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1082 lines
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<a href="sparse_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">//</span></div>
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<div class="line"><a id="l00015" 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 id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// and algorithms:</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">//</span></div>
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<div class="line"><a id="l00018" 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 id="l00019" 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 id="l00020" 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 id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">//</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">//</span></div>
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<div class="line"><a id="l00023" 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 id="l00024" 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 id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">//</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">//</span></div>
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<div class="line"><a id="l00027" 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 id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#ifndef OR_TOOLS_LP_DATA_SPARSE_H_</span></div>
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<div class="line"><a id="l00030" 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 id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include <string></span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</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 id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include "<a class="code" href="lp__types_8h.html">ortools/lp_data/lp_types.h</a>"</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="preprocessor">#include "<a class="code" href="lp__data_2permutation_8h.html">ortools/lp_data/permutation.h</a>"</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include "<a class="code" href="scattered__vector_8h.html">ortools/lp_data/scattered_vector.h</a>"</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#include "<a class="code" href="sparse__column_8h.html">ortools/lp_data/sparse_column.h</a>"</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</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 id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="keyword">class </span>CompactSparseMatrixView;</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// --------------------------------------------------------</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// SparseMatrix</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// --------------------------------------------------------</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// SparseMatrix is a class for sparse matrices suitable for computation.</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</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 id="l00052" name="l00052"></a><span class="lineno"> 52</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 id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">//</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</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 id="l00055" name="l00055"></a><span class="lineno"> 55</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 id="l00056" name="l00056"></a><span class="lineno"> 56</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 id="l00057" name="l00057"></a><span class="lineno"> 57</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 id="l00058" name="l00058"></a><span class="lineno"> 58</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 id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// coefficients may also be entries.</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">//</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// Note that no special ordering of entries is assumed.</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html"> 62</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a> {</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a79446a803c1bed8b17c8ac937d07be39">SparseMatrix</a>();</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// Useful for testing. This makes it possible to write:</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// SparseMatrix matrix {</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// {1, 2, 3},</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// {4, 5, 6},</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// {7, 8, 9}};</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="preprocessor">#if (!defined(_MSC_VER) || _MSC_VER >= 1800)</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a79446a803c1bed8b17c8ac937d07be39">SparseMatrix</a>(</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> std::initializer_list<std::initializer_list<Fractional>> init_list);</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="preprocessor">#endif</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</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 id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// the number of rows to zero.</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Returns true if the matrix is empty.</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// That is if num_rows() OR num_cols() are zero.</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</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 id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// entries and sorts remaining entries in increasing row order.</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</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 id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// cleanup running in O(num_entries * log(num_entries)).</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#abfc30f91ab75c6f4552003f777672e74">CleanUp</a>();</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// Call CheckNoDuplicates() on all columns, useful for doing a DCHECK.</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// Call IsCleanedUp() on all columns, useful for doing a DCHECK.</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// Change the number of row of this matrix.</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a55265e26d9e69e2d7a882bab054b8139">SetNumRows</a>(RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>);</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// Appends an empty column and returns its index.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a86fd105be79f4f2dbaf3a21e64e4d022">AppendEmptyColumn</a>();</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> </div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</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 id="l00102" name="l00102"></a><span class="lineno"> 102</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 id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a06d22c92f8b45b18560b46797f98a81b">AppendUnitVector</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</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 id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// Works in O(1).</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6052657cbffbe19decf328bf369d58e1">Swap</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* matrix);</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</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 id="l00110" name="l00110"></a><span class="lineno"> 110</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 id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Previous columns/values are deleted.</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ae1b90982a83e1b025ebbc1c446980640">PopulateFromZero</a>(RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>, ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>);</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</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 id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// Previous columns/values are deleted.</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a323801972c3d6de340e260de4582c34b">PopulateFromIdentity</a>(ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>);</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// Populates the matrix from the transposed of the given matrix.</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</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 id="l00120" name="l00120"></a><span class="lineno"> 120</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 id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// sorts the entries in each columns by their indices.</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Matrix></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a2fe6f7470512f5301031480737375c88">PopulateFromTranspose</a>(<span class="keyword">const</span> Matrix& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</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 id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// O(number of entries in the matrix).</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#acbbc88405e6db3fe77064e1a3d4e402a">PopulateFromSparseMatrix</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix);</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</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 id="l00130" name="l00130"></a><span class="lineno"> 130</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 id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Matrix></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a29edb960f882c54b9652853e94988e79">PopulateFromPermutedMatrix</a>(<span class="keyword">const</span> Matrix& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>,</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& inverse_col_perm);</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> </div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// Populates a SparseMatrix from the result of alpha * A + beta * B,</span></div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</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 id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a0c406d94c3586159071e0b370a5a02fb">PopulateFromLinearCombination</a>(<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> alpha, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>,</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> beta, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>);</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// Multiplies SparseMatrix a by SparseMatrix b.</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#aa1c2872fa7d491d4c093c8b2124a53b9">PopulateFromProduct</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>);</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</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 id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// This runs in O(num_cols).</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ac59fd9cddfe284bf9dc7581ed631ce8d">DeleteColumns</a>(<span class="keyword">const</span> <a class="code hl_class" 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 id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="comment">// Applies the given row permutation and deletes the rows for which</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</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 id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="comment">// This runs in O(num_entries).</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a860e7a37e8c7c2f5f7f0a73d3e3473f0">DeleteRows</a>(RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& permutation);</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// Appends all rows from the given matrix to the calling object after the last</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</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 id="l00155" name="l00155"></a><span class="lineno"> 155</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 id="l00156" name="l00156"></a><span class="lineno"> 156</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 id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// matrices are different.</span></div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ab2d8beb101c26b08a8af602300da1748">AppendRowsFromSparseMatrix</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix);</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// Applies the row permutation.</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#ace1973900f4d921a7bedbcbe36e1bcad">ApplyRowPermutation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm);</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> </div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// Returns the coefficient at position row in column col.</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</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 id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a566008ab9fd3e3dbec96263bc3c45061">LookUpValue</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</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 id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// given the tolerance).</span></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#af782744bdb01cf56841a0de18ccca3ce">Equals</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> </div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</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 id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// magnitudes of the non-zero coefficients of the calling object.</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6ae7b0836055b9b6d182115027d496f9">ComputeMinAndMaxMagnitudes</a>(<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>* min_magnitude,</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <a class="code hl_typedef" 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 id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// Return the matrix dimension.</span></div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd"> 177</a></span> RowIndex <a class="code hl_function" 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 id="l00178" name="l00178"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813"> 178</a></span> ColIndex <a class="code hl_function" 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 id="l00179" name="l00179"></a><span class="lineno"> 179</span> </div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// Access the underlying sparse columns.</span></div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502"> 181</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]; }</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa"> 182</a></span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) { <span class="keywordflow">return</span> &(columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]); }</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> </div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// Returns the total numbers of entries in the matrix.</span></div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// Runs in O(num_cols).