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<a href="sharded__optimization__utils_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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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="sharded__optimization__utils_8h.html">ortools/pdlp/sharded_optimization_utils.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 <cstdint></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <cstdlib></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <numeric></span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <random></span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "Eigen/Core"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include "Eigen/SparseCore"</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include "absl/algorithm/container.h"</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include "absl/random/distributions.h"</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include "absl/types/optional.h"</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</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="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include "<a class="code" href="mathutil_8h.html">ortools/base/mathutil.h</a>"</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include "<a class="code" href="quadratic__program_8h.html">ortools/pdlp/quadratic_program.h</a>"</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#include "<a class="code" href="sharded__quadratic__program_8h.html">ortools/pdlp/sharded_quadratic_program.h</a>"</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="preprocessor">#include "<a class="code" href="sharder_8h.html">ortools/pdlp/sharder.h</a>"</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research_1_1pdlp.html">operations_research::pdlp</a> {</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1"> 39</a></span><span class="keyword">constexpr</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span>using ::Eigen::ColMajor;</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span>using ::Eigen::SparseMatrix;</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span>using ::Eigen::VectorXd;</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>using ::Eigen::VectorXi;</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#a1e57e9610f2a8aef08167fe8f0501eb8"> 45</a></span><a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#a1e57e9610f2a8aef08167fe8f0501eb8">ShardedWeightedAverage::ShardedWeightedAverage</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>* sharder)</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> : sharder_(sharder) {</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> average_ = <a class="code hl_function" href="namespaceoperations__research.html#a5a9881f8a07b166ef2cbde572cea27b6">VectorXd::Zero</a>(sharder-><a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#ada07b6c423e2d359a22b11df7c9fef0a">NumElements</a>());</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span>}</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// We considered the five averaging algorithms M_* listed on the first page of</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// https://www.jstor.org/stable/2286154 and the Kahan summation algorithm</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// (https://en.wikipedia.org/wiki/Kahan_summation_algorithm). Of these only M_14</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// satisfies our desired property that a constant sequence is averaged without</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// roundoff while requiring only a single vector be stored. We therefore use</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// M_14 (actually a natural weighted generalization, see below).</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#a67840b47c5130550899905f06eba16da"> 56</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#a67840b47c5130550899905f06eba16da">ShardedWeightedAverage::Add</a>(<span class="keyword">const</span> VectorXd& datapoint, <span class="keywordtype">double</span> <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>) {</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(<a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>, 0.0);</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(datapoint.size(), average_.size());</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keyword">const</span> <span class="keywordtype">double</span> weight_ratio = <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a> / (sum_weights_ + <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>);</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> sharder_-><a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>([&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> shard(average_) += weight_ratio * (shard(datapoint) - shard(average_));</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> });</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> sum_weights_ += <a class="code hl_variable" href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a>;</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> ++num_terms_;</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>}</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#aa71d36872f416feaa853788a7a7a7ef8"> 67</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#aa71d36872f416feaa853788a7a7a7ef8">ShardedWeightedAverage::Clear</a>() {</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// TODO(user): There may be a performance gain from using the sharder to</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// zero-out the vectors.</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> average_.setZero();</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> sum_weights_ = 0.0;</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> num_terms_ = 0;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span>}</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#ab1e40710c900002a2cf0af3e6c490bde"> 75</a></span>VectorXd <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#ab1e40710c900002a2cf0af3e6c490bde">ShardedWeightedAverage::ComputeAverage</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> VectorXd result;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// TODO(user): consider returning a reference to avoid this copy.