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<a href="sparse_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="comment">//</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// The following are very good references for terminology, data structures,</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// and algorithms:</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// I.S. Duff, A.M. Erisman and J.K. Reid, "Direct Methods for Sparse Matrices",</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// Clarendon, Oxford, UK, 1987, ISBN 0-19-853421-3,</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// http://www.amazon.com/dp/0198534213.</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// T.A. Davis, "Direct methods for Sparse Linear Systems", SIAM, Philadelphia,</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// 2006, ISBN-13: 978-0-898716-13, http://www.amazon.com/dp/0898716136.</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// Both books also contain a wealth of references.</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  </div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#ifndef OR_TOOLS_LP_DATA_SPARSE_H_</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#define OR_TOOLS_LP_DATA_SPARSE_H_</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  </div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <string></span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  </div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</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="l00036"></a><span class="lineno"> 36</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="l00037"></a><span class="lineno"> 37</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="l00038"></a><span class="lineno"> 38</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="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#include "<a class="code" href="return__macros_8h.html">ortools/util/return_macros.h</a>"</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</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="l00042"></a><span class="lineno"> 42</span> <span class="keyword">namespace </span>glop {</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">class </span>CompactSparseMatrixView;</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// --------------------------------------------------------</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// SparseMatrix</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// --------------------------------------------------------</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// SparseMatrix is a class for sparse matrices suitable for computation.</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// Data is represented using the so-called compressed-column storage scheme.</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// Entries (row, col, value) are stored by column using a SparseColumn.</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// Citing [Duff et al, 1987], a matrix is sparse if many of its coefficients are</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// zero and if there is an advantage in exploiting its zeros.</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// For practical reasons, not all zeros are exploited (for example those that</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// result from calculations.) The term entry refers to those coefficients that</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// are handled explicitly. All non-zeros are entries while some zero</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// coefficients may also be entries.</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// Note that no special ordering of entries is assumed.</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html"> 61</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a> {</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a79446a803c1bed8b17c8ac937d07be39">SparseMatrix</a>();</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// Useful for testing. This makes it possible to write:</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// SparseMatrix matrix {</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// {1, 2, 3},</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// {4, 5, 6},</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// {7, 8, 9}};</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="preprocessor">#if (!defined(_MSC_VER) || _MSC_VER >= 1800)</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a79446a803c1bed8b17c8ac937d07be39">SparseMatrix</a>(</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  std::initializer_list<std::initializer_list<Fractional>> init_list);</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// Clears internal data structure, i.e. erases all the columns and set</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// the number of rows to zero.</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_sparse_matrix.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</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">// Returns true if the matrix is empty.</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// That is if num_rows() OR num_cols() are zero.</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  </div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// Cleans the columns, i.e. removes zero-values entries, removes duplicates</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// entries and sorts remaining entries in increasing row order.</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// Call with care: Runs in O(num_cols * column_cleanup), with each column</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">// cleanup running in O(num_entries * log(num_entries)).</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#abfc30f91ab75c6f4552003f777672e74">CleanUp</a>();</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  </div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">// Call CheckNoDuplicates() on all columns, useful for doing a DCHECK.</span></div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a2e5611d47d02e1029b98a8e9bee3469f">CheckNoDuplicates</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// Call IsCleanedUp() on all columns, useful for doing a DCHECK.</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a5e016d204d43b2cc4a2773c25462968a">IsCleanedUp</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  </div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">// Change the number of row of this matrix.</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_sparse_matrix.html#a55265e26d9e69e2d7a882bab054b8139">SetNumRows</a>(RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>);</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// Appends an empty column and returns its index.</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a86fd105be79f4f2dbaf3a21e64e4d022">AppendEmptyColumn</a>();</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  </div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">// Appends a unit vector defined by the single entry (row, value).</span></div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// Note that the row should be smaller than the number of rows of the matrix.</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a06d22c92f8b45b18560b46797f98a81b">AppendUnitVector</a>(RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>);</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="comment">// Swaps the content of this SparseMatrix with the one passed as argument.</span></div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// Works in O(1).</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_sparse_matrix.html#a6052657cbffbe19decf328bf369d58e1">Swap</a>(<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* matrix);</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">// Populates the matrix with num_cols columns of zeros. As the number of rows</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// is specified by num_rows, the matrix is not necessarily square.</span></div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// Previous columns/values are deleted.</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ae1b90982a83e1b025ebbc1c446980640">PopulateFromZero</a>(RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>, ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>);</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">// Populates the matrix from the Identity matrix of size num_cols.</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="comment">// Previous columns/values are deleted.</span></div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a323801972c3d6de340e260de4582c34b">PopulateFromIdentity</a>(ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>);</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// Populates the matrix from the transposed of the given matrix.</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// Note that this preserve the property of lower/upper triangular matrix</span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// to have the diagonal coefficients first/last in each columns. It actually</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// sorts the entries in each columns by their indices.</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Matrix></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a2fe6f7470512f5301031480737375c88">PopulateFromTranspose</a>(<span class="keyword">const</span> Matrix& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// Populates a SparseMatrix from another one (copy), note that this run in</span></div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">// O(number of entries in the matrix).</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#acbbc88405e6db3fe77064e1a3d4e402a">PopulateFromSparseMatrix</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix);</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">// Populates a SparseMatrix from the image of a matrix A through the given</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// row_perm and inverse_col_perm. See permutation.h for more details.</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Matrix></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a29edb960f882c54b9652853e94988e79">PopulateFromPermutedMatrix</a>(<span class="keyword">const</span> Matrix& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>,</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& inverse_col_perm);</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">// Populates a SparseMatrix from the result of alpha * A + beta * B,</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">// where alpha and beta are Fractionals, A and B are sparse matrices.</span></div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a0c406d94c3586159071e0b370a5a02fb">PopulateFromLinearCombination</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> alpha, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>,</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> beta, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>);</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  </div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">// Multiplies SparseMatrix a by SparseMatrix b.</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#aa1c2872fa7d491d4c093c8b2124a53b9">PopulateFromProduct</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>);</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  </div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// Removes the marked columns from the matrix and adjust its size.</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">// This runs in O(num_cols).</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ac59fd9cddfe284bf9dc7581ed631ce8d">DeleteColumns</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanRow</a>& columns_to_delete);</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  </div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// Applies the given row permutation and deletes the rows for which</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="comment">// permutation[row] is kInvalidRow. Sets the new number of rows to num_rows.</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// This runs in O(num_entries).</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a860e7a37e8c7c2f5f7f0a73d3e3473f0">DeleteRows</a>(RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& permutation);</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  </div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// Appends all rows from the given matrix to the calling object after the last</span></div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// row of the calling object. Both matrices must have the same number of</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// columns. The method returns true if the rows were added successfully and</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// false if it can't add the rows because the number of columns of the</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// matrices are different.</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ab2d8beb101c26b08a8af602300da1748">AppendRowsFromSparseMatrix</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix);</div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  </div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">// Applies the row permutation.</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ace1973900f4d921a7bedbcbe36e1bcad">ApplyRowPermutation</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm);</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// Returns the coefficient at position row in column col.</span></div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// Call with care: runs in O(num_entries_in_col) as entries may not be sorted.</span></div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a566008ab9fd3e3dbec96263bc3c45061">LookUpValue</a>(RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</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="l00165"></a><span class="lineno"> 165</span>  </div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="comment">// Returns true if the matrix equals a (with a maximum error smaller than</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="comment">// given the tolerance).</span></div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#af782744bdb01cf56841a0de18ccca3ce">Equals</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, <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="l00169"></a><span class="lineno"> 169</span>  </div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// Returns, in min_magnitude and max_magnitude, the minimum and maximum</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// magnitudes of the non-zero coefficients of the calling object.</span></div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6ae7b0836055b9b6d182115027d496f9">ComputeMinAndMaxMagnitudes</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>* min_magnitude,</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>* max_magnitude) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  </div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">// Return the matrix dimension.</span></div>
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<div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd"> 176</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_rows_; }</div>
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<div class="line"><a name="l00177"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813"> 177</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> ColIndex(columns_.size()); }</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  </div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// Access the underlying sparse columns.</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac"> 180</a></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_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> columns_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]; }</div>
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<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a1e9f788d4507f2461b4f775755aaf82e"> 181</a></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_sparse_matrix.html#a1e9f788d4507f2461b4f775755aaf82e">mutable_column</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) { <span class="keywordflow">return</span> &(columns_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]); }</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  </div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// Returns the total numbers of entries in the matrix.</span></div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="comment">// Runs in O(num_cols).</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  EntryIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="comment">// Computes the 1-norm of the matrix.</span></div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="comment">// The 1-norm |A| is defined as max_j sum_i |a_ij| or</span></div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="comment">// max_col sum_row |a(row,col)|.</span></div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a64fea3282d498f3eb2d4af70692bb117">ComputeOneNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  </div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">// Computes the oo-norm (infinity-norm) of the matrix.</span></div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">// The oo-norm |A| is defined as max_i sum_j |a_ij| or</span></div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="comment">// max_row sum_col |a(row,col)|.</span></div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a3f219a081f88c22ae282ada4f0bdddd3">ComputeInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  </div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="comment">// Returns a dense representation of the matrix.</span></div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  std::string <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ab4a8456683d4572bd9426efab8489e99">Dump</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  </div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// Resets the internal data structure and create an empty rectangular</span></div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// matrix of size num_rows x num_cols.</span></div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordtype">void</span> Reset(ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>, RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>);</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  </div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="comment">// Vector of sparse columns.</span></div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, SparseColumn></a> columns_;</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>  <span class="comment">// Number of rows. This is needed as sparse columns don't have a maximum</span></div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// number of rows.</span></div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  RowIndex num_rows_;</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  </div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  DISALLOW_COPY_AND_ASSIGN(<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>);</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="comment">// A matrix constructed from a list of already existing SparseColumn. This class</span></div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// does not take ownership of the underlying columns, and thus they must outlive</span></div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">// this class (and keep the same address in memory).</span></div>
