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<div class="headertitle"><div class="title">matrix_utils.cc</div></div>
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<a href="matrix__utils_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
<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 &quot;License&quot;);</span></div>
<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>
<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>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<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>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<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>
<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 &quot;AS IS&quot; BASIS,</span></div>
<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>
<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>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &quot;<a class="code" href="matrix__utils_8h.html">ortools/lp_data/matrix_utils.h</a>&quot;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include &quot;<a class="code" href="hash_8h.html">ortools/base/hash.h</a>&quot;</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="keyword">namespace </span>glop {</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// Returns true iff the two given sparse columns are proportional. The two</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// sparse columns must be ordered by row and must not contain any zero entry.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">//</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// See the header comment on FindProportionalColumns() for the exact definition</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// of two proportional columns with a given tolerance.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keywordtype">bool</span> AreColumnsProportional(<span class="keyword">const</span> SparseColumn&amp; <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <span class="keyword">const</span> SparseColumn&amp; <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.IsCleanedUp());</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.IsCleanedUp());</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.num_entries() != <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.num_entries()) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> multiple = 0.0;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">bool</span> a_is_larger = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.AllEntryIndices()) {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.EntryRow(i) != <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.EntryRow(i)) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff_a = <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.EntryCoefficient(i);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff_b = <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.EntryCoefficient(i);</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">if</span> (multiple == 0.0) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> a_is_larger = std::abs(coeff_a) &gt; std::abs(coeff_b);</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> multiple = a_is_larger ? coeff_a / coeff_b : coeff_b / coeff_a;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">if</span> (a_is_larger) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">if</span> (std::abs(coeff_a / coeff_b - multiple) &gt; tolerance) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">if</span> (std::abs(coeff_b / coeff_a - multiple) &gt; tolerance) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> }</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>}</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// A column index together with its fingerprint. See ComputeFingerprint().</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="keyword">struct </span>ColumnFingerprint {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> ColumnFingerprint(ColIndex _col, int64_t _hash, <span class="keywordtype">double</span> _value)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> : <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(_col), <a class="code hl_variable" href="matrix__utils_8cc.html#a95d4078c018ac04247ee3785eab30e7b">hash</a>(_hash), <a class="code hl_variable" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a>(_value) {}</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"><a class="line" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c"> 60</a></span> ColIndex <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"><a class="line" href="matrix__utils_8cc.html#a95d4078c018ac04247ee3785eab30e7b"> 61</a></span> int64_t <a class="code hl_variable" href="matrix__utils_8cc.html#a95d4078c018ac04247ee3785eab30e7b">hash</a>;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c"> 62</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a>;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// This order has the property that if AreProportionalCandidates() is true for</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// two given columns, then in a sorted list of columns</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// AreProportionalCandidates() will be true for all the pairs of columns</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// between the two given ones (included).</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordtype">bool</span> operator&lt;(<span class="keyword">const</span> ColumnFingerprint&amp; other)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="matrix__utils_8cc.html#a95d4078c018ac04247ee3785eab30e7b">hash</a> == other.hash) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a> &lt; other.value;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="matrix__utils_8cc.html#a95d4078c018ac04247ee3785eab30e7b">hash</a> &lt; other.hash;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>};</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// Two columns can be proportional only if:</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// - Their non-zero pattern hashes are the same.</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">// - Their double fingerprints are close to each other.</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="keywordtype">bool</span> AreProportionalCandidates(ColumnFingerprint <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, ColumnFingerprint <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.hash != <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.hash) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> std::abs(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>.value - <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.value) &lt; tolerance;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">// The fingerprint of a column has two parts:</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// - A hash value of the column non-zero pattern.</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">// - A double value which should be the same for two proportional columns</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment">// modulo numerical errors.