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<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 name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
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<div class="line"><a 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 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 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 name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a 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 name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a 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 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 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 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 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 name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a 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 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 name="l00016"></a><span class="lineno"> 16</span>  </div>
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<div class="line"><a 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 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 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 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 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 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 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 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 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 name="l00026"></a><span class="lineno"> 26</span>  </div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span>glop {</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  </div>
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<div class="line"><a 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 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 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 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 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" href="classoperations__research_1_1glop_1_1_lu_factorization.html">LuFactorization</a> {</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">LuFactorization</a>();</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div>
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<div class="line"><a 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 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 name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">// vector dimension.</span></div>
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<div class="line"><a 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" 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 name="l00042"></a><span class="lineno"> 42</span>  </div>
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<div class="line"><a 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 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 name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
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<div class="line"><a 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 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 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 name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">//</span></div>
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<div class="line"><a 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 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 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 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 name="l00055"></a><span class="lineno"> 55</span>  ABSL_MUST_USE_RESULT <a class="code" href="classoperations__research_1_1glop_1_1_status.html">Status</a></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4">ComputeFactorization</a>(<span class="keyword">const</span> <a class="code" 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 name="l00057"></a><span class="lineno"> 57</span>  </div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// Returns the column permutation used by the LU factorization.</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a56d08f5289eea3f018dca5b93b6fca6b"> 59</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a56d08f5289eea3f018dca5b93b6fca6b">GetColumnPermutation</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> col_perm_; }</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</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 name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// the column permutation can be incorporated in the basis RowToColMapping,</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</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 name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">// the need for a column permutation on each solve.</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58"> 65</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58">SetColumnPermutationToIdentity</a>() {</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  col_perm_.<a class="code" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  inverse_col_perm_.<a class="code" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</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 name="l00071"></a><span class="lineno"> 71</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 name="l00072"></a><span class="lineno"> 72</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 name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// 2/ solve L.z = y for z,</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// 3/ solve U.t = z for t,</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</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 name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">RightSolve</a>(<a class="code" 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 name="l00077"></a><span class="lineno"> 77</span>  </div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</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 name="l00079"></a><span class="lineno"> 79</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 name="l00080"></a><span class="lineno"> 80</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 name="l00081"></a><span class="lineno"> 81</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 name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// The procedure is thus:</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</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 name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// 2/ solve U^T.z = y for z,</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">// 3/ solve L^T.t = z for t,</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</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 name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">LeftSolve</a>(<a class="code" 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 name="l00088"></a><span class="lineno"> 88</span>  </div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</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 name="l00090"></a><span class="lineno"> 90</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 name="l00091"></a><span class="lineno"> 91</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 name="l00092"></a><span class="lineno"> 92</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 name="l00093"></a><span class="lineno"> 93</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 name="l00094"></a><span class="lineno"> 94</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 name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424">RightSolveLWithNonZeros</a>(<a class="code" 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 name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac">RightSolveUWithNonZeros</a>(<a class="code" 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 name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108">LeftSolveUWithNonZeros</a>(<a class="code" 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 name="l00098"></a><span class="lineno"> 98</span>  </div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</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 name="l00100"></a><span class="lineno"> 100</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 name="l00101"></a><span class="lineno"> 101</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 name="l00102"></a><span class="lineno"> 102</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 name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// then false is returned.</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LeftSolveLWithNonZeros</a>(<a class="code" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y,</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <a class="code" 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 name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LeftSolveLWithNonZeros</a>(<a class="code" 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 name="l00107"></a><span class="lineno"> 107</span>  </div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Specialized version of RightSolveLWithNonZeros() that takes a SparseColumn</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</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 name="l00110"></a><span class="lineno"> 110</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 name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// size and all zero.