</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> EntryIndex <a class="code hl_function" 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 id="l00187" name="l00187"></a><span class="lineno"> 187</span> </div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// Computes the 1-norm of the matrix.</span></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</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 id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// max_col sum_row |a(row,col)|.</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a64fea3282d498f3eb2d4af70692bb117">ComputeOneNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> </div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="comment">// Computes the oo-norm (infinity-norm) of the matrix.</span></div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</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 id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// max_row sum_col |a(row,col)|.</span></div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" 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 id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// Returns a dense representation of the matrix.</span></div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> std::string <a class="code hl_function" 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 id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="comment">// Resets the internal data structure and create an empty rectangular</span></div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// matrix of size num_rows x num_cols.</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordtype">void</span> Reset(ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>, RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>);</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> </div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// Vector of sparse columns.</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <a class="code hl_class" 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 id="l00208" name="l00208"></a><span class="lineno"> 208</span> </div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</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 id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="comment">// number of rows.</span></div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> RowIndex num_rows_;</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>);</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span>};</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> </div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span><span class="comment">// A matrix constructed from a list of already existing SparseColumn. This class</span></div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</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 id="l00218" name="l00218"></a><span class="lineno"> 218</span><span class="comment">// this class (and keep the same address in memory).</span></div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html"> 219</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a> {</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a1f0797ca04f7cb50938328e7e027a18b"> 221</a></span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a1f0797ca04f7cb50938328e7e027a18b">MatrixView</a>() {}</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#ac220f9bed6efccb65c2514e90d702638"> 222</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#ac220f9bed6efccb65c2514e90d702638">MatrixView</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001">PopulateFromMatrix</a>(matrix);</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> }</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> </div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="comment">// Takes all the columns of the given matrix.</span></div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001"> 227</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a495dfea7028bd3b07c1485d5c66b7001">PopulateFromMatrix</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keyword">const</span> ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a> = matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> columns_.resize(<a class="code hl_function" 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 id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = &matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> }</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> num_rows_ = matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> }</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// Takes all the columns of the first matrix followed by the columns of the</span></div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="comment">// second matrix.</span></div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a87c606b7a9b920de2d4b6aa5c3bc1a45"> 238</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a87c606b7a9b920de2d4b6aa5c3bc1a45">PopulateFromMatrixPair</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix_a,</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix_b) {</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">const</span> ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a> = matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() + matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> columns_.resize(<a class="code hl_function" 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 id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(); ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = &matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> }</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(); ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> columns_[matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() + <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = &matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> }</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> num_rows_ = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>());</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> }</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> </div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</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 id="l00252" name="l00252"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#adc9aa1d344fe9442ac3ba673b939db7c"> 252</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#adc9aa1d344fe9442ac3ba673b939db7c">PopulateFromBasis</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a>& matrix,</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keyword">const</span> <a class="code hl_class" 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 id="l00254" name="l00254"></a><span class="lineno"> 254</span> columns_.resize(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(basis.<a class="code hl_function" 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 id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < basis.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(); ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> columns_[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)] = &matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(basis[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> }</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> num_rows_ = matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> }</div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// Same behavior as the SparseMatrix functions above.</span></div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a8e12342fc420701fbffd97025421575a"> 262</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00263" name="l00263"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a960110e64357a3e69162ebf1f71959dd"> 263</a></span> RowIndex <a class="code hl_function" 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 id="l00264" name="l00264"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a41741829541d089f1c4d34f190884813"> 264</a></span> ColIndex <a class="code hl_function" 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 id="l00265" name="l00265"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_matrix_view.html#a7273cc492a51a1c5d45c620b32fce502"> 265</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> *columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]; }</div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> EntryIndex <a class="code hl_function" 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 id="l00267" name="l00267"></a><span class="lineno"> 267</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a64fea3282d498f3eb2d4af70692bb117">ComputeOneNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_matrix_view.html#a3f219a081f88c22ae282ada4f0bdddd3">ComputeInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> RowIndex num_rows_;</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <a class="code hl_class" 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 id="l00273" name="l00273"></a><span class="lineno"> 273</span>};</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> </div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</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 id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">const</span> SparseMatrix& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span><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 id="l00278" name="l00278"></a><span class="lineno"> 278</span> <span class="keyword">const</span> SparseMatrix& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a>& inverse_col_perm);</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</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 id="l00281" name="l00281"></a><span class="lineno"> 281</span>SparseMatrix::PopulateFromPermutedMatrix<CompactSparseMatrixView>(</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keyword">const</span> CompactSparseMatrixView& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">ColumnPermutation</a>& inverse_col_perm);</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> </div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span><span class="comment">// Another matrix representation which is more efficient than a SparseMatrix but</span></div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</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 id="l00287" name="l00287"></a><span class="lineno"> 287</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 id="l00288" name="l00288"></a><span class="lineno"> 288</span><span class="comment">// of the matrix columns.</span></div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html"> 289</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a> {</div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a319ffa92d03907ee98b5f3da18421af3"> 291</a></span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a319ffa92d03907ee98b5f3da18421af3">CompactSparseMatrix</a>() {}</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> </div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// Convenient constructors for tests.</span></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</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 id="l00295" name="l00295"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a9f271f559e0d1e794a2ecc76d919db68"> 295</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a9f271f559e0d1e794a2ecc76d919db68">CompactSparseMatrix</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> PopulateFromMatrixView(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a>(matrix));</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> }</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> </div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <span class="comment">// Creates a CompactSparseMatrix from the given MatrixView. The matrices are</span></div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</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 id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="comment">// each column is preserved.</span></div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keywordtype">void</span> PopulateFromMatrixView(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_matrix_view.html">MatrixView</a>& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> </div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="comment">// Creates a CompactSparseMatrix by copying the input and adding an identity</span></div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="comment">// matrix to the left of it.</span></div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordtype">void</span> PopulateFromSparseMatrixAndAddSlacks(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> </div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="comment">// Creates a CompactSparseMatrix from the transpose of the given</span></div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</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 id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="comment">// by row indices.</span></div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keywordtype">void</span> PopulateFromTranspose(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> </div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</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 id="l00314" name="l00314"></a><span class="lineno"> 314</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 id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="comment">// Add*() functions below.</span></div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="keywordtype">void</span> Reset(RowIndex num_rows);</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> </div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</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 id="l00319" name="l00319"></a><span class="lineno"> 319</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 id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="comment">// added column.</span></div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> ColIndex AddDenseColumn(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& dense_column);</div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> </div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</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 id="l00324" name="l00324"></a><span class="lineno"> 324</span> ColIndex AddDenseColumnPrefix(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& dense_column,</div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> RowIndex start);</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> </div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</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 id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="comment">// If non_zeros is empty, this actually calls AddDenseColumn().</span></div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> ColIndex AddDenseColumnWithNonZeros(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& dense_column,</div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> <span class="keyword">const</span> std::vector<RowIndex>& non_zeros);</div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> </div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</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 id="l00333" name="l00333"></a><span class="lineno"> 333</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 id="l00334" name="l00334"></a><span class="lineno"> 334</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 id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="comment">// will be cleared. Returns the index of the added column.