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<div class="headertitle"><div class="title">lu_factorization.h</div></div>
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<a href="lu__factorization_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#ifndef OR_TOOLS_GLOP_LU_FACTORIZATION_H_</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_GLOP_LU_FACTORIZATION_H_</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include "<a class="code" href="markowitz_8h.html">ortools/glop/markowitz.h</a>"</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include "<a class="code" href="parameters_8pb_8h.html">ortools/glop/parameters.pb.h</a>"</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include "<a class="code" href="status_8h.html">ortools/glop/status.h</a>"</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_2permutation_8h.html">ortools/lp_data/permutation.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="scattered__vector_8h.html">ortools/lp_data/scattered_vector.h</a>"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="sparse_8h.html">ortools/lp_data/sparse.h</a>"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="sparse__column_8h.html">ortools/lp_data/sparse_column.h</a>"</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include "<a class="code" href="stats_8h.html">ortools/util/stats.h</a>"</span></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"> 27</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="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// An LU-Factorization class encapsulating the LU factorization data and</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// algorithms. The actual algorithm is in markowitz.h and .cc. This class holds</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// all the Solve() functions that deal with the permutations and the L and U</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// factors once they are computed.</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html"> 34</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_lu_factorization.html">LuFactorization</a> {</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">LuFactorization</a>();</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Returns true if the LuFactorization is a factorization of the identity</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// matrix. In this state, all the Solve() functions will work for any</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// vector dimension.</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#adbf20cf678d328e6b36c8bb43dc499cf"> 41</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#adbf20cf678d328e6b36c8bb43dc499cf">IsIdentityFactorization</a>() { <span class="keywordflow">return</span> is_identity_factorization_; }</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// Clears internal data structure and reset this class to the factorization</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// of an identity matrix.</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Computes an LU-decomposition for a given matrix B. If for some reason,</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// there was an error, then the factorization is reset to the one of the</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// identity matrix, and an error is reported.</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// Note(user): Since a client must use the result, there is little chance of</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// it being confused by this revert to identity factorization behavior. The</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// reason behind it is that this way, calling any public function of this</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// class will never cause a crash of the program.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> ABSL_MUST_USE_RESULT <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4">ComputeFactorization</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>& compact_matrix);</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">// Given a set of columns, find a maximum linearly independent subset that can</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// be factorized in a stable way, and complete it into a square matrix using</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// slack columns. The initial set can have less, more or the same number of</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// columns as the number of rows.</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3c3fa8faef594bd4a249b4aaa5e32d8e">ComputeInitialBasis</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& matrix,</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">const</span> std::vector<ColIndex>& candidates);</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// Returns the column permutation used by the LU factorization.</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3deeb8998f541c08d96dc079591a54"> 66</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3deeb8998f541c08d96dc079591a54">GetColumnPermutation</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> col_perm_; }</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// Sets the column permutation to the identity permutation. The idea is that</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// the column permutation can be incorporated in the basis RowToColMapping,</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// and once this is done, then a client can call this and effectively remove</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// the need for a column permutation on each solve.</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58"> 72</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58">SetColumnPermutationToIdentity</a>() {</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> inverse_col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> }</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Solves 'B.x = b', x initially contains b, and is replaced by 'B^{-1}.b'.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// Since P.B.Q^{-1} = L.U, we have B = P^{-1}.L.U.Q.</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// 1/ Solve P^{-1}.y = b for y by computing y = P.b,</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// 2/ solve L.z = y for z,</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// 3/ solve U.t = z for t,</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// 4/ finally solve Q.x = t, by computing x = Q^{-1}.t.</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">RightSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// Solves 'y.B = r', y initially contains r, and is replaced by r.B^{-1}.