</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661">RightSolveLForColumnView</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>, <a class="code" 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 name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a">RightSolveLForScatteredColumn</a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>,</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <a class="code" 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 name="l00115"></a><span class="lineno"> 115</span>  </div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// Specialized version of RightSolveLWithNonZeros() where x is originaly equal</span></div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// to 'a' permuted by row_perm_. Note that 'a' is only used for DCHECK.</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83">RightSolveLWithPermutedInput</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>,</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <a class="code" 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 name="l00120"></a><span class="lineno"> 120</span>  </div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// Specialized version of LeftSolveU() for an unit right-hand side.</span></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</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 name="l00123"></a><span class="lineno"> 123</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 name="l00124"></a><span class="lineno"> 124</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 name="l00125"></a><span class="lineno"> 125</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 name="l00126"></a><span class="lineno"> 126</span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0">LeftSolveUForUnitRow</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code" 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 name="l00127"></a><span class="lineno"> 127</span>  </div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// Returns the given column of U.</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</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 name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a">GetColumnOfU</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// Returns the norm of B^{-1}.a</span></div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d">RightSolveSquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  </div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</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 name="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">DualEdgeSquaredNorm</a>(RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  </div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</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 name="l00139"></a><span class="lineno"> 139</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 name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">// the number of entries in the initial matrix B.</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</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 name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// the number of entries in B.</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordtype">double</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425">GetFillInPercentage</a>(<span class="keyword">const</span> <a class="code" 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 name="l00145"></a><span class="lineno"> 145</span>  </div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// Returns the number of entries in L + U.</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// If the factorization is the identity, this returns 0.</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  EntryIndex <a class="code" 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 name="l00149"></a><span class="lineno"> 149</span>  </div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">// Computes the determinant of the input matrix B.</span></div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</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 name="l00152"></a><span class="lineno"> 152</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 name="l00153"></a><span class="lineno"> 153</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 name="l00154"></a><span class="lineno"> 154</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 name="l00155"></a><span class="lineno"> 155</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 name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// upper-triangular matrix.</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">// Taking all this into account:</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</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 name="l00159"></a><span class="lineno"> 159</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" 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 name="l00160"></a><span class="lineno"> 160</span>  </div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</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 name="l00162"></a><span class="lineno"> 162</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 name="l00163"></a><span class="lineno"> 163</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 name="l00164"></a><span class="lineno"> 164</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 name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// http://en.wikipedia.org/wiki/Matrix_norm</span></div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" 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 name="l00167"></a><span class="lineno"> 167</span>  </div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</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 name="l00169"></a><span class="lineno"> 169</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 name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// http://en.wikipedia.org/wiki/Matrix_norm</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" 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 name="l00172"></a><span class="lineno"> 172</span>  </div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">// Computes the condition number of the input matrix B.</span></div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</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 name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="comment">// Note that because the LuFactorization class does not keep the</span></div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</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 name="l00178"></a><span class="lineno"> 178</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 name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// for ComputeFactorization().</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="comment">// TODO(user): separate this from LuFactorization.</span></div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8">ComputeOneNormConditionNumber</a>(</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keyword">const</span> <a class="code" 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 name="l00184"></a><span class="lineno"> 184</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657">ComputeInfinityNormConditionNumber</a>(</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keyword">const</span> <a class="code" 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 name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" 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 name="l00187"></a><span class="lineno"> 187</span>  </div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="comment">// Sets the current parameters.</span></div>
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<div class="line"><a name="l00189"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea"> 189</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">SetParameters</a>(<span class="keyword">const</span> GlopParameters& <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>) {</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  parameters_ = <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>;</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  markowitz_.<a class="code" href="classoperations__research_1_1glop_1_1_markowitz.html#ae7202d055b6b172a8a1da4f5b136f9ea">SetParameters</a>(<a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>);</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  }</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  </div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="comment">// Returns a string containing the statistics for this class.</span></div>