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<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html"> 218</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a> {</div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00220"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a1f0797ca04f7cb50938328e7e027a18b"> 220</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a1f0797ca04f7cb50938328e7e027a18b">MatrixView</a>() {}</div>
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<div class="line"><a name="l00221"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#ac220f9bed6efccb65c2514e90d702638"> 221</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#ac220f9bed6efccb65c2514e90d702638">MatrixView</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001">PopulateFromMatrix</a>(matrix);</div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  }</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>  <span class="comment">// Takes all the columns of the given matrix.</span></div>
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<div class="line"><a name="l00226"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001"> 226</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001">PopulateFromMatrix</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">const</span> ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a> = matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  columns_.resize(<a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>, <span class="keyword">nullptr</span>);</div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>; ++<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  columns_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = &matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  }</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  num_rows_ = matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  }</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  </div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="comment">// Takes all the columns of the first matrix followed by the columns of the</span></div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">// second matrix.</span></div>
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<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a87c606b7a9b920de2d4b6aa5c3bc1a45"> 237</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a87c606b7a9b920de2d4b6aa5c3bc1a45">PopulateFromMatrixPair</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix_a,</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix_b) {</div>
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keyword">const</span> ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a> = matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() + matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  columns_.resize(<a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>, <span class="keyword">nullptr</span>);</div>
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<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(); ++<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  columns_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = &matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</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="keywordflow">for</span> (ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(); ++<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  columns_[matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() + <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = &matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  }</div>
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<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  num_rows_ = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>());</div>
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<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  }</div>
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<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  </div>
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="comment">// Takes only the columns of the given matrix that belongs to the given basis.</span></div>
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<div class="line"><a name="l00251"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#adc9aa1d344fe9442ac3ba673b939db7c"> 251</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#adc9aa1d344fe9442ac3ba673b939db7c">PopulateFromBasis</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a>& matrix,</div>
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<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a>& basis) {</div>
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<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  columns_.resize(<a class="code" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(basis.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>()), <span class="keyword">nullptr</span>);</div>
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<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">for</span> (RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < basis.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(); ++<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  columns_[<a class="code" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)] = &matrix.<a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(basis[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  }</div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  num_rows_ = matrix.<a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</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">// Same behavior as the SparseMatrix functions above.</span></div>
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<div class="line"><a name="l00261"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a8e12342fc420701fbffd97025421575a"> 261</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> columns_.empty(); }</div>
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<div class="line"><a name="l00262"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a960110e64357a3e69162ebf1f71959dd"> 262</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_rows_; }</div>
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<div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813"> 263</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> columns_.size(); }</div>
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<div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#adc6b282d2cc7afc75b60ee44a6bfb2ac"> 264</a></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_matrix_view.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> *columns_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]; }</div>
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<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  EntryIndex <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() <span class="keyword">const</span>;</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#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a64fea3282d498f3eb2d4af70692bb117">ComputeOneNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html#a3f219a081f88c22ae282ada4f0bdddd3">ComputeInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  </div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  RowIndex num_rows_;</div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, SparseColumn const*></a> columns_;</div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> };</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="keyword">extern</span> <span class="keyword">template</span> <span class="keywordtype">void</span> SparseMatrix::PopulateFromTranspose<SparseMatrix>(</div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keyword">const</span> SparseMatrix& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">extern</span> <span class="keyword">template</span> <span class="keywordtype">void</span> SparseMatrix::PopulateFromPermutedMatrix<SparseMatrix>(</div>
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<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">const</span> SparseMatrix& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, <span class="keyword">const</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="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">const</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="l00279"></a><span class="lineno"> 279</span> <span class="keyword">extern</span> <span class="keyword">template</span> <span class="keywordtype">void</span></div>
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<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> SparseMatrix::PopulateFromPermutedMatrix<CompactSparseMatrixView>(</div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">const</span> CompactSparseMatrixView& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, <span class="keyword">const</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="l00282"></a><span class="lineno"> 282</span>  <span class="keyword">const</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="l00283"></a><span class="lineno"> 283</span>  </div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// Another matrix representation which is more efficient than a SparseMatrix but</span></div>
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<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment">// doesn't allow matrix modification. It is faster to construct, uses less</span></div>
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<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// memory and provides a better cache locality when iterating over the non-zeros</span></div>
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<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// of the matrix columns.</span></div>
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<div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html"> 288</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a> {</div>
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<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00290"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a319ffa92d03907ee98b5f3da18421af3"> 290</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a319ffa92d03907ee98b5f3da18421af3">CompactSparseMatrix</a>() {}</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">// Convenient constructors for tests.</span></div>
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<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="comment">// TODO(user): If this is needed in production code, it can be done faster.</span></div>
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<div class="line"><a name="l00294"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a9f271f559e0d1e794a2ecc76d919db68"> 294</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a9f271f559e0d1e794a2ecc76d919db68">CompactSparseMatrix</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  PopulateFromMatrixView(<a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a>(matrix));</div>
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<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  }</div>
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<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  </div>
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<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// Creates a CompactSparseMatrix from the given MatrixView. The matrices are</span></div>
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<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">// the same, only the representation differ. Note that the entry order in</span></div>
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<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="comment">// each column is preserved.</span></div>
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<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordtype">void</span> PopulateFromMatrixView(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  </div>
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<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="comment">// Creates a CompactSparseMatrix from the transpose of the given</span></div>
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<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">// CompactSparseMatrix. Note that the entries in each columns will be ordered</span></div>
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<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// by row indices.</span></div>
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<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keywordtype">void</span> PopulateFromTranspose(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  </div>
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<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="comment">// Clears the matrix and sets its number of rows. If none of the Populate()</span></div>
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<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// function has been called, Reset() must be called before calling any of the</span></div>
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<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// Add*() functions below.</span></div>
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<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="keywordtype">void</span> Reset(RowIndex num_rows);</div>
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<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  </div>
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<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="comment">// Adds a dense column to the CompactSparseMatrix (only the non-zero will be</span></div>
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<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// actually stored). This work in O(input.size()) and returns the index of the</span></div>
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<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="comment">// added column.</span></div>
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<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  ColIndex AddDenseColumn(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& dense_column);</div>
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<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  </div>
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<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="comment">// Same as AddDenseColumn(), but only adds the non-zero from the given start.</span></div>
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<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  ColIndex AddDenseColumnPrefix(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& dense_column,</div>
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<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  RowIndex start);</div>
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<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  </div>
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<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="comment">// Same as AddDenseColumn(), but uses the given non_zeros pattern of input.</span></div>
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<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="comment">// If non_zeros is empty, this actually calls AddDenseColumn().</span></div>
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<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  ColIndex AddDenseColumnWithNonZeros(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& dense_column,</div>
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<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keyword">const</span> std::vector<RowIndex>& non_zeros);</div>
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<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  </div>
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<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="comment">// Adds a dense column for which we know the non-zero positions and clears it.</span></div>
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<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="comment">// Note that this function supports duplicate indices in non_zeros. The</span></div>
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<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="comment">// complexity is in O(non_zeros.size()). Only the indices present in non_zeros</span></div>
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<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="comment">// will be cleared. Returns the index of the added column.</span></div>
