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<a href="matrix__scaler_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "<a class="code" href="matrix__scaler_8h.html">ortools/lp_data/matrix_scaler.h</a>"</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include "absl/strings/str_format.h"</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "<a class="code" href="strong__vector_8h.html">ortools/base/strong_vector.h</a>"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="revised__simplex_8h.html">ortools/glop/revised_simplex.h</a>"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="lp__data_2lp__utils_8h.html">ortools/lp_data/lp_utils.h</a>"</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include "<a class="code" href="sparse_8h.html">ortools/lp_data/sparse.h</a>"</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "<a class="code" href="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa5d52693bed51c5fb6e84c99a23799b5"> 31</a></span><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa5d52693bed51c5fb6e84c99a23799b5">SparseMatrixScaler::SparseMatrixScaler</a>()</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> : matrix_(nullptr), row_scale_(), col_scale_() {}</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a2dd7d09e2fe8d71850baa854b0edbf27"> 34</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a2dd7d09e2fe8d71850baa854b0edbf27">SparseMatrixScaler::Init</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_matrix.html">SparseMatrix</a>* matrix) {</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> matrix_ = matrix;</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> row_scale_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), 1.0);</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> col_scale_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(), 1.0);</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span>}</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa71d36872f416feaa853788a7a7a7ef8"> 41</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa71d36872f416feaa853788a7a7a7ef8">SparseMatrixScaler::Clear</a>() {</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> matrix_ = <span class="keyword">nullptr</span>;</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> row_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> col_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>}</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ada52fc5d004939ec0a71b5302434af02"> 47</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ada52fc5d004939ec0a71b5302434af02">SparseMatrixScaler::RowUnscalingFactor</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, 0);</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < row_scale_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>() ? row_scale_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] : 1.0;</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span>}</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ac9e0ca12adc5a8695b7c203049ae6f56"> 52</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ac9e0ca12adc5a8695b7c203049ae6f56">SparseMatrixScaler::ColUnscalingFactor</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, 0);</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < col_scale_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>() ? col_scale_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] : 1.0;</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span>}</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a00be4687c662ab91018b1901422968ef"> 57</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a00be4687c662ab91018b1901422968ef">SparseMatrixScaler::RowScalingFactor</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ada52fc5d004939ec0a71b5302434af02">RowUnscalingFactor</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>}</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a0fda0916591d196bc6a237a40c89dc2b"> 61</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a0fda0916591d196bc6a237a40c89dc2b">SparseMatrixScaler::ColScalingFactor</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ac9e0ca12adc5a8695b7c203049ae6f56">ColUnscalingFactor</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>}</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>std::string SparseMatrixScaler::DebugInformationString()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// Note that some computations are redundant with the computations made in</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// some callees, but we do not care as this function is supposed to be called</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// with FLAGS_v set to 1.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(!row_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>());</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(!col_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>());</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_magnitude;</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> min_magnitude;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6ae7b0836055b9b6d182115027d496f9">ComputeMinAndMaxMagnitudes</a>(&min_magnitude, &max_magnitude);</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> dynamic_range = max_magnitude / min_magnitude;</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> std::string output = absl::StrFormat(</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="stringliteral">"Min magnitude = %g, max magnitude = %g\n"</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="stringliteral">"Dynamic range = %g\n"</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="stringliteral">"Variance = %g\n"</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="stringliteral">"Minimum row scale = %g, maximum row scale = %g\n"</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="stringliteral">"Minimum col scale = %g, maximum col scale = %g\n"</span>,</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> min_magnitude, max_magnitude, dynamic_range,</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3">VarianceOfAbsoluteValueOfNonZeros</a>(),</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> *std::min_element(row_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ad69bd11391be1a1dba5c8202259664f8">begin</a>(), row_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#acad38d52497a975bfb6f2f6acd76631f">end</a>()),</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> *std::max_element(row_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ad69bd11391be1a1dba5c8202259664f8">begin</a>(), row_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#acad38d52497a975bfb6f2f6acd76631f">end</a>()),</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> *std::min_element(col_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ad69bd11391be1a1dba5c8202259664f8">begin</a>(), col_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#acad38d52497a975bfb6f2f6acd76631f">end</a>()),</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> *std::max_element(col_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#ad69bd11391be1a1dba5c8202259664f8">begin</a>(), col_scale_.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#acad38d52497a975bfb6f2f6acd76631f">end</a>()));</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">return</span> output;</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span>}</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#abc0a90242ca4f46222e707202f7918b0"> 90</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#abc0a90242ca4f46222e707202f7918b0">SparseMatrixScaler::Scale</a>(<a class="code hl_enumeration" href="namespaceoperations__research_1_1glop.html#a8d4212c24c21b25a11a4c119273df998">GlopParameters::ScalingAlgorithm</a> method) {</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// This is an implementation of the algorithm described in</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// Benichou, M., Gauthier, J-M., Hentges, G., and Ribiere, G.,</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// "The efficient solution of large-scale linear programming problems —</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// some algorithmic techniques and computational results,"</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// Mathematical Programming 13(3) (December 1977).