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<a href="markowitz_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="markowitz_8h.html">ortools/glop/markowitz.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 <cstdint></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include "absl/strings/str_format.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="lp__types_8h.html">ortools/lp_data/lp_types.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="lp__data_2lp__utils_8h.html">ortools/lp_data/lp_utils.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="sparse_8h.html">ortools/lp_data/sparse.h</a>"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="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="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_markowitz.html#afd3f022e573b8f4f0901624a813ade07"> 27</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#afd3f022e573b8f4f0901624a813ade07">Markowitz::ComputeRowAndColumnPermutation</a>(</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& basis_matrix, <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>* row_perm,</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</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="l00030" name="l00030"></a><span class="lineno"> 30</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="l00031" name="l00031"></a><span class="lineno"> 31</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">const</span> RowIndex num_rows = basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">const</span> ColIndex num_cols = basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> col_perm-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#acb8f594fc0399176a6201d6c66eb0419">assign</a>(num_cols, <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> row_perm-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#acb8f594fc0399176a6201d6c66eb0419">assign</a>(num_rows, <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>);</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// Get the empty matrix corner case out of the way.</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> (basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> basis_matrix_ = &basis_matrix;</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Initialize all the matrices.</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">Reset</a>(num_rows, num_cols);</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">Reset</a>(num_rows, num_cols);</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a1eb060a55278923620fda32549d18ae7">Reset</a>(num_cols);</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a1eb060a55278923620fda32549d18ae7">Reset</a>(num_cols);</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> permuted_lower_column_needs_solve_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#af8d7048738ceb4c753b040e6d29db79c">assign</a>(num_cols, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> contains_only_singleton_columns_ = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// Start by moving the singleton columns to the front and by putting their</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// non-zero coefficient on the diagonal. The general algorithm below would</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// have the same effect, but this function is a lot faster.</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = 0;</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> ExtractSingletonColumns(basis_matrix, row_perm, col_perm, &<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> ExtractResidualSingletonColumns(basis_matrix, row_perm, col_perm, &<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">int</span> stats_num_pivots_without_fill_in = <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>;</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">int</span> stats_degree_two_pivot_columns = 0;</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// Initialize residual_matrix_non_zero_ with the submatrix left after we</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// removed the singleton and residual singleton columns.</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af6141c80a5d2f56d86f149c822065cc5">InitializeFromMatrixSubset</a>(</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> basis_matrix, *row_perm, *col_perm, &singleton_column_, &singleton_row_);</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// Perform Gaussian elimination.</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">const</span> <span class="keywordtype">int</span> end_index = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(num_rows.value(), num_cols.value());</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> singularity_threshold =</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> parameters_.markowitz_singularity_threshold();</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">while</span> (<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < end_index) {</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> pivot_coefficient = 0.0;</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> RowIndex pivot_row = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>;</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> ColIndex pivot_col = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// TODO(user): If we don't need L and U, we can abort when the residual</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// matrix becomes dense (i.e. when its density factor is above a certain</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// threshold). The residual size is 'end_index - index' and the</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// density can either be computed exactly or estimated from min_markowitz.</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> int64_t min_markowitz = FindPivot(*row_perm, *col_perm, &pivot_row,</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> &pivot_col, &pivot_coefficient);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Singular matrix? No pivot will be selected if a column has no entries. If</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// a column has some entries, then we are sure that a pivot will be selected</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// but its magnitude can be really close to zero. In both cases, we</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// report the singularity of the matrix.</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">if</span> (pivot_row == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a> || pivot_col == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a> ||</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> std::abs(pivot_coefficient) <= singularity_threshold) {</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">const</span> std::string error_message = absl::StrFormat(</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="stringliteral">"The matrix is singular! pivot = %E"</span>, pivot_coefficient);</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"ERROR_LU: "</span> << error_message;</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a>(<a class="code hl_enumvalue" href="classoperations__research_1_1glop_1_1_status.html#a59e56af19e754a6aa26a612ebf91d05fafa2ff9c081445bfbfbda10bc41b76a87">Status::ERROR_LU</a>, error_message);</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>((*row_perm)[pivot_row], <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>);</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>((*col_perm)[pivot_col], <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// Update residual_matrix_non_zero_.</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// TODO(user): This step can be skipped, once a fully dense matrix is</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// obtained. But note that permuted_lower_column_needs_solve_ needs to be</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// updated.</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">const</span> <span class="keywordtype">int</span> pivot_col_degree = residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(pivot_col);</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">const</span> <span class="keywordtype">int</span> pivot_row_degree = residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a44badccd63c183b774ba7bfb005aac9f">RowDegree</a>(pivot_row);</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a437a888007d0475cfaf07ac70538c458">DeleteRowAndColumn</a>(pivot_row, pivot_col);</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">if</span> (min_markowitz == 0) {</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> ++stats_num_pivots_without_fill_in;</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">if</span> (pivot_col_degree == 1) {</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> RemoveRowFromResidualMatrix(pivot_row, pivot_col);</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> } <span class="keywordflow">else</span> {</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="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(pivot_row_degree, 1);</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> RemoveColumnFromResidualMatrix(pivot_row, pivot_col);</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> }</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// TODO(user): Note that in some rare cases, because of numerical</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// cancellation, the column degree may actually be smaller than</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// pivot_col_degree. Exploit that better?</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_define" href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a>(</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordflow">if</span> (pivot_col_degree == 2) { ++stats_degree_two_pivot_columns; });</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> UpdateResidualMatrix(pivot_row, pivot_col);</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</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> <span class="keywordflow">if</span> (contains_only_singleton_columns_) {</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(pivot_col).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>());</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ae95eb4b81113f212b6aae874a15808df">AddDiagonalOnlyColumn</a>(1.0);</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab5a8a005f27ece21134c277a33057c70">AddTriangularColumn</a>(basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(pivot_col), pivot_row);</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8d3594198944bf0a6ac2669581085683">AddAndNormalizeTriangularColumn</a>(permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(pivot_col),</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> pivot_row, pivot_coefficient);</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a4d3e4198a395b77980b341d40ddb8b3c">ClearAndReleaseColumn</a>(pivot_col);</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> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a2ffa6dbb95dfb7e397bf69fd1ddd188e">AddTriangularColumnWithGivenDiagonalEntry</a>(</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(pivot_col), pivot_row, pivot_coefficient);</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a4d3e4198a395b77980b341d40ddb8b3c">ClearAndReleaseColumn</a>(pivot_col);</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</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">// Update the permutations.</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> (*col_perm)[pivot_col] = ColIndex(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> (*row_perm)[pivot_row] = RowIndex(<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>;</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// To get a better deterministic time, we add a factor that depend on the</span></div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// final number of entries in the result.</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> num_fp_operations_ += 10 * lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>().value();</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> num_fp_operations_ += 10 * upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>().value();</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> stats_.pivots_without_fill_in_ratio.Add(</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> 1.0 * stats_num_pivots_without_fill_in / num_rows.value());</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> stats_.degree_two_pivot_columns.Add(1.0 * stats_degree_two_pivot_columns /</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> num_rows.value());</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span>}</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_markowitz.html#a7ac2557be8cf0394f9953fbdac2f18f4"> 149</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#a7ac2557be8cf0394f9953fbdac2f18f4">Markowitz::ComputeLU</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& basis_matrix,</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>* row_perm,</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</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="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>* <a class="code hl_variable" href="glpk__solver_8cc.html#abb82b111deb51f3a5917cf8780fee484">lower</a>, <a class="code hl_class" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>* <a class="code hl_variable" href="glpk__solver_8cc.html#ae0e265c074f457e193b30ff0d77c750b">upper</a>) {</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// The two first swaps allow to use less memory since this way upper_</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// and lower_ will always stay empty at the end of this function.</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3e1b01501c922d36c55fb59cfc18e630">Swap</a>(<a class="code hl_variable" href="glpk__solver_8cc.html#abb82b111deb51f3a5917cf8780fee484">lower</a>);</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3e1b01501c922d36c55fb59cfc18e630">Swap</a>(<a class="code hl_variable" href="glpk__solver_8cc.html#ae0e265c074f457e193b30ff0d77c750b">upper</a>);</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_define" href="status_8h.html#a3efb1c6250c02a5b881f8b82f75f9822">GLOP_RETURN_IF_ERROR</a>(</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#afd3f022e573b8f4f0901624a813ade07">ComputeRowAndColumnPermutation</a>(basis_matrix, row_perm, col_perm));</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</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="l00160" name="l00160"></a><span class="lineno"> 160</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ad001a49701677a22b4efd9186b97ae05">ApplyRowPermutationToNonDiagonalEntries</a>(*row_perm);</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ad001a49701677a22b4efd9186b97ae05">ApplyRowPermutationToNonDiagonalEntries</a>(*row_perm);</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3e1b01501c922d36c55fb59cfc18e630">Swap</a>(<a class="code hl_variable" href="glpk__solver_8cc.html#abb82b111deb51f3a5917cf8780fee484">lower</a>);</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3e1b01501c922d36c55fb59cfc18e630">Swap</a>(<a class="code hl_variable" href="glpk__solver_8cc.html#ae0e265c074f457e193b30ff0d77c750b">upper</a>);</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_variable" href="glpk__solver_8cc.html#abb82b111deb51f3a5917cf8780fee484">lower</a>->IsLowerTriangular());</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_variable" href="glpk__solver_8cc.html#ae0e265c074f457e193b30ff0d77c750b">upper</a>->IsUpperTriangular());</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span>}</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_markowitz.html#aa71d36872f416feaa853788a7a7a7ef8"> 169</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#aa71d36872f416feaa853788a7a7a7ef8">Markowitz::Clear</a>() {</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</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="l00171" name="l00171"></a><span class="lineno"> 171</span> permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> col_by_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> examined_col_.clear();</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> num_fp_operations_ = 0;</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> is_col_by_degree_initialized_ = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span>}</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><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="keyword">struct </span>MatrixEntry {</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"><a class="line" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52"> 182</a></span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>;</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"><a class="line" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c"> 183</a></span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"><a class="line" href="markowitz_8cc.html#a722e11301e7de93191aa47dbd3ecb4d8"> 184</a></span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_variable" href="markowitz_8cc.html#a722e11301e7de93191aa47dbd3ecb4d8">coefficient</a>;</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> MatrixEntry(RowIndex r, ColIndex c, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_variable" href="variable__and__expressions_8cc.html#a2091cd7d80fdd31762020bce86138587">coeff</a>)</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> : <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(r), <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(c), <a class="code hl_variable" href="markowitz_8cc.html#a722e11301e7de93191aa47dbd3ecb4d8">coefficient</a>(<a class="code hl_variable" href="variable__and__expressions_8cc.html#a2091cd7d80fdd31762020bce86138587">coeff</a>) {}</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordtype">bool</span> operator<(<span class="keyword">const</span> MatrixEntry& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> == o.row) ? <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < o.col : <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < o.row;</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> }</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> </div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="keywordtype">void</span> Markowitz::ExtractSingletonColumns(</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keyword">const</span> CompactSparseMatrixView& basis_matrix, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>* row_perm,</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a>* col_perm, <span class="keywordtype">int</span>* <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</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="l00198" name="l00198"></a><span class="lineno"> 198</span> std::vector<MatrixEntry> singleton_entries;</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keyword">const</span> ColIndex num_cols = basis_matrix.num_cols();</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keyword">const</span> ColumnView& column = basis_matrix.column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keywordflow">if</span> (column.num_entries().value() == 1) {</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> singleton_entries.push_back(</div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> MatrixEntry(column.GetFirstRow(), <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, column.GetFirstCoefficient()));</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> }</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// Sorting the entries by row indices allows the row_permutation to be closer</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// to identity which seems like a good idea.