</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// Internally, it takes x = y^T, b = r^T and solves B^T.x = b.</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// We have P.B.Q^{-1} = P.B.Q^T = L.U, thus (L.U)^T = Q.B^T.P^T.</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// Therefore B^T = Q^{-1}.U^T.L^T.P^T.P^{-1} = Q^{-1}.U^T.L^T.P</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// The procedure is thus:</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// 1/ Solve Q^{-1}.y = b for y, by computing y = Q.b,</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// 2/ solve U^T.z = y for z,</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// 3/ solve L^T.t = z for t,</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// 4/ finally, solve P.x = t for x by computing x = P^{-1}.t.</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">LeftSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// More fine-grained right/left solve functions that may exploit the initial</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// non-zeros of the input vector if non-empty. Note that a solve involving L</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// actually solves P^{-1}.L and a solve involving U actually solves U.Q. To</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// solve a system with the initial matrix B, one needs to call:</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// - RightSolveL() and then RightSolveU() for a right solve (B.x = initial x).</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// - LeftSolveU() and then LeftSolveL() for a left solve (y.B = initial y).</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424">RightSolveLWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac">RightSolveUWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108">LeftSolveUWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// Specialized version of LeftSolveL() that may exploit the initial non_zeros</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// of y if it is non empty. Moreover, if result_before_permutation is not</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// NULL, it might be filled with the result just before row_perm_ is applied</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// to it and true is returned. If result_before_permutation is not filled,</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// then false is returned.</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LeftSolveLWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y,</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* result_before_permutation) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LeftSolveLWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// Specialized version of RightSolveLWithNonZeros() that takes a SparseColumn</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// or a ScatteredColumn as input. non_zeros will either be cleared or set to</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// the non zeros of the result. Important: the output x must be of the correct</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// size and all zero.</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661">RightSolveLForColumnView</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a">RightSolveLForScatteredColumn</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// Specialized version of RightSolveLWithNonZeros() where x is originally</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="comment">// equal to 'a' permuted by row_perm_. Note that 'a' is only used for DCHECK.</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83">RightSolveLWithPermutedInput</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>,</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// Specialized version of LeftSolveU() for an unit right-hand side.</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// non_zeros will either be cleared or set to the non zeros of the results.</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// It also returns the value of col permuted by Q (which is the position</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// of the unit-vector rhs in the solve system: y.U = rhs).</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// Important: the output y must be of the correct size and all zero.</span></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0">LeftSolveUForUnitRow</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// Returns the given column of U.</span></div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// It will only be valid until the next call to GetColumnOfU().</span></div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</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_lu_factorization.html#a3042b0778d3d901556345438e482d88a">GetColumnOfU</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="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// Returns the norm of B^{-1}.a</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d">RightSolveSquaredNorm</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a id="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> <span class="comment">// Returns the norm of (B^T)^{-1}.e_row where e is an unit vector.</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">DualEdgeSquaredNorm</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> </div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// The fill-in of the LU-factorization is defined as the sum of the number</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// of entries of both the lower- and upper-triangular matrices L and U minus</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// the number of entries in the initial matrix B.</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// This returns the number of entries in lower + upper as the percentage of</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="comment">// the number of entries in B.</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425">GetFillInPercentage</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>& matrix) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// Returns the number of entries in L + U.</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// If the factorization is the identity, this returns 0.</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> EntryIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1">NumberOfEntries</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> </div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// Computes the determinant of the input matrix B.</span></div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// Since P.B.Q^{-1} = L.U, det(P) * det(B) * det(Q^{-1}) = det(L) * det(U).