</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// http://www.springerlink.com/content/j3367676856m0064/</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_magnitude;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> min_magnitude;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6ae7b0836055b9b6d182115027d496f9">ComputeMinAndMaxMagnitudes</a>(&min_magnitude, &max_magnitude);</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (min_magnitude == 0.0) {</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(0.0, max_magnitude);</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">return</span>; <span class="comment">// Null matrix: nothing to do.</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> }</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Before scaling:\n"</span> << DebugInformationString();</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">if</span> (method == <a class="code hl_variable" href="classoperations__research_1_1glop_1_1_glop_parameters.html#a210d1aecb683a5dbbe8b91cd2df107c8">GlopParameters::LINEAR_PROGRAM</a>) {</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> lp_status = <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a4eedd0e414498a0b6bc4f2ce2143da72">LPScale</a>();</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// Revert to the default scaling method if there is an error with the LP.</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">if</span> (lp_status.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a03cb7eaa663dc83af68bc28a596d09e6">ok</a>()) {</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Error with LP scaling: "</span> << lp_status.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#abc9cf268b3c06dff63be23f21995a892">error_message</a>();</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> }</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// TODO(user): Decide precisely for which value of dynamic range we should cut</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// off geometric scaling.</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> dynamic_range = max_magnitude / min_magnitude;</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kMaxDynamicRangeForGeometricScaling = 1e20;</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (dynamic_range < kMaxDynamicRangeForGeometricScaling) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">const</span> <span class="keywordtype">int</span> kScalingIterations = 4;</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kVarianceThreshold(10.0);</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> iteration = 0; iteration < kScalingIterations; ++iteration) {</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keyword">const</span> RowIndex num_rows_scaled = <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aeaa021fae3560c48754bc32bfc54978c">ScaleRowsGeometrically</a>();</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">const</span> ColIndex num_cols_scaled = <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a8b4373d64f8f8f3a6480e9ae4e2a6a2e">ScaleColumnsGeometrically</a>();</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> variance = <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3">VarianceOfAbsoluteValueOfNonZeros</a>();</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Geometric scaling iteration "</span> << iteration</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> << <span class="stringliteral">". Rows scaled = "</span> << num_rows_scaled</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> << <span class="stringliteral">", columns scaled = "</span> << num_cols_scaled << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << DebugInformationString();</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">if</span> (variance < kVarianceThreshold ||</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> (num_cols_scaled == 0 && num_rows_scaled == 0)) {</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> }</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> }</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> RowIndex rows_equilibrated = <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a89b5d413f7e1aa8426e85143a37b54dc">EquilibrateRows</a>();</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> ColIndex cols_equilibrated = <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a6a8ddd97065e27d7f8e5013aaa59fb24">EquilibrateColumns</a>();</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Equilibration step: Rows scaled = "</span> << rows_equilibrated</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> << <span class="stringliteral">", columns scaled = "</span> << cols_equilibrated << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << DebugInformationString();</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span>}</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="keyword">template</span> <<span class="keyword">class</span> I></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="keywordtype">void</span> ScaleVector(<span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<I, Fractional></a>& scale, <span class="keywordtype">bool</span> up,</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<I, Fractional></a>* vector_to_scale) {</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <a class="code hl_define" href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a>(vector_to_scale);</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keyword">const</span> I size(<a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(scale.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a60304b65bf89363bcc3165d3cde67f86">size</a>(), vector_to_scale-><a class="code hl_function" href="classabsl_1_1_strong_vector.html#a60304b65bf89363bcc3165d3cde67f86">size</a>()));</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">if</span> (up) {</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">for</span> (I i(0); i < size; ++i) {</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> (*vector_to_scale)[i] *= scale[i];</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> }</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">for</span> (I i(0); i < size; ++i) {</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> (*vector_to_scale)[i] /= scale[i];</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> }</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> }</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span>}</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="keyword">template</span> <<span class="keyword">typename</span> InputIndexType></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span>ColIndex CreateOrGetScaleIndex(</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> InputIndexType num, LinearProgram* lp,</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<InputIndexType, ColIndex></a>* scale_var_indices) {</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">if</span> ((*scale_var_indices)[num] == -1) {</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> (*scale_var_indices)[num] = lp->CreateNewVariable();</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> }</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">return</span> (*scale_var_indices)[num];</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span>}</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span>} <span class="comment">// anonymous namespace</span></div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> </div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a57b3fbbeb1e0b5a127cc94694aad586e"> 171</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a57b3fbbeb1e0b5a127cc94694aad586e">SparseMatrixScaler::ScaleRowVector</a>(<span class="keywordtype">bool</span> up, <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* row_vector)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(row_vector != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> ScaleVector(col_scale_, up, row_vector);</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span>}</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a150a7b18071b89f90d47aa00b679edc9"> 176</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a150a7b18071b89f90d47aa00b679edc9">SparseMatrixScaler::ScaleColumnVector</a>(<span class="keywordtype">bool</span> up,</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* column_vector)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(column_vector != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> ScaleVector(row_scale_, up, column_vector);</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span>}</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> </div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3"> 182</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3">SparseMatrixScaler::VarianceOfAbsoluteValueOfNonZeros</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sigma_square(0.0);</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sigma_abs(0.0);</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordtype">double</span> n = 0.0; <span class="comment">// n is used in a calculation involving doubles.</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> magnitude = fabs(e.coefficient());</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordflow">if</span> (magnitude != 0.0) {</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> sigma_square += magnitude * magnitude;</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> sigma_abs += magnitude;</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> ++n;</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> }</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> }</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">if</span> (n == 0.0) <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// Since we know all the population (the non-zeros) and we are not using a</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// sample, the variance is defined as below.</span></div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// For an explanation, see:</span></div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="comment">// http://en.wikipedia.org/wiki/Variance</span></div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// #Population_variance_and_sample_variance</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordflow">return</span> (sigma_square - sigma_abs * sigma_abs / n) / n;</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span>}</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> </div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span><span class="comment">// For geometric scaling, we compute the maximum and minimum magnitudes</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span><span class="comment">// of non-zeros in a row (resp. column). Let us denote these numbers as</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="comment">// max and min. We then scale the row (resp. column) by dividing the</span></div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="comment">// coefficients by sqrt(min * max).</span></div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aeaa021fae3560c48754bc32bfc54978c"> 212</a></span>RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aeaa021fae3560c48754bc32bfc54978c">SparseMatrixScaler::ScaleRowsGeometrically</a>() {</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> max_in_row(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), 0.0);</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> min_in_row(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), <a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> magnitude = fabs(e.coefficient());</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordflow">if</span> (magnitude != 0.0) {</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> max_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>], magnitude);</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> min_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(min_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>], magnitude);</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> }</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> }</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> }</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keyword">const</span> RowIndex num_rows = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> scaling_factor(num_rows, 0.0);</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">if</span> (max_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == 0.0) {</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> scaling_factor[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = 1.0;</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(<a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>, min_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> scaling_factor[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = sqrt(max_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] * min_in_row[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> }</div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> }</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keywordflow">return</span> ScaleMatrixRows(scaling_factor);</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span>}</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a8b4373d64f8f8f3a6480e9ae4e2a6a2e"> 240</a></span>ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a8b4373d64f8f8f3a6480e9ae4e2a6a2e">SparseMatrixScaler::ScaleColumnsGeometrically</a>() {</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> ColIndex num_cols_scaled(0);</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_in_col(0.0);</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> min_in_col(<a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> magnitude = fabs(e.coefficient());</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keywordflow">if</span> (magnitude != 0.0) {</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> max_in_col = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_in_col, magnitude);</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> min_in_col = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(min_in_col, magnitude);</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> }</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> }</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordflow">if</span> (max_in_col != 0.0) {</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> factor(sqrt(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afd6d278f9d061a91716c6770f2d723e8">ToDouble</a>(max_in_col * min_in_col)));</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> ScaleMatrixColumn(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, factor);</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> num_cols_scaled++;</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> }</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> }</div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="keywordflow">return</span> num_cols_scaled;</div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span>}</div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> </div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span><span class="comment">// For equilibration, we compute the maximum magnitude of non-zeros</span></div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span><span class="comment">// in a row (resp. column), and then scale the row (resp. column) by dividing</span></div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span><span class="comment">// the coefficients this maximum magnitude.