</span></div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> std::sort(singleton_entries.begin(), singleton_entries.end());</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> MatrixEntry e : singleton_entries) {</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">if</span> ((*row_perm)[e.row] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) {</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> (*col_perm)[e.col] = ColIndex(*<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> (*row_perm)[e.row] = RowIndex(*<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ae95eb4b81113f212b6aae874a15808df">AddDiagonalOnlyColumn</a>(1.0);</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ae95eb4b81113f212b6aae874a15808df">AddDiagonalOnlyColumn</a>(e.coefficient);</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> ++(*index);</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> }</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> }</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> stats_.basis_singleton_column_ratio.Add(<span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(*<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) /</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> basis_matrix.num_rows().value());</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span>}</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> </div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span><span class="keywordtype">bool</span> Markowitz::IsResidualSingletonColumn(<span class="keyword">const</span> ColumnView& column,</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> RowIndex* <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keywordtype">int</span> residual_degree = 0;</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> e : column) {</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">if</span> (row_perm[e.row()] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> ++residual_degree;</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordflow">if</span> (residual_degree > 1) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> *<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> }</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keywordflow">return</span> residual_degree == 1;</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span>}</div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> </div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span><span class="keywordtype">void</span> Markowitz::ExtractResidualSingletonColumns(</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">const</span> CompactSparseMatrixView& basis_matrix, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>* row_perm,</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a>* col_perm, <span class="keywordtype">int</span>* <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</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="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">const</span> ColIndex num_cols = basis_matrix.num_cols();</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>;</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordflow">if</span> ((*col_perm)[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keyword">const</span> ColumnView& column = basis_matrix.column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keywordflow">if</span> (!IsResidualSingletonColumn(column, *row_perm, &<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> (*col_perm)[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = ColIndex(*<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> (*row_perm)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = RowIndex(*<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ae95eb4b81113f212b6aae874a15808df">AddDiagonalOnlyColumn</a>(1.0);</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab5a8a005f27ece21134c277a33057c70">AddTriangularColumn</a>(column, <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> ++(*index);</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> }</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> stats_.basis_residual_singleton_column_ratio.Add(</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(*<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) / basis_matrix.num_rows().value());</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span>}</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> </div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span><span class="keyword">const</span> SparseColumn& Markowitz::ComputeColumn(<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <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="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="comment">// Is this the first time ComputeColumn() sees this column? This is a bit</span></div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// tricky because just one of the tests is not sufficient in case the matrix</span></div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="comment">// is degenerate.</span></div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> first_time = permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>() &&</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>();</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">// If !permuted_lower_column_needs_solve_[col] then the result of the</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="comment">// PermutedLowerSparseSolve() below is already stored in</span></div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="comment">// permuted_lower_.column(col) and we just need to split this column. Note</span></div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="comment">// that this is just an optimization and the code would work if we just</span></div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="comment">// assumed permuted_lower_column_needs_solve_[col] to be always true.</span></div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> SparseColumn* lower_column = permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keywordflow">if</span> (permuted_lower_column_needs_solve_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// Solve a sparse triangular system. If the column 'col' of permuted_lower_</span></div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="comment">// was never computed before by ComputeColumn(), we use the column 'col' of</span></div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="comment">// the matrix to factorize.</span></div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">const</span> ColumnView& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a> =</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> first_time ? basis_matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) : ColumnView(*lower_column);</div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#abedd52dbc024598bf0189235764f734a">PermutedLowerSparseSolve</a>(<a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>, row_perm, lower_column,</div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>));</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> permuted_lower_column_needs_solve_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> num_fp_operations_ +=</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aec8942e8b01f9aed2abc24de9acfb6ab">NumFpOperationsInLastPermutedLowerSparseSolve</a>();</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">return</span> *lower_column;</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> }</div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> </div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// All the symbolic non-zeros are always present in lower. So if this test is</span></div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// true, we can conclude that there is no entries from upper that need to be</span></div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// moved by a cardinality argument.</span></div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordflow">if</span> (lower_column->num_entries() == residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="keywordflow">return</span> *lower_column;</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> </div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// In this case, we just need to "split" the lower column. We copy from the</span></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="comment">// appropriate ColumnView in basis_matrix_.</span></div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="comment">// TODO(user): add PopulateFromColumnView if it is useful elsewhere.</span></div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">if</span> (first_time) {</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keyword">const</span> EntryIndex <a class="code hl_variable" href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a> = basis_matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>();</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> num_fp_operations_ += <a class="code hl_variable" href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a>.value();</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> lower_column->Reserve(<a class="code hl_variable" href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a>);</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> e : basis_matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> lower_column->SetCoefficient(e.row(), e.coefficient());</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</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> num_fp_operations_ += lower_column->num_entries().value();</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> lower_column->MoveTaggedEntriesTo(row_perm,</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> permuted_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>));</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keywordflow">return</span> *lower_column;</div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span>}</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>int64_t Markowitz::FindPivot(<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a>& col_perm,</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> RowIndex* pivot_row, ColIndex* pivot_col,</div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>* pivot_coefficient) {</div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</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="l00315" name="l00315"></a><span class="lineno"> 315</span> </div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="comment">// Fast track for singleton columns.</span></div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keywordflow">while</span> (!singleton_column_.empty()) {</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = singleton_column_.back();</div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> singleton_column_.pop_back();</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>, col_perm[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]);</div>
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<div class="line"><a id="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">// This can only happen if the matrix is singular. Continuing will cause</span></div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="comment">// the algorithm to detect the singularity at the end when we stop before</span></div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <span class="comment">// the end.</span></div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> <span class="comment">// TODO(user): We could detect the singularity at this point, but that</span></div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="comment">// may make the code more complex.</span></div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="keywordflow">if</span> (residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) != 1) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> </div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> <span class="comment">// ComputeColumn() is not used as long as only singleton columns of the</span></div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> <span class="comment">// residual matrix are used. See the other condition in</span></div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="comment">// ComputeRowAndColumnPermutation().</span></div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="keywordflow">if</span> (contains_only_singleton_columns_) {</div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> *pivot_col = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : basis_matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keywordflow">if</span> (row_perm[e.row()] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) {</div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> *pivot_row = e.row();</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> *pivot_coefficient = e.coefficient();</div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> }</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="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> }</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="keyword">const</span> SparseColumn& column = ComputeColumn(row_perm, <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keywordflow">if</span> (column.IsEmpty()) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> *pivot_col = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> *pivot_row = column.GetFirstRow();</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> *pivot_coefficient = column.GetFirstCoefficient();</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> }</div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> contains_only_singleton_columns_ = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> </div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="comment">// Fast track for singleton rows. Note that this is actually more than a fast</span></div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="comment">// track because of the Zlatev heuristic. Such rows may not be processed as</span></div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="comment">// soon as possible otherwise, resulting in more fill-in.</span></div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="keywordflow">while</span> (!singleton_row_.empty()) {</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = singleton_row_.back();</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> singleton_row_.pop_back();</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> </div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// A singleton row could have been processed when processing a singleton</span></div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="comment">// column. Skip if this is the case.</span></div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="keywordflow">if</span> (row_perm[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> </div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="comment">// This shows that the matrix is singular, see comment above for the same</span></div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="comment">// case when processing singleton columns.</span></div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keywordflow">if</span> (residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a44badccd63c183b774ba7bfb005aac9f">RowDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) != 1) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> <span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> =</div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af14468b811c1218ef477ccbd170e6f8d">GetFirstNonDeletedColumnFromRow</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="keyword">const</span> SparseColumn& column = ComputeColumn(row_perm, <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="keywordflow">if</span> (column.IsEmpty()) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> </div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> *pivot_col = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> *pivot_row = <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>;</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> *pivot_coefficient = column.LookUpCoefficient(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> }</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> </div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="comment">// col_by_degree_ is not needed before we reach this point. Exploit this with</span></div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="comment">// a lazy initialization.