</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>ColumnFingerprint ComputeFingerprint(ColIndex <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <span class="keyword">const</span> SparseColumn&amp; column) {</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> int64_t non_zero_pattern_hash = 0;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> min_abs = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits&lt;Fractional&gt;::max</a>();</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_abs = 0.0;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sum = 0.0;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : column) {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> non_zero_pattern_hash =</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_function" href="namespaceutil__hash.html#a17715af1c1bc575a706eb167371b81e9">util_hash::Hash</a>(e.row().value(), non_zero_pattern_hash);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> sum += e.coefficient();</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> min_abs = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(min_abs, std::abs(e.coefficient()));</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> max_abs = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_abs, std::abs(e.coefficient()));</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// The two scaled values are in [0, 1].</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// TODO(user): A better way to discriminate columns would be to take the</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// scalar product with a constant but random vector scaled by max_abs.</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(0.0, max_abs);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">const</span> <span class="keywordtype">double</span> inverse_dynamic_range = min_abs / max_abs;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">const</span> <span class="keywordtype">double</span> scaled_average =</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::abs(sum) /</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> (<span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(column.num_entries().value()) * max_abs);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">return</span> ColumnFingerprint(<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, non_zero_pattern_hash,</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> inverse_dynamic_range + scaled_average);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span>}</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>} <span class="comment">// namespace</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#ac9bef291f9b941569978d0f075144abf"> 116</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ac9bef291f9b941569978d0f075144abf">FindProportionalColumns</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>&amp; matrix,</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">const</span> ColIndex num_cols = matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> mapping(num_cols, <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> </div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// Compute the fingerprint of each columns and sort them.</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> std::vector&lt;ColumnFingerprint&gt; fingerprints;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> &lt; num_cols; ++<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (!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="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) {</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> fingerprints.push_back(ComputeFingerprint(<a class="code hl_variable" href="matrix__utils_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="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)));</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> std::sort(fingerprints.begin(), fingerprints.end());</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// Find a representative of each proportional columns class. This only</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// compares columns with a close-enough fingerprint.</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; fingerprints.size(); ++i) {</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">const</span> ColIndex col_a = fingerprints[i].col;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">if</span> (mapping[col_a] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j &lt; fingerprints.size(); ++j) {</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keyword">const</span> ColIndex col_b = fingerprints[j].col;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">if</span> (mapping[col_b] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// Note that we use the same tolerance for the fingerprints.</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// TODO(user): Derive precise bounds on what this tolerance should be so</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// that no proportional columns are missed.</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordflow">if</span> (!AreProportionalCandidates(fingerprints[i], fingerprints[j],</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> tolerance)) {</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> }</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">if</span> (AreColumnsProportional(matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(col_a), matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(col_b),</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> tolerance)) {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> mapping[col_b] = col_a;</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> }</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> }</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// Sort the mapping so that the representative of each class is the smallest</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// column. To achieve this, the current representative is used as a pointer</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// to the new one, a bit like in an union find algorithm.</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> &lt; num_cols; ++<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">if</span> (mapping[<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keyword">const</span> ColIndex new_representative = mapping[mapping[<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]];</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">if</span> (new_representative != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> mapping[<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = new_representative;</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">if</span> (mapping[<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] &gt; <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> mapping[mapping[<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]] = <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> mapping[<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> }</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> }</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">return</span> mapping;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span>}</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a1ee4943cf389e6ff8159924ea5b048e1"> 172</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a1ee4943cf389e6ff8159924ea5b048e1">FindProportionalColumnsUsingSimpleAlgorithm</a>(</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>&amp; matrix, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keyword">const</span> ColIndex num_cols = matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> mapping(num_cols, <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordflow">for</span> (ColIndex col_a(0); col_a &lt; num_cols; ++col_a) {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordflow">if</span> (matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(col_a).