</span></div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span><span class="comment">// This brings the largest coefficient in a row equal to 1.0.</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> </div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a89b5d413f7e1aa8426e85143a37b54dc"> 268</a></span>RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a89b5d413f7e1aa8426e85143a37b54dc">SparseMatrixScaler::EquilibrateRows</a>() {</div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">const</span> RowIndex num_rows = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> max_magnitude(num_rows, 0.0);</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> magnitude = fabs(e.coefficient());</div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keywordflow">if</span> (magnitude != 0.0) {</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> max_magnitude[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_magnitude[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>], magnitude);</div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> }</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> }</div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> }</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">if</span> (max_magnitude[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == 0.0) {</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> max_magnitude[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = 1.0;</div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> }</div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> }</div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="keywordflow">return</span> ScaleMatrixRows(max_magnitude);</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span>}</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> </div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a6a8ddd97065e27d7f8e5013aaa59fb24"> 290</a></span>ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a6a8ddd97065e27d7f8e5013aaa59fb24">SparseMatrixScaler::EquilibrateColumns</a>() {</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> ColIndex num_cols_scaled(0);</div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_magnitude = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">InfinityNorm</a>(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>));</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">if</span> (max_magnitude != 0.0) {</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> ScaleMatrixColumn(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, max_magnitude);</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> num_cols_scaled++;</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> }</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> }</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="keywordflow">return</span> num_cols_scaled;</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span>}</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> </div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span>RowIndex SparseMatrixScaler::ScaleMatrixRows(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& factors) {</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="comment">// Matrix rows are scaled by dividing their coefficients by factors[row].</span></div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keyword">const</span> RowIndex num_rows = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(num_rows, factors.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>());</div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> RowIndex num_rows_scaled(0);</div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> factor = factors[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(0.0, factor);</div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> <span class="keywordflow">if</span> (factor != 1.0) {</div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> ++num_rows_scaled;</div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> row_scale_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] *= factor;</div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> }</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> }</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> </div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> SparseColumn* <span class="keyword">const</span> column = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="keywordflow">if</span> (column != <span class="keyword">nullptr</span>) {</div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#aa914fdd75c35b81e5df7fba7b9d23925">ComponentWiseDivide</a>(factors);</div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> }</div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> }</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> </div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="keywordflow">return</span> num_rows_scaled;</div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span>}</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> </div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span><span class="keywordtype">void</span> SparseMatrixScaler::ScaleMatrixColumn(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> factor) {</div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> <span class="comment">// A column is scaled by dividing by factor.</span></div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> col_scale_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] *= factor;</div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(0.0, factor);</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> </div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> SparseColumn* <span class="keyword">const</span> column = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="keywordflow">if</span> (column != <span class="keyword">nullptr</span>) {</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a88cf92566c4a4b0281ea82571f4269ad">DivideByConstant</a>(factor);</div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> }</div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span>}</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> </div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aebfa385cb902145ed371b68ce3bf579d"> 342</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aebfa385cb902145ed371b68ce3bf579d">SparseMatrixScaler::Unscale</a>() {</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="comment">// Unscaling is easier than scaling since all scaling factors are stored.</span></div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> column_scale = col_scale_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(0.0, column_scale);</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> </div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* <span class="keyword">const</span> column = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> <span class="keywordflow">if</span> (column != <span class="keyword">nullptr</span>) {</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a997af931ec11394cec3418321c2ecc4b">MultiplyByConstant</a>(column_scale);</div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#a09a2901ab63e665486a0b32347b9fab6">ComponentWiseMultiply</a>(row_scale_);</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> }</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> }</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span>}</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> </div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a4eedd0e414498a0b6bc4f2ce2143da72"> 358</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a4eedd0e414498a0b6bc4f2ce2143da72">SparseMatrixScaler::LPScale</a>() {</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(matrix_ != <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> </div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="keyword">auto</span> linear_program = absl::make_unique<LinearProgram>();</div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_glop_parameters.html">GlopParameters</a> params;</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> <span class="keyword">auto</span> simplex = absl::make_unique<RevisedSimplex>();</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> simplex->SetParameters(params);</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> </div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="comment">// Begin linear program construction.