</span></div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="keywordflow">if</span> (!is_col_by_degree_initialized_) {</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> is_col_by_degree_initialized_ = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> <span class="keyword">const</span> ColIndex num_cols = col_perm.size();</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> col_by_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a026a7cba6cd132662dae0468f395d3cf">Reset</a>(row_perm.size().value(), num_cols);</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <span class="keywordflow">if</span> (col_perm[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> <span class="keyword">const</span> <span class="keywordtype">int</span> degree = residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(degree, 1);</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> UpdateDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, degree);</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> }</div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> }</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> </div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> <span class="comment">// Note(user): we use int64_t since this is a product of two ints, moreover</span></div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="comment">// the ints should be relatively small, so that should be fine for a while.</span></div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> int64_t min_markowitz_number = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<int64_t>::max</a>();</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> examined_col_.clear();</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_columns_to_examine = parameters_.markowitz_zlatev_parameter();</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> threshold = parameters_.lu_factorization_pivot_threshold();</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> <span class="keywordflow">while</span> (examined_col_.size() < num_columns_to_examine) {</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = col_by_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a49e7d07685ccac64b842fa1b1cc9a3cc">Pop</a>();</div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> <span class="keywordflow">if</span> (col_perm[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> <span class="keyword">const</span> <span class="keywordtype">int</span> col_degree = residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> examined_col_.push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> </div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="comment">// Because of the two singleton special cases at the beginning of this</span></div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <span class="comment">// function and because we process columns by increasing degree, we can</span></div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> <span class="comment">// derive a lower bound on the best markowitz number we can get by exploring</span></div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="comment">// this column. If we cannot beat this number, we can stop here.</span></div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="comment">// Note(user): we still process extra column if we can meet the lower bound</span></div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <span class="comment">// to eventually have a better pivot.</span></div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="comment">// Todo(user): keep the minimum row degree to have a better bound?</span></div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="keyword">const</span> int64_t markowitz_lower_bound = col_degree - 1;</div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="keywordflow">if</span> (min_markowitz_number < markowitz_lower_bound) <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> </div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="comment">// TODO(user): col_degree (which is the same as column.num_entries()) is</span></div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="comment">// actually an upper bound on the number of non-zeros since there may be</span></div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <span class="comment">// numerical cancellations. Exploit this here? Note that it is already used</span></div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="comment">// when we update the non_zero pattern of the residual matrix.</span></div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <span class="keyword">const</span> SparseColumn& column = ComputeColumn(row_perm, <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(column.num_entries(), col_degree);</div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> </div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_magnitude = 0.0;</div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : column) {</div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> max_magnitude = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_magnitude, std::abs(e.coefficient()));</div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> }</div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="keywordflow">if</span> (max_magnitude == 0.0) {</div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// All symbolic non-zero entries have been cancelled!</span></div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> <span class="comment">// The matrix is singular, but we continue with the other columns.</span></div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> examined_col_.pop_back();</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> }</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> </div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> skip_threshold = threshold * max_magnitude;</div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : column) {</div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> magnitude = std::abs(e.coefficient());</div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="keywordflow">if</span> (magnitude < skip_threshold) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> </div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <span class="keyword">const</span> <span class="keywordtype">int</span> row_degree = residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a44badccd63c183b774ba7bfb005aac9f">RowDegree</a>(e.row());</div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> <span class="keyword">const</span> int64_t markowitz_number = (col_degree - 1) * (row_degree - 1);</div>
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<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(markowitz_number, 0);</div>
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<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keywordflow">if</span> (markowitz_number < min_markowitz_number ||</div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> ((markowitz_number == min_markowitz_number) &&</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> magnitude > std::abs(*pivot_coefficient))) {</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> min_markowitz_number = markowitz_number;</div>
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<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> *pivot_col = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> *pivot_row = e.row();</div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> *pivot_coefficient = e.coefficient();</div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> </div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <span class="comment">// Note(user): We could abort early here if the markowitz_lower_bound is</span></div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="comment">// reached, but finishing to loop over this column is fast and may lead</span></div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="comment">// to a pivot with a greater magnitude (i.e. a more robust</span></div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="comment">// factorization).</span></div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> }</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> }</div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(min_markowitz_number, 0);</div>
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(min_markowitz_number, markowitz_lower_bound);</div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> }</div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> </div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> <span class="comment">// Push back the columns that we just looked at in the queue since they</span></div>
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|
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="comment">// are candidates for the next pivot.</span></div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <span class="comment">// TODO(user): Do that after having updated the matrix? Rationale:</span></div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="comment">// - col_by_degree_ is LIFO, so that may save work in ComputeColumn() by</span></div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="comment">// calling it again on the same columns.</span></div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> <span class="comment">// - Maybe the earliest low-degree columns have a better precision? This</span></div>
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|
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="comment">// actually depends on the number of operations so is not really true.</span></div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="comment">// - Maybe picking the column randomly from the ones with lowest degree would</span></div>
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|
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> <span class="comment">// help having more diversity from one factorization to the next. This is</span></div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> <span class="comment">// for the case we do implement this TODO.</span></div>
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<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : examined_col_) {</div>
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<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> != *pivot_col) {</div>
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<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <span class="keyword">const</span> <span class="keywordtype">int</span> degree = residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> col_by_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a0a601ea6856d6a6162a705fe6ab48cbc">PushOrAdjust</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, degree);</div>
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|
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> }</div>
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<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> }</div>
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<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> <span class="keywordflow">return</span> min_markowitz_number;</div>
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<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span>}</div>
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<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> </div>
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<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span><span class="keywordtype">void</span> Markowitz::UpdateDegree(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <span class="keywordtype">int</span> degree) {</div>
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<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(is_col_by_degree_initialized_);</div>
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|
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> </div>
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<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> <span class="comment">// Separating the degree one columns work because we always select such</span></div>
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|
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> <span class="comment">// a column first and pivoting by such columns does not affect the degree of</span></div>
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|
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> <span class="comment">// any other singleton columns (except if the matrix is not inversible).</span></div>
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|
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> <span class="comment">// Note that using this optimization does change the order in which the</span></div>
|
|
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> <span class="comment">// degree one columns are taken compared to pushing them in the queue.</span></div>
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<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> <span class="keywordflow">if</span> (degree == 1) {</div>
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|
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> <span class="comment">// Note that there is no need to remove this column from col_by_degree_</span></div>
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|
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> <span class="comment">// because it will be processed before col_by_degree_.Pop() is called and</span></div>
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|
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <span class="comment">// then just be ignored.</span></div>
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<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> singleton_column_.push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> col_by_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a0a601ea6856d6a6162a705fe6ab48cbc">PushOrAdjust</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, degree);</div>
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|
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> }</div>
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<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span>}</div>
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<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> </div>
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<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span><span class="keywordtype">void</span> Markowitz::RemoveRowFromResidualMatrix(RowIndex pivot_row,</div>
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|
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> ColIndex pivot_col) {</div>
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|
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</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="l00504" name="l00504"></a><span class="lineno"> 504</span> <span class="comment">// Note that instead of calling:</span></div>
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|
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> <span class="comment">// residual_matrix_non_zero_.RemoveDeletedColumnsFromRow(pivot_row);</span></div>
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|
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> <span class="comment">// it is a bit faster to test each position with IsColumnDeleted() since we</span></div>
|
|
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> <span class="comment">// will not need the pivot row anymore.</span></div>
|
|
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> <span class="keywordflow">if</span> (is_col_by_degree_initialized_) {</div>
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|
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a28a4e2ca582ad13d6ab28d1c757934c0">RowNonZero</a>(pivot_row)) {</div>
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|
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> <span class="keywordflow">if</span> (residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a1f59bbe4cda31ad0ee8a91c4bd57e945">IsColumnDeleted</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) <span class="keywordflow">continue</span>;</div>
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|
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> UpdateDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a25db8d6277cbd4811441929a1817dea0">DecreaseColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>));</div>
|
|
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> }</div>
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<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> } <span class="keywordflow">else</span> {</div>
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|
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a28a4e2ca582ad13d6ab28d1c757934c0">RowNonZero</a>(pivot_row)) {</div>
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<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> <span class="keywordflow">if</span> (residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a1f59bbe4cda31ad0ee8a91c4bd57e945">IsColumnDeleted</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) <span class="keywordflow">continue</span>;</div>
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|
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> <span class="keywordflow">if</span> (residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a25db8d6277cbd4811441929a1817dea0">DecreaseColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) == 1) {</div>
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<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> singleton_column_.push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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|
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> }</div>