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordflow">if</span> (mapping[col_a] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordflow">for</span> (ColIndex col_b(col_a + 1); col_b &lt; num_cols; ++col_b) {</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">if</span> (matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(col_b).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">if</span> (mapping[col_b] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">if</span> (AreColumnsProportional(matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(col_a), matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(col_b),</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> tolerance)) {</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> mapping[col_b] = col_a;</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> }</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> }</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> }</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">return</span> mapping;</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span>}</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a9f2b788a9c67a4c71cb7e75b54aea27f"> 191</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a9f2b788a9c67a4c71cb7e75b54aea27f">AreFirstColumnsAndRowsExactlyEquals</a>(RowIndex num_rows, ColIndex num_cols,</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>&amp; matrix_a,</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>&amp; matrix_b) {</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="comment">// TODO(user): Also DCHECK() that matrix_b is ordered by rows.</span></div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a5e016d204d43b2cc4a2773c25462968a">IsCleanedUp</a>());</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordflow">if</span> (num_rows &gt; matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>() || num_rows &gt; matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>() ||</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> num_cols &gt; matrix_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() || num_cols &gt; matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>()) {</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> }</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> &lt; num_cols; ++<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>&amp; 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="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>&amp; col_b = matrix_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(<a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="keyword">const</span> EntryIndex <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>(), col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>());</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a> &lt; col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() &amp;&amp; col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(<a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a>) &lt; num_rows) {</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> }</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a> &lt; col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() &amp;&amp; col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(<a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a>) &lt; num_rows) {</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> }</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordflow">for</span> (EntryIndex i(0); i &lt; <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a>; ++i) {</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordflow">if</span> (col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i) != col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i)) {</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">if</span> (col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i) &lt; num_rows || col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i) &lt; num_rows) {</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> }</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">if</span> (col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(i) != col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(i)) {</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> }</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordflow">if</span> (col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() &gt; <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a> &amp;&amp; col_a.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(<a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a>) &lt; num_rows) {</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> }</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <span class="keywordflow">if</span> (col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() &gt; <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a> &amp;&amp; col_b.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(<a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a>) &lt; num_rows) {</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> }</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> }</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> }</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span>}</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a15dfa7820af8e00b9624297be497f95a"> 232</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a15dfa7820af8e00b9624297be497f95a">IsRightMostSquareMatrixIdentity</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>&amp; matrix) {</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a5e016d204d43b2cc4a2773c25462968a">IsCleanedUp</a>());</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keywordflow">if</span> (matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>().value() &gt; matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>().value()) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="keyword">const</span> ColIndex first_identity_col =</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() - <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>());</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = first_identity_col; <a class="code hl_variable" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> &lt; matrix.<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="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>&amp; column = 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="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keywordflow">if</span> (column.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() != 1 ||</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> column.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(EntryIndex(0)) != 1.0) {</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> }</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> }</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span>}</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span>} <span class="comment">// namespace glop</span></div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span>} <span class="comment">// namespace operations_research</span></div>
<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>
<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
2022-03-04 00:11:33 +01:00
<div class="ttc" id="abase_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0"><div class="ttname"><a href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a></div><div class="ttdeci">#define DCHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00892">base/logging.h:892</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_ae17f8119c108cf3070bad3449c7e0006"><div class="ttname"><a href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a></div><div class="ttdeci">#define DCHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