</span></div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> <span class="comment">// Beta represents the largest distance from zero among the constraint pairs.</span></div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> <span class="comment">// It resembles a slack variable because the 'objective' of each constraint is</span></div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="comment">// to cancel out the log "w" of the original nonzero |a_ij| (a.k.a. |a_rc|).</span></div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="comment">// Approaching 0 by addition in log space is the same as approaching 1 by</span></div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="comment">// multiplication in linear space. Hence, each variable's log magnitude is</span></div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="comment">// subtracted from the log row scale and log column scale. If the sum is</span></div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// positive, the positive constraint is trivially satisfied, but the negative</span></div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="comment">// constraint will determine the minimum necessary value of beta for that</span></div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="comment">// variable and scaling factors, and vice versa.</span></div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="comment">// For an MxN matrix, the resulting scaling LP has M+N+1 variables and</span></div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="comment">// O(M*N) constraints (2*M*N at maximum). As a result, using this LP to scale</span></div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <span class="comment">// another linear program, will typically increase the time to</span></div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="comment">// optimization by a factor of 4, and has increased the time of some benchmark</span></div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="comment">// LPs by up to 10.</span></div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> </div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="comment">// Indices to variables in the LinearProgram populated by</span></div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> <span class="comment">// GenerateLinearProgram.</span></div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<ColIndex, ColIndex></a> col_scale_var_indices;</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<RowIndex, ColIndex></a> row_scale_var_indices;</div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> row_scale_var_indices.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a4e3670a285a3642eaa07f66766cffa72">resize</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#af2ae3ca10438618ca2fc81f38dcb80e1">RowToIntIndex</a>(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()), <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> col_scale_var_indices.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a4e3670a285a3642eaa07f66766cffa72">resize</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a62b2a1c80c429da3975f1d948f7c27df">ColToIntIndex</a>(matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>()), <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="keyword">const</span> ColIndex beta = linear_program->CreateNewVariable();</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> linear_program->SetVariableBounds(beta, -<a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>, <a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="comment">// Default objective is to minimize.</span></div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> linear_program->SetObjectiveCoefficient(beta, 1);</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#abfc30f91ab75c6f4552003f777672e74">CleanUp</a>();</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>* <span class="keyword">const</span> column = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">mutable_column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="comment">// This is the variable representing the log of the scale factor for col.</span></div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="keyword">const</span> ColIndex column_scale = CreateOrGetScaleIndex<ColIndex>(</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, linear_program.get(), &col_scale_var_indices);</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> linear_program->SetVariableBounds(column_scale, -<a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>, <a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="keywordflow">for</span> (EntryIndex i : column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab8c57a207c9a5d77dd268bd7018c4971">AllEntryIndices</a>()) {</div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> log_magnitude =</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> log2(std::abs(column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aaef7fc778a29bb3bb3040c0423937f6e">EntryCoefficient</a>(i)));</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> <span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = column-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_column.html#aedc46de5199e203b77de2eae2e4c100d">EntryRow</a>(i);</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <span class="comment">// This is the variable representing the log of the scale factor for row.</span></div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="keyword">const</span> ColIndex row_scale = CreateOrGetScaleIndex<RowIndex>(</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, linear_program.get(), &row_scale_var_indices);</div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> </div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> linear_program->SetVariableBounds(row_scale, -<a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>, <a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="comment">// This is derived from the formulation in</span></div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="comment">// min β</span></div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="comment">// Subject to:</span></div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <span class="comment">// ∀ c∈C, v∈V, p_{c,v} ≠ 0.0, w_{c,v} + s^{var}_v + s^{comb}_c + β ≥ 0.0</span></div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="comment">// ∀ c∈C, v∈V, p_{c,v} ≠ 0.0, w_{c,v} + s^{var}_v + s^{comb}_c ≤ β</span></div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="comment">// If a variable is integer, its scale factor is zero.</span></div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> </div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="comment">// Start with the constraint w_cv + s_c + s_v + beta >= 0.</span></div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> <span class="keyword">const</span> RowIndex positive_constraint =</div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> linear_program->CreateNewConstraint();</div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="comment">// Subtract the constant w_cv from both sides.</span></div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> linear_program->SetConstraintBounds(positive_constraint, -log_magnitude,</div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <span class="comment">// +s_c, meaning (log) scale of the constraint C, pointed by row_scale.</span></div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> linear_program->SetCoefficient(positive_constraint, row_scale, 1);</div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <span class="comment">// +s_v, meaning (log) scale of the variable V, pointed by column_scale.