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<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  ColIndex AddAndClearColumnWithNonZeros(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* column,</div>
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<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  std::vector<RowIndex>* non_zeros);</div>
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<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  </div>
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<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="comment">// Returns the number of entries (i.e. degree) of the given column.</span></div>
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<div class="line"><a name="l00335"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afe3d36f3ba4f04442fbb36f8726f8baf"> 335</a></span>  EntryIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afe3d36f3ba4f04442fbb36f8726f8baf">ColumnNumEntries</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="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">return</span> starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1] - starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  }</div>
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<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  </div>
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<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">// Returns the matrix dimensions. See same functions in SparseMatrix.</span></div>
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<div class="line"><a name="l00340"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#af69d9b7065a8f31604a8134be4307749"> 340</a></span>  EntryIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(coefficients_.size(), rows_.size());</div>
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<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">return</span> coefficients_.size();</div>
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<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  }</div>
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<div class="line"><a name="l00344"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd"> 344</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_rows_; }</div>
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<div class="line"><a name="l00345"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813"> 345</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_cols_; }</div>
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<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  </div>
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<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="comment">// Returns whether or not this matrix contains any non-zero entries.</span></div>
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<div class="line"><a name="l00348"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8e12342fc420701fbffd97025421575a"> 348</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(coefficients_.size(), rows_.size());</div>
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<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keywordflow">return</span> coefficients_.empty();</div>
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<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  }</div>
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<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  </div>
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<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">// Functions to iterate on the entries of a given column:</span></div>
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<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="comment">// for (const EntryIndex i : compact_matrix_.Column(col)) {</span></div>
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<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="comment">// const RowIndex row = compact_matrix_.EntryRow(i);</span></div>
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<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="comment">// const Fractional coefficient = compact_matrix_.EntryCoefficient(i);</span></div>
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<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="comment">// }</span></div>
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<div class="line"><a name="l00358"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a60771349d1fcf262313b13a6a857c140"> 358</a></span>  <a class="code" href="classutil_1_1_integer_range.html">::util::IntegerRange<EntryIndex></a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a60771349d1fcf262313b13a6a857c140">Column</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="l00359"></a><span class="lineno"> 359</span>  return ::util::IntegerRange<EntryIndex>(starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1]);</div>
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<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  }</div>
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<div class="line"><a name="l00361"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aaef7fc778a29bb3bb3040c0423937f6e"> 361</a></span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(EntryIndex i)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> coefficients_[i]; }</div>
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<div class="line"><a name="l00362"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aedc46de5199e203b77de2eae2e4c100d"> 362</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(EntryIndex i)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> rows_[i]; }</div>
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<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  </div>
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<div class="line"><a name="l00364"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59"> 364</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</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="l00365"></a><span class="lineno"> 365</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, num_cols_);</div>
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<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  </div>
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<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="comment">// Note that the start may be equal to row.size() if the last columns</span></div>
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<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="comment">// are empty, it is why we don't use &row[start].</span></div>
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<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">const</span> EntryIndex start = starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>(starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1] - start, rows_.data() + start.value(),</div>
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<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  coefficients_.data() + start.value());</div>
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<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  }</div>
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<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  </div>
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<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="comment">// Returns true if the given column is empty. Note that for triangular matrix</span></div>
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<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="comment">// this does not include the diagonal coefficient (see below).</span></div>
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<div class="line"><a name="l00376"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda"> 376</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda">ColumnIsEmpty</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="l00377"></a><span class="lineno"> 377</span>  <span class="keywordflow">return</span> starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1] == starts_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  }</div>
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<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  </div>
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<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="comment">// Returns the scalar product of the given row vector with the column of index</span></div>
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<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="comment">// col of this matrix. This function is declared in the .h for efficiency.</span></div>
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<div class="line"><a name="l00382"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#abdd940ad64b555052b33e763b80aea26"> 382</a></span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#abdd940ad64b555052b33e763b80aea26">ColumnScalarProduct</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& vector)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> result = 0.0;</div>
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<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  result += EntryCoefficient(i) * vector[<a class="code" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(EntryRow(i))];</div>
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<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  }</div>
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<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="keywordflow">return</span> result;</div>
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<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  }</div>
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<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  </div>
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<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="comment">// Adds a multiple of the given column of this matrix to the given</span></div>
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<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="comment">// dense_column. If multiplier is 0.0, this function does nothing. This</span></div>
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<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="comment">// function is declared in the .h for efficiency.</span></div>
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<div class="line"><a name="l00393"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aea0e9a84b41c95c874f171cae97cf31b"> 393</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aea0e9a84b41c95c874f171cae97cf31b">ColumnAddMultipleToDenseColumn</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> multiplier,</div>
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<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* dense_column)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="keywordflow">if</span> (multiplier == 0.0) <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <a class="code" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  (*dense_column)[EntryRow(i)] += multiplier * EntryCoefficient(i);</div>
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<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  }</div>
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<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  }</div>
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<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  </div>
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<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="comment">// Same as ColumnAddMultipleToDenseColumn() but also adds the new non-zeros to</span></div>
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<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="comment">// the non_zeros vector. A non-zero is "new" if is_non_zero[row] was false,</span></div>
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<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="comment">// and we update dense_column[row]. This function also updates is_non_zero.</span></div>
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<div class="line"><a name="l00405"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a6e49e4127a33039fcccc6e50380faefa"> 405</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a6e49e4127a33039fcccc6e50380faefa">ColumnAddMultipleToSparseScatteredColumn</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>,</div>
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<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> multiplier,</div>
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<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <a class="code" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* column)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="keywordflow">if</span> (multiplier == 0.0) <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <a class="code" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(column);</div>
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<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keyword">const</span> RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = EntryRow(i);</div>
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<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  column-><a class="code" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a9bb4f0967311f0f79a279879c4d69678">Add</a>(<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, multiplier * EntryCoefficient(i));</div>
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<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  }</div>
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<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  }</div>
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<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  </div>
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<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="comment">// Copies the given column of this matrix into the given dense_column.</span></div>
|
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<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="comment">// This function is declared in the .h for efficiency.</span></div>
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<div class="line"><a name="l00418"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a28058c5e9ff6638ea1ea210b49a4e7bc"> 418</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a28058c5e9ff6638ea1ea210b49a4e7bc">ColumnCopyToDenseColumn</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* dense_column)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <a class="code" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  dense_column-><a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">AssignToZero</a>(num_rows_);</div>
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<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  ColumnCopyToClearedDenseColumn(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, dense_column);</div>
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<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  }</div>
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<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  </div>
|
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<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="comment">// Same as ColumnCopyToDenseColumn() but assumes the column to be initially</span></div>
|
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<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="comment">// all zero.</span></div>
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<div class="line"><a name="l00426"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab9bd1cef3f6a18704cb7d9ce6201e106"> 426</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab9bd1cef3f6a18704cb7d9ce6201e106">ColumnCopyToClearedDenseColumn</a>(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>,</div>
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<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* dense_column)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <a class="code" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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|
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  dense_column-><a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows_, 0.0);</div>
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<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  (*dense_column)[EntryRow(i)] = EntryCoefficient(i);</div>
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|
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  }</div>
|
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<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  }</div>
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<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  </div>
|
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<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="comment">// Same as ColumnCopyToClearedDenseColumn() but also fills non_zeros.</span></div>
|
|
<div class="line"><a name="l00436"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8a0e8a1a3afc70e2678d046feb11d024"> 436</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8a0e8a1a3afc70e2678d046feb11d024">ColumnCopyToClearedDenseColumnWithNonZeros</a>(</div>
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<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* dense_column,</div>
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<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zeros)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <a class="code" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  dense_column-><a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows_, 0.0);</div>
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<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  non_zeros->clear();</div>
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<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="keyword">const</span> RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = EntryRow(i);</div>