</span></div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// det(L) = 1 since L is a lower-triangular matrix with 1 on the diagonal.</span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// det(P) = +1 or -1 (by definition it is the sign of the permutation P)</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="comment">// det(Q^{-1}) = +1 or -1 (the sign of the permutation Q^{-1})</span></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// Finally det(U) = product of the diagonal elements of U, since U is an</span></div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// upper-triangular matrix.</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="comment">// Taking all this into account:</span></div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// det(B) = sign(P) * sign(Q^{-1}) * prod_i u_ii .</span></div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e">ComputeDeterminant</a>() <span class="keyword">const</span>;</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> <span class="comment">// Computes the 1-norm of the inverse of the input matrix B.</span></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="comment">// For this we iteratively solve B.x = e_j, where e_j is the jth unit vector.</span></div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// The result of this computation is the jth column of B^-1.</span></div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// The 1-norm |B| is defined as max_j sum_i |a_ij|</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// http://en.wikipedia.org/wiki/Matrix_norm</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937">ComputeInverseOneNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// Computes the infinity-norm of the inverse of the input matrix B.</span></div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// The infinity-norm |B| is defined as max_i sum_j |a_ij|</span></div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// http://en.wikipedia.org/wiki/Matrix_norm</span></div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">ComputeInverseInfinityNorm</a>() <span class="keyword">const</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="comment">// Computes the condition number of the input matrix B.</span></div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// For a given norm, this is the matrix norm times the norm of its inverse.</span></div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// Note that because the LuFactorization class does not keep the</span></div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// non-factorized matrix in memory, it needs to be passed to these functions.</span></div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// It is up to the client to pass exactly the same matrix as the one used</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// for ComputeFactorization().</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// TODO(user): separate this from LuFactorization.</span></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8">ComputeOneNormConditionNumber</a>(</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</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>& matrix) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657">ComputeInfinityNormConditionNumber</a>(</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</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>& matrix) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38">ComputeInverseInfinityNormUpperBound</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// Sets the current parameters.</span></div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea"> 196</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">SetParameters</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_glop_parameters.html">GlopParameters</a>& <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>) {</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> parameters_ = <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>;</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> markowitz_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#ae7202d055b6b172a8a1da4f5b136f9ea">SetParameters</a>(<a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>);</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> }</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// Returns a string containing the statistics for this class.</span></div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f"> 202</a></span> std::string <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f">StatString</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="keywordflow">return</span> stats_.StatString() + markowitz_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#af9bc435481ae9e6e60d66a65d5394a7f">StatString</a>();</div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> }</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> </div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// This is only used for testing and in debug mode.</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// TODO(user): avoid the matrix conversion by multiplying TriangularMatrix</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// directly.</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305"> 209</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305">ComputeLowerTimesUpper</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* product)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a> temp_lower, temp_upper;</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e">CopyToSparseMatrix</a>(&temp_lower);</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e">CopyToSparseMatrix</a>(&temp_upper);</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> product-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#aa1c2872fa7d491d4c093c8b2124a53b9">PopulateFromProduct</a>(temp_lower, temp_upper);</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> }</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> </div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// Returns the deterministic time of the last factorization.</span></div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2">DeterministicTimeOfLastFactorization</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="comment">// Visible for testing.</span></div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af2e901d9cdc8f3f36f5b54ef1455c712"> 220</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af2e901d9cdc8f3f36f5b54ef1455c712">row_perm</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> row_perm_; }</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a41e666f39c778c69ade38b4db0c223ec"> 221</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a41e666f39c778c69ade38b4db0c223ec">inverse_col_perm</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">return</span> inverse_col_perm_;</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> </div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="comment">// Statistics about this class.