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<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 name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "<a class="code" href="matrix__utils_8h.html">ortools/lp_data/matrix_utils.h</a>"</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  </div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  </div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "<a class="code" href="hash_8h.html">ortools/base/hash.h</a>"</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">namespace </span>glop {</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  </div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">namespace </span>{</div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  </div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// Returns true iff the two given sparse columns are proportional. The two</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// sparse columns must be ordered by row and must not contain any zero entry.</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// See the header comment on FindProportionalColumns() for the exact definition</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// of two proportional columns with a given tolerance.</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keywordtype">bool</span> AreColumnsProportional(<span class="keyword">const</span> SparseColumn& <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, <span class="keyword">const</span> SparseColumn& <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>,</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.IsCleanedUp());</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>.IsCleanedUp());</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">if</span> (<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.num_entries() != <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>.num_entries()) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> multiple = 0.0;</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordtype">bool</span> a_is_larger = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> EntryIndex i : <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.AllEntryIndices()) {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordflow">if</span> (<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.EntryRow(i) != <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>.EntryRow(i)) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff_a = <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.EntryCoefficient(i);</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff_b = <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>.EntryCoefficient(i);</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">if</span> (multiple == 0.0) {</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  a_is_larger = std::abs(coeff_a) > std::abs(coeff_b);</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  multiple = a_is_larger ? coeff_a / coeff_b : coeff_b / coeff_a;</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">if</span> (a_is_larger) {</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">if</span> (std::abs(coeff_a / coeff_b - multiple) > tolerance) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">if</span> (std::abs(coeff_b / coeff_a - multiple) > tolerance) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  }</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  }</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  }</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> }</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  </div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// A column index together with its fingerprint. See ComputeFingerprint().</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">struct </span>ColumnFingerprint {</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  ColumnFingerprint(ColIndex _col, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> _hash, <span class="keywordtype">double</span> _value)</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  : <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(_col), <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a>(_hash), <a class="code" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a>(_value) {}</div>
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<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c"> 59</a></span>  ColIndex <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89"> 60</a></span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a>;</div>
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<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c"> 61</a></span>  <span class="keywordtype">double</span> <a class="code" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a>;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// This order has the property that if AreProportionalCandidates() is true for</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">// two given columns, then in a sorted list of columns</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// AreProportionalCandidates() will be true for all the pairs of columns</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// between the two given ones (included).</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordtype">bool</span> operator<(<span class="keyword">const</span> ColumnFingerprint& other)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">if</span> (<a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a> == other.hash) {</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">return</span> <a class="code" href="matrix__utils_8cc.html#aee90379adb0307effb138f4871edbc5c">value</a> < other.value;</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">return</span> <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a> < other.hash;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> };</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  </div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// Two columns can be proportional only if:</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// - Their non-zero pattern hashes are the same.</span></div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// - Their double fingerprints are close to each other.</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="keywordtype">bool</span> AreProportionalCandidates(ColumnFingerprint <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>, ColumnFingerprint <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>,</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> (<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.hash != <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>.hash) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">return</span> std::abs(<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>.value - <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>.value) < tolerance;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> }</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  </div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// The fingerprint of a column has two parts:</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// - A hash value of the column non-zero pattern.</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// - A double value which should be the same for two proportional columns</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// modulo numerical errors.</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> ColumnFingerprint ComputeFingerprint(ColIndex <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <span class="keyword">const</span> SparseColumn& column) {</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> non_zero_pattern_hash = 0;</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> min_abs = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::numeric_limits<Fractional>::max</a>();</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_abs = 0.0;</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sum = 0.0;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : column) {</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  non_zero_pattern_hash =</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="namespaceutil__hash.html#aa2ba7114404f5416e797636b0e1eddcd">util_hash::Hash</a>(e.row().value(), non_zero_pattern_hash);</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  sum += e.coefficient();</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  min_abs = <a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">std::min</a>(min_abs, std::abs(e.coefficient()));</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  max_abs = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(max_abs, std::abs(e.coefficient()));</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// The two scaled values are in [0, 1].</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// TODO(user): A better way to discriminate columns would be to take the</span></div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// scalar product with a constant but random vector scaled by max_abs.</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <a class="code" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(0.0, max_abs);</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> inverse_dynamic_range = min_abs / max_abs;</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> scaled_average =</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  std::abs(sum) /</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  (<span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(column.num_entries().value()) * max_abs);</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">return</span> ColumnFingerprint(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, non_zero_pattern_hash,</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  inverse_dynamic_range + scaled_average);</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> }</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> } <span class="comment">// namespace</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  </div>