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<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> }</div>
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<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> }</div>
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<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span>}</div>
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<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> </div>
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<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span><span class="keywordtype">void</span> Markowitz::RemoveColumnFromResidualMatrix(RowIndex pivot_row,</div>
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<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> ColIndex pivot_col) {</div>
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<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</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="l00526" name="l00526"></a><span class="lineno"> 526</span> <span class="comment">// The entries of the pivot column are exactly the symbolic non-zeros of the</span></div>
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|
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="comment">// residual matrix, since we didn't remove the entries with a coefficient of</span></div>
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<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> <span class="comment">// zero during PermutedLowerSparseSolve().</span></div>
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<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="comment">// Note that it is okay to decrease the degree of a previous pivot row since</span></div>
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<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> <span class="comment">// it was set to 0 and will never trigger this test. Even if it triggers it,</span></div>
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<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> <span class="comment">// we just ignore such singleton rows in FindPivot().</span></div>
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<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(pivot_col)) {</div>
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<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> <span class="keywordflow">if</span> (residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa844f860b76cad2a3682e7d9b927195c">DecreaseRowDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) == 1) {</div>
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<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> singleton_row_.push_back(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> }</div>
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<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> }</div>
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<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span>}</div>
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<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> </div>
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<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span><span class="keywordtype">void</span> Markowitz::UpdateResidualMatrix(RowIndex pivot_row, ColIndex pivot_col) {</div>
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<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</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="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="keyword">const</span> SparseColumn& pivot_column = permuted_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(pivot_col);</div>
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<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a965275e22dbb55799f5b99cca98e0fbc">Update</a>(pivot_row, pivot_col, pivot_column);</div>
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<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a28a4e2ca582ad13d6ab28d1c757934c0">RowNonZero</a>(pivot_row)) {</div>
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<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, pivot_col);</div>
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<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> UpdateDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, residual_matrix_non_zero_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">ColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>));</div>
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<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> permuted_lower_column_needs_solve_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> }</div>
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<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> RemoveColumnFromResidualMatrix(pivot_row, pivot_col);</div>
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<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span>}</div>
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<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> </div>
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<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_markowitz.html#a627511bf305a6af5d7e114817c1792c2"> 553</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#a627511bf305a6af5d7e114817c1792c2">Markowitz::DeterministicTimeOfLastFactorization</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#aedb714d776d86539dbb9f42ae5d7d923">DeterministicTimeForFpOperations</a>(num_fp_operations_);</div>
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<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span>}</div>
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<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> </div>
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<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa71d36872f416feaa853788a7a7a7ef8"> 557</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa71d36872f416feaa853788a7a7a7ef8">MatrixNonZeroPattern::Clear</a>() {</div>
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<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> row_degree_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> col_degree_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> row_non_zero_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> deleted_columns_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> bool_scratchpad_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> num_non_deleted_columns_ = 0;</div>
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<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span>}</div>
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<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> </div>
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<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a85e6c7ebc5ac22d117ff412e3658c72d"> 566</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a85e6c7ebc5ac22d117ff412e3658c72d">MatrixNonZeroPattern::Reset</a>(RowIndex num_rows, ColIndex num_cols) {</div>
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<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> row_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">AssignToZero</a>(num_rows);</div>
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<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> col_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">AssignToZero</a>(num_cols);</div>
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<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> row_non_zero_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> row_non_zero_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a4e3670a285a3642eaa07f66766cffa72">resize</a>(num_rows.value());</div>
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<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> deleted_columns_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#af8d7048738ceb4c753b040e6d29db79c">assign</a>(num_cols, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> bool_scratchpad_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#af8d7048738ceb4c753b040e6d29db79c">assign</a>(num_cols, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> num_non_deleted_columns_ = num_cols;</div>
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<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span>}</div>
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<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> </div>
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<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af6141c80a5d2f56d86f149c822065cc5"> 576</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af6141c80a5d2f56d86f149c822065cc5">MatrixNonZeroPattern::InitializeFromMatrixSubset</a>(</div>
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<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& basis_matrix, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& col_perm, std::vector<ColIndex>* singleton_columns,</div>
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<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> std::vector<RowIndex>* singleton_rows) {</div>
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<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> <span class="keyword">const</span> ColIndex num_cols = basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> <span class="keyword">const</span> RowIndex num_rows = basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> </div>
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<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> <span class="comment">// Reset the matrix and initialize the vectors to the correct sizes.</span></div>
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<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a85e6c7ebc5ac22d117ff412e3658c72d">Reset</a>(num_rows, num_cols);</div>
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<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> singleton_columns->clear();</div>
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<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> singleton_rows->clear();</div>
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<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> </div>
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<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> <span class="comment">// Compute the number of entries in each row.</span></div>
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<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <span class="keywordflow">if</span> (col_perm[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
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<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> deleted_columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> --num_non_deleted_columns_;</div>
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<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> }</div>
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<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> ++row_degree_[e.row()];</div>
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<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> }</div>
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<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> }</div>
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<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> </div>
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<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> <span class="comment">// Reserve the row_non_zero_ vector sizes.</span></div>
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<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</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="l00602" name="l00602"></a><span class="lineno"> 602</span> <span class="keywordflow">if</span> (row_perm[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) {</div>
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<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>].<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a562f7b24b47d3e7632a9896935c14d8b">reserve</a>(row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> <span class="keywordflow">if</span> (row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == 1) singleton_rows->push_back(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> <span class="comment">// This is needed because in the row degree computation above, we do not</span></div>
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<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> <span class="comment">// test for row_perm[row] == kInvalidRow because it is a bit faster.</span></div>
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<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = 0;</div>
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<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> }</div>
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<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span> }</div>
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<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> </div>
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<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span> <span class="comment">// Initialize row_non_zero_.</span></div>
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<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span> <span class="keywordflow">if</span> (col_perm[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> int32_t col_degree = 0;</div>
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<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : basis_matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="keywordflow">if</span> (row_perm[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) {</div>
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<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> ++col_degree;</div>
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<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>].<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">push_back</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> }</div>
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<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> }</div>
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<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = col_degree;</div>
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<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> <span class="keywordflow">if</span> (col_degree == 1) singleton_columns-><a class="code hl_function" href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">push_back</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> }</div>
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<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span>}</div>
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<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> </div>
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<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a8036bd4d1fc8a69112a1f7ed5493a924"> 628</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a8036bd4d1fc8a69112a1f7ed5493a924">MatrixNonZeroPattern::AddEntry</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> ++row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> ++col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>].<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">push_back</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span>}</div>
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<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> </div>
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<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a25db8d6277cbd4811441929a1817dea0"> 634</a></span>int32_t <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a25db8d6277cbd4811441929a1817dea0">MatrixNonZeroPattern::DecreaseColDegree</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> <span class="keywordflow">return</span> --col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span>}</div>
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<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> </div>
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<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa844f860b76cad2a3682e7d9b927195c"> 638</a></span>int32_t <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa844f860b76cad2a3682e7d9b927195c">MatrixNonZeroPattern::DecreaseRowDegree</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> <span class="keywordflow">return</span> --row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span>}</div>
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<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> </div>
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<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a437a888007d0475cfaf07ac70538c458"> 642</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a437a888007d0475cfaf07ac70538c458">MatrixNonZeroPattern::DeleteRowAndColumn</a>(RowIndex pivot_row,</div>
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<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> ColIndex pivot_col) {</div>
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<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(!deleted_columns_[pivot_col]);</div>
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<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> deleted_columns_[pivot_col] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> --num_non_deleted_columns_;</div>
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<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> </div>
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<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span> <span class="comment">// We do that to optimize RemoveColumnFromResidualMatrix().</span></div>