</span></div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keyword">struct </span>Stats : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1_stats_group.html">StatsGroup</a> {</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> Stats()</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> : <a class="code hl_class" href="classoperations__research_1_1_stats_group.html">StatsGroup</a>(<span class="stringliteral">"LuFactorization"</span>),</div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> basis_num_entries(<span class="stringliteral">"basis_num_entries"</span>, this),</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> lu_fill_in(<span class="stringliteral">"lu_fill_in"</span>, this) {}</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <a class="code hl_class" href="classoperations__research_1_1_integer_distribution.html">IntegerDistribution</a> basis_num_entries;</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <a class="code hl_class" href="classoperations__research_1_1_ratio_distribution.html">RatioDistribution</a> lu_fill_in;</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> };</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// Internal function used in the left solve functions.</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> LeftSolveScratchpad() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> </div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="comment">// Internal function used in the right solve functions</span></div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Column></div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordtype">void</span> RightSolveLInternal(<span class="keyword">const</span> Column& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, ScatteredColumn* x) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> </div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// Fills transpose_upper_ from upper_.</span></div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordtype">void</span> ComputeTransposeUpper();</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> </div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// transpose_lower_ is only needed when we compute dual norms.</span></div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordtype">void</span> ComputeTransposeLower() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> </div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="comment">// Computes R = P.B.Q^{-1} - L.U and returns false if the largest magnitude of</span></div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// the coefficients of P.B.Q^{-1} - L.U is greater than tolerance.</span></div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keywordtype">bool</span> CheckFactorization(<span class="keyword">const</span> CompactSparseMatrixView& matrix,</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> </div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="comment">// Special case where we have nothing to do. This happens at the beginning</span></div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="comment">// when we start the problem with an all-slack basis and gives a good speedup</span></div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="comment">// on really easy problems. It is initially true and set to true each time we</span></div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="comment">// call Clear(). We set it to false if a call to ComputeFactorization()</span></div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="comment">// succeeds.</span></div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="keywordtype">bool</span> is_identity_factorization_;</div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// The triangular factor L and U (and its transpose).</span></div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> TriangularMatrix lower_;</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> TriangularMatrix upper_;</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> TriangularMatrix transpose_upper_;</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">// The transpose of lower_. It is just used by DualEdgeSquaredNorm()</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="comment">// and mutable so it can be lazily initialized.</span></div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keyword">mutable</span> TriangularMatrix transpose_lower_;</div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="comment">// The column permutation Q and its inverse Q^{-1} in P.B.Q^{-1} = L.U.</span></div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</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="l00272" name="l00272"></a><span class="lineno"> 272</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a> inverse_col_perm_;</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> </div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="comment">// The row permutation P and its inverse P^{-1} in P.B.Q^{-1} = L.U.</span></div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</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="l00276" name="l00276"></a><span class="lineno"> 276</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a> inverse_row_perm_;</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> </div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <span class="comment">// Temporary storage used by LeftSolve()/RightSolve().</span></div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keyword">mutable</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a> dense_column_scratchpad_;</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> </div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="comment">// Temporary storage used by GetColumnOfU().</span></div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keyword">mutable</span> SparseColumn column_of_upper_;</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> </div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// Same as dense_column_scratchpad_ but this vector is always reset to zero by</span></div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="comment">// the functions that use it. non_zero_rows_ is used to track the</span></div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// non_zero_rows_ position of dense_column_scratchpad_.</span></div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="keyword">mutable</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a> dense_zero_scratchpad_;</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keyword">mutable</span> std::vector<RowIndex> non_zero_rows_;</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> </div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="comment">// Statistics, mutable so const functions can still update it.