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142 lines
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<a href="lp__data_2lp__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 2010-2021 Google LLC</span></div><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><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><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><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><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><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><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><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><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><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><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "<a class="code" href="lp__data_2lp__utils_8h.html">ortools/lp_data/lp_utils.h</a>"</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include "<a class="code" href="sparse__column_8h.html">ortools/lp_data/sparse_column.h</a>"</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span>glop {</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SparseColumnLike></div><div class="line"><a name="l00022"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a8398b224d64679ea8551369a9a060ef0"> 22</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a8398b224d64679ea8551369a9a060ef0">SquaredNormTemplate</a>(<span class="keyword">const</span> SparseColumnLike& column) {</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sum(0.0);</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</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><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  sum += <a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(e.coefficient());</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  }</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordflow">return</span> sum;</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> }</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> </div><div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77"> 30</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">SquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& v) {</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">return</span> SquaredNormTemplate<SparseColumn>(v);</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> }</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#aa5483e2b5fdf708e43f09d5d8b0173dd"> 34</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">SquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& v) {</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">return</span> SquaredNormTemplate<ColumnView>(v);</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> }</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div><div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1"> 38</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">PreciseSquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& v) {</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <a class="code" href="classoperations__research_1_1_accurate_sum.html">KahanSum</a> sum;</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</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 : v) {</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  sum.<a class="code" href="classoperations__research_1_1_accurate_sum.html#acc8fad1f98b885fa7d0504f4dfc71f08">Add</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(e.coefficient()));</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">return</span> sum.<a class="code" href="classoperations__research_1_1_accurate_sum.html#a176a3e919acd979b67cea1ede094cdaa">Value</a>();</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> }</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div><div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a933fb20dae58928ca1840e8c52d2e715"> 46</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">PreciseSquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& v) {</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordflow">if</span> (v.<a class="code" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a73934bd40690bdc3cbe36d6fbb0ecad5">ShouldUseDenseIteration</a>()) {</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">PreciseSquaredNorm</a>(v.<a class="code" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  }</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <a class="code" href="classoperations__research_1_1_accurate_sum.html">KahanSum</a> sum;</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> : v.<a class="code" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>) {</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  sum.<a class="code" href="classoperations__research_1_1_accurate_sum.html#acc8fad1f98b885fa7d0504f4dfc71f08">Add</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(v[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]));</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  }</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">return</span> sum.<a class="code" href="classoperations__research_1_1_accurate_sum.html#a176a3e919acd979b67cea1ede094cdaa">Value</a>();</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> }</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div><div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a30f9e66ddf3f771b82fd3aebe39f9a00"> 57</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">SquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& column) {</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sum(0.0);</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0);</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">const</span> <span class="keywordtype">size_t</span> num_blocks = column.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>().value() / 4;</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < num_blocks; ++i) {</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// See the comment in ScalarProduct in the header for some notes about the</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// effect of adding up several squares at a time.</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  sum += <a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(column[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>++]) + <a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(column[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>++]) +</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(column[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>++]) + <a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(column[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>++]);</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  }</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">while</span> (<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < column.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>()) {</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  sum += <a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(column[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>++]);</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  }</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">return</span> sum;</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> }</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div><div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a1e19c170ba82a38048a3f8ef9139da64"> 73</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">PreciseSquaredNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& column) {</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="code" href="classoperations__research_1_1_accurate_sum.html">KahanSum</a> sum;</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">for</span> (RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < column.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(); ++<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  sum.<a class="code" href="classoperations__research_1_1_accurate_sum.html#acc8fad1f98b885fa7d0504f4dfc71f08">Add</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(column[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]));</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">return</span> sum.