</span></div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> ColIndex AddAndClearColumnWithNonZeros(<a class="code hl_class" 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 id="l00337" name="l00337"></a><span class="lineno"> 337</span> std::vector<RowIndex>* non_zeros);</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> </div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</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 id="l00340" name="l00340"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afe3d36f3ba4f04442fbb36f8726f8baf"> 340</a></span> EntryIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afe3d36f3ba4f04442fbb36f8726f8baf">ColumnNumEntries</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <span class="keywordflow">return</span> starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1] - starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> }</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="comment">// Returns the matrix dimensions. See same functions in SparseMatrix.</span></div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#af69d9b7065a8f31604a8134be4307749"> 345</a></span> EntryIndex <a class="code hl_function" 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 id="l00346" name="l00346"></a><span class="lineno"> 346</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(coefficients_.size(), rows_.size());</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <span class="keywordflow">return</span> coefficients_.size();</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> }</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd"> 349</a></span> RowIndex <a class="code hl_function" 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 id="l00350" name="l00350"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813"> 350</a></span> ColIndex <a class="code hl_function" 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 id="l00351" name="l00351"></a><span class="lineno"> 351</span> </div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</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 id="l00353" name="l00353"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8e12342fc420701fbffd97025421575a"> 353</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00354" name="l00354"></a><span class="lineno"> 354</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(coefficients_.size(), rows_.size());</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="keywordflow">return</span> coefficients_.empty();</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> }</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> </div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="comment">// Functions to iterate on the entries of a given column:</span></div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="comment">// for (const EntryIndex i : compact_matrix_.Column(col)) {</span></div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// const RowIndex row = compact_matrix_.EntryRow(i);</span></div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="comment">// const Fractional coefficient = compact_matrix_.EntryCoefficient(i);</span></div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="comment">// }</span></div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#acedaf830dd26be6213e4665f088c5aa4"> 363</a></span> <a class="code hl_class" href="classutil_1_1_integer_range.html">::util::IntegerRange<EntryIndex></a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#acedaf830dd26be6213e4665f088c5aa4">Column</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> return ::util::IntegerRange<EntryIndex>(starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>], starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1]);</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> }</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aaef7fc778a29bb3bb3040c0423937f6e"> 366</a></span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_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 id="l00367" name="l00367"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aedc46de5199e203b77de2eae2e4c100d"> 367</a></span> RowIndex <a class="code hl_function" 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 id="l00368" name="l00368"></a><span class="lineno"> 368</span> </div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59"> 369</a></span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, num_cols_);</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> </div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</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 id="l00373" name="l00373"></a><span class="lineno"> 373</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 id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="keyword">const</span> EntryIndex start = starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>(starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1] - start, rows_.data() + start.value(),</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> coefficients_.data() + start.value());</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> }</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> </div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="comment">// Returns true if the given column is empty. Note that for triangular matrix</span></div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="comment">// this does not include the diagonal coefficient (see below).</span></div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda"> 381</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda">ColumnIsEmpty</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="keywordflow">return</span> starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 1] == starts_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> }</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> </div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</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 id="l00386" name="l00386"></a><span class="lineno"> 386</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 id="l00387" name="l00387"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#abdd940ad64b555052b33e763b80aea26"> 387</a></span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#abdd940ad64b555052b33e763b80aea26">ColumnScalarProduct</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <span class="keyword">const</span> <a class="code hl_class" 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 id="l00388" name="l00388"></a><span class="lineno"> 388</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> result = 0.0;</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> result += EntryCoefficient(i) * vector[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(EntryRow(i))];</div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> }</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> }</div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> </div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</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 id="l00396" name="l00396"></a><span class="lineno"> 396</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 id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="comment">// function is declared in the .h for efficiency.</span></div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aea0e9a84b41c95c874f171cae97cf31b"> 398</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#aea0e9a84b41c95c874f171cae97cf31b">ColumnAddMultipleToDenseColumn</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> multiplier,</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> <a class="code hl_class" 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 id="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="keywordflow">if</span> (multiplier == 0.0) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <a class="code hl_define" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> (*dense_column)[EntryRow(i)] += multiplier * EntryCoefficient(i);</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> }</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> }</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> </div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</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 id="l00408" name="l00408"></a><span class="lineno"> 408</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 id="l00409" name="l00409"></a><span class="lineno"> 409</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 id="l00410" name="l00410"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a6e49e4127a33039fcccc6e50380faefa"> 410</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a6e49e4127a33039fcccc6e50380faefa">ColumnAddMultipleToSparseScatteredColumn</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>,</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> multiplier,</div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <a class="code hl_struct" 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 id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keywordflow">if</span> (multiplier == 0.0) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <a class="code hl_define" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(column);</div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = EntryRow(i);</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> column-><a class="code hl_function" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a9bb4f0967311f0f79a279879c4d69678">Add</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, multiplier * EntryCoefficient(i));</div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> }</div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> }</div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> </div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</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 id="l00422" name="l00422"></a><span class="lineno"> 422</span> <span class="comment">// This function is declared in the .h for efficiency.</span></div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a28058c5e9ff6638ea1ea210b49a4e7bc"> 423</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a28058c5e9ff6638ea1ea210b49a4e7bc">ColumnCopyToDenseColumn</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_class" 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 id="l00424" name="l00424"></a><span class="lineno"> 424</span> <a class="code hl_define" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> dense_column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">AssignToZero</a>(num_rows_);</div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> ColumnCopyToClearedDenseColumn(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, dense_column);</div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> }</div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> </div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="comment">// Same as ColumnCopyToDenseColumn() but assumes the column to be initially</span></div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// all zero.</span></div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab9bd1cef3f6a18704cb7d9ce6201e106"> 431</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab9bd1cef3f6a18704cb7d9ce6201e106">ColumnCopyToClearedDenseColumn</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>,</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <a class="code hl_class" 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 id="l00433" name="l00433"></a><span class="lineno"> 433</span> <a class="code hl_define" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> dense_column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows_, 0.0);</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> (*dense_column)[EntryRow(i)] = EntryCoefficient(i);</div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> }</div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> }</div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> </div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <span class="comment">// Same as ColumnCopyToClearedDenseColumn() but also fills non_zeros.</span></div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8a0e8a1a3afc70e2678d046feb11d024"> 441</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8a0e8a1a3afc70e2678d046feb11d024">ColumnCopyToClearedDenseColumnWithNonZeros</a>(</div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_class" 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 id="l00443" name="l00443"></a><span class="lineno"> 443</span> <a class="code hl_typedef" 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 id="l00444" name="l00444"></a><span class="lineno"> 444</span> <a class="code hl_define" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(dense_column);</div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> dense_column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows_, 0.0);</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> non_zeros->clear();</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : Column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = EntryRow(i);</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> (*dense_column)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = EntryCoefficient(i);</div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> non_zeros->push_back(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> }</div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> }</div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> </div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="keywordtype">void</span> Swap(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>* other);</div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> </div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="keyword">protected</span>:</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="comment">// The matrix dimensions, properly updated by full and incremental builders.</span></div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a5d6d5d7a7944b09bd0df4b7132fe5f7e"> 458</a></span> RowIndex <a class="code hl_variable" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a5d6d5d7a7944b09bd0df4b7132fe5f7e">num_rows_</a>;</div>