</span></div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> linear_program->SetCoefficient(positive_constraint, column_scale, 1);</div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <span class="comment">// +beta</span></div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> linear_program->SetCoefficient(positive_constraint, beta, 1);</div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> </div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="comment">// Construct the constraint w_cv + s_c + s_v <= beta.</span></div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="keyword">const</span> RowIndex negative_constraint =</div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> linear_program->CreateNewConstraint();</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="comment">// Subtract w (and beta) from both sides.</span></div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> linear_program->SetConstraintBounds(negative_constraint, -<a class="code hl_variable" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>,</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> -log_magnitude);</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> <span class="comment">// +s_c, meaning (log) scale of the constraint C, pointed by row_scale.</span></div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> linear_program->SetCoefficient(negative_constraint, row_scale, 1);</div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="comment">// +s_v, meaning (log) scale of the variable V, pointed by column_scale.</span></div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> linear_program->SetCoefficient(negative_constraint, column_scale, 1);</div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="comment">// -beta</span></div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> linear_program->SetCoefficient(negative_constraint, beta, -1);</div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> }</div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> }</div>
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<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="comment">// End linear program construction.</span></div>
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<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> </div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> linear_program->AddSlackVariablesWhereNecessary(<span class="keyword">false</span>);</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> simplex_status =</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> simplex->Solve(*linear_program, <a class="code hl_function" href="classoperations__research_1_1_time_limit.html#a8e8e386d8f916b1fefb983118cbdf0a6">TimeLimit::Infinite</a>().get());</div>
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<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> <span class="keywordflow">if</span> (!simplex_status.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a03cb7eaa663dc83af68bc28a596d09e6">ok</a>()) {</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> <span class="keywordflow">return</span> simplex_status;</div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> <span class="comment">// Now the solution variables can be interpreted and translated from log</span></div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <span class="comment">// space.</span></div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="comment">// For each row scale, unlog it and scale the constraints and constraint</span></div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="comment">// bounds.</span></div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="keyword">const</span> ColIndex num_cols = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> column_scale =</div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> exp2(-simplex->GetVariableValue(CreateOrGetScaleIndex<ColIndex>(</div>
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, linear_program.get(), &col_scale_var_indices)));</div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> ScaleMatrixColumn(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, column_scale);</div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> }</div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> <span class="keyword">const</span> RowIndex num_rows = matrix_-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> row_scale(num_rows, 0.0);</div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> row_scale[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] =</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> exp2(-simplex->GetVariableValue(CreateOrGetScaleIndex<RowIndex>(</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, linear_program.get(), &row_scale_var_indices)));</div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> }</div>
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<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> ScaleMatrixRows(row_scale);</div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div>
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<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> }</div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span>}</div>
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<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> </div>
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<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</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#l00887">base/logging.h:887</a></div></div>
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<div class="ttc" id="abase_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="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#l00885">base/logging.h:885</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00886">base/logging.h:886</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_afcaa7cadd41741bb855c2ada1d2ef927"><div class="ttname"><a href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a></div><div class="ttdeci">#define VLOG(verboselevel)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00979">base/logging.h:979</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html"><div class="ttname"><a href="classabsl_1_1_strong_vector.html">absl::StrongVector</a></div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00076">strong_vector.h:76</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a4e3670a285a3642eaa07f66766cffa72"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a4e3670a285a3642eaa07f66766cffa72">absl::StrongVector::resize</a></div><div class="ttdeci">void resize(size_type new_size)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00150">strong_vector.h:150</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a60304b65bf89363bcc3165d3cde67f86"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a60304b65bf89363bcc3165d3cde67f86">absl::StrongVector::size</a></div><div class="ttdeci">size_type size() const</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00147">strong_vector.h:147</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a644718bb2fb240de962dc3c9a1fdf0dc"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a644718bb2fb240de962dc3c9a1fdf0dc">absl::StrongVector::empty</a></div><div class="ttdeci">bool empty() const</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00156">strong_vector.h:156</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_ac8bb3912a3ce86b15842e79d0b421204"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">absl::StrongVector::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00170">strong_vector.h:170</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_acad38d52497a975bfb6f2f6acd76631f"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#acad38d52497a975bfb6f2f6acd76631f">absl::StrongVector::end</a></div><div class="ttdeci">iterator end()</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00140">strong_vector.h:140</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_ad69bd11391be1a1dba5c8202259664f8"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#ad69bd11391be1a1dba5c8202259664f8">absl::StrongVector::begin</a></div><div class="ttdeci">iterator begin()</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00138">strong_vector.h:138</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_time_limit_html_a8e8e386d8f916b1fefb983118cbdf0a6"><div class="ttname"><a href="classoperations__research_1_1_time_limit.html#a8e8e386d8f916b1fefb983118cbdf0a6">operations_research::TimeLimit::Infinite</a></div><div class="ttdeci">static std::unique_ptr< TimeLimit > Infinite()</div><div class="ttdoc">Creates a time limit object that uses infinite time for wall time, deterministic time and instruction...