</span></div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keyword">mutable</span> Stats stats_;</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">// Proto holding all the parameters of this algorithm.</span></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> GlopParameters parameters_;</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> </div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="comment">// The class doing the Markowitz LU factorization.</span></div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> Markowitz markowitz_;</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> </div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">LuFactorization</a>);</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span>};</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> </div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_GLOP_LU_FACTORIZATION_H_</span></div>
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<div class="ttc" id="aclassoperations__research_1_1_integer_distribution_html"><div class="ttname"><a href="classoperations__research_1_1_integer_distribution.html">operations_research::IntegerDistribution</a></div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00287">stats.h:287</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_ratio_distribution_html"><div class="ttname"><a href="classoperations__research_1_1_ratio_distribution.html">operations_research::RatioDistribution</a></div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00263">stats.h:263</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_stats_group_html"><div class="ttname"><a href="classoperations__research_1_1_stats_group.html">operations_research::StatsGroup</a></div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00131">stats.h:131</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html">operations_research::glop::ColumnView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00065">sparse_column.h:65</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">operations_research::glop::CompactSparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00289">sparse.h:289</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_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_glop_parameters_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html">operations_research::glop::GlopParameters</a></div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l00194">parameters.pb.h:195</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html">operations_research::glop::LuFactorization</a></div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00034">lu_factorization.h:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a05d6979828b99ac719553f75335a1937"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937">operations_research::glop::LuFactorization::ComputeInverseOneNorm</a></div><div class="ttdeci">Fractional ComputeInverseOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00491">lu_factorization.cc:491</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a1ea8d0a49dad57416810ab7b1a2e2108"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108">operations_research::glop::LuFactorization::LeftSolveUWithNonZeros</a></div><div class="ttdeci">void LeftSolveUWithNonZeros(ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00317">lu_factorization.cc:317</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3042b0778d3d901556345438e482d88a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a">operations_research::glop::LuFactorization::GetColumnOfU</a></div><div class="ttdeci">const SparseColumn & GetColumnOfU(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00453">lu_factorization.cc:453</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3a6bb95b9009b1c578a27e6139d52696"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">operations_research::glop::LuFactorization::ComputeInverseInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInverseInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00512">lu_factorization.cc:512</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3c3fa8faef594bd4a249b4aaa5e32d8e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3c3fa8faef594bd4a249b4aaa5e32d8e">operations_research::glop::LuFactorization::ComputeInitialBasis</a></div><div class="ttdeci">RowToColMapping ComputeInitialBasis(const CompactSparseMatrix &matrix, const std::vector< ColIndex > &candidates)</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00068">lu_factorization.cc:68</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a40757145002c85d47ad8df1b53707661"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661">operations_research::glop::LuFactorization::RightSolveLForColumnView</a></div><div class="ttdeci">void RightSolveLForColumnView(const ColumnView &b, ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00263">lu_factorization.cc:263</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a41e666f39c778c69ade38b4db0c223ec"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a41e666f39c778c69ade38b4db0c223ec">operations_research::glop::LuFactorization::inverse_col_perm</a></div><div class="ttdeci">const ColumnPermutation & inverse_col_perm() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00221">lu_factorization.h:221</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a43e095088501053427e317e905d5fc83"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83">operations_research::glop::LuFactorization::RightSolveLWithPermutedInput</a></div><div class="ttdeci">void RightSolveLWithPermutedInput(const DenseColumn &a, ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00215">lu_factorization.cc:215</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a4523b56a271bfeb588757e64e4bf1425"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425">operations_research::glop::LuFactorization::GetFillInPercentage</a></div><div class="ttdeci">double GetFillInPercentage(const CompactSparseMatrixView &matrix) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00464">lu_factorization.cc:464</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a4bf241af6b1844669171d6e170ef991d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d">operations_research::glop::LuFactorization::RightSolveSquaredNorm</a></div><div class="ttdeci">Fractional RightSolveSquaredNorm(const ColumnView &a) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00141">lu_factorization.cc:141</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a577c37faff9567f86849dd74c3fcf4ac"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac">operations_research::glop::LuFactorization::RightSolveUWithNonZeros</a></div><div class="ttdeci">void