<a class="code" href="classoperations__research_1_1_accurate_sum.html#a176a3e919acd979b67cea1ede094cdaa">Value</a>();</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> }</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div><div class="line"><a name="l00081"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb"> 81</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">InfinityNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& v) {</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> infinity_norm = 0.0;</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">for</span> (RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < v.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(); ++<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  infinity_norm = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(infinity_norm, fabs(v[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]));</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  }</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">return</span> infinity_norm;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> }</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SparseColumnLike></div><div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a62aa07f8404dcd8e900f6f7b2d85c47f"> 90</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a62aa07f8404dcd8e900f6f7b2d85c47f">InfinityNormTemplate</a>(<span class="keyword">const</span> SparseColumnLike& column) {</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> infinity_norm = 0.0;</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</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><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  infinity_norm = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(infinity_norm, fabs(e.coefficient()));</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  }</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> infinity_norm;</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> }</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div><div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a65e1aee226f34cc6b121b4296ad8851e"> 98</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">InfinityNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& v) {</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">return</span> InfinityNormTemplate<SparseColumn>(v);</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> }</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div><div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a45cc06be815d8ff90e4b808625b2e75f"> 102</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">InfinityNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& v) {</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">return</span> InfinityNormTemplate<ColumnView>(v);</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> }</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div><div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a6b36bbbcd695191600dab9b88487ff18"> 106</a></span> <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a6b36bbbcd695191600dab9b88487ff18">Density</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">if</span> (<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>.empty()) <span class="keywordflow">return</span> 0.0;</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordtype">int</span> sum = 0.0;</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>.size(); ++<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">if</span> (<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(0.0)) ++sum;</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> static_cast<double>(sum) / <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>.size().value();</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> }</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div><div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a5e79e30b7239adc4fb2a27778335bca0"> 115</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a5e79e30b7239adc4fb2a27778335bca0">RemoveNearZeroEntries</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> threshold, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">if</span> (threshold == <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(0.0)) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">for</span> (ColIndex <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>->size(); ++<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">if</span> (fabs((*<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) < threshold) {</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  (*row)[<a class="code" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(0.0);</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  }</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span> }</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> </div><div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#ab6584860b9b9b015f69a69dd42fdf098"> 124</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a5e79e30b7239adc4fb2a27778335bca0">RemoveNearZeroEntries</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> threshold, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* column) {</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">if</span> (threshold == <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(0.0)) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">for</span> (RowIndex <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < column-><a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(); ++<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">if</span> (fabs((*column)[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]) < threshold) {</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  (*column)[<a class="code" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(0.0);</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  }</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  }</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> }</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> </div><div class="line"><a name="l00133"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#ad8019bac1bde0ead6ff32980cd5bff52"> 133</a></span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="namespaceoperations__research_1_1glop.html#ad8019bac1bde0ead6ff32980cd5bff52">RestrictedInfinityNorm</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& column,</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a>& rows_to_consider,</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  RowIndex* row_index) {</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> infinity_norm = 0.0;</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</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><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">if</span> (rows_to_consider[e.row()] && fabs(e.coefficient()) > infinity_norm) {</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  infinity_norm = fabs(e.coefficient());</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  *row_index = e.row();</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  }</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  }</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">return</span> infinity_norm;</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> }</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div><div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a82b6c13b99cf0a0c7c92f4f1e44eda29"> 146</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a82b6c13b99cf0a0c7c92f4f1e44eda29">SetSupportToFalse</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& column, <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a>* <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</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><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">if</span> (e.coefficient() != 0.0) {</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  (*b)[e.row()] = <span class="keyword">false</span>;</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  }</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> }</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div><div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1glop.html#a9a9b90bb0105347953a41ae1d6f4dce3"> 154</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a9a9b90bb0105347953a41ae1d6f4dce3">IsDominated</a>(<span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& column, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& radius) {</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</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><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(radius[e.row()], 0.0);</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">if</span> (fabs(e.coefficient()) > radius[e.row()]) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  }</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> }</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> </div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> } <span class="comment">// namespace glop</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> } <span class="comment">// namespace operations_research</span></div><div class="ttc" id="namespaceoperations__research_1_1glop_html_a2ad7ea612bc859f5b637d5029fb875fb"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">operations_research::glop::InfinityNorm</a></div><div class="ttdeci">Fractional InfinityNorm(const DenseColumn &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00081">lp_data/lp_utils.cc:81</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_accurate_sum_html_acc8fad1f98b885fa7d0504f4dfc71f08"><div class="ttname"><a href="classoperations__research_1_1_accurate_sum.html#acc8fad1f98b885fa7d0504f4dfc71f08">operations_research::AccurateSum::Add</a></div><div class="ttdeci">void Add(const FpNumber &value)</div><div class="ttdef"><b>Definition:</b> <a href="accurate__sum_8h_source.html#l00029">accurate_sum.h:29</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_accurate_sum_html"><div class="ttname"><a href="classoperations__research_1_1_accurate_sum.html">operations_research::AccurateSum< Fractional ></a></div></div>