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<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span> row_degree_[pivot_row] = 0;</div>
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<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span>}</div>
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<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> </div>
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<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a1f59bbe4cda31ad0ee8a91c4bd57e945"> 652</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a1f59bbe4cda31ad0ee8a91c4bd57e945">MatrixNonZeroPattern::IsColumnDeleted</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> <span class="keywordflow">return</span> deleted_columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span>}</div>
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<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> </div>
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<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a2527e336adfc8144ee253eed236fa699"> 656</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a2527e336adfc8144ee253eed236fa699">MatrixNonZeroPattern::RemoveDeletedColumnsFromRow</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> <span class="keyword">auto</span>& ref = row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> <span class="keywordtype">int</span> new_index = 0;</div>
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<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a> = ref.size();</div>
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<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a>; ++i) {</div>
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<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> <span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = ref[i];</div>
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<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="keywordflow">if</span> (!deleted_columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div>
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<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> ref[new_index] = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> ++new_index;</div>
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<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> }</div>
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<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> }</div>
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<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> ref.resize(new_index);</div>
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<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span>}</div>
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<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> </div>
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<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af14468b811c1218ef477ccbd170e6f8d"> 670</a></span>ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af14468b811c1218ef477ccbd170e6f8d">MatrixNonZeroPattern::GetFirstNonDeletedColumnFromRow</a>(</div>
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<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> 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="l00672" name="l00672"></a><span class="lineno"> 672</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a28a4e2ca582ad13d6ab28d1c757934c0">RowNonZero</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)) {</div>
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<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a1f59bbe4cda31ad0ee8a91c4bd57e945">IsColumnDeleted</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) <span class="keywordflow">return</span> <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> }</div>
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<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div>
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<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span>}</div>
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<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> </div>
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<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a965275e22dbb55799f5b99cca98e0fbc"> 678</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a965275e22dbb55799f5b99cca98e0fbc">MatrixNonZeroPattern::Update</a>(RowIndex pivot_row, ColIndex pivot_col,</div>
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<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& column) {</div>
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<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> <span class="comment">// Since DeleteRowAndColumn() must be called just before this function,</span></div>
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<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> <span class="comment">// the pivot column has been marked as deleted but degrees have not been</span></div>
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<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> <span class="comment">// updated yet. Hence the +1.</span></div>
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<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(deleted_columns_[pivot_col]);</div>
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<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> <span class="keyword">const</span> <span class="keywordtype">int</span> max_row_degree = num_non_deleted_columns_.value() + 1;</div>
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<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> </div>
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<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a2527e336adfc8144ee253eed236fa699">RemoveDeletedColumnsFromRow</a>(pivot_row);</div>
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<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : row_non_zero_[pivot_row]) {</div>
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<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a25db8d6277cbd4811441929a1817dea0">DecreaseColDegree</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> bool_scratchpad_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> }</div>
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<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> </div>
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<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> <span class="comment">// We only need to merge the row for the position with a coefficient different</span></div>
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<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> <span class="comment">// from 0.0. Note that the column must contain all the symbolic non-zeros for</span></div>
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<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> <span class="comment">// the row degree to be updated correctly. Note also that decreasing the row</span></div>
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<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> <span class="comment">// degrees due to the deletion of pivot_col will happen outside this function.</span></div>
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<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : column) {</div>
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<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> == pivot_row) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> </div>
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<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span> <span class="comment">// If the row is fully dense, there is nothing to do (the merge below will</span></div>
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<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span> <span class="comment">// not change anything). This is a small price to pay for a huge gain when</span></div>
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<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span> <span class="comment">// the matrix becomes dense.</span></div>
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<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> <span class="keywordflow">if</span> (e.coefficient() == 0.0 || row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == max_row_degree) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>], max_row_degree);</div>
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<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> </div>
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<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> <span class="comment">// We only clean row_non_zero_[row] if there are more than 4 entries to</span></div>
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<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> <span class="comment">// delete. Note(user): the 4 is somewhat arbitrary, but gives good results</span></div>
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<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> <span class="comment">// on the Netlib (23/04/2013). Note that calling</span></div>
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<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> <span class="comment">// RemoveDeletedColumnsFromRow() is not mandatory and does not change the LU</span></div>
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<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> <span class="comment">// decomposition, so we could call it all the time or never and the</span></div>
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<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> <span class="comment">// algorithm would still work.</span></div>
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<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> <span class="keyword">const</span> <span class="keywordtype">int</span> kDeletionThreshold = 4;</div>
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<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> <span class="keywordflow">if</span> (row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>].size() > row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] + kDeletionThreshold) {</div>
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<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a2527e336adfc8144ee253eed236fa699">RemoveDeletedColumnsFromRow</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> }</div>
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<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> <span class="comment">// TODO(user): Special case if row_non_zero_[pivot_row].size() == 1?</span></div>
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<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> <span class="keywordflow">if</span> (<span class="comment">/* DISABLES CODE */</span> (<span class="keyword">true</span>)) {</div>
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<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> MergeInto(pivot_row, <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> } <span class="keywordflow">else</span> {</div>
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|
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> <span class="comment">// This is currently not used, but kept as an alternative algorithm to</span></div>
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|
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> <span class="comment">// investigate. The performance is really similar, but the final L.U is</span></div>
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|
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> <span class="comment">// different. Note that when this is used, there is no need to modify</span></div>
|
|
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> <span class="comment">// bool_scratchpad_ at the beginning of this function.</span></div>
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|
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> <span class="comment">// TODO(user): Add unit tests before using this.</span></div>
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<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> MergeIntoSorted(pivot_row, <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> }</div>
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<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> }</div>
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<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span>}</div>
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<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> </div>
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<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span><span class="keywordtype">void</span> MatrixNonZeroPattern::MergeInto(RowIndex pivot_row, RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> <span class="comment">// Note that bool_scratchpad_ must be already false on the positions in</span></div>
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<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> <span class="comment">// row_non_zero_[pivot_row].</span></div>
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<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]) {</div>
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<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> bool_scratchpad_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> }</div>
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<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> </div>
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<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> <span class="keyword">auto</span>& non_zero = row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span> <span class="keyword">const</span> <span class="keywordtype">int</span> old_size = non_zero.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a60304b65bf89363bcc3165d3cde67f86">size</a>();</div>
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<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : row_non_zero_[pivot_row]) {</div>
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<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"> 741</span> <span class="keywordflow">if</span> (bool_scratchpad_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div>
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<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span> bool_scratchpad_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> non_zero.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">push_back</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span> ++col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> }</div>
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<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> }</div>
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<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span> row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] += non_zero.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>() - old_size;</div>
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<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span>}</div>
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<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span> </div>
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<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00752" name="l00752"></a><span class="lineno"> 752</span> </div>
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<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span><span class="comment">// Given two sorted vectors (the second one is the initial value of out), merges</span></div>
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<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"> 754</span><span class="comment">// them and outputs the sorted result in out. The merge is stable and an element</span></div>
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<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span><span class="comment">// of input_a will appear before the identical elements of the second input.</span></div>
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<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span><span class="keyword">template</span> <<span class="keyword">typename</span> V, <span class="keyword">typename</span> W></div>
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<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span><span class="keywordtype">void</span> MergeSortedVectors(<span class="keyword">const</span> V& input_a, W* out) {</div>
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<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span> <span class="keywordflow">if</span> (input_a.empty()) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00759" name="l00759"></a><span class="lineno"> 759</span> <span class="keyword">const</span> <span class="keyword">auto</span>& input_b = *out;</div>
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<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span> <span class="keywordtype">int</span> index_a = input_a.size() - 1;</div>
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<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span> <span class="keywordtype">int</span> index_b = input_b.size() - 1;</div>
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<div class="line"><a id="l00762" name="l00762"></a><span class="lineno"> 762</span> <span class="keywordtype">int</span> index_out = input_a.size() + input_b.size();</div>
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<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span> out->resize(index_out);</div>
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<div class="line"><a id="l00764" name="l00764"></a><span class="lineno"> 764</span> <span class="keywordflow">while</span> (index_a >= 0) {</div>