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a0358eb2d6ea480b59d89dc42326cf840"> 459</a></span> ColIndex <a class="code hl_variable" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a0358eb2d6ea480b59d89dc42326cf840">num_cols_</a>;</div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> </div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> <span class="comment">// Holds the columns non-zero coefficients and row positions.</span></div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</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 id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="comment">// [starts_[col], starts_[col + 1]).</span></div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab392807d136adb480aedec7750cbbb18"> 464</a></span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<EntryIndex, Fractional></a> <a class="code hl_variable" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#ab392807d136adb480aedec7750cbbb18">coefficients_</a>;</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8da36920b149053499a21e50fc859a93"> 465</a></span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<EntryIndex, RowIndex></a> <a class="code hl_variable" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a8da36920b149053499a21e50fc859a93">rows_</a>;</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a37ac057f213297550a26947d551324a3"> 466</a></span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, EntryIndex></a> <a class="code hl_variable" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a37ac057f213297550a26947d551324a3">starts_</a>;</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> </div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <a class="code hl_define" href="macros_8h.html#af8df3547bfde53a5acb93e2607b0034a">DISALLOW_COPY_AND_ASSIGN</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>);</div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span>};</div>
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<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> </div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</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 id="l00473" name="l00473"></a><span class="lineno"> 473</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 id="l00474" name="l00474"></a><span class="lineno"> 474</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 id="l00475" name="l00475"></a><span class="lineno"> 475</span><span class="comment">// the same address in memory).</span></div>
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<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html"> 476</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a> {</div>
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<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6e483ed6906f126dc6fa63d198c8f907"> 478</a></span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6e483ed6906f126dc6fa63d198c8f907">CompactSparseMatrixView</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>* compact_matrix,</div>
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<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> <span class="keyword">const</span> <a class="code hl_class" 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 id="l00480" name="l00480"></a><span class="lineno"> 480</span> : compact_matrix_(*compact_matrix),</div>
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<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> columns_(basis->data(), basis->size().<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>()) {}</div>
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<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a7a56df5528de85e8d1b588d6a50e6948"> 482</a></span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a7a56df5528de85e8d1b588d6a50e6948">CompactSparseMatrixView</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>* compact_matrix,</div>
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<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <span class="keyword">const</span> std::vector<ColIndex>* columns)</div>
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<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> : compact_matrix_(*compact_matrix), columns_(*columns) {}</div>
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<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> </div>
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<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> <span class="comment">// Same behavior as the SparseMatrix functions above.</span></div>
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<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a"> 487</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00488" name="l00488"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd"> 488</a></span> RowIndex <a class="code hl_function" 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 id="l00489" name="l00489"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813"> 489</a></span> ColIndex <a class="code hl_function" 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> ColIndex(columns_.size()); }</div>
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<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c"> 490</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">column</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> <span class="keywordflow">return</span> compact_matrix_.column(columns_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>.value()]);</div>
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<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> }</div>
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<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> EntryIndex <a class="code hl_variable" href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeOneNorm() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#acb294633c7688f918623b3b0e09aec43">ComputeInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> </div>
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<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> <span class="comment">// We require that the underlying CompactSparseMatrix and RowToColMapping</span></div>
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<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</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 id="l00500" name="l00500"></a><span class="lineno"> 500</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& compact_matrix_;</div>
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<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> <span class="keyword">const</span> absl::Span<const ColIndex> columns_;</div>
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<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span>};</div>
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<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> </div>
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<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span><span class="comment">// Specialization of a CompactSparseMatrix used for triangular matrices.</span></div>
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<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</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 id="l00506" name="l00506"></a><span class="lineno"> 506</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 id="l00507" name="l00507"></a><span class="lineno"> 507</span><span class="comment">// CompactSparseMatrix.</span></div>
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<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span><span class="comment">//</span></div>
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<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</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 id="l00510" name="l00510"></a><span class="lineno"> 510</span><span class="comment">// triangular matrix and some functions work directly on such matrices.</span></div>
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<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html"> 511</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a> : <span class="keyword">private</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a> {</div>
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<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ab8101094fb842f9cb500b3dfadc325d3"> 513</a></span> <a class="code hl_function" 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 id="l00514" name="l00514"></a><span class="lineno"> 514</span> </div>
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<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</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 id="l00516" name="l00516"></a><span class="lineno"> 516</span> <span class="comment">// the private inheritance). They are extended to deal with diagonal</span></div>
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<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <span class="comment">// coefficients properly.</span></div>
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<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> <span class="keywordtype">void</span> PopulateFromTranspose(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> <span class="keywordtype">void</span> Swap(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>* other);</div>
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<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8e12342fc420701fbffd97025421575a"> 520</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" 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 id="l00521" name="l00521"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd"> 521</a></span> RowIndex <a class="code hl_function" 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 id="l00522" name="l00522"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813"> 522</a></span> ColIndex <a class="code hl_function" 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 id="l00523" name="l00523"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749"> 523</a></span> EntryIndex <a class="code hl_function" 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 id="l00524" name="l00524"></a><span class="lineno"> 524</span> <span class="keywordflow">return</span> EntryIndex(num_cols_.value()) + coefficients_.size();</div>
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<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> }</div>
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<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> </div>
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<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="comment">// On top of the CompactSparseMatrix functionality, TriangularMatrix::Reset()</span></div>
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<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</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 id="l00529" name="l00529"></a><span class="lineno"> 529</span> <span class="comment">// This helps reduce costly push_back operations for large problems.</span></div>
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<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</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 id="l00532" name="l00532"></a><span class="lineno"> 532</span> <span class="comment">// prior to any Add* calls (e.g., AddTriangularColumn).</span></div>
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<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> <span class="keywordtype">void</span> Reset(RowIndex num_rows, ColIndex col_capacity);</div>
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<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> </div>
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<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</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 id="l00536" name="l00536"></a><span class="lineno"> 536</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 id="l00537" name="l00537"></a><span class="lineno"> 537</span> <span class="comment">// checked in debug mode.</span></div>
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<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <span class="keywordtype">void</span> PopulateFromTriangularSparseMatrix(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& <a class="code hl_function" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>);</div>
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<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> </div>
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<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> <span class="comment">// Functions to create a triangular matrix incrementally, column by column.</span></div>
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<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</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 id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="comment">// added by calling one of the 3 functions below.</span></div>
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<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</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 id="l00545" name="l00545"></a><span class="lineno"> 545</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 id="l00546" name="l00546"></a><span class="lineno"> 546</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 id="l00547" name="l00547"></a><span class="lineno"> 547</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 id="l00548" name="l00548"></a><span class="lineno"> 548</span> <span class="comment">// ApplyRowPermutationToNonDiagonalEntries() or accounted directly in the case</span></div>
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<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> <span class="comment">// of PermutedLowerSparseSolve().</span></div>
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<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> <span class="keywordtype">void</span> AddTriangularColumn(<span class="keyword">const</span> <a class="code hl_class" 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 id="l00551" name="l00551"></a><span class="lineno"> 551</span> <span class="keywordtype">void</span> AddTriangularColumnWithGivenDiagonalEntry(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& column,</div>
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<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> RowIndex diagonal_row,</div>
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<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_value);</div>
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<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> <span class="keywordtype">void</span> AddDiagonalOnlyColumn(<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_value);</div>
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<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> </div>
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<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> <span class="comment">// Adds the given sparse column divided by diagonal_coefficient.</span></div>
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<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</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 id="l00558" name="l00558"></a><span class="lineno"> 558</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 id="l00559" name="l00559"></a><span class="lineno"> 559</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 id="l00560" name="l00560"></a><span class="lineno"> 560</span> <span class="keywordtype">void</span> AddAndNormalizeTriangularColumn(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& column,</div>
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<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> RowIndex diagonal_row,</div>
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<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_coefficient);</div>
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<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> </div>