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<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  (*dense_column)[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = EntryCoefficient(i);</div>
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<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  non_zeros->push_back(<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  }</div>
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<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  }</div>
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<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  </div>
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<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordtype">void</span> Swap(<a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>* other);</div>
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<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  </div>
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<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keyword">protected</span>:</div>
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<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="comment">// The matrix dimensions, properly updated by full and incremental builders.</span></div>
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<div class="line"><a name="l00453"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a5d6d5d7a7944b09bd0df4b7132fe5f7e"> 453</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a5d6d5d7a7944b09bd0df4b7132fe5f7e">num_rows_</a>;</div>
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<div class="line"><a name="l00454"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a0358eb2d6ea480b59d89dc42326cf840"> 454</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a0358eb2d6ea480b59d89dc42326cf840">num_cols_</a>;</div>
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<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  </div>
|
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<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="comment">// Holds the columns non-zero coefficients and row positions.</span></div>
|
|
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="comment">// The entries for the column of index col are stored in the entries</span></div>
|
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<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// [starts_[col], starts_[col + 1]).</span></div>
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<div class="line"><a name="l00459"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab392807d136adb480aedec7750cbbb18"> 459</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<EntryIndex, Fractional></a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab392807d136adb480aedec7750cbbb18">coefficients_</a>;</div>
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<div class="line"><a name="l00460"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8da36920b149053499a21e50fc859a93"> 460</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<EntryIndex, RowIndex></a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8da36920b149053499a21e50fc859a93">rows_</a>;</div>
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<div class="line"><a name="l00461"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a37ac057f213297550a26947d551324a3"> 461</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, EntryIndex></a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a37ac057f213297550a26947d551324a3">starts_</a>;</div>
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<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  </div>
|
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<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <a class="code" href="macros_8h.html#af8df3547bfde53a5acb93e2607b0034a">DISALLOW_COPY_AND_ASSIGN</a>(<a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>);</div>
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<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> };</div>
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<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  </div>
|
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<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="comment">// A matrix view of the basis columns of a CompactSparseMatrix, with basis</span></div>
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<div class="line"><a name="l00468"></a><span class="lineno"> 468</span> <span class="comment">// specified as a RowToColMapping. This class does not take ownership of the</span></div>
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<div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="comment">// underlying matrix or basis, and thus they must outlive this class (and keep</span></div>
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<div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="comment">// the same address in memory).</span></div>
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<div class="line"><a name="l00471"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html"> 471</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a> {</div>
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<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00473"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6e483ed6906f126dc6fa63d198c8f907"> 473</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6e483ed6906f126dc6fa63d198c8f907">CompactSparseMatrixView</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>* compact_matrix,</div>
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<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a>* basis)</div>
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<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  : compact_matrix_(*compact_matrix), basis_(*basis) {}</div>
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<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  </div>
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<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="comment">// Same behavior as the SparseMatrix functions above.</span></div>
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<div class="line"><a name="l00478"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a"> 478</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> compact_matrix_.IsEmpty(); }</div>
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<div class="line"><a name="l00479"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd"> 479</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> compact_matrix_.num_rows(); }</div>
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<div class="line"><a name="l00480"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813"> 480</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(basis_.size()); }</div>
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<div class="line"><a name="l00481"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c"> 481</a></span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</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="l00482"></a><span class="lineno"> 482</span>  <span class="keywordflow">return</span> compact_matrix_.column(basis_[<a class="code" href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">ColToRowIndex</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)]);</div>
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<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  }</div>
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<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  EntryIndex <a class="code" href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeOneNorm() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1sat.html#acb294633c7688f918623b3b0e09aec43">ComputeInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  </div>
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<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="comment">// We require that the underlying CompactSparseMatrix and RowToColMapping</span></div>
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<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="comment">// continue to own the (potentially large) data accessed via this view.</span></div>
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<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& compact_matrix_;</div>
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<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a>& basis_;</div>
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<div class="line"><a name="l00493"></a><span class="lineno"> 493</span> };</div>
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<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  </div>
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<div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="comment">// Specialization of a CompactSparseMatrix used for triangular matrices.</span></div>
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<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="comment">// To be able to solve triangular systems as efficiently as possible, the</span></div>
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<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="comment">// diagonal entries are stored in a separate vector and not in the underlying</span></div>
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<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="comment">// CompactSparseMatrix.</span></div>
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<div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment">// Advanced usage: this class also support matrices that can be permuted into a</span></div>
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<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="comment">// triangular matrix and some functions work directly on such matrices.</span></div>
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<div class="line"><a name="l00502"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html"> 502</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a> : <span class="keyword">private</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a> {</div>
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<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00504"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab8101094fb842f9cb500b3dfadc325d3"> 504</a></span>  <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab8101094fb842f9cb500b3dfadc325d3">TriangularMatrix</a>() : all_diagonal_coefficients_are_one_(true) {}</div>
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<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  </div>
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<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="comment">// Only a subset of the functions from CompactSparseMatrix are exposed (note</span></div>
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<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="comment">// the private inheritance). They are extended to deal with diagonal</span></div>
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<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="comment">// coefficients properly.</span></div>
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<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keywordtype">void</span> PopulateFromTranspose(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordtype">void</span> Swap(<a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>* other);</div>
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<div class="line"><a name="l00511"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8e12342fc420701fbffd97025421575a"> 511</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> diagonal_coefficients_.empty(); }</div>
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<div class="line"><a name="l00512"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd"> 512</a></span>  RowIndex <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_rows_; }</div>
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<div class="line"><a name="l00513"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813"> 513</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_cols_; }</div>
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<div class="line"><a name="l00514"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749"> 514</a></span>  EntryIndex <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordflow">return</span> EntryIndex(num_cols_.value()) + coefficients_.size();</div>
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<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  }</div>
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<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  </div>
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<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="comment">// On top of the CompactSparseMatrix functionality, TriangularMatrix::Reset()</span></div>
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<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="comment">// also pre-allocates space of size col_size for a number of internal vectors.</span></div>
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<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="comment">// This helps reduce costly push_back operations for large problems.</span></div>
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<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="comment">// WARNING: Reset() must be called with a sufficiently large col_capacity</span></div>
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<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="comment">// prior to any Add* calls (e.g., AddTriangularColumn).</span></div>
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<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordtype">void</span> Reset(RowIndex num_rows, ColIndex col_capacity);</div>
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<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  </div>
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<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="comment">// Constructs a triangular matrix from the given SparseMatrix. The input is</span></div>
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<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="comment">// assumed to be lower or upper triangular without any permutations. This is</span></div>
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<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="comment">// checked in debug mode.</span></div>
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<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keywordtype">void</span> PopulateFromTriangularSparseMatrix(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  </div>
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<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="comment">// Functions to create a triangular matrix incrementally, column by column.</span></div>
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<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="comment">// A client needs to call Reset(num_rows) first, and then each column must be</span></div>
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<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <span class="comment">// added by calling one of the 3 functions below.</span></div>
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<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="comment">// Note that the row indices of the columns are allowed to be permuted: the</span></div>
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<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="comment">// diagonal entry of the column #col not being necessarily on the row #col.</span></div>
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<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="comment">// This is why these functions require the 'diagonal_row' parameter. The</span></div>
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<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="comment">// permutation can be fixed at the end by a call to</span></div>
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<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="comment">// ApplyRowPermutationToNonDiagonalEntries() or accounted directly in the case</span></div>
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<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="comment">// of PermutedLowerSparseSolve().</span></div>
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<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="keywordtype">void</span> AddTriangularColumn(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& column, RowIndex diagonal_row);</div>
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<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keywordtype">void</span> AddTriangularColumnWithGivenDiagonalEntry(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& column,</div>
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<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  RowIndex diagonal_row,</div>
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<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_value);</div>
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<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="keywordtype">void</span> AddDiagonalOnlyColumn(<a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_value);</div>
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<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  </div>
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<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="comment">// Adds the given sparse column divided by diagonal_coefficient.</span></div>
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<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <span class="comment">// The diagonal_row is assumed to be present and its value should be the</span></div>