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<div class="line"><a id="l00765" name="l00765"></a><span class="lineno"> 765</span> <span class="keywordflow">if</span> (index_b < 0) {</div>
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<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span> <span class="keywordflow">while</span> (index_a >= 0) {</div>
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<div class="line"><a id="l00767" name="l00767"></a><span class="lineno"> 767</span> --index_out;</div>
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<div class="line"><a id="l00768" name="l00768"></a><span class="lineno"> 768</span> (*out)[index_out] = input_a[index_a];</div>
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<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"> 769</span> --index_a;</div>
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<div class="line"><a id="l00770" name="l00770"></a><span class="lineno"> 770</span> }</div>
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<div class="line"><a id="l00771" name="l00771"></a><span class="lineno"> 771</span> <span class="keywordflow">return</span>;</div>
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|
<div class="line"><a id="l00772" name="l00772"></a><span class="lineno"> 772</span> }</div>
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<div class="line"><a id="l00773" name="l00773"></a><span class="lineno"> 773</span> --index_out;</div>
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<div class="line"><a id="l00774" name="l00774"></a><span class="lineno"> 774</span> <span class="keywordflow">if</span> (input_a[index_a] > input_b[index_b]) {</div>
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<div class="line"><a id="l00775" name="l00775"></a><span class="lineno"> 775</span> (*out)[index_out] = input_a[index_a];</div>
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<div class="line"><a id="l00776" name="l00776"></a><span class="lineno"> 776</span> --index_a;</div>
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<div class="line"><a id="l00777" name="l00777"></a><span class="lineno"> 777</span> } <span class="keywordflow">else</span> {</div>
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|
<div class="line"><a id="l00778" name="l00778"></a><span class="lineno"> 778</span> (*out)[index_out] = input_b[index_b];</div>
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|
<div class="line"><a id="l00779" name="l00779"></a><span class="lineno"> 779</span> --index_b;</div>
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<div class="line"><a id="l00780" name="l00780"></a><span class="lineno"> 780</span> }</div>
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<div class="line"><a id="l00781" name="l00781"></a><span class="lineno"> 781</span> }</div>
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|
<div class="line"><a id="l00782" name="l00782"></a><span class="lineno"> 782</span>}</div>
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|
<div class="line"><a id="l00783" name="l00783"></a><span class="lineno"> 783</span> </div>
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<div class="line"><a id="l00784" name="l00784"></a><span class="lineno"> 784</span>} <span class="comment">// namespace</span></div>
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|
<div class="line"><a id="l00785" name="l00785"></a><span class="lineno"> 785</span> </div>
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<div class="line"><a id="l00786" name="l00786"></a><span class="lineno"> 786</span><span class="comment">// The algorithm first computes into col_scratchpad_ the entries in pivot_row</span></div>
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<div class="line"><a id="l00787" name="l00787"></a><span class="lineno"> 787</span><span class="comment">// that are not in the row (i.e. the fill-in). It then updates the non-zero</span></div>
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<div class="line"><a id="l00788" name="l00788"></a><span class="lineno"> 788</span><span class="comment">// pattern using this temporary vector.</span></div>
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|
<div class="line"><a id="l00789" name="l00789"></a><span class="lineno"> 789</span><span class="keywordtype">void</span> MatrixNonZeroPattern::MergeIntoSorted(RowIndex pivot_row, RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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|
<div class="line"><a id="l00790" name="l00790"></a><span class="lineno"> 790</span> <span class="comment">// We want to add the entries of the input not already in the output.</span></div>
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<div class="line"><a id="l00791" name="l00791"></a><span class="lineno"> 791</span> <span class="keyword">const</span> <span class="keyword">auto</span>& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a> = row_non_zero_[pivot_row];</div>
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|
<div class="line"><a id="l00792" name="l00792"></a><span class="lineno"> 792</span> <span class="keyword">const</span> <span class="keyword">auto</span>& output = row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00793" name="l00793"></a><span class="lineno"> 793</span> </div>
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<div class="line"><a id="l00794" name="l00794"></a><span class="lineno"> 794</span> <span class="comment">// These two resizes are because of the set_difference() output iterator api.</span></div>
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<div class="line"><a id="l00795" name="l00795"></a><span class="lineno"> 795</span> col_scratchpad_.resize(<a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>.size());</div>
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<div class="line"><a id="l00796" name="l00796"></a><span class="lineno"> 796</span> col_scratchpad_.resize(std::set_difference(<a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>.begin(), <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>.end(),</div>
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|
<div class="line"><a id="l00797" name="l00797"></a><span class="lineno"> 797</span> output.begin(), output.end(),</div>
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|
<div class="line"><a id="l00798" name="l00798"></a><span class="lineno"> 798</span> col_scratchpad_.begin()) -</div>
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|
<div class="line"><a id="l00799" name="l00799"></a><span class="lineno"> 799</span> col_scratchpad_.begin());</div>
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<div class="line"><a id="l00800" name="l00800"></a><span class="lineno"> 800</span> </div>
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<div class="line"><a id="l00801" name="l00801"></a><span class="lineno"> 801</span> <span class="comment">// Add the fill-in to the pattern.</span></div>
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<div class="line"><a id="l00802" name="l00802"></a><span class="lineno"> 802</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : col_scratchpad_) {</div>
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<div class="line"><a id="l00803" name="l00803"></a><span class="lineno"> 803</span> ++col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00804" name="l00804"></a><span class="lineno"> 804</span> }</div>
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<div class="line"><a id="l00805" name="l00805"></a><span class="lineno"> 805</span> row_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] += col_scratchpad_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>();</div>
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<div class="line"><a id="l00806" name="l00806"></a><span class="lineno"> 806</span> MergeSortedVectors(col_scratchpad_, &row_non_zero_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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|
<div class="line"><a id="l00807" name="l00807"></a><span class="lineno"> 807</span>}</div>
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<div class="line"><a id="l00808" name="l00808"></a><span class="lineno"> 808</span> </div>
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<div class="line"><a id="l00809" name="l00809"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#aa71d36872f416feaa853788a7a7a7ef8"> 809</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#aa71d36872f416feaa853788a7a7a7ef8">ColumnPriorityQueue::Clear</a>() {</div>
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<div class="line"><a id="l00810" name="l00810"></a><span class="lineno"> 810</span> col_degree_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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|
<div class="line"><a id="l00811" name="l00811"></a><span class="lineno"> 811</span> col_index_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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|
<div class="line"><a id="l00812" name="l00812"></a><span class="lineno"> 812</span> col_by_degree_.clear();</div>
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|
<div class="line"><a id="l00813" name="l00813"></a><span class="lineno"> 813</span>}</div>
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<div class="line"><a id="l00814" name="l00814"></a><span class="lineno"> 814</span> </div>
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<div class="line"><a id="l00815" name="l00815"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a026a7cba6cd132662dae0468f395d3cf"> 815</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a026a7cba6cd132662dae0468f395d3cf">ColumnPriorityQueue::Reset</a>(<span class="keywordtype">int</span> max_degree, ColIndex num_cols) {</div>
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<div class="line"><a id="l00816" name="l00816"></a><span class="lineno"> 816</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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|
<div class="line"><a id="l00817" name="l00817"></a><span class="lineno"> 817</span> col_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#af8d7048738ceb4c753b040e6d29db79c">assign</a>(num_cols, 0);</div>
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|
<div class="line"><a id="l00818" name="l00818"></a><span class="lineno"> 818</span> col_index_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#af8d7048738ceb4c753b040e6d29db79c">assign</a>(num_cols, -1);</div>
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|
<div class="line"><a id="l00819" name="l00819"></a><span class="lineno"> 819</span> col_by_degree_.resize(max_degree + 1);</div>
|
|
<div class="line"><a id="l00820" name="l00820"></a><span class="lineno"> 820</span> min_degree_ = max_degree + 1;</div>
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|
<div class="line"><a id="l00821" name="l00821"></a><span class="lineno"> 821</span>}</div>
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|
<div class="line"><a id="l00822" name="l00822"></a><span class="lineno"> 822</span> </div>
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|
<div class="line"><a id="l00823" name="l00823"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a0a601ea6856d6a6162a705fe6ab48cbc"> 823</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a0a601ea6856d6a6162a705fe6ab48cbc">ColumnPriorityQueue::PushOrAdjust</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, int32_t degree) {</div>
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<div class="line"><a id="l00824" name="l00824"></a><span class="lineno"> 824</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(degree, 0);</div>
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<div class="line"><a id="l00825" name="l00825"></a><span class="lineno"> 825</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(degree, col_by_degree_.size());</div>
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<div class="line"><a id="l00826" name="l00826"></a><span class="lineno"> 826</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, 0);</div>
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|
<div class="line"><a id="l00827" name="l00827"></a><span class="lineno"> 827</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, col_degree_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>());</div>
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|
<div class="line"><a id="l00828" name="l00828"></a><span class="lineno"> 828</span> </div>
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|
<div class="line"><a id="l00829" name="l00829"></a><span class="lineno"> 829</span> <span class="keyword">const</span> int32_t old_degree = col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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|
<div class="line"><a id="l00830" name="l00830"></a><span class="lineno"> 830</span> <span class="keywordflow">if</span> (degree != old_degree) {</div>
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<div class="line"><a id="l00831" name="l00831"></a><span class="lineno"> 831</span> <span class="keyword">const</span> int32_t old_index = col_index_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00832" name="l00832"></a><span class="lineno"> 832</span> <span class="keywordflow">if</span> (old_index != -1) {</div>
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<div class="line"><a id="l00833" name="l00833"></a><span class="lineno"> 833</span> col_by_degree_[old_degree][old_index] = col_by_degree_[old_degree].back();</div>
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<div class="line"><a id="l00834" name="l00834"></a><span class="lineno"> 834</span> col_index_[col_by_degree_[old_degree].back()] = old_index;</div>
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<div class="line"><a id="l00835" name="l00835"></a><span class="lineno"> 835</span> col_by_degree_[old_degree].<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a058bda4957df6a97b1ea6c9fd783f672">pop_back</a>();</div>
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<div class="line"><a id="l00836" name="l00836"></a><span class="lineno"> 836</span> }</div>
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<div class="line"><a id="l00837" name="l00837"></a><span class="lineno"> 837</span> <span class="keywordflow">if</span> (degree > 0) {</div>
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<div class="line"><a id="l00838" name="l00838"></a><span class="lineno"> 838</span> col_index_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = col_by_degree_[degree].size();</div>
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<div class="line"><a id="l00839" name="l00839"></a><span class="lineno"> 839</span> col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = degree;</div>
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<div class="line"><a id="l00840" name="l00840"></a><span class="lineno"> 840</span> col_by_degree_[degree].push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00841" name="l00841"></a><span class="lineno"> 841</span> min_degree_ = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(min_degree_, degree);</div>
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<div class="line"><a id="l00842" name="l00842"></a><span class="lineno"> 842</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00843" name="l00843"></a><span class="lineno"> 843</span> col_index_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = -1;</div>
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<div class="line"><a id="l00844" name="l00844"></a><span class="lineno"> 844</span> col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = 0;</div>
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<div class="line"><a id="l00845" name="l00845"></a><span class="lineno"> 845</span> }</div>
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<div class="line"><a id="l00846" name="l00846"></a><span class="lineno"> 846</span> }</div>
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<div class="line"><a id="l00847" name="l00847"></a><span class="lineno"> 847</span>}</div>
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<div class="line"><a id="l00848" name="l00848"></a><span class="lineno"> 848</span> </div>
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<div class="line"><a id="l00849" name="l00849"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a49e7d07685ccac64b842fa1b1cc9a3cc"> 849</a></span>ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a49e7d07685ccac64b842fa1b1cc9a3cc">ColumnPriorityQueue::Pop</a>() {</div>
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<div class="line"><a id="l00850" name="l00850"></a><span class="lineno"> 850</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(min_degree_, 0);</div>
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<div class="line"><a id="l00851" name="l00851"></a><span class="lineno"> 851</span> <a class="code hl_define" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(min_degree_, col_by_degree_.size());</div>
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<div class="line"><a id="l00852" name="l00852"></a><span class="lineno"> 852</span> <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
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<div class="line"><a id="l00853" name="l00853"></a><span class="lineno"> 853</span> <span class="keywordflow">if</span> (min_degree_ == col_by_degree_.size()) <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div>
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<div class="line"><a id="l00854" name="l00854"></a><span class="lineno"> 854</span> <span class="keywordflow">if</span> (!col_by_degree_[min_degree_].empty()) <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00855" name="l00855"></a><span class="lineno"> 855</span> min_degree_++;</div>
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<div class="line"><a id="l00856" name="l00856"></a><span class="lineno"> 856</span> }</div>
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<div class="line"><a id="l00857" name="l00857"></a><span class="lineno"> 857</span> <span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = col_by_degree_[min_degree_].back();</div>