RightSolveUWithNonZeros(ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00333">lu_factorization.cc:333</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a5a3deeb8998f541c08d96dc079591a54"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3deeb8998f541c08d96dc079591a54">operations_research::glop::LuFactorization::GetColumnPermutation</a></div><div class="ttdeci">const ColumnPermutation & GetColumnPermutation() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00066">lu_factorization.h:66</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a627511bf305a6af5d7e114817c1792c2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2">operations_research::glop::LuFactorization::DeterministicTimeOfLastFactorization</a></div><div class="ttdeci">double DeterministicTimeOfLastFactorization() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00095">lu_factorization.cc:95</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6b5f31c4068711b8e6823f4888f410ce"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">operations_research::glop::LuFactorization::LeftSolve</a></div><div class="ttdeci">void LeftSolve(DenseRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00109">lu_factorization.cc:109</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6c5735e4c25655dd4533504d22b1d66c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">operations_research::glop::LuFactorization::LeftSolveLWithNonZeros</a></div><div class="ttdeci">bool LeftSolveLWithNonZeros(ScatteredRow *y, ScatteredColumn *result_before_permutation) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00351">lu_factorization.cc:351</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6ec53ed3afa3d8affb6941568dcfec76"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">operations_research::glop::LuFactorization::RightSolve</a></div><div class="ttdeci">void RightSolve(DenseColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00099">lu_factorization.cc:99</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a9438a3ceb0327c1bd75ff3b4fa58d3b0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0">operations_research::glop::LuFactorization::LeftSolveUForUnitRow</a></div><div class="ttdeci">ColIndex LeftSolveUForUnitRow(ColIndex col, ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00420">lu_factorization.cc:420</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a9b738f6b485a4d4ef866b8d82ac07876"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">operations_research::glop::LuFactorization::DualEdgeSquaredNorm</a></div><div class="ttdeci">Fractional DualEdgeSquaredNorm(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00172">lu_factorization.cc:172</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa1222207079d0d679ef52f8b465cd00a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a">operations_research::glop::LuFactorization::RightSolveLForScatteredColumn</a></div><div class="ttdeci">void RightSolveLForScatteredColumn(const ScatteredColumn &b, ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00298">lu_factorization.cc:298</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa35c31899babb961a8100bc605136424"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424">operations_research::glop::LuFactorization::RightSolveLWithNonZeros</a></div><div class="ttdeci">void RightSolveLWithNonZeros(ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00279">lu_factorization.cc:279</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa40655f0310c3616632354ffeb7d466e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e">operations_research::glop::LuFactorization::ComputeDeterminant</a></div><div class="ttdeci">Fractional ComputeDeterminant() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00480">lu_factorization.cc:480</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::LuFactorization::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00031">lu_factorization.cc:31</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ac22943ff00ae631c58ad2c42932d4657"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657">operations_research::glop::LuFactorization::ComputeInfinityNormConditionNumber</a></div><div class="ttdeci">Fractional ComputeInfinityNormConditionNumber(const CompactSparseMatrixView &matrix) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00541">lu_factorization.cc:541</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_acd3d874c6fe9195587688508b6cd0305"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305">operations_research::glop::LuFactorization::ComputeLowerTimesUpper</a></div><div class="ttdeci">void ComputeLowerTimesUpper(SparseMatrix *product) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00209">lu_factorization.h:209</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ace58a4f9d6a147c3455ff8dc029537c4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4">operations_research::glop::LuFactorization::ComputeFactorization</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ComputeFactorization(const CompactSparseMatrixView &compact_matrix)</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00044">lu_factorization.cc:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ad91a397910de30b87b9fb45298fa5c58"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58">operations_research::glop::LuFactorization::SetColumnPermutationToIdentity</a></div><div class="ttdeci">void SetColumnPermutationToIdentity()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00072">lu_factorization.h:72</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ad9e11229fed5416bf22fb3b4fa65f4c1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1">operations_research::glop::LuFactorization::NumberOfEntries</a></div><div class="ttdeci">EntryIndex NumberOfEntries() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00474">lu_factorization.cc:474</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ada69c9026d5d933471bf27c9ad2d1b38"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38">operations_research::glop::LuFactorization::ComputeInverseInfinityNormUpperBound</a></div><div class="ttdeci">Fractional ComputeInverseInfinityNormUpperBound() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00547">lu_factorization.cc:547</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_adbf20cf678d328e6b36c8bb43dc499cf"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#adbf20cf678d328e6b36c8bb43dc499cf">operations_research::glop::LuFactorization::IsIdentityFactorization</a></div><div class="ttdeci">bool IsIdentityFactorization()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00041">lu_factorization.h:41</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ae7202d055b6b172a8a1da4f5b136f9ea"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">operations_research::glop::LuFactorization::SetParameters</a></div><div class="ttdeci">void