</div><div class="ttdef"><b>Definition:</b> <a href="time__limit_8h_source.html#l00134">time_limit.h:134</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_glop_parameters_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html">operations_research::glop::GlopParameters</a></div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l00194">parameters.pb.h:195</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_glop_parameters_html_a210d1aecb683a5dbbe8b91cd2df107c8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_glop_parameters.html#a210d1aecb683a5dbbe8b91cd2df107c8">operations_research::glop::GlopParameters::LINEAR_PROGRAM</a></div><div class="ttdeci">static constexpr ScalingAlgorithm LINEAR_PROGRAM</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l00322">parameters.pb.h:322</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#l00062">sparse.h:62</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::SparseMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00178">sparse.h:178</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a564caf35589006190ef4985fbda74faa"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a564caf35589006190ef4985fbda74faa">operations_research::glop::SparseMatrix::mutable_column</a></div><div class="ttdeci">SparseColumn * mutable_column(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00182">sparse.h:182</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a6ae7b0836055b9b6d182115027d496f9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a6ae7b0836055b9b6d182115027d496f9">operations_research::glop::SparseMatrix::ComputeMinAndMaxMagnitudes</a></div><div class="ttdeci">void ComputeMinAndMaxMagnitudes(Fractional *min_magnitude, Fractional *max_magnitude) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00369">sparse.cc:369</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a7273cc492a51a1c5d45c620b32fce502"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a7273cc492a51a1c5d45c620b32fce502">operations_research::glop::SparseMatrix::column</a></div><div class="ttdeci">const SparseColumn & column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00181">sparse.h:181</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::SparseMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00177">sparse.h:177</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_html_abfc30f91ab75c6f4552003f777672e74"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix.html#abfc30f91ab75c6f4552003f777672e74">operations_research::glop::SparseMatrix::CleanUp</a></div><div class="ttdeci">void CleanUp()</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00119">sparse.cc:119</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a00be4687c662ab91018b1901422968ef"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a00be4687c662ab91018b1901422968ef">operations_research::glop::SparseMatrixScaler::RowScalingFactor</a></div><div class="ttdeci">Fractional RowScalingFactor(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00057">matrix_scaler.cc:57</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a0fda0916591d196bc6a237a40c89dc2b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a0fda0916591d196bc6a237a40c89dc2b">operations_research::glop::SparseMatrixScaler::ColScalingFactor</a></div><div class="ttdeci">Fractional ColScalingFactor(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00061">matrix_scaler.cc:61</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a150a7b18071b89f90d47aa00b679edc9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a150a7b18071b89f90d47aa00b679edc9">operations_research::glop::SparseMatrixScaler::ScaleColumnVector</a></div><div class="ttdeci">void ScaleColumnVector(bool up, DenseColumn *column_vector) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00176">matrix_scaler.cc:176</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a2dd7d09e2fe8d71850baa854b0edbf27"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a2dd7d09e2fe8d71850baa854b0edbf27">operations_research::glop::SparseMatrixScaler::Init</a></div><div class="ttdeci">void Init(SparseMatrix *matrix)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00034">matrix_scaler.cc:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a4eedd0e414498a0b6bc4f2ce2143da72"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a4eedd0e414498a0b6bc4f2ce2143da72">operations_research::glop::SparseMatrixScaler::LPScale</a></div><div class="ttdeci">Status LPScale()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00358">matrix_scaler.cc:358</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a57b3fbbeb1e0b5a127cc94694aad586e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a57b3fbbeb1e0b5a127cc94694aad586e">operations_research::glop::SparseMatrixScaler::ScaleRowVector</a></div><div class="ttdeci">void ScaleRowVector(bool up, DenseRow *row_vector) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00171">matrix_scaler.cc:171</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a6a8ddd97065e27d7f8e5013aaa59fb24"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a6a8ddd97065e27d7f8e5013aaa59fb24">operations_research::glop::SparseMatrixScaler::EquilibrateColumns</a></div><div class="ttdeci">ColIndex EquilibrateColumns()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00290">matrix_scaler.cc:290</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a89b5d413f7e1aa8426e85143a37b54dc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a89b5d413f7e1aa8426e85143a37b54dc">operations_research::glop::SparseMatrixScaler::EquilibrateRows</a></div><div class="ttdeci">RowIndex EquilibrateRows()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00268">matrix_scaler.cc:268</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_a8b4373d64f8f8f3a6480e9ae4e2a6a2e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#a8b4373d64f8f8f3a6480e9ae4e2a6a2e">operations_research::glop::SparseMatrixScaler::ScaleColumnsGeometrically</a></div><div class="ttdeci">ColIndex ScaleColumnsGeometrically()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00240">matrix_scaler.cc:240</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aa5d52693bed51c5fb6e84c99a23799b5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa5d52693bed51c5fb6e84c99a23799b5">operations_research::glop::SparseMatrixScaler::SparseMatrixScaler</a></div><div class="ttdeci">SparseMatrixScaler()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00031">matrix_scaler.cc:31</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::SparseMatrixScaler::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00041">matrix_scaler.cc:41</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_abc0a90242ca4f46222e707202f7918b0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#abc0a90242ca4f46222e707202f7918b0">operations_research::glop::SparseMatrixScaler::Scale</a></div><div class="ttdeci">void Scale(GlopParameters::ScalingAlgorithm method)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00090">matrix_scaler.cc:90</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_ac9e0ca12adc5a8695b7c203049ae6f56"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ac9e0ca12adc5a8695b7c203049ae6f56">operations_research::glop::SparseMatrixScaler::ColUnscalingFactor</a></div><div class="ttdeci">Fractional