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<div class="line"><a id="l00858" name="l00858"></a><span class="lineno"> 858</span> col_by_degree_[min_degree_].pop_back();</div>
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<div class="line"><a id="l00859" name="l00859"></a><span class="lineno"> 859</span> col_index_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = -1;</div>
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<div class="line"><a id="l00860" name="l00860"></a><span class="lineno"> 860</span> col_degree_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = 0;</div>
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<div class="line"><a id="l00861" name="l00861"></a><span class="lineno"> 861</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00862" name="l00862"></a><span class="lineno"> 862</span>}</div>
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<div class="line"><a id="l00863" name="l00863"></a><span class="lineno"> 863</span> </div>
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<div class="line"><a id="l00864" name="l00864"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a1eb060a55278923620fda32549d18ae7"> 864</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a1eb060a55278923620fda32549d18ae7">SparseMatrixWithReusableColumnMemory::Reset</a>(ColIndex num_cols) {</div>
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<div class="line"><a id="l00865" name="l00865"></a><span class="lineno"> 865</span> mapping_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a184fe69018ae421dcf31c964bfe40576">assign</a>(num_cols.value(), -1);</div>
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<div class="line"><a id="l00866" name="l00866"></a><span class="lineno"> 866</span> free_columns_.clear();</div>
|
|
<div class="line"><a id="l00867" name="l00867"></a><span class="lineno"> 867</span> columns_.clear();</div>
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|
<div class="line"><a id="l00868" name="l00868"></a><span class="lineno"> 868</span>}</div>
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|
<div class="line"><a id="l00869" name="l00869"></a><span class="lineno"> 869</span> </div>
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<div class="line"><a id="l00870" name="l00870"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502"> 870</a></span><span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">SparseMatrixWithReusableColumnMemory::column</a>(</div>
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<div class="line"><a id="l00871" name="l00871"></a><span class="lineno"> 871</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00872" name="l00872"></a><span class="lineno"> 872</span> <span class="keywordflow">if</span> (mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] == -1) <span class="keywordflow">return</span> empty_column_;</div>
|
|
<div class="line"><a id="l00873" name="l00873"></a><span class="lineno"> 873</span> <span class="keywordflow">return</span> columns_[mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]];</div>
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|
<div class="line"><a id="l00874" name="l00874"></a><span class="lineno"> 874</span>}</div>
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|
<div class="line"><a id="l00875" name="l00875"></a><span class="lineno"> 875</span> </div>
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<div class="line"><a id="l00876" name="l00876"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a564caf35589006190ef4985fbda74faa"> 876</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a564caf35589006190ef4985fbda74faa">SparseMatrixWithReusableColumnMemory::mutable_column</a>(</div>
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<div class="line"><a id="l00877" name="l00877"></a><span class="lineno"> 877</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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|
<div class="line"><a id="l00878" name="l00878"></a><span class="lineno"> 878</span> <span class="keywordflow">if</span> (mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != -1) <span class="keywordflow">return</span> &columns_[mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]];</div>
|
|
<div class="line"><a id="l00879" name="l00879"></a><span class="lineno"> 879</span> <span class="keywordtype">int</span> new_col_index;</div>
|
|
<div class="line"><a id="l00880" name="l00880"></a><span class="lineno"> 880</span> <span class="keywordflow">if</span> (free_columns_.empty()) {</div>
|
|
<div class="line"><a id="l00881" name="l00881"></a><span class="lineno"> 881</span> new_col_index = columns_.size();</div>
|
|
<div class="line"><a id="l00882" name="l00882"></a><span class="lineno"> 882</span> columns_.push_back(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>());</div>
|
|
<div class="line"><a id="l00883" name="l00883"></a><span class="lineno"> 883</span> } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><a id="l00884" name="l00884"></a><span class="lineno"> 884</span> new_col_index = free_columns_.back();</div>
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|
<div class="line"><a id="l00885" name="l00885"></a><span class="lineno"> 885</span> free_columns_.pop_back();</div>
|
|
<div class="line"><a id="l00886" name="l00886"></a><span class="lineno"> 886</span> }</div>
|
|
<div class="line"><a id="l00887" name="l00887"></a><span class="lineno"> 887</span> mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = new_col_index;</div>
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|
<div class="line"><a id="l00888" name="l00888"></a><span class="lineno"> 888</span> <span class="keywordflow">return</span> &columns_[new_col_index];</div>
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|
<div class="line"><a id="l00889" name="l00889"></a><span class="lineno"> 889</span>}</div>
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|
<div class="line"><a id="l00890" name="l00890"></a><span class="lineno"> 890</span> </div>
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<div class="line"><a id="l00891" name="l00891"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a4d3e4198a395b77980b341d40ddb8b3c"> 891</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a4d3e4198a395b77980b341d40ddb8b3c">SparseMatrixWithReusableColumnMemory::ClearAndReleaseColumn</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00892" name="l00892"></a><span class="lineno"> 892</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], -1);</div>
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<div class="line"><a id="l00893" name="l00893"></a><span class="lineno"> 893</span> free_columns_.push_back(mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]);</div>
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<div class="line"><a id="l00894" name="l00894"></a><span class="lineno"> 894</span> columns_[mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]].Clear();</div>
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<div class="line"><a id="l00895" name="l00895"></a><span class="lineno"> 895</span> mapping_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = -1;</div>
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<div class="line"><a id="l00896" name="l00896"></a><span class="lineno"> 896</span>}</div>
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|
<div class="line"><a id="l00897" name="l00897"></a><span class="lineno"> 897</span> </div>
|
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<div class="line"><a id="l00898" name="l00898"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#aa71d36872f416feaa853788a7a7a7ef8"> 898</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#aa71d36872f416feaa853788a7a7a7ef8">SparseMatrixWithReusableColumnMemory::Clear</a>() {</div>
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<div class="line"><a id="l00899" name="l00899"></a><span class="lineno"> 899</span> mapping_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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|
<div class="line"><a id="l00900" name="l00900"></a><span class="lineno"> 900</span> free_columns_.clear();</div>
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<div class="line"><a id="l00901" name="l00901"></a><span class="lineno"> 901</span> columns_.clear();</div>
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|
<div class="line"><a id="l00902" name="l00902"></a><span class="lineno"> 902</span>}</div>
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<div class="line"><a id="l00903" name="l00903"></a><span class="lineno"> 903</span> </div>
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<div class="line"><a id="l00904" name="l00904"></a><span class="lineno"> 904</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00905" name="l00905"></a><span class="lineno"> 905</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a4395e95bab44e222cb2e77251017a0e2"><div class="ttname"><a href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a></div><div class="ttdeci">#define DCHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00893">base/logging.h:893</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0"><div class="ttname"><a href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a></div><div class="ttdeci">#define DCHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00892">base/logging.h:892</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295"><div class="ttname"><a href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a></div><div class="ttdeci">#define DCHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00895">base/logging.h:895</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ab62f5ed8f2d48e29802be0cbbcd1359a"><div class="ttname"><a href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a></div><div class="ttdeci">#define DCHECK_LT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00894">base/logging.h:894</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="abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00891">base/logging.h:891</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="aclassabsl_1_1_strong_vector_html_a058bda4957df6a97b1ea6c9fd783f672"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a058bda4957df6a97b1ea6c9fd783f672">absl::StrongVector::pop_back</a></div><div class="ttdeci">void pop_back()</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00168">strong_vector.h:168</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a184fe69018ae421dcf31c964bfe40576"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a184fe69018ae421dcf31c964bfe40576">absl::StrongVector::assign</a></div><div class="ttdeci">void assign(size_type n, const value_type &val)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00131">strong_vector.h:131</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a4e3670a285a3642eaa07f66766cffa72"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a4e3670a285a3642eaa07f66766cffa72">absl::StrongVector::resize</a></div><div class="ttdeci">void resize(size_type new_size)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00150">strong_vector.h:150</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a562f7b24b47d3e7632a9896935c14d8b"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a562f7b24b47d3e7632a9896935c14d8b">absl::StrongVector::reserve</a></div><div class="ttdeci">void reserve(size_type n)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00157">strong_vector.h:157</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a60304b65bf89363bcc3165d3cde67f86"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a60304b65bf89363bcc3165d3cde67f86">absl::StrongVector::size</a></div><div class="ttdeci">size_type size() const</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00147">strong_vector.h:147</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a9263000d449fdccb6cb70b303063e60b"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">absl::StrongVector::push_back</a></div><div class="ttdeci">void push_back(const value_type &x)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00158">strong_vector.h:158</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_ac8bb3912a3ce86b15842e79d0b421204"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">absl::StrongVector::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00170">strong_vector.h:170</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_priority_queue_html_a026a7cba6cd132662dae0468f395d3cf"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a026a7cba6cd132662dae0468f395d3cf">operations_research::glop::ColumnPriorityQueue::Reset</a></div><div class="ttdeci">void Reset(int32_t max_degree, ColIndex num_cols)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00815">markowitz.cc:815</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_priority_queue_html_a0a601ea6856d6a6162a705fe6ab48cbc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a0a601ea6856d6a6162a705fe6ab48cbc">operations_research::glop::ColumnPriorityQueue::PushOrAdjust</a></div><div class="ttdeci">void PushOrAdjust(ColIndex col, int32_t degree)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00823">markowitz.cc:823</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_priority_queue_html_a49e7d07685ccac64b842fa1b1cc9a3cc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_priority_queue.html#a49e7d07685ccac64b842fa1b1cc9a3cc">operations_research::glop::ColumnPriorityQueue::Pop</a></div><div class="ttdeci">ColIndex Pop()</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00849">markowitz.cc:849</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_priority_queue_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_priority_queue.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::ColumnPriorityQueue::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00809">markowitz.cc:809</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::ColumnView::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00082">sparse_column.h:82</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">operations_research::glop::CompactSparseMatrixView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00476">sparse.h:476</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrixView::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00489">sparse.h:489</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a6c2cb025b83ee5d5365eb0b419a0298c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">operations_research::glop::CompactSparseMatrixView::column</a></div><div class="ttdeci">const ColumnView column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00490">sparse.h:490</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::CompactSparseMatrixView::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00487">sparse.h:487</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrixView::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00488">sparse.h:488</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_a627511bf305a6af5d7e114817c1792c2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#a627511bf305a6af5d7e114817c1792c2">operations_research::glop::Markowitz::DeterministicTimeOfLastFactorization</a></div><div class="ttdeci">double DeterministicTimeOfLastFactorization() const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00553">markowitz.cc:553</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_a7ac2557be8cf0394f9953fbdac2f18f4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#a7ac2557be8cf0394f9953fbdac2f18f4">operations_research::glop::Markowitz::ComputeLU</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ComputeLU(const CompactSparseMatrixView &basis_matrix, RowPermutation *row_perm, ColumnPermutation *col_perm, TriangularMatrix *lower, TriangularMatrix *upper)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00149">markowitz.cc:149</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::Markowitz::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00169">markowitz.cc:169</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_afd3f022e573b8f4f0901624a813ade07"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#afd3f022e573b8f4f0901624a813ade07">operations_research::glop::Markowitz::ComputeRowAndColumnPermutation</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ComputeRowAndColumnPermutation(const CompactSparseMatrixView &basis_matrix, RowPermutation *row_perm, ColumnPermutation *col_perm)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00027">markowitz.cc:27</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a1f59bbe4cda31ad0ee8a91c4bd57e945"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a1f59bbe4cda31ad0ee8a91c4bd57e945">operations_research::glop::MatrixNonZeroPattern::IsColumnDeleted</a></div><div class="ttdeci">bool IsColumnDeleted(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00652">markowitz.cc:652</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a2527e336adfc8144ee253eed236fa699"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a2527e336adfc8144ee253eed236fa699">operations_research::glop::MatrixNonZeroPattern::RemoveDeletedColumnsFromRow</a></div><div class="ttdeci">void RemoveDeletedColumnsFromRow(RowIndex row)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00656">markowitz.cc:656</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a25db8d6277cbd4811441929a1817dea0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a25db8d6277cbd4811441929a1817dea0">operations_research::glop::MatrixNonZeroPattern::DecreaseColDegree</a></div><div class="ttdeci">int32_t DecreaseColDegree(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00634">markowitz.cc:634</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a28a4e2ca582ad13d6ab28d1c757934c0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a28a4e2ca582ad13d6ab28d1c757934c0">operations_research::glop::MatrixNonZeroPattern::RowNonZero</a></div><div class="ttdeci">const absl::InlinedVector< ColIndex, 6 > & RowNonZero(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8h_source.html#l00168">markowitz.h:168</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a437a888007d0475cfaf07ac70538c458"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a437a888007d0475cfaf07ac70538c458">operations_research::glop::MatrixNonZeroPattern::DeleteRowAndColumn</a></div><div