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<div class="line"><a name="l00195"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f"> 195</a></span>  std::string <a class="code" 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 name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">return</span> stats_.StatString() + markowitz_.<a class="code" href="classoperations__research_1_1glop_1_1_markowitz.html#af9bc435481ae9e6e60d66a65d5394a7f">StatString</a>();</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  }</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  </div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// This is only used for testing and in debug mode.</span></div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// TODO(user): avoid the matrix conversion by multiplying TriangularMatrix</span></div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// directly.</span></div>
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<div class="line"><a name="l00202"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305"> 202</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305">ComputeLowerTimesUpper</a>(<a class="code" 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 name="l00203"></a><span class="lineno"> 203</span>  <a class="code" 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 name="l00204"></a><span class="lineno"> 204</span>  lower_.<a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e">CopyToSparseMatrix</a>(&temp_lower);</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  upper_.<a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e">CopyToSparseMatrix</a>(&temp_upper);</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  product-><a class="code" 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 name="l00207"></a><span class="lineno"> 207</span>  }</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  </div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// Visible for testing.</span></div>
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<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3f1ad730713e296dcbbed8b1123130"> 210</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3f1ad730713e296dcbbed8b1123130">row_perm</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> row_perm_; }</div>
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<div class="line"><a name="l00211"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a864ad5596d017729a4ca349fed8949a8"> 211</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& <a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a864ad5596d017729a4ca349fed8949a8">inverse_col_perm</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">return</span> inverse_col_perm_;</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  }</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  </div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// Statistics about this class.</span></div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keyword">struct </span>Stats : <span class="keyword">public</span> <a class="code" href="classoperations__research_1_1_stats_group.html">StatsGroup</a> {</div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  Stats()</div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  : <a class="code" href="classoperations__research_1_1_stats_group.html">StatsGroup</a>(<span class="stringliteral">"LuFactorization"</span>),</div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  basis_num_entries(<span class="stringliteral">"basis_num_entries"</span>, this),</div>
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  lu_fill_in(<span class="stringliteral">"lu_fill_in"</span>, this) {}</div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <a class="code" href="classoperations__research_1_1_integer_distribution.html">IntegerDistribution</a> basis_num_entries;</div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <a class="code" href="classoperations__research_1_1_ratio_distribution.html">RatioDistribution</a> lu_fill_in;</div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  };</div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  </div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// Internal function used in the left solve functions.</span></div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordtype">void</span> LeftSolveScratchpad() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  </div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">// Internal function used in the right solve functions</span></div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Column></div>
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordtype">void</span> RightSolveLInternal(<span class="keyword">const</span> Column& <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>, ScatteredColumn* x) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  </div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">// Fills transpose_upper_ from upper_.</span></div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordtype">void</span> ComputeTransposeUpper();</div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  </div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">// transpose_lower_ is only needed when we compute dual norms.</span></div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordtype">void</span> ComputeTransposeLower() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  </div>
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</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 name="l00240"></a><span class="lineno"> 240</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 name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordtype">bool</span> CheckFactorization(<span class="keyword">const</span> CompactSparseMatrixView& matrix,</div>
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<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  </div>
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<div class="line"><a name="l00244"></a><span class="lineno"> 244</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 name="l00245"></a><span class="lineno"> 245</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 name="l00246"></a><span class="lineno"> 246</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 name="l00247"></a><span class="lineno"> 247</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 name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">// succeeds.</span></div>
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<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">bool</span> is_identity_factorization_;</div>
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  </div>
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<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="comment">// The triangular factor L and U (and its transpose).</span></div>
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<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  TriangularMatrix lower_;</div>
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<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  TriangularMatrix upper_;</div>
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<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  TriangularMatrix transpose_upper_;</div>
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<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  </div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="comment">// The transpose of lower_. It is just used by DualEdgeSquaredNorm()</span></div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="comment">// and mutable so it can be lazily initialized.</span></div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">mutable</span> TriangularMatrix transpose_lower_;</div>
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  </div>
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</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 name="l00261"></a><span class="lineno"> 261</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a> col_perm_;</div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a> inverse_col_perm_;</div>
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<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  </div>
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<div class="line"><a name="l00264"></a><span class="lineno"> 264</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 name="l00265"></a><span class="lineno"> 265</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a> row_perm_;</div>
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<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a> inverse_row_perm_;</div>
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<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  </div>
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<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="comment">// Temporary storage used by LeftSolve()/RightSolve().</span></div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keyword">mutable</span> <a class="code" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a> dense_column_scratchpad_;</div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  </div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">// Temporary storage used by GetColumnOfU().</span></div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keyword">mutable</span> SparseColumn column_of_upper_;</div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  </div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</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 name="l00275"></a><span class="lineno"> 275</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 name="l00276"></a><span class="lineno"> 276</span>  <span class="comment">// non_zero_rows_ position of dense_column_scratchpad_.</span></div>