SetParameters(const GlopParameters &parameters)</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00196">lu_factorization.h:196</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af03b66d5eb557d6d95ad01d446c2cba8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8">operations_research::glop::LuFactorization::ComputeOneNormConditionNumber</a></div><div class="ttdeci">Fractional ComputeOneNormConditionNumber(const CompactSparseMatrixView &matrix) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00535">lu_factorization.cc:535</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af0b37b89dc1909384e822287c1091aa0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">operations_research::glop::LuFactorization::LuFactorization</a></div><div class="ttdeci">LuFactorization()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00024">lu_factorization.cc:24</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af2e901d9cdc8f3f36f5b54ef1455c712"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af2e901d9cdc8f3f36f5b54ef1455c712">operations_research::glop::LuFactorization::row_perm</a></div><div class="ttdeci">const RowPermutation & row_perm() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00220">lu_factorization.h:220</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af9bc435481ae9e6e60d66a65d5394a7f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f">operations_research::glop::LuFactorization::StatString</a></div><div class="ttdeci">std::string StatString() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00202">lu_factorization.h:202</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_ae7202d055b6b172a8a1da4f5b136f9ea"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#ae7202d055b6b172a8a1da4f5b136f9ea">operations_research::glop::Markowitz::SetParameters</a></div><div class="ttdeci">void SetParameters(const GlopParameters &parameters)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8h_source.html#l00313">markowitz.h:313</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_af9bc435481ae9e6e60d66a65d5394a7f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#af9bc435481ae9e6e60d66a65d5394a7f">operations_research::glop::Markowitz::StatString</a></div><div class="ttdeci">std::string StatString() const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8h_source.html#l00310">markowitz.h:310</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html">operations_research::glop::Permutation< ColIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_ac8bb3912a3ce86b15842e79d0b421204"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">operations_research::glop::Permutation::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00053">lp_data/permutation.h:53</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_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html">operations_research::glop::SparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00062">sparse.h:62</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_aa1c2872fa7d491d4c093c8b2124a53b9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#aa1c2872fa7d491d4c093c8b2124a53b9">operations_research::glop::SparseMatrix::PopulateFromProduct</a></div><div class="ttdeci">void PopulateFromProduct(const SparseMatrix &a, const SparseMatrix &b)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00250">sparse.cc:250</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#l00024">status.h:24</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector< RowIndex, ColIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a138580a401252ec46ad8e08925e4e92e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e">operations_research::glop::TriangularMatrix::CopyToSparseMatrix</a></div><div class="ttdeci">void CopyToSparseMatrix(SparseMatrix *output) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00757">sparse.cc:757</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a></div><div class="ttdeci">int64_t a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00046">constraint_solver/table.cc:46</a></div></div>
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<div class="ttc" id="acp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219"><div class="ttname"><a href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a></div><div class="ttdeci">SatParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__fz__solver_8cc_source.html#l00116">cp_model_fz_solver.cc:116</a></div></div>
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<div class="ttc" id="alp__data_2permutation_8h_html"><div class="ttname"><a href="lp__data_2permutation_8h.html">permutation.h</a></div></div>
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<div class="ttc" id="alp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="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_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_ae5fa9e57c2d31b294195ed8a9e17bfac"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">operations_research::glop::DenseColumn</a></div><div class="ttdeci">StrictITIVector< RowIndex, Fractional > DenseColumn</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00332">lp_types.h:332</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_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_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="aparameters_8pb_8h_html"><div class="ttname"><a href="parameters_8pb_8h.html">parameters.pb.h</a></div></div>
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<div class="ttc" id="ascattered__vector_8h_html"><div class="ttname"><a href="scattered__vector_8h.html">scattered_vector.h</a></div></div>
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<div class="ttc" id="asparse_8h_html"><div class="ttname"><a href="sparse_8h.html">sparse.h</a></div></div>
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<div class="ttc" id="asparse__column_8h_html"><div class="ttname"><a href="sparse__column_8h.html">sparse_column.h</a></div></div>
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<div class="ttc" id="astats_8h_html"><div class="ttname"><a href="stats_8h.html">stats.h</a></div></div>
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<div class="ttc" id="astatus_8h_html"><div class="ttname"><a href="status_8h.html">status.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_column_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_column.html">operations_research::glop::ScatteredColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00196">scattered_vector.h:197</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_row_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_row.html">operations_research::glop::ScatteredRow</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00198">scattered_vector.h:198</a></div></div>
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