class="ttdeci">void DeleteRowAndColumn(RowIndex pivot_row, ColIndex pivot_col)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00642">markowitz.cc:642</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a44badccd63c183b774ba7bfb005aac9f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a44badccd63c183b774ba7bfb005aac9f">operations_research::glop::MatrixNonZeroPattern::RowDegree</a></div><div class="ttdeci">int32_t RowDegree(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8h_source.html#l00163">markowitz.h:163</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a8036bd4d1fc8a69112a1f7ed5493a924"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a8036bd4d1fc8a69112a1f7ed5493a924">operations_research::glop::MatrixNonZeroPattern::AddEntry</a></div><div class="ttdeci">void AddEntry(RowIndex row, ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00628">markowitz.cc:628</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a85e6c7ebc5ac22d117ff412e3658c72d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a85e6c7ebc5ac22d117ff412e3658c72d">operations_research::glop::MatrixNonZeroPattern::Reset</a></div><div class="ttdeci">void Reset(RowIndex num_rows, ColIndex num_cols)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00566">markowitz.cc:566</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_a965275e22dbb55799f5b99cca98e0fbc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#a965275e22dbb55799f5b99cca98e0fbc">operations_research::glop::MatrixNonZeroPattern::Update</a></div><div class="ttdeci">void Update(RowIndex pivot_row, ColIndex pivot_col, const SparseColumn &column)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00678">markowitz.cc:678</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::MatrixNonZeroPattern::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00557">markowitz.cc:557</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_aa844f860b76cad2a3682e7d9b927195c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#aa844f860b76cad2a3682e7d9b927195c">operations_research::glop::MatrixNonZeroPattern::DecreaseRowDegree</a></div><div class="ttdeci">int32_t DecreaseRowDegree(RowIndex row)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00638">markowitz.cc:638</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_ac6fdf4b27f37d788a51ff50a47d0a3df"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#ac6fdf4b27f37d788a51ff50a47d0a3df">operations_research::glop::MatrixNonZeroPattern::ColDegree</a></div><div class="ttdeci">int32_t ColDegree(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8h_source.html#l00156">markowitz.h:156</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_af14468b811c1218ef477ccbd170e6f8d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af14468b811c1218ef477ccbd170e6f8d">operations_research::glop::MatrixNonZeroPattern::GetFirstNonDeletedColumnFromRow</a></div><div class="ttdeci">ColIndex GetFirstNonDeletedColumnFromRow(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00670">markowitz.cc:670</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_non_zero_pattern_html_af6141c80a5d2f56d86f149c822065cc5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_non_zero_pattern.html#af6141c80a5d2f56d86f149c822065cc5">operations_research::glop::MatrixNonZeroPattern::InitializeFromMatrixSubset</a></div><div class="ttdeci">void InitializeFromMatrixSubset(const CompactSparseMatrixView &basis_matrix, const RowPermutation &row_perm, const ColumnPermutation &col_perm, std::vector< ColIndex > *singleton_columns, std::vector< RowIndex > *singleton_rows)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00576">markowitz.cc:576</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html">operations_research::glop::Permutation< RowIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_acb8f594fc0399176a6201d6c66eb0419"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#acb8f594fc0399176a6201d6c66eb0419">operations_research::glop::Permutation::assign</a></div><div class="ttdeci">void assign(IndexType size, IndexType value)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00059">lp_data/permutation.h:59</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html">operations_research::glop::SparseColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00044">sparse_column.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory_html_a1eb060a55278923620fda32549d18ae7"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a1eb060a55278923620fda32549d18ae7">operations_research::glop::SparseMatrixWithReusableColumnMemory::Reset</a></div><div class="ttdeci">void Reset(ColIndex num_cols)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00864">markowitz.cc:864</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory_html_a4d3e4198a395b77980b341d40ddb8b3c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a4d3e4198a395b77980b341d40ddb8b3c">operations_research::glop::SparseMatrixWithReusableColumnMemory::ClearAndReleaseColumn</a></div><div class="ttdeci">void ClearAndReleaseColumn(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00891">markowitz.cc:891</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory_html_a564caf35589006190ef4985fbda74faa"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a564caf35589006190ef4985fbda74faa">operations_research::glop::SparseMatrixWithReusableColumnMemory::mutable_column</a></div><div class="ttdeci">SparseColumn * mutable_column(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00876">markowitz.cc:876</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory_html_a7273cc492a51a1c5d45c620b32fce502"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#a7273cc492a51a1c5d45c620b32fce502">operations_research::glop::SparseMatrixWithReusableColumnMemory::column</a></div><div class="ttdeci">const SparseColumn & column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00870">markowitz.cc:870</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_with_reusable_column_memory.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::SparseMatrixWithReusableColumnMemory::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00898">markowitz.cc:898</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::SparseVector::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00529">lp_data/sparse_vector.h:529</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_ab38326ea6cb6187267665dd8b2748f3d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">operations_research::glop::SparseVector< RowIndex, SparseColumnIterator >::Entry</a></div><div class="ttdeci">typename Iterator::Entry Entry</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00091">lp_data/sparse_vector.h:91</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html">operations_research::glop::Status</a></div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00026">status.h:26</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_a071b1d04197c0ac6e7a4d0ec0b91ff43"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">operations_research::glop::Status::OK</a></div><div class="ttdeci">static const Status OK()</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00056">status.h:56</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_a59e56af19e754a6aa26a612ebf91d05fafa2ff9c081445bfbfbda10bc41b76a87"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a59e56af19e754a6aa26a612ebf91d05fafa2ff9c081445bfbfbda10bc41b76a87">operations_research::glop::Status::ERROR_LU</a></div><div class="ttdeci">@ ERROR_LU</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00034">status.h:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a3de922485ca2c30f3e07d959dd97cdd0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">operations_research::glop::StrictITIVector::AssignToZero</a></div><div class="ttdeci">void AssignToZero(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00294">lp_types.h:294</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00280">lp_types.h:280</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_af8d7048738ceb4c753b040e6d29db79c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#af8d7048738ceb4c753b040e6d29db79c">operations_research::glop::StrictITIVector::assign</a></div><div class="ttdeci">void assign(IntType size, const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00278">lp_types.h:278</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html">operations_research::glop::TriangularMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00511">sparse.h:511</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a2ffa6dbb95dfb7e397bf69fd1ddd188e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a2ffa6dbb95dfb7e397bf69fd1ddd188e">operations_research::glop::TriangularMatrix::AddTriangularColumnWithGivenDiagonalEntry</a></div><div class="ttdeci">void AddTriangularColumnWithGivenDiagonalEntry(const SparseColumn &column, RowIndex diagonal_row, Fractional diagonal_value)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00699">sparse.cc:699</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a3e1b01501c922d36c55fb59cfc18e630"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3e1b01501c922d36c55fb59cfc18e630">operations_research::glop::TriangularMatrix::Swap</a></div><div class="ttdeci">void Swap(TriangularMatrix *other)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00620">sparse.cc:620</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a8d3594198944bf0a6ac2669581085683"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8d3594198944bf0a6ac2669581085683">operations_research::glop::TriangularMatrix::AddAndNormalizeTriangularColumn</a></div><div class="ttdeci">void AddAndNormalizeTriangularColumn(const SparseColumn &column, RowIndex diagonal_row, Fractional diagonal_coefficient)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00682">sparse.cc:682</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_ab5a8a005f27ece21134c277a33057c70"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab5a8a005f27ece21134c277a33057c70">operations_research::glop::TriangularMatrix::AddTriangularColumn</a></div><div class="ttdeci">void AddTriangularColumn(const ColumnView &column, RowIndex diagonal_row)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00667">sparse.cc:667</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_abedd52dbc024598bf0189235764f734a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#abedd52dbc024598bf0189235764f734a">operations_research::glop::TriangularMatrix::PermutedLowerSparseSolve</a></div><div class="ttdeci">void PermutedLowerSparseSolve(const ColumnView &rhs, const RowPermutation &row_perm, SparseColumn *lower, SparseColumn *upper)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l01065">sparse.cc:1065</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_ad001a49701677a22b4efd9186b97ae05"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ad001a49701677a22b4efd9186b97ae05">operations_research::glop::TriangularMatrix::ApplyRowPermutationToNonDiagonalEntries</a></div><div class="ttdeci">void ApplyRowPermutationToNonDiagonalEntries(const RowPermutation &row_perm)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00739">sparse.cc:739</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_ae95eb4b81113f212b6aae874a15808df"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ae95eb4b81113f212b6aae874a15808df">operations_research::glop::TriangularMatrix::AddDiagonalOnlyColumn</a></div><div class="ttdeci">void AddDiagonalOnlyColumn(Fractional diagonal_value)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00663">sparse.cc:663</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_aec8942e8b01f9aed2abc24de9acfb6ab"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aec8942e8b01f9aed2abc24de9acfb6ab">operations_research::glop::TriangularMatrix::NumFpOperationsInLastPermutedLowerSparseSolve</a></div><div class="ttdeci">int64_t NumFpOperationsInLastPermutedLowerSparseSolve() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00709">sparse.h:709</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_aeebcdc829c541f3ca21a15784f02fe9c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">operations_research::glop::TriangularMatrix::Reset</a></div><div class="ttdeci">void Reset(RowIndex num_rows, ColIndex col_capacity)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00551">sparse.cc:551</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::TriangularMatrix::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00523">sparse.h:523</a></div></div>
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<div class="ttc" id="aglpk__solver_8cc_html_abb82b111deb51f3a5917cf8780fee484"><div class="ttname"><a href="glpk__solver_8cc.html#abb82b111deb51f3a5917cf8780fee484">lower</a></div><div class="ttdeci">double lower</div><div class="ttdef"><b>Definition:</b> <a href="glpk__solver_8cc_source.html#l00075">glpk_solver.cc:75</a></div></div>
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<div class="ttc" id="aglpk__solver_8cc_html_ae0e265c074f457e193b30ff0d77c750b"><div class="ttname"><a href="glpk__solver_8cc.html#ae0e265c074f457e193b30ff0d77c750b">upper</a></div><div class="ttdeci">double upper</div><div class="ttdef"><b>Definition:</b> <a href="glpk__solver_8cc_source.html#l00076">glpk_solver.cc:76</a></div></div>
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<div class="ttc" id="alocal__search_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="local__search_8cc_source.html#l02750">local_search.cc:2750</a></div></div>
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<div class="ttc" id="alp__data_2lp__utils_8h_html"><div class="ttname"><a href="lp__data_2lp__utils_8h.html">lp_utils.h</a></div></div>
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<div class="ttc" id="alp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_a722e11301e7de93191aa47dbd3ecb4d8"><div class="ttname"><a href="markowitz_8cc.html#a722e11301e7de93191aa47dbd3ecb4d8">coefficient</a></div><div class="ttdeci">Fractional coefficient</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00184">markowitz.cc:184</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
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<div class="ttc" id="amarkowitz_8h_html"><div class="ttname"><a href="markowitz_8h.html">markowitz.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a31ee82f6ef05c3da492c0376f910d015"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">operations_research::glop::kInvalidRow</a></div><div class="ttdeci">const RowIndex kInvalidRow(-1)</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a6b1b56ad0cb77edbd314f2bec33b467a"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">operations_research::glop::ColumnPermutation</a></div><div class="ttdeci">Permutation< ColIndex > ColumnPermutation</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00095">lp_data/permutation.h:95</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_ae69267cf0653a77925ee13121b9857ec"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">operations_research::glop::RowPermutation</a></div><div class="ttdeci">Permutation< RowIndex > RowPermutation</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00094">lp_data/permutation.h:94</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_aedb714d776d86539dbb9f42ae5d7d923"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#aedb714d776d86539dbb9f42ae5d7d923">operations_research::glop::DeterministicTimeForFpOperations</a></div><div class="ttdeci">static double DeterministicTimeForFpOperations(int64_t n)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00383">lp_types.h:383</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_afb755b7934d8679476e2f05a89739bcd"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">operations_research::glop::kInvalidCol</a></div><div class="ttdeci">const ColIndex kInvalidCol(-1)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="aparser_8yy_8cc_html_a5a634cf4429798b1c921a81de8250051"><div class="ttname"><a href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a></div><div class="ttdeci">static int input(yyscan_t yyscanner)</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="asparse_8h_html"><div class="ttname"><a href="sparse_8h.html">sparse.h</a></div></div>
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<div class="ttc" id="asparse__submatrix_8cc_html_a4d53eac2ef2732c28fa9fb663e0c19a7"><div class="ttname"><a href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a></div><div class="ttdeci">std::optional< int64_t > end</div><div class="ttdef"><b>Definition:</b> <a href="sparse__submatrix_8cc_source.html#l00036">sparse_submatrix.cc:36</a></div></div>
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<div class="ttc" id="astats_8h_html_a3c3e6b102f0d91c523099325c98e1887"><div class="ttname"><a href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a></div><div class="ttdeci">#define IF_STATS_ENABLED(instructions)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00437">stats.h:437</a></div></div>
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<div class="ttc" id="astats_8h_html_a9995704aaaf45fc21e08c847551a8d04"><div class="ttname"><a href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a></div><div class="ttdeci">#define SCOPED_TIME_STAT(stats)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00438">stats.h:438</a></div></div>
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<div class="ttc" id="astatus_8h_html_a3efb1c6250c02a5b881f8b82f75f9822"><div class="ttname"><a href="status_8h.html#a3efb1c6250c02a5b881f8b82f75f9822">GLOP_RETURN_IF_ERROR</a></div><div class="ttdeci">#define GLOP_RETURN_IF_ERROR(function_call)</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00072">status.h:72</a></div></div>
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<div class="ttc" id="avariable__and__expressions_8cc_html_a2091cd7d80fdd31762020bce86138587"><div class="ttname"><a href="variable__and__expressions_8cc.html#a2091cd7d80fdd31762020bce86138587">coeff</a></div><div class="ttdeci">const double coeff</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8cc_source.html#l00105">variable_and_expressions.cc:105</a></div></div>
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