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<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="comment">// same as the one given in diagonal_coefficient. Note that this function</span></div>
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<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="comment">// tests for zero coefficients in the input column and removes them.</span></div>
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<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordtype">void</span> AddAndNormalizeTriangularColumn(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& column,</div>
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<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  RowIndex diagonal_row,</div>
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<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_coefficient);</div>
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<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  </div>
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<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="comment">// Applies the given row permutation to all entries except the diagonal ones.</span></div>
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<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordtype">void</span> ApplyRowPermutationToNonDiagonalEntries(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm);</div>
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<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  </div>
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<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="comment">// Copy a triangular column with its diagonal entry to the given SparseColumn.</span></div>
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<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordtype">void</span> CopyColumnToSparseColumn(ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* output) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  </div>
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<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="comment">// Copy a triangular matrix to the given SparseMatrix.</span></div>
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<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="keywordtype">void</span> CopyToSparseMatrix(<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* output) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  </div>
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<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="comment">// Returns the index of the first column which is not an identity column (i.e.</span></div>
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<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="comment">// a column j with only one entry of value 1 at the j-th row). This is always</span></div>
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<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="comment">// zero if the matrix is not triangular.</span></div>
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<div class="line"><a name="l00567"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3d3abc3e6b522dc60fd8c1168522e09d"> 567</a></span>  ColIndex <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3d3abc3e6b522dc60fd8c1168522e09d">GetFirstNonIdentityColumn</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="keywordflow">return</span> first_non_identity_column_;</div>
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<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  }</div>
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<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  </div>
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<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <span class="comment">// Returns the diagonal coefficient of the given column.</span></div>
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<div class="line"><a name="l00572"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84"> 572</a></span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">GetDiagonalCoefficient</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="l00573"></a><span class="lineno"> 573</span>  <span class="keywordflow">return</span> diagonal_coefficients_[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  }</div>
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<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  </div>
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<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <span class="comment">// Returns true iff the column contains no non-diagonal entries.</span></div>
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<div class="line"><a name="l00577"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6"> 577</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6">ColumnIsDiagonalOnly</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="l00578"></a><span class="lineno"> 578</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda">CompactSparseMatrix::ColumnIsEmpty</a>(<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  }</div>
|
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<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  </div>
|
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<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="comment">// --------------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="comment">// Triangular solve functions.</span></div>
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<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="comment">// All the functions containing the word Lower (resp. Upper) require the</span></div>
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<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="comment">// matrix to be lower (resp. upper_) triangular without any permutation.</span></div>
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<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="comment">// --------------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  </div>
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<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  <span class="comment">// Solve the system L.x = rhs for a lower triangular matrix.</span></div>
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<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="comment">// The result overwrite rhs.</span></div>
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<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <span class="keywordtype">void</span> LowerSolve(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  </div>
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<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="comment">// Solves the system U.x = rhs for an upper triangular matrix.</span></div>
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<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <span class="keywordtype">void</span> UpperSolve(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  </div>
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<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="comment">// Solves the system Transpose(U).x = rhs where U is upper triangular.</span></div>
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<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  <span class="comment">// This can be used to do a left-solve for a row vector (i.e. y.Y = rhs).</span></div>
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<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keywordtype">void</span> TransposeUpperSolve(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  </div>
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<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  <span class="comment">// This assumes that the rhs is all zero before the given position.</span></div>
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<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  <span class="keywordtype">void</span> LowerSolveStartingAt(ColIndex start, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  </div>
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<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  <span class="comment">// Solves the system Transpose(L).x = rhs, where L is lower triangular.</span></div>
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<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <span class="comment">// This can be used to do a left-solve for a row vector (i.e., y.Y = rhs).</span></div>
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<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  <span class="keywordtype">void</span> TransposeLowerSolve(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  </div>
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<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="comment">// Hyper-sparse version of the triangular solve functions. The passed</span></div>
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|
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="comment">// non_zero_rows should contain the positions of the symbolic non-zeros of the</span></div>
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|
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <span class="comment">// result in the order in which they need to be accessed (or in the reverse</span></div>
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<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <span class="comment">// order for the Reverse*() versions).</span></div>
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|
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  <span class="comment">//</span></div>
|
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<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="comment">// The non-zero vector is mutable so that the symbolic non-zeros that are</span></div>
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<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="comment">// actually zero because of numerical cancellations can be removed.</span></div>
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<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="comment">// The non-zeros can be computed by one of these two methods:</span></div>
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|
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="comment">// - ComputeRowsToConsiderWithDfs() which will give them in the reverse order</span></div>
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|
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  <span class="comment">// of the one they need to be accessed in. This is only a topological order,</span></div>
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<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <span class="comment">// and it will not necessarily be "sorted".</span></div>
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|
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="comment">// - ComputeRowsToConsiderInSortedOrder() which will always give them in</span></div>
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<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="comment">// increasing order.</span></div>
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|
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  <span class="comment">// Note that if the non-zeros are given in a sorted order, then the</span></div>
|
|
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  <span class="comment">// hyper-sparse functions will return EXACTLY the same results as the non</span></div>
|
|
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="comment">// hyper-sparse version above.</span></div>
|
|
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  <span class="comment">// For a given solve, here is the required order:</span></div>
|
|
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="comment">// - For a lower solve, increasing non-zeros order.</span></div>
|
|
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  <span class="comment">// - For an upper solve, decreasing non-zeros order.</span></div>
|
|
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="comment">// - for a transpose lower solve, decreasing non-zeros order.</span></div>
|
|
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <span class="comment">// - for a transpose upper solve, increasing non_zeros order.</span></div>
|
|
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  <span class="comment">//</span></div>
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|
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <span class="comment">// For a general discussion of hyper-sparsity in LP, see:</span></div>
|
|
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="comment">// J.A.J. Hall, K.I.M. McKinnon, "Exploiting hyper-sparsity in the revised</span></div>
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|
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <span class="comment">// simplex method", December 1999, MS 99-014.</span></div>
|
|
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="comment">// http://www.maths.ed.ac.uk/hall/MS-99/MS9914.pdf</span></div>
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|
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  <span class="keywordtype">void</span> HyperSparseSolve(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  <span class="keywordtype">void</span> HyperSparseSolveWithReversedNonZeros(</div>
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|
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
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|
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  <span class="keywordtype">void</span> TransposeHyperSparseSolve(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs,</div>
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|
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
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|
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  <span class="keywordtype">void</span> TransposeHyperSparseSolveWithReversedNonZeros(</div>
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<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
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|
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  </div>
|
|
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  <span class="comment">// Given the positions of the non-zeros of a vector, computes the non-zero</span></div>
|
|
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  <span class="comment">// positions of the vector after a solve by this triangular matrix. The order</span></div>
|
|
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  <span class="comment">// of the returned non-zero positions will be in the REVERSE elimination</span></div>
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|
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="comment">// order. If the function detects that there are too many non-zeros, then it</span></div>
|
|
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="comment">// aborts early and non_zero_rows is cleared.</span></div>
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|
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  <span class="keywordtype">void</span> ComputeRowsToConsiderWithDfs(<a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  </div>
|
|
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  <span class="comment">// Same as TriangularComputeRowsToConsider() but always returns the non-zeros</span></div>
|
|
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  <span class="comment">// sorted by rows. It is up to the client to call the direct or reverse</span></div>
|
|
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  <span class="comment">// hyper-sparse solve function depending if the matrix is upper or lower</span></div>
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|
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  <span class="comment">// triangular.</span></div>
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<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  <span class="keywordtype">void</span> ComputeRowsToConsiderInSortedOrder(<a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows,</div>
|
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<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sparsity_ratio,</div>
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<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> num_ops_ratio) <span class="keyword">const</span>;</div>
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|
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  <span class="keywordtype">void</span> ComputeRowsToConsiderInSortedOrder(<a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="comment">// This is currently only used for testing. It achieves the same result as</span></div>
|
|
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <span class="comment">// PermutedLowerSparseSolve() below, but the latter exploits the sparsity of</span></div>
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|
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="comment">// rhs and is thus faster for our use case.</span></div>
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|
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="comment">//</span></div>
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|
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  <span class="comment">// Note that partial_inverse_row_perm only permutes the first k rows, where k</span></div>
|
|
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  <span class="comment">// is the same as partial_inverse_row_perm.size(). It is the inverse</span></div>
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|
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  <span class="comment">// permutation of row_perm which only permutes k rows into is [0, k), the</span></div>
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|
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  <span class="comment">// other row images beeing kInvalidRow. The other arguments are the same as</span></div>
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|