2022-01-17 21:42:14 +01:00
<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>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html_aaef7fc778a29bb3bb3040c0423937f6e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html#aaef7fc778a29bb3bb3040c0423937f6e">operations_research::glop::ColumnView::EntryCoefficient</a></div><div class="ttdeci">Fractional EntryCoefficient(EntryIndex i) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00083">sparse_column.h:83</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html_aedc46de5199e203b77de2eae2e4c100d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">operations_research::glop::ColumnView::EntryRow</a></div><div class="ttdeci">RowIndex EntryRow(EntryIndex i) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00089">sparse_column.h:89</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::ColumnView::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00082">sparse_column.h:82</a></div></div>
<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>
<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>
<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>
<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>
<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>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html_aaef7fc778a29bb3bb3040c0423937f6e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html#aaef7fc778a29bb3bb3040c0423937f6e">operations_research::glop::SparseColumn::EntryCoefficient</a></div><div class="ttdeci">Fractional EntryCoefficient(EntryIndex i) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00052">sparse_column.h:52</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html_aedc46de5199e203b77de2eae2e4c100d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">operations_research::glop::SparseColumn::EntryRow</a></div><div class="ttdeci">RowIndex EntryRow(EntryIndex i) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00051">sparse_column.h:51</a></div></div>
<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>
<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>
<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>
<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 &amp; column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00181">sparse.h:181</a></div></div>
<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>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_a8e12342fc420701fbffd97025421575a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">operations_research::glop::SparseVector::IsEmpty</a></div><div class="ttdeci">bool IsEmpty() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00529">lp_data/sparse_vector.h:529</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_ab38326ea6cb6187267665dd8b2748f3d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">operations_research::glop::SparseVector&lt; RowIndex, SparseColumnIterator &gt;::Entry</a></div><div class="ttdeci">typename Iterator::Entry Entry</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00091">lp_data/sparse_vector.h:91</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::SparseVector::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00270">lp_data/sparse_vector.h:270</a></div></div>
<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&lt; ColIndex, ColIndex &gt;</a></div></div>
<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>
<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>
<div class="ttc" id="ahash_8h_html"><div class="ttname"><a href="hash_8h.html">hash.h</a></div></div>
<div class="ttc" id="amatrix__utils_8cc_html_a95d4078c018ac04247ee3785eab30e7b"><div class="ttname"><a href="matrix__utils_8cc.html#a95d4078c018ac04247ee3785eab30e7b">hash</a></div><div class="ttdeci">int64_t hash</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00061">matrix_utils.cc:61</a></div></div>
<div class="ttc" id="amatrix__utils_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00060">matrix_utils.cc:60</a></div></div>
<div class="ttc" id="amatrix__utils_8cc_html_aee90379adb0307effb138f4871edbc5c"><div class="ttname"><a href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a></div><div class="ttdeci">double value</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00062">matrix_utils.cc:62</a></div></div>
<div class="ttc" id="amatrix__utils_8h_html"><div class="ttname"><a href="matrix__utils_8h.html">matrix_utils.h</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a15dfa7820af8e00b9624297be497f95a"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a15dfa7820af8e00b9624297be497f95a">operations_research::glop::IsRightMostSquareMatrixIdentity</a></div><div class="ttdeci">bool IsRightMostSquareMatrixIdentity(const SparseMatrix &amp;matrix)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00232">matrix_utils.cc:232</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a1ee4943cf389e6ff8159924ea5b048e1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1ee4943cf389e6ff8159924ea5b048e1">operations_research::glop::FindProportionalColumnsUsingSimpleAlgorithm</a></div><div class="ttdeci">ColMapping FindProportionalColumnsUsingSimpleAlgorithm(const SparseMatrix &amp;matrix, Fractional tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00172">matrix_utils.cc:172</a></div></div>
<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>
<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>
<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a9f2b788a9c67a4c71cb7e75b54aea27f"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a9f2b788a9c67a4c71cb7e75b54aea27f">operations_research::glop::AreFirstColumnsAndRowsExactlyEquals</a></div><div class="ttdeci">bool AreFirstColumnsAndRowsExactlyEquals(RowIndex num_rows, ColIndex num_cols, const SparseMatrix &amp;matrix_a, const CompactSparseMatrix &amp;matrix_b)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00191">matrix_utils.cc:191</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ac9bef291f9b941569978d0f075144abf"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ac9bef291f9b941569978d0f075144abf">operations_research::glop::FindProportionalColumns</a></div><div class="ttdeci">ColMapping FindProportionalColumns(const SparseMatrix &amp;matrix, Fractional tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00116">matrix_utils.cc:116</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1glop_html_afb755b7934d8679476e2f05a89739bcd"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">operations_research::glop::kInvalidCol</a></div><div class="ttdeci">const ColIndex kInvalidCol(-1)</div></div>
<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>
<div class="ttc" id="anamespaceutil__hash_html_a17715af1c1bc575a706eb167371b81e9"><div class="ttname"><a href="namespaceutil__hash.html#a17715af1c1bc575a706eb167371b81e9">util_hash::Hash</a></div><div class="ttdeci">uint64_t Hash(uint64_t num, uint64_t c)</div><div class="ttdef"><b>Definition:</b> <a href="hash_8h_source.html#l00150">hash.h:150</a></div></div>
<div class="ttc" id="asparse__submatrix_8cc_html_a4d53eac2ef2732c28fa9fb663e0c19a7"><div class="ttname"><a href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a></div><div class="ttdeci">std::optional&lt; int64_t &gt; end</div><div class="ttdef"><b>Definition:</b> <a href="sparse__submatrix_8cc_source.html#l00036">sparse_submatrix.cc:36</a></div></div>
2021-01-26 11:28:50 +01:00
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