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<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#ac9bef291f9b941569978d0f075144abf"> 115</a></span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> <a class="code" href="namespaceoperations__research_1_1glop.html#ac9bef291f9b941569978d0f075144abf">FindProportionalColumns</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix,</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keyword">const</span> ColIndex num_cols = matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> mapping(num_cols, <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// Compute the fingerprint of each columns and sort them.</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  std::vector<ColumnFingerprint> fingerprints;</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">if</span> (!matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) {</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  fingerprints.push_back(ComputeFingerprint(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)));</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  }</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  std::sort(fingerprints.begin(), fingerprints.end());</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  </div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// Find a representative of each proportional columns class. This only</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">// compares columns with a close-enough fingerprint.</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < fingerprints.size(); ++i) {</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keyword">const</span> ColIndex col_a = fingerprints[i].col;</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">if</span> (mapping[col_a] != <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < fingerprints.size(); ++j) {</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keyword">const</span> ColIndex col_b = fingerprints[j].col;</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keywordflow">if</span> (mapping[col_b] != <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  </div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// Note that we use the same tolerance for the fingerprints.</span></div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// TODO(user): Derive precise bounds on what this tolerance should be so</span></div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">// that no proportional columns are missed.</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">if</span> (!AreProportionalCandidates(fingerprints[i], fingerprints[j],</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  tolerance)) {</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">if</span> (AreColumnsProportional(matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(col_a), matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(col_b),</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  tolerance)) {</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  mapping[col_b] = col_a;</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  }</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  }</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  }</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  </div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// Sort the mapping so that the representative of each class is the smallest</span></div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// column. To achieve this, the current representative is used as a pointer</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// to the new one, a bit like in an union find algorithm.</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">if</span> (mapping[<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] == <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keyword">const</span> ColIndex new_representative = mapping[mapping[<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]];</div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">if</span> (new_representative != <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  mapping[<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = new_representative;</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">if</span> (mapping[<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] > <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  mapping[mapping[<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]] = <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  mapping[<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>;</div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  }</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  }</div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">return</span> mapping;</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> }</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  </div>
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<div class="line"><a name="l00171"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a1ee4943cf389e6ff8159924ea5b048e1"> 171</a></span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a1ee4943cf389e6ff8159924ea5b048e1">FindProportionalColumnsUsingSimpleAlgorithm</a>(</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance) {</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">const</span> ColIndex num_cols = matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">ColMapping</a> mapping(num_cols, <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">for</span> (ColIndex col_a(0); col_a < num_cols; ++col_a) {</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">if</span> (matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(col_a).<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">if</span> (mapping[col_a] != <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">for</span> (ColIndex col_b(col_a + 1); col_b < num_cols; ++col_b) {</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">if</span> (matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(col_b).<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a8e12342fc420701fbffd97025421575a">IsEmpty</a>()) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">if</span> (mapping[col_b] != <a class="code" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">if</span> (AreColumnsProportional(matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(col_a), matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(col_b),</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  tolerance)) {</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  mapping[col_b] = col_a;</div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  }</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  }</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">return</span> mapping;</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> }</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  </div>
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<div class="line"><a name="l00190"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a9f2b788a9c67a4c71cb7e75b54aea27f"> 190</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a9f2b788a9c67a4c71cb7e75b54aea27f">AreFirstColumnsAndRowsExactlyEquals</a>(RowIndex num_rows, ColIndex num_cols,</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix_a,</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& matrix_b) {</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="comment">// TODO(user): Also DCHECK() that matrix_b is ordered by rows.</span></div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a5e016d204d43b2cc4a2773c25462968a">IsCleanedUp</a>());</div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">if</span> (num_rows > matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>() || num_rows > matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>() ||</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  num_cols > matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() || num_cols > matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>()) {</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& col_a = matrix_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& col_b = matrix_b.<a class="code" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">const</span> EntryIndex end = <a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">std::min</a>(col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>(), col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>());</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordflow">if</span> (end < col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() && col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(end) < num_rows) {</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  }</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">if</span> (end < col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() && col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(end) < num_rows) {</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  }</div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keywordflow">for</span> (EntryIndex i(0); i < end; ++i) {</div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">if</span> (col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i) != col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i)) {</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordflow">if</span> (col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i) < num_rows || col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i) < num_rows) {</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  }</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  }</div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">if</span> (col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(i) != col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(i)) {</div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  }</div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">if</span> (col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() > end && col_a.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(end) < num_rows) {</div>