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<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</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 id="l00565" name="l00565"></a><span class="lineno"> 565</span> <span class="keywordtype">void</span> ApplyRowPermutationToNonDiagonalEntries(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm);</div>
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<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> </div>
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<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</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 id="l00568" name="l00568"></a><span class="lineno"> 568</span> <span class="keywordtype">void</span> CopyColumnToSparseColumn(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_class" 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 id="l00569" name="l00569"></a><span class="lineno"> 569</span> </div>
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<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> <span class="comment">// Copy a triangular matrix to the given SparseMatrix.</span></div>
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<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> <span class="keywordtype">void</span> CopyToSparseMatrix(<a class="code hl_class" 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 id="l00572" name="l00572"></a><span class="lineno"> 572</span> </div>
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<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</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 id="l00574" name="l00574"></a><span class="lineno"> 574</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 id="l00575" name="l00575"></a><span class="lineno"> 575</span> <span class="comment">// zero if the matrix is not triangular.</span></div>
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<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3d3abc3e6b522dc60fd8c1168522e09d"> 576</a></span> ColIndex <a class="code hl_function" 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 id="l00577" name="l00577"></a><span class="lineno"> 577</span> <span class="keywordflow">return</span> first_non_identity_column_;</div>
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<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> }</div>
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<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> </div>
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<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> <span class="comment">// Returns the diagonal coefficient of the given column.</span></div>
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<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84"> 581</a></span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">GetDiagonalCoefficient</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> <span class="keywordflow">return</span> diagonal_coefficients_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> }</div>
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<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> </div>
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<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <span class="comment">// Returns true iff the column contains no non-diagonal entries.</span></div>
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<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6"> 586</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6">ColumnIsDiagonalOnly</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a1426d8ab983ec32193c571f5e8c02cda">CompactSparseMatrix::ColumnIsEmpty</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> }</div>
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<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> </div>
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<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <span class="comment">// --------------------------------------------------------------------------</span></div>
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<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> <span class="comment">// Triangular solve functions.</span></div>
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<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</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 id="l00594" name="l00594"></a><span class="lineno"> 594</span> <span class="comment">// matrix to be lower (resp. upper_) triangular without any permutation.</span></div>
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<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="comment">// --------------------------------------------------------------------------</span></div>
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<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> </div>
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<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</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 id="l00598" name="l00598"></a><span class="lineno"> 598</span> <span class="comment">// The result overwrite rhs.</span></div>
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<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keywordtype">void</span> LowerSolve(<a class="code hl_class" 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 id="l00600" name="l00600"></a><span class="lineno"> 600</span> </div>
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<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</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 id="l00602" name="l00602"></a><span class="lineno"> 602</span> <span class="keywordtype">void</span> UpperSolve(<a class="code hl_class" 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 id="l00603" name="l00603"></a><span class="lineno"> 603</span> </div>
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<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</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 id="l00605" name="l00605"></a><span class="lineno"> 605</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 id="l00606" name="l00606"></a><span class="lineno"> 606</span> <span class="keywordtype">void</span> TransposeUpperSolve(<a class="code hl_class" 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 id="l00607" name="l00607"></a><span class="lineno"> 607</span> </div>
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<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</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 id="l00609" name="l00609"></a><span class="lineno"> 609</span> <span class="keywordtype">void</span> LowerSolveStartingAt(ColIndex start, <a class="code hl_class" 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 id="l00610" name="l00610"></a><span class="lineno"> 610</span> </div>
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<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> <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 id="l00612" name="l00612"></a><span class="lineno"> 612</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 id="l00613" name="l00613"></a><span class="lineno"> 613</span> <span class="keywordtype">void</span> TransposeLowerSolve(<a class="code hl_class" 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 id="l00614" name="l00614"></a><span class="lineno"> 614</span> </div>
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<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> <span class="comment">// Hyper-sparse version of the triangular solve functions. The passed</span></div>
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<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</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 id="l00617" name="l00617"></a><span class="lineno"> 617</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 id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="comment">// order for the Reverse*() versions).</span></div>
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<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</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 id="l00621" name="l00621"></a><span class="lineno"> 621</span> <span class="comment">// actually zero because of numerical cancellations can be removed.</span></div>
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<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</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 id="l00624" name="l00624"></a><span class="lineno"> 624</span> <span class="comment">// - ComputeRowsToConsiderWithDfs() which will give them in the reverse order</span></div>
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<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</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 id="l00626" name="l00626"></a><span class="lineno"> 626</span> <span class="comment">// and it will not necessarily be "sorted".</span></div>
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|
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <span class="comment">// - ComputeRowsToConsiderInSortedOrder() which will always give them in</span></div>
|
|
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> <span class="comment">// increasing order.</span></div>
|
|
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> <span class="comment">// Note that if the non-zeros are given in a sorted order, then the</span></div>
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|
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> <span class="comment">// hyper-sparse functions will return EXACTLY the same results as the non</span></div>
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|
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> <span class="comment">// hyper-sparse version above.</span></div>
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|
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> <span class="comment">// For a given solve, here is the required order:</span></div>
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|
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> <span class="comment">// - For a lower solve, increasing non-zeros order.</span></div>
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|
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> <span class="comment">// - For an upper solve, decreasing non-zeros order.</span></div>
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|
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> <span class="comment">// - for a transpose lower solve, decreasing non-zeros order.</span></div>
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|
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> <span class="comment">// - for a transpose upper solve, increasing non_zeros order.</span></div>
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|
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> <span class="comment">// For a general discussion of hyper-sparsity in LP, see:</span></div>
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<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</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 id="l00642" name="l00642"></a><span class="lineno"> 642</span> <span class="comment">// simplex method", December 1999, MS 99-014.</span></div>
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|
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</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 id="l00644" name="l00644"></a><span class="lineno"> 644</span> <span class="keywordtype">void</span> HyperSparseSolve(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code hl_typedef" 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 id="l00645" name="l00645"></a><span class="lineno"> 645</span> <span class="keywordtype">void</span> HyperSparseSolveWithReversedNonZeros(</div>
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|
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code hl_typedef" 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 id="l00647" name="l00647"></a><span class="lineno"> 647</span> <span class="keywordtype">void</span> TransposeHyperSparseSolve(<a class="code hl_class" 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 id="l00648" name="l00648"></a><span class="lineno"> 648</span> <a class="code hl_typedef" 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 id="l00649" name="l00649"></a><span class="lineno"> 649</span> <span class="keywordtype">void</span> TransposeHyperSparseSolveWithReversedNonZeros(</div>
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<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code hl_typedef" 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 id="l00651" name="l00651"></a><span class="lineno"> 651</span> </div>
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|
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span> <span class="comment">// Given the positions of the non-zeros of a vector, computes the non-zero</span></div>
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|
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> <span class="comment">// positions of the vector after a solve by this triangular matrix. The order</span></div>
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|
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</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 id="l00655" name="l00655"></a><span class="lineno"> 655</span> <span class="comment">// order. If the function detects that there are too many non-zeros, then it</span></div>
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<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> <span class="comment">// aborts early and non_zero_rows is cleared.</span></div>
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<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> <span class="keywordtype">void</span> ComputeRowsToConsiderWithDfs(<a class="code hl_typedef" 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 id="l00658" name="l00658"></a><span class="lineno"> 658</span> </div>
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|
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> <span class="comment">// Same as TriangularComputeRowsToConsider() but always returns the non-zeros</span></div>
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|
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> <span class="comment">// sorted by rows. It is up to the client to call the direct or reverse</span></div>
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|
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</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 id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="comment">// triangular.</span></div>
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<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> <span class="keywordtype">void</span> ComputeRowsToConsiderInSortedOrder(<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* non_zero_rows,</div>
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|
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sparsity_ratio,</div>