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <span class="comment">// for PermutedLowerSparseSolve() and described there.</span></div>
|
|
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="comment">// IMPORTANT: lower will contain all the "symbolic" non-zero entries.</span></div>
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|
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="comment">// A "symbolic" zero entry is one that will be zero whatever the coefficients</span></div>
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|
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  <span class="comment">// of the rhs entries. That is it only depends on the position of its</span></div>
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|
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <span class="comment">// entries, not on their values. Thus, some of its coefficients may be zero.</span></div>
|
|
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="comment">// This fact is exploited by the LU factorization code. The zero coefficients</span></div>
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|
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <span class="comment">// of upper will be cleaned, however.</span></div>
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|
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordtype">void</span> PermutedLowerSolve(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& rhs,</div>
|
|
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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|
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowMapping</a>& partial_inverse_row_perm,</div>
|
|
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* lower, <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* upper) <span class="keyword">const</span>;</div>
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|
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  </div>
|
|
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  <span class="comment">// This solves a lower triangular system with only ones on the diagonal where</span></div>
|
|
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <span class="comment">// the matrix and the input rhs are permuted by the inverse of row_perm. Note</span></div>
|
|
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="comment">// that the output will also be permuted by the inverse of row_perm. The</span></div>
|
|
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  <span class="comment">// function also supports partial permutation. That is if row_perm[i] < 0 then</span></div>
|
|
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  <span class="comment">// column row_perm[i] is assumed to be an identity column.</span></div>
|
|
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  <span class="comment">// The output is given as follow:</span></div>
|
|
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <span class="comment">// - lower is cleared, and receives the rows for which row_perm[row] < 0</span></div>
|
|
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  <span class="comment">// meaning not yet examined as a pivot (see markowitz.cc).</span></div>
|
|
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  <span class="comment">// - upper is NOT cleared, and the other rows (row_perm[row] >= 0) are</span></div>
|
|
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="comment">// appended to it.</span></div>
|
|
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  <span class="comment">// - Note that lower and upper can point to the same SparseColumn.</span></div>
|
|
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  <span class="comment">// Note: This function is non-const because ComputeRowsToConsider() also</span></div>
|
|
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="comment">// prunes the underlying dependency graph of the lower matrix while doing a</span></div>
|
|
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="comment">// solve. See marked_ and pruned_ends_ below.</span></div>
|
|
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  <span class="keywordtype">void</span> PermutedLowerSparseSolve(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& rhs,</div>
|
|
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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|
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* lower, <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* upper);</div>
|
|
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  </div>
|
|
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  <span class="comment">// To be used in DEBUG mode by the client code. This check that the matrix is</span></div>
|
|
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  <span class="comment">// lower- (resp. upper-) triangular without any permutation and that there is</span></div>
|
|
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  <span class="comment">// no zero on the diagonal. We can't do that on each Solve() that require so,</span></div>
|
|
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="comment">// otherwise it will be too slow in debug.</span></div>
|
|
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  <span class="keywordtype">bool</span> IsLowerTriangular() <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  <span class="keywordtype">bool</span> IsUpperTriangular() <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  </div>
|
|
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <span class="comment">// Visible for testing. This is used by PermutedLowerSparseSolve() to compute</span></div>
|
|
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <span class="comment">// the non-zero indices of the result. The output is as follow:</span></div>
|
|
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="comment">// - lower_column_rows will contains the rows for which row_perm[row] < 0.</span></div>
|
|
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="comment">// - upper_column_rows will contains the other rows in the reverse topological</span></div>
|
|
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  <span class="comment">// order in which they should be considered in PermutedLowerSparseSolve().</span></div>
|
|
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="comment">// This function is non-const because it prunes the underlying dependency</span></div>
|
|
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  <span class="comment">// graph of the lower matrix while doing a solve. See marked_ and pruned_ends_</span></div>
|
|
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  <span class="comment">// below.</span></div>
|
|
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <span class="comment">// Pruning the graph at the same time is slower but not by too much (< 2x) and</span></div>
|
|
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <span class="comment">// seems worth doing. Note that when the lower matrix is dense, most of the</span></div>
|
|
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  <span class="comment">// graph will likely be pruned. As a result, the symbolic phase will be</span></div>
|
|
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  <span class="comment">// negligible compared to the numerical phase so we don't really need a dense</span></div>
|
|
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  <span class="comment">// version of PermutedLowerSparseSolve().</span></div>
|
|
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  <span class="keywordtype">void</span> PermutedComputeRowsToConsider(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& rhs,</div>
|
|
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
|
|
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* lower_column_rows,</div>
|
|
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* upper_column_rows);</div>
|
|
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  </div>
|
|
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  <span class="comment">// The upper bound is computed using one of the algorithm presented in</span></div>
|
|
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="comment">// "A Survey of Condition Number Estimation for Triangular Matrices"</span></div>
|
|
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <span class="comment">// https:epubs.siam.org/doi/pdf/10.1137/1029112/</span></div>
|
|
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeInverseInfinityNormUpperBound() <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeInverseInfinityNorm() <span class="keyword">const</span>;</div>
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|
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  </div>
|
|
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  <span class="keyword">private</span>:</div>
|
|
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  <span class="comment">// Internal versions of some Solve() functions to avoid code duplication.</span></div>
|
|
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  <span class="keywordtype">void</span> LowerSolveStartingAtInternal(ColIndex start, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <span class="keywordtype">void</span> UpperSolveInternal(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  <span class="keywordtype">void</span> TransposeLowerSolveInternal(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  <span class="keywordtype">void</span> TransposeUpperSolveInternal(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  <span class="keywordtype">void</span> HyperSparseSolveInternal(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs,</div>
|
|
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  <span class="keywordtype">void</span> HyperSparseSolveWithReversedNonZerosInternal(</div>
|
|
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <span class="keywordtype">void</span> TransposeHyperSparseSolveInternal(<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs,</div>
|
|
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
|
|
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="keywordtype">void</span> TransposeHyperSparseSolveWithReversedNonZerosInternal(</div>
|
|
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows) <span class="keyword">const</span>;</div>
|
|
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  </div>
|
|
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  <span class="comment">// Internal function used by the Add*() functions to finish adding</span></div>
|
|
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="comment">// a new column to a triangular matrix.</span></div>
|
|
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <span class="keywordtype">void</span> CloseCurrentColumn(<a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_value);</div>
|
|
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  </div>
|
|
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  <span class="comment">// Extra data for "triangular" matrices. The diagonal coefficients are</span></div>
|
|
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  <span class="comment">// stored in a separate vector instead of beeing stored in each column.</span></div>
|
|
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, Fractional></a> diagonal_coefficients_;</div>
|
|
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  </div>
|
|
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  <span class="comment">// Index of the first column which is not a diagonal only column with a</span></div>
|
|
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span>  <span class="comment">// coefficient of 1. This is used to optimize the solves.</span></div>
|
|
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  ColIndex first_non_identity_column_;</div>
|
|
<div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  </div>
|
|
<div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  <span class="comment">// This common case allows for more efficient Solve() functions.</span></div>
|
|
<div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  <span class="comment">// TODO(user): Do not even construct diagonal_coefficients_ in this case?</span></div>
|
|
<div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  <span class="keywordtype">bool</span> all_diagonal_coefficients_are_one_;</div>
|
|
<div class="line"><a name="l00770"></a><span class="lineno"> 770</span>  </div>
|
|
<div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  <span class="comment">// For the hyper-sparse version. These are used to implement a DFS, see</span></div>
|
|
<div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  <span class="comment">// TriangularComputeRowsToConsider() for more details.</span></div>
|
|
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  <span class="keyword">mutable</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> stored_;</div>
|
|
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  <span class="keyword">mutable</span> std::vector<RowIndex> nodes_to_explore_;</div>
|
|
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  </div>
|
|
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  <span class="comment">// For PermutedLowerSparseSolve().</span></div>
|
|
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  <span class="keyword">mutable</span> std::vector<RowIndex> lower_column_rows_;</div>
|
|
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  <span class="keyword">mutable</span> std::vector<RowIndex> upper_column_rows_;</div>
|
|
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  <span class="keyword">mutable</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> initially_all_zero_scratchpad_;</div>
|
|
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  </div>
|
|
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  <span class="comment">// This boolean vector is used to detect entries that can be pruned during</span></div>
|
|
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  <span class="comment">// the DFS used for the symbolic phase of ComputeRowsToConsider().</span></div>
|
|
<div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00784"></a><span class="lineno"> 784</span>  <span class="comment">// Problem: We have a DAG where each node has outgoing arcs towards other</span></div>
|
|
<div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  <span class="comment">// nodes (this adjacency list is NOT sorted by any order). We want to compute</span></div>
|
|
<div class="line"><a name="l00786"></a><span class="lineno"> 786</span>  <span class="comment">// the reachability of a set of nodes S and its topological order. While doing</span></div>
|
|
<div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  <span class="comment">// this, we also want to prune the adjacency lists to exploit the simple fact</span></div>
|
|
<div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  <span class="comment">// that if a -> (b, c) and b -> (c) then c can be removed from the adjacency</span></div>
|
|
<div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  <span class="comment">// list of a since it will be implied through b. Note that this doesn't change</span></div>
|
|
<div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  <span class="comment">// the reachability of any set nor a valid topological ordering of such a set.</span></div>
|
|
<div class="line"><a name="l00791"></a><span class="lineno"> 791</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  <span class="comment">// The concept is known as the transitive reduction of a DAG, see</span></div>
|
|
<div class="line"><a name="l00793"></a><span class="lineno"> 793</span>  <span class="comment">// http://en.wikipedia.org/wiki/Transitive_reduction.</span></div>
|
|
<div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  <span class="comment">// Heuristic algorithm: While doing the DFS to compute Reach(S) and its</span></div>
|
|
<div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  <span class="comment">// topological order, each time we process a node, we mark all its adjacent</span></div>
|
|
<div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <span class="comment">// node while going down in the DFS, and then we unmark all of them when we go</span></div>
|
|
<div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  <span class="comment">// back up. During the un-marking, if a node is already un-marked, it means</span></div>
|
|
<div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  <span class="comment">// that it was implied by some other path starting at the current node and we</span></div>
|
|
<div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  <span class="comment">// can prune it and remove it from the adjacency list of the current node.</span></div>
|
|
<div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  <span class="comment">// Note(user): I couldn't find any reference for this algorithm, even though</span></div>
|
|
<div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  <span class="comment">// I suspect I am not the first one to need someting similar.</span></div>
|
|
<div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  <span class="keyword">mutable</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> marked_;</div>
|
|
<div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  </div>
|
|
<div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  <span class="comment">// This is used to represent a pruned sub-matrix of the current matrix that</span></div>
|
|
<div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  <span class="comment">// corresponds to the pruned DAG as described in the comment above for</span></div>
|
|
<div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  <span class="comment">// marked_. This vector is used to encode the sub-matrix as follow:</span></div>
|
|
<div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  <span class="comment">// - Both the rows and the coefficients of the pruned matrix are still stored</span></div>
|
|
<div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  <span class="comment">// in rows_ and coefficients_.</span></div>
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<div class="line"><a name="l00811"></a><span class="lineno"> 811</span>  <span class="comment">// - The data of column 'col' is still stored starting at starts_[col].</span></div>