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  }</div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">if</span> (col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() > end && col_b.<a class="code" href="classoperations__research_1_1glop_1_1_column_view.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(end) < num_rows) {</div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  }</div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  }</div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  }</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> }</div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div>
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<div class="line"><a name="l00231"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a15dfa7820af8e00b9624297be497f95a"> 231</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a15dfa7820af8e00b9624297be497f95a">IsRightMostSquareMatrixIdentity</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>& matrix) {</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a5e016d204d43b2cc4a2773c25462968a">IsCleanedUp</a>());</div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">if</span> (matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>().value() > matrix.<a class="code" 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>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">const</span> ColIndex first_identity_col =</div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() - <a class="code" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>());</div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = first_identity_col; <a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(); ++<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& column = matrix.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">column</a>(<a class="code" href="matrix__utils_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">if</span> (column.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_vector.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() != 1 ||</div>
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  column.<a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(EntryIndex(0)) != 1.0) {</div>
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<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div>
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<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  }</div>
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<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> }</div>
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<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  </div>
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<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> } <span class="comment">// namespace glop</span></div>
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<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a021e695f54a13bd809c34b2f4ca87c37"><div class="ttname"><a href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a></div><div class="ttdeci">int64 min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00138">alldiff_cst.cc:138</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a9d0c202d5fdd62f4fa2c613339ff168a"><div class="ttname"><a href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a></div><div class="ttdeci">int64 max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="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#l00886">base/logging.h:886</a></div></div>
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<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#l00884">base/logging.h:884</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_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>
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<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>
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<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>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">operations_research::glop::CompactSparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00288">sparse.h:288</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00345">sparse.h:345</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00344">sparse.h:344</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_afbe7c81d6b4066bf7874299a0f7c0d59"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">operations_research::glop::CompactSparseMatrix::column</a></div><div class="ttdeci">ColumnView column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00364">sparse.h:364</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_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_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>
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<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>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html">operations_research::glop::SparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00061">sparse.h:61</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::SparseMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00177">sparse.h:177</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_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_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::SparseMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00176">sparse.h:176</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_adc6b282d2cc7afc75b60ee44a6bfb2ac"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#adc6b282d2cc7afc75b60ee44a6bfb2ac">operations_research::glop::SparseMatrix::column</a></div><div class="ttdeci">const SparseColumn & column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00180">sparse.h:180</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_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="sparse__vector_8h_source.html#l00529">sparse_vector.h:529</a></div></div>
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<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< RowIndex, SparseColumnIterator >::Entry</a></div><div class="ttdeci">typename Iterator::Entry Entry</div><div class="ttdef"><b>Definition:</b> <a href="sparse__vector_8h_source.html#l00091">sparse_vector.h:91</a></div></div>
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<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="sparse__vector_8h_source.html#l00270">sparse_vector.h:270</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, ColIndex ></a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a344010e26426d6a13411648d988bc9b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a></div><div class="ttdeci">int64 b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00043">constraint_solver/table.cc:43</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_af730895c6c6ef6e03caaf6251192dfd2"><div class="ttname"><a href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a></div><div class="ttdeci">int64 a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00042">constraint_solver/table.cc:42</a></div></div>
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<div class="ttc" id="ahash_8h_html"><div class="ttname"><a href="hash_8h.html">hash.h</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_a7cde0074dfd288f2d70c0e035dacb28a"><div class="ttname"><a href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a></div><div class="ttdeci">int64_t int64</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00034">integral_types.h:34</a></div></div>
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<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#l00059">matrix_utils.cc:59</a></div></div>
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<div class="ttc" id="amatrix__utils_8cc_html_ad96c5e641806a06a23e5d5b9fca20e89"><div class="ttname"><a href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a></div><div class="ttdeci">int64 hash</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00060">matrix_utils.cc:60</a></div></div>
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<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#l00061">matrix_utils.cc:61</a></div></div>
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<div class="ttc" id="amatrix__utils_8h_html"><div class="ttname"><a href="matrix__utils_8h.html">matrix_utils.h</a></div></div>
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<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 &matrix)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00231">matrix_utils.cc:231</a></div></div>
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<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 &matrix, Fractional tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00171">matrix_utils.cc:171</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00077">lp_types.h:77</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a8fbc9efd86a3cc862a9079d86ab8b524"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">operations_research::glop::RowToColIndex</a></div><div class="ttdeci">ColIndex RowToColIndex(RowIndex row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00048">lp_types.h:48</a></div></div>
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<div class="ttc" id="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 &matrix_a, const CompactSparseMatrix &matrix_b)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00190">matrix_utils.cc:190</a></div></div>
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<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 &matrix, Fractional tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__utils_8cc_source.html#l00115">matrix_utils.cc:115</a></div></div>
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<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>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="anamespaceutil__hash_html_aa2ba7114404f5416e797636b0e1eddcd"><div class="ttname"><a href="namespaceutil__hash.html#aa2ba7114404f5416e797636b0e1eddcd">util_hash::Hash</a></div><div class="ttdeci">uint64 Hash(uint64 num, uint64 c)</div><div class="ttdef"><b>Definition:</b> <a href="hash_8h_source.html#l00150">hash.h:150</a></div></div>
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