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<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> <a class="code hl_typedef" 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 id="l00666" name="l00666"></a><span class="lineno"> 666</span> <span class="keywordtype">void</span> ComputeRowsToConsiderInSortedOrder(<a class="code hl_typedef" 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 id="l00667" name="l00667"></a><span class="lineno"> 667</span> <span class="comment">// This is currently only used for testing. It achieves the same result as</span></div>
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|
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> <span class="comment">// PermutedLowerSparseSolve() below, but the latter exploits the sparsity of</span></div>
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|
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> <span class="comment">// rhs and is thus faster for our use case.</span></div>
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|
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> <span class="comment">// Note that partial_inverse_row_perm only permutes the first k rows, where k</span></div>
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|
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</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 id="l00673" name="l00673"></a><span class="lineno"> 673</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 id="l00674" name="l00674"></a><span class="lineno"> 674</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 id="l00675" name="l00675"></a><span class="lineno"> 675</span> <span class="comment">// for PermutedLowerSparseSolve() and described there.</span></div>
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|
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> <span class="comment">// IMPORTANT: lower will contain all the "symbolic" non-zero entries.</span></div>
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|
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</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 id="l00679" name="l00679"></a><span class="lineno"> 679</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 id="l00680" name="l00680"></a><span class="lineno"> 680</span> <span class="comment">// entries, not on their values. Thus, some of its coefficients may be zero.</span></div>
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|
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</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 id="l00682" name="l00682"></a><span class="lineno"> 682</span> <span class="comment">// of upper will be cleaned, however.</span></div>
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<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> <span class="keywordtype">void</span> PermutedLowerSolve(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& rhs,</div>
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<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowMapping</a>& partial_inverse_row_perm,</div>
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<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* lower, <a class="code hl_class" 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 id="l00687" name="l00687"></a><span class="lineno"> 687</span> </div>
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<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> <span class="comment">// This solves a lower triangular system with only ones on the diagonal where</span></div>
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<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> <span class="comment">// the matrix and the input rhs are permuted by the inverse of row_perm. Note</span></div>
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<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> <span class="comment">// that the output will also be permuted by the inverse of row_perm. The</span></div>
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<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> <span class="comment">// function also supports partial permutation. That is if row_perm[i] < 0 then</span></div>
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<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> <span class="comment">// column row_perm[i] is assumed to be an identity column.</span></div>
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<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> <span class="comment">// The output is given as follow:</span></div>
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<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> <span class="comment">// - lower is cleared, and receives the rows for which row_perm[row] < 0</span></div>
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<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> <span class="comment">// meaning not yet examined as a pivot (see markowitz.cc).</span></div>
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<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> <span class="comment">// - upper is NOT cleared, and the other rows (row_perm[row] >= 0) are</span></div>
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<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span> <span class="comment">// appended to it.</span></div>
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<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> <span class="comment">// - Note that lower and upper can point to the same SparseColumn.</span></div>
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<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span> <span class="comment">// Note: This function is non-const because ComputeRowsToConsider() also</span></div>
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<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span> <span class="comment">// prunes the underlying dependency graph of the lower matrix while doing a</span></div>
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<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> <span class="comment">// solve. See marked_ and pruned_ends_ below.</span></div>
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<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> <span class="keywordtype">void</span> PermutedLowerSparseSolve(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& rhs,</div>
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<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* lower, <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* upper);</div>
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<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> </div>
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<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> <span class="comment">// This is used to compute the deterministic time of a matrix factorization.</span></div>
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<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aec8942e8b01f9aed2abc24de9acfb6ab"> 709</a></span> int64_t <a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aec8942e8b01f9aed2abc24de9acfb6ab">NumFpOperationsInLastPermutedLowerSparseSolve</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> <span class="keywordflow">return</span> num_fp_operations_;</div>
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<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> }</div>
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<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> </div>
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<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> <span class="comment">// To be used in DEBUG mode by the client code. This check that the matrix is</span></div>
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<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> <span class="comment">// lower- (resp. upper-) triangular without any permutation and that there is</span></div>
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<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> <span class="comment">// no zero on the diagonal. We can't do that on each Solve() that require so,</span></div>
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<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> <span class="comment">// otherwise it will be too slow in debug.</span></div>
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<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> <span class="keywordtype">bool</span> IsLowerTriangular() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> <span class="keywordtype">bool</span> IsUpperTriangular() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> </div>
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<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> <span class="comment">// Visible for testing. This is used by PermutedLowerSparseSolve() to compute</span></div>
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<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> <span class="comment">// the non-zero indices of the result. The output is as follow:</span></div>
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<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> <span class="comment">// - lower_column_rows will contains the rows for which row_perm[row] < 0.</span></div>
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<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> <span class="comment">// - upper_column_rows will contains the other rows in the reverse topological</span></div>
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<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> <span class="comment">// order in which they should be considered in PermutedLowerSparseSolve().</span></div>
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<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> <span class="comment">// This function is non-const because it prunes the underlying dependency</span></div>
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<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> <span class="comment">// graph of the lower matrix while doing a solve. See marked_ and pruned_ends_</span></div>
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<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> <span class="comment">// below.</span></div>
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<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> <span class="comment">// Pruning the graph at the same time is slower but not by too much (< 2x) and</span></div>
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<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span> <span class="comment">// seems worth doing. Note that when the lower matrix is dense, most of the</span></div>
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<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> <span class="comment">// graph will likely be pruned. As a result, the symbolic phase will be</span></div>
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<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> <span class="comment">// negligible compared to the numerical phase so we don't really need a dense</span></div>
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<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> <span class="comment">// version of PermutedLowerSparseSolve().</span></div>
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<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> <span class="keywordtype">void</span> PermutedComputeRowsToConsider(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& rhs,</div>
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<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm,</div>
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<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* lower_column_rows,</div>
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<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* upper_column_rows);</div>
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|
<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span> </div>
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<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> <span class="comment">// The upper bound is computed using one of the algorithm presented in</span></div>
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<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"> 741</span> <span class="comment">// "A Survey of Condition Number Estimation for Triangular Matrices"</span></div>
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<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span> <span class="comment">// https:epubs.siam.org/doi/pdf/10.1137/1029112/</span></div>
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<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeInverseInfinityNormUpperBound() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeInverseInfinityNorm() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span> </div>
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<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> <span class="comment">// Internal versions of some Solve() functions to avoid code duplication.</span></div>
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<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span> <span class="keywordtype">void</span> LowerSolveStartingAtInternal(ColIndex start, <a class="code hl_class" 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 id="l00750" name="l00750"></a><span class="lineno"> 750</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span> <span class="keywordtype">void</span> UpperSolveInternal(<a class="code hl_class" 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 id="l00752" name="l00752"></a><span class="lineno"> 752</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span> <span class="keywordtype">void</span> TransposeLowerSolveInternal(<a class="code hl_class" 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 id="l00754" name="l00754"></a><span class="lineno"> 754</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> <span class="keywordtype">void</span> TransposeUpperSolveInternal(<a class="code hl_class" 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 id="l00756" name="l00756"></a><span class="lineno"> 756</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> <span class="keywordtype">void</span> HyperSparseSolveInternal(<a class="code hl_class" 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 id="l00758" name="l00758"></a><span class="lineno"> 758</span> <a class="code hl_typedef" 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 id="l00759" name="l00759"></a><span class="lineno"> 759</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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|
<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span> <span class="keywordtype">void</span> HyperSparseSolveWithReversedNonZerosInternal(</div>
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<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code hl_typedef" 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 id="l00762" name="l00762"></a><span class="lineno"> 762</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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|