ColUnscalingFactor(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00052">matrix_scaler.cc:52</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_ada52fc5d004939ec0a71b5302434af02"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#ada52fc5d004939ec0a71b5302434af02">operations_research::glop::SparseMatrixScaler::RowUnscalingFactor</a></div><div class="ttdeci">Fractional RowUnscalingFactor(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00047">matrix_scaler.cc:47</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aeaa021fae3560c48754bc32bfc54978c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aeaa021fae3560c48754bc32bfc54978c">operations_research::glop::SparseMatrixScaler::ScaleRowsGeometrically</a></div><div class="ttdeci">RowIndex ScaleRowsGeometrically()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00212">matrix_scaler.cc:212</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_aebfa385cb902145ed371b68ce3bf579d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#aebfa385cb902145ed371b68ce3bf579d">operations_research::glop::SparseMatrixScaler::Unscale</a></div><div class="ttdeci">void Unscale()</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00342">matrix_scaler.cc:342</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_matrix_scaler_html_af9524ee82f45fb16c26a3e6eb6f32ef3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_matrix_scaler.html#af9524ee82f45fb16c26a3e6eb6f32ef3">operations_research::glop::SparseMatrixScaler::VarianceOfAbsoluteValueOfNonZeros</a></div><div class="ttdeci">Fractional VarianceOfAbsoluteValueOfNonZeros() const</div><div class="ttdef"><b>Definition:</b> <a href="matrix__scaler_8cc_source.html#l00182">matrix_scaler.cc:182</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_a09a2901ab63e665486a0b32347b9fab6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#a09a2901ab63e665486a0b32347b9fab6">operations_research::glop::SparseVector::ComponentWiseMultiply</a></div><div class="ttdeci">void ComponentWiseMultiply(const DenseVector &factors)</div><div class="ttdef"><b>Definition:</b> <a href="sparse__vector_8h_source.html#l00770">sparse_vector.h:770</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_a88cf92566c4a4b0281ea82571f4269ad"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#a88cf92566c4a4b0281ea82571f4269ad">operations_research::glop::SparseVector::DivideByConstant</a></div><div class="ttdeci">void DivideByConstant(Fractional factor)</div><div class="ttdef"><b>Definition:</b> <a href="sparse__vector_8h_source.html#l00778">sparse_vector.h:778</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_a997af931ec11394cec3418321c2ecc4b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#a997af931ec11394cec3418321c2ecc4b">operations_research::glop::SparseVector::MultiplyByConstant</a></div><div class="ttdeci">void MultiplyByConstant(Fractional factor)</div><div class="ttdef"><b>Definition:</b> <a href="sparse__vector_8h_source.html#l00762">sparse_vector.h:762</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_aa914fdd75c35b81e5df7fba7b9d23925"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#aa914fdd75c35b81e5df7fba7b9d23925">operations_research::glop::SparseVector::ComponentWiseDivide</a></div><div class="ttdeci">void ComponentWiseDivide(const DenseVector &factors)</div><div class="ttdef"><b>Definition:</b> <a href="sparse__vector_8h_source.html#l00786">sparse_vector.h:786</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_ab8c57a207c9a5d77dd268bd7018c4971"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab8c57a207c9a5d77dd268bd7018c4971">operations_research::glop::SparseVector::AllEntryIndices</a></div><div class="ttdeci">::util::IntegerRange< EntryIndex > AllEntryIndices() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__vector_8h_source.html#l00302">sparse_vector.h:302</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html">operations_research::glop::Status</a></div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00024">status.h:24</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_a03cb7eaa663dc83af68bc28a596d09e6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a03cb7eaa663dc83af68bc28a596d09e6">operations_research::glop::Status::ok</a></div><div class="ttdeci">bool ok() const</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00059">status.h:59</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_a071b1d04197c0ac6e7a4d0ec0b91ff43"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">operations_research::glop::Status::OK</a></div><div class="ttdeci">static const Status OK()</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00054">status.h:54</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_abc9cf268b3c06dff63be23f21995a892"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#abc9cf268b3c06dff63be23f21995a892">operations_research::glop::Status::error_message</a></div><div class="ttdeci">const std::string & error_message() const</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00058">status.h:58</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, Fractional ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a64b6b04f3a519d2c61d49daaa88bf06e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">operations_research::glop::StrictITIVector::resize</a></div><div class="ttdeci">void resize(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00273">lp_types.h:273</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00280">lp_types.h:280</a></div></div>
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<div class="ttc" id="alp__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="amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
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<div class="ttc" id="amatrix__scaler_8h_html"><div class="ttname"><a href="matrix__scaler_8h.html">matrix_scaler.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__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="anamespaceoperations__research_1_1glop_html_a62b2a1c80c429da3975f1d948f7c27df"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a62b2a1c80c429da3975f1d948f7c27df">operations_research::glop::ColToIntIndex</a></div><div class="ttdeci">Index ColToIntIndex(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00055">lp_types.h:55</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a8d4212c24c21b25a11a4c119273df998"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a8d4212c24c21b25a11a4c119273df998">operations_research::glop::GlopParameters_ScalingAlgorithm</a></div><div class="ttdeci">GlopParameters_ScalingAlgorithm</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8pb_8h_source.html#l00070">parameters.pb.h:70</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_af2ae3ca10438618ca2fc81f38dcb80e1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#af2ae3ca10438618ca2fc81f38dcb80e1">operations_research::glop::RowToIntIndex</a></div><div class="ttdeci">Index RowToIntIndex(RowIndex row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00058">lp_types.h:58</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_af9a790b7e8c5b0c6d55b336177378e78"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">operations_research::glop::kInfinity</a></div><div class="ttdeci">const double kInfinity</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00084">lp_types.h:84</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_1_1glop_html_afd6d278f9d061a91716c6770f2d723e8"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#afd6d278f9d061a91716c6770f2d723e8">operations_research::glop::ToDouble</a></div><div class="ttdeci">static double ToDouble(double f)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00069">lp_types.h:69</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="areturn__macros_8h_html_a6009315499028d98072d8f31834cf4f9"><div class="ttname"><a href="return__macros_8h.html#a6009315499028d98072d8f31834cf4f9">RETURN_IF_NULL</a></div><div class="ttdeci">#define RETURN_IF_NULL(x)</div><div class="ttdef"><b>Definition:</b> <a href="return__macros_8h_source.html#l00020">return_macros.h:20</a></div></div>
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