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<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">mutable</span> <a class="code" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a> dense_zero_scratchpad_;</div>
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<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">mutable</span> std::vector<RowIndex> non_zero_rows_;</div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  </div>
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<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="comment">// Statistics, mutable so const functions can still update it.</span></div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">mutable</span> Stats stats_;</div>
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  </div>
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="comment">// Proto holding all the parameters of this algorithm.</span></div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  GlopParameters parameters_;</div>
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<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  </div>
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<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// The class doing the Markowitz LU factorization.</span></div>
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<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  Markowitz markowitz_;</div>
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<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  </div>
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<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  DISALLOW_COPY_AND_ASSIGN(<a class="code" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">LuFactorization</a>);</div>
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<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> };</div>
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<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  </div>
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<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> } <span class="comment">// namespace glop</span></div>
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<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="preprocessor">#endif // OR_TOOLS_GLOP_LU_FACTORIZATION_H_</span></div>
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</div><!-- fragment --></div><!-- contents -->
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</div><!-- doc-content -->
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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#l00065">lu_factorization.h:65</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#l00510">lu_factorization.cc:510</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#l00110">lu_factorization.cc:110</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_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_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#l00471">sparse.h:471</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#l00232">lu_factorization.cc:232</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_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#l00267">lu_factorization.cc:267</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">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</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="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_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#l00504">lu_factorization.cc:504</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#l00286">lu_factorization.cc:286</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_lu_factorization_html_a864ad5596d017729a4ca349fed8949a8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a864ad5596d017729a4ca349fed8949a8">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#l00211">lu_factorization.h:211</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#l00308">markowitz.h:308</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#l00077">lp_types.h:77</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_integer_distribution_html"><div class="ttname"><a href="classoperations__research_1_1_integer_distribution.html">operations_research::IntegerDistribution</a></div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00287">stats.h:287</a></div></div>
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<div class="ttc" id="astats_8h_html"><div class="ttname"><a href="stats_8h.html">stats.h</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#l00320">lu_factorization.cc:320</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_af730895c6c6ef6e03caaf6251192dfd2"><div class="ttname"><a href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a></div><div class="ttdeci">int64 a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00042">constraint_solver/table.cc:42</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#l00078">lu_factorization.cc:78</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#l00443">lu_factorization.cc:443</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#l00248">lu_factorization.cc:248</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_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#l00061">sparse.h:61</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#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_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_a56d08f5289eea3f018dca5b93b6fca6b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a56d08f5289eea3f018dca5b93b6fca6b">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#l00059">lu_factorization.h:59</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</a></div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00252">lp_types.h:252</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#l00193">scattered_vector.h:193</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#l00302">lu_factorization.cc:302</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#l00093">lp_data/permutation.h:93</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#l00141">lu_factorization.cc:141</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#l00305">markowitz.h:305</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="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="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#l00094">lp_data/permutation.h:94</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_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#l00516">lu_factorization.cc:516</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#l00189">lu_factorization.h:189</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#l00176">markowitz.cc:176</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="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#l00175">markowitz.cc:175</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#l00191">scattered_vector.h:192</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#l00422">lu_factorization.cc:422</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#l00328">lp_types.h:328</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a344010e26426d6a13411648d988bc9b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a></div><div class="ttdeci">int64 b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00043">constraint_solver/table.cc:43</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_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#l00052">lp_data/permutation.h:52</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#l00433">lu_factorization.cc:433</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#l00730">sparse.cc:730</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="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="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#l00449">lu_factorization.cc:449</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="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#l00202">lu_factorization.h:202</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#l00460">lu_factorization.cc:460</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#l00184">lu_factorization.cc:184</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="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#l00481">lu_factorization.cc:481</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#l00389">lu_factorization.cc:389</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#l00107">cp_model_fz_solver.cc:107</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="astatus_8h_html"><div class="ttname"><a href="status_8h.html">status.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="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="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#l00195">lu_factorization.h:195</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a5a3f1ad730713e296dcbbed8b1123130"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3f1ad730713e296dcbbed8b1123130">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#l00210">lu_factorization.h:210</a></div></div>
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