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<div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  <span class="comment">// - But, its end is given by pruned_ends_[col] instead of starts_[col + 1].</span></div>
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<div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  <span class="comment">// The idea of using a smaller graph for the symbolic phase is well known in</span></div>
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<div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  <span class="comment">// sparse linear algebra. See:</span></div>
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<div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  <span class="comment">// - John R. Gilbert and Joseph W. H. Liu, "Elimination structures for</span></div>
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<div class="line"><a name="l00817"></a><span class="lineno"> 817</span>  <span class="comment">// unsymmetric sparse LU factors", Tech. Report CS-90-11. Departement of</span></div>
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<div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  <span class="comment">// Computer Science, York University, North York. Ontario, Canada, 1990.</span></div>
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<div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  <span class="comment">// - Stanley C. Eisenstat and Joseph W. H. Liu, "Exploiting structural</span></div>
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<div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  <span class="comment">// symmetry in a sparse partial pivoting code". SIAM J. Sci. Comput. Vol</span></div>
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<div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  <span class="comment">// 14, No 1, pp. 253-257, January 1993.</span></div>
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<div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  <span class="comment">// Note that we use an original algorithm and prune the graph while performing</span></div>
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<div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  <span class="comment">// the symbolic phase. Hence the pruning will only benefit the next symbolic</span></div>
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<div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  <span class="comment">// phase. This is different from Eisenstat-Liu's symmetric pruning. It is</span></div>
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<div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  <span class="comment">// still a heuristic and will not necessarily find the minimal graph that</span></div>
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<div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <span class="comment">// has the same result for the symbolic phase though.</span></div>
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<div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  <span class="comment">// TODO(user): Use this during the "normal" hyper-sparse solves so that</span></div>
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<div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  <span class="comment">// we can benefit from the pruned lower matrix there?</span></div>
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<div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, EntryIndex></a> pruned_ends_;</div>
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<div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  </div>
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<div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  <a class="code" href="macros_8h.html#af8df3547bfde53a5acb93e2607b0034a">DISALLOW_COPY_AND_ASSIGN</a>(<a class="code" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>);</div>
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<div class="line"><a name="l00834"></a><span class="lineno"> 834</span> };</div>
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<div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  </div>
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<div class="line"><a name="l00836"></a><span class="lineno"> 836</span> } <span class="comment">// namespace glop</span></div>
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<div class="line"><a name="l00837"></a><span class="lineno"> 837</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  </div>
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<div class="line"><a name="l00839"></a><span class="lineno"> 839</span> <span class="preprocessor">#endif // OR_TOOLS_LP_DATA_SPARSE_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_matrix_view_html_adc9aa1d344fe9442ac3ba673b939db7c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#adc9aa1d344fe9442ac3ba673b939db7c">operations_research::glop::MatrixView::PopulateFromBasis</a></div><div class="ttdeci">void PopulateFromBasis(const MatrixView &matrix, const RowToColMapping &basis)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00251">sparse.h:251</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a1426d8ab983ec32193c571f5e8c02cda"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda">operations_research::glop::CompactSparseMatrix::ColumnIsEmpty</a></div><div class="ttdeci">bool ColumnIsEmpty(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00376">sparse.h:376</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a37ac057f213297550a26947d551324a3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a37ac057f213297550a26947d551324a3">operations_research::glop::CompactSparseMatrix::starts_</a></div><div class="ttdeci">StrictITIVector< ColIndex, EntryIndex > starts_</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00461">sparse.h:461</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_ae1b90982a83e1b025ebbc1c446980640"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ae1b90982a83e1b025ebbc1c446980640">operations_research::glop::SparseMatrix::PopulateFromZero</a></div><div class="ttdeci">void PopulateFromZero(RowIndex num_rows, ColIndex num_cols)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00164">sparse.cc:164</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::CompactSparseMatrix::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00348">sparse.h:348</a></div></div>
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<div class="ttc" id="aclassutil_1_1_integer_range_html"><div class="ttname"><a href="classutil_1_1_integer_range.html">util::IntegerRange</a></div><div class="ttdef"><b>Definition:</b> <a href="iterators_8h_source.html#l00146">iterators.h:146</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">operations_research::glop::CompactSparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00288">sparse.h:288</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a64b6b04f3a519d2c61d49daaa88bf06e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">operations_research::glop::StrictITIVector::resize</a></div><div class="ttdeci">void resize(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00269">lp_types.h:269</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html"><div class="ttname"><a href="integral__types_8h.html">integral_types.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ab62f5ed8f2d48e29802be0cbbcd1359a"><div class="ttname"><a href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a></div><div class="ttdeci">#define DCHECK_LT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00888">base/logging.h:888</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_ab2d8beb101c26b08a8af602300da1748"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ab2d8beb101c26b08a8af602300da1748">operations_research::glop::SparseMatrix::AppendRowsFromSparseMatrix</a></div><div class="ttdeci">bool AppendRowsFromSparseMatrix(const SparseMatrix &matrix)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00302">sparse.cc:302</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a9d0c202d5fdd62f4fa2c613339ff168a"><div class="ttname"><a href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a></div><div class="ttdeci">int64 max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_ac220f9bed6efccb65c2514e90d702638"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#ac220f9bed6efccb65c2514e90d702638">operations_research::glop::MatrixView::MatrixView</a></div><div class="ttdeci">MatrixView(const SparseMatrix &matrix)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00221">sparse.h:221</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a28058c5e9ff6638ea1ea210b49a4e7bc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a28058c5e9ff6638ea1ea210b49a4e7bc">operations_research::glop::CompactSparseMatrix::ColumnCopyToDenseColumn</a></div><div class="ttdeci">void ColumnCopyToDenseColumn(ColIndex col, DenseColumn *dense_column) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00418">sparse.h:418</a></div></div>
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<div class="ttc" id="apreprocessor_8cc_html_a2babe18010525bbf13c2fa5a959971e4"><div class="ttname"><a href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a></div><div class="ttdeci">EntryIndex num_entries</div><div class="ttdef"><b>Definition:</b> <a href="preprocessor_8cc_source.html#l01306">preprocessor.cc:1306</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::MatrixView::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00262">sparse.h:262</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a06d22c92f8b45b18560b46797f98a81b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a06d22c92f8b45b18560b46797f98a81b">operations_research::glop::SparseMatrix::AppendUnitVector</a></div><div class="ttdeci">void AppendUnitVector(RowIndex row, Fractional value)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00151">sparse.cc:151</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_vector_html_a9bb4f0967311f0f79a279879c4d69678"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#a9bb4f0967311f0f79a279879c4d69678">operations_research::glop::ScatteredVector::Add</a></div><div class="ttdeci">void Add(Index index, Fractional value)</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00099">scattered_vector.h:99</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_afbe7c81d6b4066bf7874299a0f7c0d59"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">operations_research::glop::CompactSparseMatrix::column</a></div><div class="ttdeci">ColumnView column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00364">sparse.h:364</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::MatrixView::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00261">sparse.h:261</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_af782744bdb01cf56841a0de18ccca3ce"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#af782744bdb01cf56841a0de18ccca3ce">operations_research::glop::SparseMatrix::Equals</a></div><div class="ttdeci">bool Equals(const SparseMatrix &a, Fractional tolerance) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00327">sparse.cc:327</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_aea0e9a84b41c95c874f171cae97cf31b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aea0e9a84b41c95c874f171cae97cf31b">operations_research::glop::CompactSparseMatrix::ColumnAddMultipleToDenseColumn</a></div><div class="ttdeci">void ColumnAddMultipleToDenseColumn(ColIndex col, Fractional multiplier, DenseColumn *dense_column) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00393">sparse.h:393</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a64fea3282d498f3eb2d4af70692bb117"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a64fea3282d498f3eb2d4af70692bb117">operations_research::glop::MatrixView::ComputeOneNorm</a></div><div class="ttdeci">Fractional ComputeOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00420">sparse.cc:420</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="ademon__profiler_8cc_html_a21edc7ca4cc5802c8779d68556bc09cf"><div class="ttname"><a href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a></div><div class="ttdeci">int64 value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00043">demon_profiler.cc:43</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00344">sparse.h:344</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_aaef7fc778a29bb3bb3040c0423937f6e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aaef7fc778a29bb3bb3040c0423937f6e">operations_research::glop::CompactSparseMatrix::EntryCoefficient</a></div><div class="ttdeci">Fractional EntryCoefficient(EntryIndex i) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00361">sparse.h:361</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00276">lp_types.h:276</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_sparse_matrix_html_a566008ab9fd3e3dbec96263bc3c45061"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a566008ab9fd3e3dbec96263bc3c45061">operations_research::glop::SparseMatrix::LookUpValue</a></div><div class="ttdeci">Fractional LookUpValue(RowIndex row, ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00323">sparse.cc:323</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html">operations_research::glop::MatrixView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00218">sparse.h:218</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::TriangularMatrix::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00514">sparse.h:514</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_acbbc88405e6db3fe77064e1a3d4e402a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#acbbc88405e6db3fe77064e1a3d4e402a">operations_research::glop::SparseMatrix::PopulateFromSparseMatrix</a></div><div class="ttdeci">void PopulateFromSparseMatrix(const SparseMatrix &matrix)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00206">sparse.cc:206</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00345">sparse.h:345</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::CompactSparseMatrix::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00340">sparse.h:340</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::TriangularMatrix::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00511">sparse.h:511</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a860e7a37e8c7c2f5f7f0a73d3e3473f0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a860e7a37e8c7c2f5f7f0a73d3e3473f0">operations_research::glop::SparseMatrix::DeleteRows</a></div><div class="ttdeci">void DeleteRows(RowIndex num_rows, const RowPermutation &permutation)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00289">sparse.cc:289</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html">operations_research::glop::SparseColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00044">sparse_column.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a3f219a081f88c22ae282ada4f0bdddd3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a3f219a081f88c22ae282ada4f0bdddd3">operations_research::glop::SparseMatrix::ComputeInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00395">sparse.cc:395</a></div></div>
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<div class="ttc" id="areturn__macros_8h_html_a6009315499028d98072d8f31834cf4f9"><div class="ttname"><a href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a></div><div class="ttdeci">#define RETURN_IF_NULL(x)</div><div class="ttdef"><b>Definition:</b> <a href="return__macros_8h_source.html#l00020">return_macros.h:20</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a5d6d5d7a7944b09bd0df4b7132fe5f7e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a5d6d5d7a7944b09bd0df4b7132fe5f7e">operations_research::glop::CompactSparseMatrix::num_rows_</a></div><div class="ttdeci">RowIndex num_rows_</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00453">sparse.h:453</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_1glop_1_1_compact_sparse_matrix_view_html_a6c2cb025b83ee5d5365eb0b419a0298c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">operations_research::glop::CompactSparseMatrixView::column</a></div><div class="ttdeci">const ColumnView column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00481">sparse.h:481</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_ace1973900f4d921a7bedbcbe36e1bcad"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ace1973900f4d921a7bedbcbe36e1bcad">operations_research::glop::SparseMatrix::ApplyRowPermutation</a></div><div class="ttdeci">void ApplyRowPermutation(const RowPermutation &row_perm)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00316">sparse.cc:316</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a8fbc9efd86a3cc862a9079d86ab8b524"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">operations_research::glop::RowToColIndex</a></div><div class="ttdeci">ColIndex RowToColIndex(RowIndex row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00048">lp_types.h:48</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_compact_sparse_matrix_html_a9f271f559e0d1e794a2ecc76d919db68"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a9f271f559e0d1e794a2ecc76d919db68">operations_research::glop::CompactSparseMatrix::CompactSparseMatrix</a></div><div class="ttdeci">CompactSparseMatrix(const SparseMatrix &matrix)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00294">sparse.h:294</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a86fd105be79f4f2dbaf3a21e64e4d022"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a86fd105be79f4f2dbaf3a21e64e4d022">operations_research::glop::SparseMatrix::AppendEmptyColumn</a></div><div class="ttdeci">ColIndex AppendEmptyColumn()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00145">sparse.cc:145</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::TriangularMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00513">sparse.h:513</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::SparseMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00177">sparse.h:177</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_ac59fd9cddfe284bf9dc7581ed631ce8d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ac59fd9cddfe284bf9dc7581ed631ce8d">operations_research::glop::SparseMatrix::DeleteColumns</a></div><div class="ttdeci">void DeleteColumns(const DenseBooleanRow &columns_to_delete)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00276">sparse.cc:276</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_aedc46de5199e203b77de2eae2e4c100d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aedc46de5199e203b77de2eae2e4c100d">operations_research::glop::CompactSparseMatrix::EntryRow</a></div><div class="ttdeci">RowIndex EntryRow(EntryIndex i) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00362">sparse.h:362</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_abfc30f91ab75c6f4552003f777672e74"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#abfc30f91ab75c6f4552003f777672e74">operations_research::glop::SparseMatrix::CleanUp</a></div><div class="ttdeci">void CleanUp()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00119">sparse.cc:119</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a323801972c3d6de340e260de4582c34b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a323801972c3d6de340e260de4582c34b">operations_research::glop::SparseMatrix::PopulateFromIdentity</a></div><div class="ttdeci">void PopulateFromIdentity(ColIndex num_cols)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00172">sparse.cc:172</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_sparse_matrix_html_a1e9f788d4507f2461b4f775755aaf82e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a1e9f788d4507f2461b4f775755aaf82e">operations_research::glop::SparseMatrix::mutable_column</a></div><div class="ttdeci">SparseColumn * mutable_column(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00181">sparse.h:181</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a29edb960f882c54b9652853e94988e79"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a29edb960f882c54b9652853e94988e79">operations_research::glop::SparseMatrix::PopulateFromPermutedMatrix</a></div><div class="ttdeci">void PopulateFromPermutedMatrix(const Matrix &a, const RowPermutation &row_perm, const ColumnPermutation &inverse_col_perm)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00212">sparse.cc:212</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a5e016d204d43b2cc4a2773c25462968a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a5e016d204d43b2cc4a2773c25462968a">operations_research::glop::SparseMatrix::IsCleanedUp</a></div><div class="ttdeci">bool IsCleanedUp() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00135">sparse.cc:135</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::TriangularMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00512">sparse.h:512</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a79446a803c1bed8b17c8ac937d07be39"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a79446a803c1bed8b17c8ac937d07be39">operations_research::glop::SparseMatrix::SparseMatrix</a></div><div class="ttdeci">SparseMatrix()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00087">sparse.cc:87</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::SparseMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00176">sparse.h:176</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector< ColIndex, bool ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::SparseMatrix::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00110">sparse.cc:110</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a2e5611d47d02e1029b98a8e9bee3469f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a2e5611d47d02e1029b98a8e9bee3469f">operations_research::glop::SparseMatrix::CheckNoDuplicates</a></div><div class="ttdeci">bool CheckNoDuplicates() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00126">sparse.cc:126</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrixView::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00479">sparse.h:479</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a87c606b7a9b920de2d4b6aa5c3bc1a45"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a87c606b7a9b920de2d4b6aa5c3bc1a45">operations_research::glop::MatrixView::PopulateFromMatrixPair</a></div><div class="ttdeci">void PopulateFromMatrixPair(const SparseMatrix &matrix_a, const SparseMatrix &matrix_b)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00237">sparse.h:237</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a64fea3282d498f3eb2d4af70692bb117"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a64fea3282d498f3eb2d4af70692bb117">operations_research::glop::SparseMatrix::ComputeOneNorm</a></div><div class="ttdeci">Fractional ComputeOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00392">sparse.cc:392</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a6052657cbffbe19decf328bf369d58e1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6052657cbffbe19decf328bf369d58e1">operations_research::glop::SparseMatrix::Swap</a></div><div class="ttdeci">void Swap(SparseMatrix *matrix)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00158">sparse.cc:158</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a1f0797ca04f7cb50938328e7e027a18b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a1f0797ca04f7cb50938328e7e027a18b">operations_research::glop::MatrixView::MatrixView</a></div><div class="ttdeci">MatrixView()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00220">sparse.h:220</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a6e483ed6906f126dc6fa63d198c8f907"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6e483ed6906f126dc6fa63d198c8f907">operations_research::glop::CompactSparseMatrixView::CompactSparseMatrixView</a></div><div class="ttdeci">CompactSparseMatrixView(const CompactSparseMatrix *compact_matrix, const RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00473">sparse.h:473</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a3de922485ca2c30f3e07d959dd97cdd0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">operations_research::glop::StrictITIVector::AssignToZero</a></div><div class="ttdeci">void AssignToZero(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00290">lp_types.h:290</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a8da36920b149053499a21e50fc859a93"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8da36920b149053499a21e50fc859a93">operations_research::glop::CompactSparseMatrix::rows_</a></div><div class="ttdeci">StrictITIVector< EntryIndex, RowIndex > rows_</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00460">sparse.h:460</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_afe3d36f3ba4f04442fbb36f8726f8baf"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afe3d36f3ba4f04442fbb36f8726f8baf">operations_research::glop::CompactSparseMatrix::ColumnNumEntries</a></div><div class="ttdeci">EntryIndex ColumnNumEntries(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00335">sparse.h:335</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html">operations_research::glop::TriangularMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00502">sparse.h:502</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a0c406d94c3586159071e0b370a5a02fb"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a0c406d94c3586159071e0b370a5a02fb">operations_research::glop::SparseMatrix::PopulateFromLinearCombination</a></div><div class="ttdeci">void PopulateFromLinearCombination(Fractional alpha, const SparseMatrix &a, Fractional beta, const SparseMatrix &b)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00225">sparse.cc:225</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_sparse_matrix_html_adc6b282d2cc7afc75b60ee44a6bfb2ac"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">operations_research::glop::SparseMatrix::column</a></div><div class="ttdeci">const SparseColumn & column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00180">sparse.h:180</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">operations_research::glop::MatrixView::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00263">sparse.h:263</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a4a34504e7ba1673cf24f745d162fda84"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">operations_research::glop::TriangularMatrix::GetDiagonalCoefficient</a></div><div class="ttdeci">Fractional GetDiagonalCoefficient(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00572">sparse.h:572</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a2fe6f7470512f5301031480737375c88"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a2fe6f7470512f5301031480737375c88">operations_research::glop::SparseMatrix::PopulateFromTranspose</a></div><div class="ttdeci">void PopulateFromTranspose(const Matrix &input)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00181">sparse.cc:181</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html">operations_research::glop::Permutation< RowIndex ></a></div></div>
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<div class="ttc" id="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_matrix_view_html_a495dfea7028bd3b07c1485d5c66b7001"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001">operations_research::glop::MatrixView::PopulateFromMatrix</a></div><div class="ttdeci">void PopulateFromMatrix(const SparseMatrix &matrix)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00226">sparse.h:226</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a8a0e8a1a3afc70e2678d046feb11d024"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8a0e8a1a3afc70e2678d046feb11d024">operations_research::glop::CompactSparseMatrix::ColumnCopyToClearedDenseColumnWithNonZeros</a></div><div class="ttdeci">void ColumnCopyToClearedDenseColumnWithNonZeros(ColIndex col, DenseColumn *dense_column, RowIndexVector *non_zeros) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00436">sparse.h:436</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_ab8101094fb842f9cb500b3dfadc325d3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab8101094fb842f9cb500b3dfadc325d3">operations_research::glop::TriangularMatrix::TriangularMatrix</a></div><div class="ttdeci">TriangularMatrix()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00504">sparse.h:504</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::CompactSparseMatrixView::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00478">sparse.h:478</a></div></div>
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<div class="ttc" id="areturn__macros_8h_html"><div class="ttname"><a href="return__macros_8h.html">return_macros.h</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_ab392807d136adb480aedec7750cbbb18"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab392807d136adb480aedec7750cbbb18">operations_research::glop::CompactSparseMatrix::coefficients_</a></div><div class="ttdeci">StrictITIVector< EntryIndex, Fractional > coefficients_</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00459">sparse.h:459</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_compact_sparse_matrix_html_a60771349d1fcf262313b13a6a857c140"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a60771349d1fcf262313b13a6a857c140">operations_research::glop::CompactSparseMatrix::Column</a></div><div class="ttdeci">::util::IntegerRange< EntryIndex > Column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00358">sparse.h:358</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_ab9bd1cef3f6a18704cb7d9ce6201e106"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab9bd1cef3f6a18704cb7d9ce6201e106">operations_research::glop::CompactSparseMatrix::ColumnCopyToClearedDenseColumn</a></div><div class="ttdeci">void ColumnCopyToClearedDenseColumn(ColIndex col, DenseColumn *dense_column) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00426">sparse.h:426</a></div></div>
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<div class="ttc" id="aparser_8yy_8cc_html_a5a634cf4429798b1c921a81de8250051"><div class="ttname"><a href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a></div><div class="ttdeci">static int input(yyscan_t yyscanner)</div></div>
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<div class="ttc" id="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="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a6ae7b0836055b9b6d182115027d496f9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6ae7b0836055b9b6d182115027d496f9">operations_research::glop::SparseMatrix::ComputeMinAndMaxMagnitudes</a></div><div class="ttdeci">void ComputeMinAndMaxMagnitudes(Fractional *min_magnitude, Fractional *max_magnitude) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00369">sparse.cc:369</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a319ffa92d03907ee98b5f3da18421af3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a319ffa92d03907ee98b5f3da18421af3">operations_research::glop::CompactSparseMatrix::CompactSparseMatrix</a></div><div class="ttdeci">CompactSparseMatrix()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00290">sparse.h:290</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_matrix_view_html_adc6b282d2cc7afc75b60ee44a6bfb2ac"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">operations_research::glop::MatrixView::column</a></div><div class="ttdeci">const SparseColumn & column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00264">sparse.h:264</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a6e49e4127a33039fcccc6e50380faefa"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a6e49e4127a33039fcccc6e50380faefa">operations_research::glop::CompactSparseMatrix::ColumnAddMultipleToSparseScatteredColumn</a></div><div class="ttdeci">void ColumnAddMultipleToSparseScatteredColumn(ColIndex col, Fractional multiplier, ScatteredColumn *column) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00405">sparse.h:405</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00885">base/logging.h:885</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="amacros_8h_html_af8df3547bfde53a5acb93e2607b0034a"><div class="ttname"><a href="macros_8h.html#af8df3547bfde53a5acb93e2607b0034a">DISALLOW_COPY_AND_ASSIGN</a></div><div class="ttdeci">#define DISALLOW_COPY_AND_ASSIGN(TypeName)</div><div class="ttdef"><b>Definition:</b> <a href="macros_8h_source.html#l00029">macros.h:29</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_a3f219a081f88c22ae282ada4f0bdddd3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a3f219a081f88c22ae282ada4f0bdddd3">operations_research::glop::MatrixView::ComputeInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00423">sparse.cc:423</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_matrix_view_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::MatrixView::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00419">sparse.cc:419</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::SparseMatrix::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00115">sparse.cc:115</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a0358eb2d6ea480b59d89dc42326cf840"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a0358eb2d6ea480b59d89dc42326cf840">operations_research::glop::CompactSparseMatrix::num_cols_</a></div><div class="ttdeci">ColIndex num_cols_</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00454">sparse.h:454</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_abdd940ad64b555052b33e763b80aea26"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#abdd940ad64b555052b33e763b80aea26">operations_research::glop::CompactSparseMatrix::ColumnScalarProduct</a></div><div class="ttdeci">Fractional ColumnScalarProduct(ColIndex col, const DenseRow &vector) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00382">sparse.h:382</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_acb294633c7688f918623b3b0e09aec43"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#acb294633c7688f918623b3b0e09aec43">operations_research::sat::ComputeInfinityNorm</a></div><div class="ttdeci">IntegerValue ComputeInfinityNorm(const LinearConstraint &constraint)</div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint_8cc_source.html#l00140">linear_constraint.cc:140</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_triangular_matrix_html_a3d3abc3e6b522dc60fd8c1168522e09d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3d3abc3e6b522dc60fd8c1168522e09d">operations_research::glop::TriangularMatrix::GetFirstNonIdentityColumn</a></div><div class="ttdeci">ColIndex GetFirstNonIdentityColumn() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00567">sparse.h:567</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::SparseMatrix::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00389">sparse.cc:389</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_sparse_matrix_html_ab4a8456683d4572bd9426efab8489e99"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ab4a8456683d4572bd9426efab8489e99">operations_research::glop::SparseMatrix::Dump</a></div><div class="ttdeci">std::string Dump() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00399">sparse.cc:399</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ab65a327cfc2a74c15fa26b91f19acc64"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">operations_research::glop::ColToRowIndex</a></div><div class="ttdeci">RowIndex ColToRowIndex(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00051">lp_types.h:51</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af0dafb025bcf4174501a93fb91ca4bb6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6">operations_research::glop::TriangularMatrix::ColumnIsDiagonalOnly</a></div><div class="ttdeci">bool ColumnIsDiagonalOnly(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00577">sparse.h:577</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ac014de658aabf122011e8fb07b6f4612"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">operations_research::glop::RowIndexVector</a></div><div class="ttdeci">std::vector< RowIndex > RowIndexVector</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00309">lp_types.h:309</a></div></div>
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<div class="ttc" id="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_compact_sparse_matrix_view_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrixView::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00480">sparse.h:480</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="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a55265e26d9e69e2d7a882bab054b8139"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a55265e26d9e69e2d7a882bab054b8139">operations_research::glop::SparseMatrix::SetNumRows</a></div><div class="ttdeci">void SetNumRows(RowIndex num_rows)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00143">sparse.cc:143</a></div></div>
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