<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span> <span class="keywordtype">void</span> TransposeHyperSparseSolveInternal(<a class="code hl_class" 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 id="l00764" name="l00764"></a><span class="lineno"> 764</span> <a class="code hl_typedef" 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 id="l00765" name="l00765"></a><span class="lineno"> 765</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> diagonal_of_ones></div>
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|
<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span> <span class="keywordtype">void</span> TransposeHyperSparseSolveWithReversedNonZerosInternal(</div>
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|
<div class="line"><a id="l00767" name="l00767"></a><span class="lineno"> 767</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* rhs, <a class="code hl_typedef" 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 id="l00768" name="l00768"></a><span class="lineno"> 768</span> </div>
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|
<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"> 769</span> <span class="comment">// Internal function used by the Add*() functions to finish adding</span></div>
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|
<div class="line"><a id="l00770" name="l00770"></a><span class="lineno"> 770</span> <span class="comment">// a new column to a triangular matrix.</span></div>
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<div class="line"><a id="l00771" name="l00771"></a><span class="lineno"> 771</span> <span class="keywordtype">void</span> CloseCurrentColumn(<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> diagonal_value);</div>
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|
<div class="line"><a id="l00772" name="l00772"></a><span class="lineno"> 772</span> </div>
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|
<div class="line"><a id="l00773" name="l00773"></a><span class="lineno"> 773</span> <span class="comment">// Extra data for "triangular" matrices. The diagonal coefficients are</span></div>
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|
<div class="line"><a id="l00774" name="l00774"></a><span class="lineno"> 774</span> <span class="comment">// stored in a separate vector instead of beeing stored in each column.</span></div>
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<div class="line"><a id="l00775" name="l00775"></a><span class="lineno"> 775</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<ColIndex, Fractional></a> diagonal_coefficients_;</div>
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|
<div class="line"><a id="l00776" name="l00776"></a><span class="lineno"> 776</span> </div>
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<div class="line"><a id="l00777" name="l00777"></a><span class="lineno"> 777</span> <span class="comment">// Index of the first column which is not a diagonal only column with a</span></div>
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|
<div class="line"><a id="l00778" name="l00778"></a><span class="lineno"> 778</span> <span class="comment">// coefficient of 1. This is used to optimize the solves.</span></div>
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|
<div class="line"><a id="l00779" name="l00779"></a><span class="lineno"> 779</span> ColIndex first_non_identity_column_;</div>
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|
<div class="line"><a id="l00780" name="l00780"></a><span class="lineno"> 780</span> </div>
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|
<div class="line"><a id="l00781" name="l00781"></a><span class="lineno"> 781</span> <span class="comment">// This common case allows for more efficient Solve() functions.</span></div>
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|
<div class="line"><a id="l00782" name="l00782"></a><span class="lineno"> 782</span> <span class="comment">// TODO(user): Do not even construct diagonal_coefficients_ in this case?</span></div>
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|
<div class="line"><a id="l00783" name="l00783"></a><span class="lineno"> 783</span> <span class="keywordtype">bool</span> all_diagonal_coefficients_are_one_;</div>
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|
<div class="line"><a id="l00784" name="l00784"></a><span class="lineno"> 784</span> </div>
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|
<div class="line"><a id="l00785" name="l00785"></a><span class="lineno"> 785</span> <span class="comment">// For the hyper-sparse version. These are used to implement a DFS, see</span></div>
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|
<div class="line"><a id="l00786" name="l00786"></a><span class="lineno"> 786</span> <span class="comment">// TriangularComputeRowsToConsider() for more details.</span></div>
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|
<div class="line"><a id="l00787" name="l00787"></a><span class="lineno"> 787</span> <span class="keyword">mutable</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> stored_;</div>
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<div class="line"><a id="l00788" name="l00788"></a><span class="lineno"> 788</span> <span class="keyword">mutable</span> std::vector<RowIndex> nodes_to_explore_;</div>
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<div class="line"><a id="l00789" name="l00789"></a><span class="lineno"> 789</span> </div>
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|
<div class="line"><a id="l00790" name="l00790"></a><span class="lineno"> 790</span> <span class="comment">// For PermutedLowerSparseSolve().</span></div>
|
|
<div class="line"><a id="l00791" name="l00791"></a><span class="lineno"> 791</span> int64_t num_fp_operations_;</div>
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|
<div class="line"><a id="l00792" name="l00792"></a><span class="lineno"> 792</span> <span class="keyword">mutable</span> std::vector<RowIndex> lower_column_rows_;</div>
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|
<div class="line"><a id="l00793" name="l00793"></a><span class="lineno"> 793</span> <span class="keyword">mutable</span> std::vector<RowIndex> upper_column_rows_;</div>
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|
<div class="line"><a id="l00794" name="l00794"></a><span class="lineno"> 794</span> <span class="keyword">mutable</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> initially_all_zero_scratchpad_;</div>
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|
<div class="line"><a id="l00795" name="l00795"></a><span class="lineno"> 795</span> </div>
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|
<div class="line"><a id="l00796" name="l00796"></a><span class="lineno"> 796</span> <span class="comment">// This boolean vector is used to detect entries that can be pruned during</span></div>
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|
<div class="line"><a id="l00797" name="l00797"></a><span class="lineno"> 797</span> <span class="comment">// the DFS used for the symbolic phase of ComputeRowsToConsider().</span></div>
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|
<div class="line"><a id="l00798" name="l00798"></a><span class="lineno"> 798</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00799" name="l00799"></a><span class="lineno"> 799</span> <span class="comment">// Problem: We have a DAG where each node has outgoing arcs towards other</span></div>
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<div class="line"><a id="l00800" name="l00800"></a><span class="lineno"> 800</span> <span class="comment">// nodes (this adjacency list is NOT sorted by any order). We want to compute</span></div>
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<div class="line"><a id="l00801" name="l00801"></a><span class="lineno"> 801</span> <span class="comment">// the reachability of a set of nodes S and its topological order. While doing</span></div>
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<div class="line"><a id="l00802" name="l00802"></a><span class="lineno"> 802</span> <span class="comment">// this, we also want to prune the adjacency lists to exploit the simple fact</span></div>
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|
<div class="line"><a id="l00803" name="l00803"></a><span class="lineno"> 803</span> <span class="comment">// that if a -> (b, c) and b -> (c) then c can be removed from the adjacency</span></div>
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<div class="line"><a id="l00804" name="l00804"></a><span class="lineno"> 804</span> <span class="comment">// list of a since it will be implied through b. Note that this doesn't change</span></div>
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<div class="line"><a id="l00805" name="l00805"></a><span class="lineno"> 805</span> <span class="comment">// the reachability of any set nor a valid topological ordering of such a set.</span></div>
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<div class="line"><a id="l00806" name="l00806"></a><span class="lineno"> 806</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00807" name="l00807"></a><span class="lineno"> 807</span> <span class="comment">// The concept is known as the transitive reduction of a DAG, see</span></div>
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<div class="line"><a id="l00808" name="l00808"></a><span class="lineno"> 808</span> <span class="comment">// http://en.wikipedia.org/wiki/Transitive_reduction.</span></div>
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<div class="line"><a id="l00809" name="l00809"></a><span class="lineno"> 809</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00810" name="l00810"></a><span class="lineno"> 810</span> <span class="comment">// Heuristic algorithm: While doing the DFS to compute Reach(S) and its</span></div>
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<div class="line"><a id="l00811" name="l00811"></a><span class="lineno"> 811</span> <span class="comment">// topological order, each time we process a node, we mark all its adjacent</span></div>
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<div class="line"><a id="l00812" name="l00812"></a><span class="lineno"> 812</span> <span class="comment">// node while going down in the DFS, and then we unmark all of them when we go</span></div>
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<div class="line"><a id="l00813" name="l00813"></a><span class="lineno"> 813</span> <span class="comment">// back up. During the un-marking, if a node is already un-marked, it means</span></div>
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<div class="line"><a id="l00814" name="l00814"></a><span class="lineno"> 814</span> <span class="comment">// that it was implied by some other path starting at the current node and we</span></div>
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|
<div class="line"><a id="l00815" name="l00815"></a><span class="lineno"> 815</span> <span class="comment">// can prune it and remove it from the adjacency list of the current node.</span></div>
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<div class="line"><a id="l00816" name="l00816"></a><span class="lineno"> 816</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00817" name="l00817"></a><span class="lineno"> 817</span> <span class="comment">// Note(user): I couldn't find any reference for this algorithm, even though</span></div>
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<div class="line"><a id="l00818" name="l00818"></a><span class="lineno"> 818</span> <span class="comment">// I suspect I am not the first one to need something similar.</span></div>
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<div class="line"><a id="l00819" name="l00819"></a><span class="lineno"> 819</span> <span class="keyword">mutable</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> marked_;</div>
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<div class="line"><a id="l00820" name="l00820"></a><span class="lineno"> 820</span> </div>
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<div class="line"><a id="l00821" name="l00821"></a><span class="lineno"> 821</span> <span class="comment">// This is used to represent a pruned sub-matrix of the current matrix that</span></div>
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<div class="line"><a id="l00822" name="l00822"></a><span class="lineno"> 822</span> <span class="comment">// corresponds to the pruned DAG as described in the comment above for</span></div>
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<div class="line"><a id="l00823" name="l00823"></a><span class="lineno"> 823</span> <span class="comment">// marked_. This vector is used to encode the sub-matrix as follow:</span></div>
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<div class="line"><a id="l00824" name="l00824"></a><span class="lineno"> 824</span> <span class="comment">// - Both the rows and the coefficients of the pruned matrix are still stored</span></div>
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<div class="line"><a id="l00825" name="l00825"></a><span class="lineno"> 825</span> <span class="comment">// in rows_ and coefficients_.</span></div>
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<div class="line"><a id="l00826" name="l00826"></a><span class="lineno"> 826</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 id="l00827" name="l00827"></a><span class="lineno"> 827</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 id="l00828" name="l00828"></a><span class="lineno"> 828</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00829" name="l00829"></a><span class="lineno"> 829</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 id="l00830" name="l00830"></a><span class="lineno"> 830</span> <span class="comment">// sparse linear algebra. See:</span></div>
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<div class="line"><a id="l00831" name="l00831"></a><span class="lineno"> 831</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 id="l00832" name="l00832"></a><span class="lineno"> 832</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 id="l00833" name="l00833"></a><span class="lineno"> 833</span> <span class="comment">// Computer Science, York University, North York. Ontario, Canada, 1990.</span></div>
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<div class="line"><a id="l00834" name="l00834"></a><span class="lineno"> 834</span> <span class="comment">// - Stanley C. Eisenstat and Joseph W. H. Liu, "Exploiting structural</span></div>
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<div class="line"><a id="l00835" name="l00835"></a><span class="lineno"> 835</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 id="l00836" name="l00836"></a><span class="lineno"> 836</span> <span class="comment">// 14, No 1, pp. 253-257, January 1993.</span></div>
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<div class="line"><a id="l00837" name="l00837"></a><span class="lineno"> 837</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00838" name="l00838"></a><span class="lineno"> 838</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 id="l00839" name="l00839"></a><span class="lineno"> 839</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 id="l00840" name="l00840"></a><span class="lineno"> 840</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 id="l00841" name="l00841"></a><span class="lineno"> 841</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 id="l00842" name="l00842"></a><span class="lineno"> 842</span> <span class="comment">// has the same result for the symbolic phase though.</span></div>