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<div class="ttc" id="structoperations__research_1_1glop_1_1_scattered_vector_html_a73934bd40690bdc3cbe36d6fbb0ecad5"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#a73934bd40690bdc3cbe36d6fbb0ecad5">operations_research::glop::ScatteredVector::ShouldUseDenseIteration</a></div><div class="ttdeci">bool ShouldUseDenseIteration(double ratio_for_using_dense_representation) const</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00119">scattered_vector.h:119</a></div></div>
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<div class="ttc" id="markowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_ad8019bac1bde0ead6ff32980cd5bff52"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ad8019bac1bde0ead6ff32980cd5bff52">operations_research::glop::RestrictedInfinityNorm</a></div><div class="ttdeci">Fractional RestrictedInfinityNorm(const ColumnView &column, const DenseBooleanColumn &rows_to_consider, RowIndex *row_index)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00133">lp_data/lp_utils.cc:133</a></div></div>
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<div class="ttc" id="markowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a8398b224d64679ea8551369a9a060ef0"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a8398b224d64679ea8551369a9a060ef0">operations_research::glop::SquaredNormTemplate</a></div><div class="ttdeci">Fractional SquaredNormTemplate(const SparseColumnLike &column)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00022">lp_data/lp_utils.cc:22</a></div></div>
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<div class="ttc" id="constraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a5e79e30b7239adc4fb2a27778335bca0"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a5e79e30b7239adc4fb2a27778335bca0">operations_research::glop::RemoveNearZeroEntries</a></div><div class="ttdeci">void RemoveNearZeroEntries(Fractional threshold, DenseRow *row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00115">lp_data/lp_utils.cc:115</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a1faa927dd93b43b3dea3eb2a993e30a1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">operations_research::glop::PreciseSquaredNorm</a></div><div class="ttdeci">Fractional PreciseSquaredNorm(const SparseColumn &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00038">lp_data/lp_utils.cc:38</a></div></div>
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<div class="ttc" id="alldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="classoperations__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="classoperations__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="structoperations__research_1_1glop_1_1_scattered_vector_html_ae0473e18a367af671dc3f08063c80da4"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">operations_research::glop::ScatteredVector::values</a></div><div class="ttdeci">StrictITIVector< Index, Fractional > values</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00057">scattered_vector.h:57</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a82b6c13b99cf0a0c7c92f4f1e44eda29"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a82b6c13b99cf0a0c7c92f4f1e44eda29">operations_research::glop::SetSupportToFalse</a></div><div class="ttdeci">void SetSupportToFalse(const ColumnView &column, DenseBooleanColumn *b)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00146">lp_data/lp_utils.cc:146</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295"><div class="ttname"><a href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a></div><div class="ttdeci">#define DCHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a6b36bbbcd695191600dab9b88487ff18"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a6b36bbbcd695191600dab9b88487ff18">operations_research::glop::Density</a></div><div class="ttdeci">double Density(const DenseRow &row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00106">lp_data/lp_utils.cc:106</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector</a></div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00256">lp_types.h:256</a></div></div>
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<div class="ttc" id="structoperations__research_1_1glop_1_1_scattered_column_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_column.html">operations_research::glop::ScatteredColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00196">scattered_vector.h:196</a></div></div>
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<div class="ttc" id="sparse__column_8h_html"><div class="ttname"><a href="sparse__column_8h.html">sparse_column.h</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a1dcd08b0f6c19cd4a302bb5a3a6ea06e"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">operations_research::glop::Square</a></div><div class="ttdeci">Fractional Square(Fractional f)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00036">lp_data/lp_utils.h:36</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a9a9b90bb0105347953a41ae1d6f4dce3"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a9a9b90bb0105347953a41ae1d6f4dce3">operations_research::glop::IsDominated</a></div><div class="ttdeci">bool IsDominated(const ColumnView &column, const DenseColumn &radius)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00154">lp_data/lp_utils.cc:154</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a2d53948bf5e999d006e781105aa8bc77"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">operations_research::glop::SquaredNorm</a></div><div class="ttdeci">Fractional SquaredNorm(const SparseColumn &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00030">lp_data/lp_utils.cc:30</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a62aa07f8404dcd8e900f6f7b2d85c47f"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a62aa07f8404dcd8e900f6f7b2d85c47f">operations_research::glop::InfinityNormTemplate</a></div><div class="ttdeci">Fractional InfinityNormTemplate(const SparseColumnLike &column)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00090">lp_data/lp_utils.cc:90</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00280">lp_types.h:280</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_accurate_sum_html_a176a3e919acd979b67cea1ede094cdaa"><div class="ttname"><a href="classoperations__research_1_1_accurate_sum.html#a176a3e919acd979b67cea1ede094cdaa">operations_research::AccurateSum::Value</a></div><div class="ttdeci">FpNumber Value() const</div><div class="ttdef"><b>Definition:</b> <a href="accurate__sum_8h_source.html#l00037">accurate_sum.h:37</a></div></div>
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<div class="ttc" id="lp__data_2lp__utils_8h_html"><div class="ttname"><a href="lp__data_2lp__utils_8h.html">lp_utils.h</a></div></div>
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<div class="ttc" id="structoperations__research_1_1glop_1_1_scattered_vector_html_ac146d47daa294f7e6546c7569c9c881b"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">operations_research::glop::ScatteredVector::non_zeros</a></div><div class="ttdeci">std::vector< Index > non_zeros</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00062">scattered_vector.h:62</a></div></div>
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<div class="ttc" id="classoperations__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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