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|
<div class="line"><a id="l00843" name="l00843"></a><span class="lineno"> 843</span> <span class="comment">//</span></div>
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|
<div class="line"><a id="l00844" name="l00844"></a><span class="lineno"> 844</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 id="l00845" name="l00845"></a><span class="lineno"> 845</span> <span class="comment">// we can benefit from the pruned lower matrix there?</span></div>
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|
<div class="line"><a id="l00846" name="l00846"></a><span class="lineno"> 846</span> <a class="code hl_class" 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 id="l00847" name="l00847"></a><span class="lineno"> 847</span> </div>
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<div class="line"><a id="l00848" name="l00848"></a><span class="lineno"> 848</span> <a class="code hl_define" href="macros_8h.html#af8df3547bfde53a5acb93e2607b0034a">DISALLOW_COPY_AND_ASSIGN</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_triangular_matrix.html">TriangularMatrix</a>);</div>
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|
<div class="line"><a id="l00849" name="l00849"></a><span class="lineno"> 849</span>};</div>
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<div class="line"><a id="l00850" name="l00850"></a><span class="lineno"> 850</span> </div>
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<div class="line"><a id="l00851" name="l00851"></a><span class="lineno"> 851</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00852" name="l00852"></a><span class="lineno"> 852</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00853" name="l00853"></a><span class="lineno"> 853</span> </div>
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<div class="line"><a id="l00854" name="l00854"></a><span class="lineno"> 854</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_LP_DATA_SPARSE_H_</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="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#l00889">base/logging.h:889</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#l00886">base/logging.h:886</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html">operations_research::glop::ColumnView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00065">sparse_column.h:65</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">operations_research::glop::CompactSparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00289">sparse.h:289</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_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#l00459">sparse.h:459</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#l00381">sparse.h:381</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#l00423">sparse.h:423</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#l00291">sparse.h:291</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#l00466">sparse.h:466</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#l00350">sparse.h:350</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#l00458">sparse.h:458</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#l00410">sparse.h:410</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#l00441">sparse.h:441</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#l00465">sparse.h:465</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#l00353">sparse.h:353</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#l00349">sparse.h:349</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#l00295">sparse.h:295</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#l00366">sparse.h:366</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#l00464">sparse.h:464</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#l00431">sparse.h:431</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#l00387">sparse.h:387</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_acedaf830dd26be6213e4665f088c5aa4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#acedaf830dd26be6213e4665f088c5aa4">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#l00363">sparse.h:363</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#l00398">sparse.h:398</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#l00367">sparse.h:367</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#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_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#l00369">sparse.h:369</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#l00340">sparse.h:340</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">operations_research::glop::CompactSparseMatrixView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00476">sparse.h:476</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrixView::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00489">sparse.h:489</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a6c2cb025b83ee5d5365eb0b419a0298c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a6c2cb025b83ee5d5365eb0b419a0298c">operations_research::glop::CompactSparseMatrixView::column</a></div><div class="ttdeci">const ColumnView column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00490">sparse.h:490</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_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#l00478">sparse.h:478</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a7a56df5528de85e8d1b588d6a50e6948"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a7a56df5528de85e8d1b588d6a50e6948">operations_research::glop::CompactSparseMatrixView::CompactSparseMatrixView</a></div><div class="ttdeci">CompactSparseMatrixView(const CompactSparseMatrix *compact_matrix, const std::vector< ColIndex > *columns)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00482">sparse.h:482</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::CompactSparseMatrixView::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00487">sparse.h:487</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrixView::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00488">sparse.h:488</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_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#l00219">sparse.h:219</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#l00221">sparse.h:221</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_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#l00264">sparse.h:264</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#l00227">sparse.h:227</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_matrix_view_html_a7273cc492a51a1c5d45c620b32fce502"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_matrix_view.html#a7273cc492a51a1c5d45c620b32fce502">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#l00265">sparse.h:265</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#l00238">sparse.h:238</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#l00262">sparse.h:262</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#l00263">sparse.h:263</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#l00222">sparse.h:222</a></div></div>
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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#l00252">sparse.h:252</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_permutation_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html">operations_research::glop::Permutation< RowIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html">operations_research::glop::SparseColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00044">sparse_column.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html">operations_research::glop::SparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00062">sparse.h:62</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_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="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="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_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_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_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_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="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#l00178">sparse.h:178</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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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a564caf35589006190ef4985fbda74faa"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">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#l00182">sparse.h:182</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_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_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_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_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_sparse_matrix_html_a7273cc492a51a1c5d45c620b32fce502"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">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#l00181">sparse.h:181</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_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_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_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_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#l00177">sparse.h:177</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_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_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="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="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_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_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_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="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_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="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_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_strict_i_t_i_vector_html_a3de922485ca2c30f3e07d959dd97cdd0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a3de922485ca2c30f3e07d959dd97cdd0">operations_research::glop::StrictITIVector::AssignToZero</a></div><div class="ttdeci">void AssignToZero(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00294">lp_types.h:294</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a64b6b04f3a519d2c61d49daaa88bf06e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">operations_research::glop::StrictITIVector::resize</a></div><div class="ttdeci">void resize(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00273">lp_types.h:273</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00280">lp_types.h:280</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html">operations_research::glop::TriangularMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00511">sparse.h:511</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_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#l00576">sparse.h:576</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#l00522">sparse.h:522</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#l00581">sparse.h:581</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#l00520">sparse.h:520</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#l00521">sparse.h:521</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#l00513">sparse.h:513</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_aec8942e8b01f9aed2abc24de9acfb6ab"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aec8942e8b01f9aed2abc24de9acfb6ab">operations_research::glop::TriangularMatrix::NumFpOperationsInLastPermutedLowerSparseSolve</a></div><div class="ttdeci">int64_t NumFpOperationsInLastPermutedLowerSparseSolve() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00709">sparse.h:709</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_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#l00586">sparse.h:586</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::TriangularMatrix::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00523">sparse.h:523</a></div></div>
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<div class="ttc" id="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="aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a></div><div class="ttdeci">int64_t a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00046">constraint_solver/table.cc:46</a></div></div>
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<div class="ttc" id="ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</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="alp__data_2permutation_8h_html"><div class="ttname"><a href="lp__data_2permutation_8h.html">permutation.h</a></div></div>
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<div class="ttc" id="alp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="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="amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a6b1b56ad0cb77edbd314f2bec33b467a"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a">operations_research::glop::ColumnPermutation</a></div><div class="ttdeci">Permutation< ColIndex > ColumnPermutation</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00095">lp_data/permutation.h:95</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_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#l00049">lp_types.h:49</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#l00313">lp_types.h:313</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ae69267cf0653a77925ee13121b9857ec"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec">operations_research::glop::RowPermutation</a></div><div class="ttdeci">Permutation< RowIndex > RowPermutation</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00094">lp_data/permutation.h:94</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_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="sat_2linear__constraint_8cc_source.html#l00182">sat/linear_constraint.cc:182</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="aparser_8yy_8cc_html_a5a634cf4429798b1c921a81de8250051"><div class="ttname"><a href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a></div><div class="ttdeci">static int input(yyscan_t yyscanner)</div></div>
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<div class="ttc" id="apreprocessor_8cc_html_a2babe18010525bbf13c2fa5a959971e4"><div class="ttname"><a href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a></div><div class="ttdeci">EntryIndex num_entries</div><div class="ttdef"><b>Definition:</b> <a href="preprocessor_8cc_source.html#l01366">preprocessor.cc:1366</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="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="ascattered__vector_8h_html"><div class="ttname"><a href="scattered__vector_8h.html">scattered_vector.h</a></div></div>
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<div class="ttc" id="asparse__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="astructoperations__research_1_1glop_1_1_scattered_column_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_column.html">operations_research::glop::ScatteredColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00196">scattered_vector.h:197</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_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#l00098">scattered_vector.h:98</a></div></div>
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