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#afca8f74da7e8301c8aee45f33c93896c">AssignVector</a>(average_, *sharder_, result);</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>}</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="keywordtype">double</span> CombineBounds(<span class="keyword">const</span> <span class="keywordtype">double</span> v1, <span class="keyword">const</span> <span class="keywordtype">double</span> v2,</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">const</span> <span class="keywordtype">double</span> infinite_bound_threshold) {</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = 0.0;</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">if</span> (std::abs(v1) < infinite_bound_threshold) {</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = std::abs(v1);</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"> 90</span> <span class="keywordflow">if</span> (std::abs(v2) < infinite_bound_threshold) {</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>, std::abs(v2));</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> }</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span>}</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="keyword">struct </span>VectorInfo {</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4"> 97</a></span> int64_t <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a> = 0;</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a4d37e0f041f757e75ba8ac17ded9cfbc"> 98</a></span> int64_t <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a4d37e0f041f757e75ba8ac17ded9cfbc">num_nonzero</a> = 0;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a90a377dabbff2504d9c2c3a51030d216"> 99</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a90a377dabbff2504d9c2c3a51030d216">largest</a> = 0.0;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a229a2d9c49444ad43e50c4efddb3b607"> 100</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a229a2d9c49444ad43e50c4efddb3b607">smallest</a> = 0.0;</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a2e50537b138c27e2e30e8d3a568fbee0"> 101</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a2e50537b138c27e2e30e8d3a568fbee0">average</a> = 0.0;</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a2a897122b37c5a906205687aecdb627b"> 102</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a2a897122b37c5a906205687aecdb627b">l2_norm</a> = 0.0;</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</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><span class="keyword">struct </span>InfNormInfo {</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#aa2e8644f5973aaf5614f7694ef29281d"> 106</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#aa2e8644f5973aaf5614f7694ef29281d">max_col_norm</a>;</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#aed33cfe7d4d1bcda205ef2b972014b69"> 107</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#aed33cfe7d4d1bcda205ef2b972014b69">min_col_norm</a>;</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a50b61c289d15248d14d7e2560242f08c"> 108</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a50b61c289d15248d14d7e2560242f08c">max_row_norm</a>;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"><a class="line" href="sharded__optimization__utils_8cc.html#a2bc5760472b765b9ccbba08b19a93ac1"> 109</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a2bc5760472b765b9ccbba08b19a93ac1">min_row_norm</a>;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>};</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment">// The functions below are used to generate default values for</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment">// QuadraticProgramStats when the underlying program is empty or has no</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment">// constraints.</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="keywordtype">double</span> MaxOrZero(<span class="keyword">const</span> VectorXd& vec) {</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">if</span> (vec.size() == 0) {</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::isinf(vec.maxCoeff())) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">return</span> vec.maxCoeff();</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span>}</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="keywordtype">double</span> MinOrZero(<span class="keyword">const</span> VectorXd& vec) {</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">if</span> (vec.size() == 0) {</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::isinf(vec.minCoeff())) {</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">return</span> vec.minCoeff();</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>VectorInfo ComputeVectorInfo(<span class="keyword">const</span> Eigen::Ref<const VectorXd>& vec,</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> VectorXd local_max(sharder.NumShards());</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> VectorXd local_min(sharder.NumShards());</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> VectorXd local_sum(sharder.NumShards());</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> VectorXd local_sum_squared(sharder.NumShards());</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> std::vector<int64_t> local_num_nonzero(sharder.NumShards());</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">const</span> VectorXd shard_abs = shard(vec).cwiseAbs();</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> local_max[shard.Index()] = shard_abs.maxCoeff();</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> local_min[shard.Index()] = shard_abs.minCoeff();</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> local_sum[shard.Index()] = shard_abs.sum();</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> local_sum_squared[shard.Index()] = shard_abs.squaredNorm();</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">for</span> (<span class="keywordtype">double</span> element : shard_abs) {</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">if</span> (element != 0) {</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> local_num_nonzero[shard.Index()] += 1;</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> }</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> });</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">const</span> int64_t num_elements = vec.size();</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">return</span> VectorInfo{</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> .num_finite = num_elements,</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> .num_nonzero = std::accumulate(local_num_nonzero.begin(),</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> local_num_nonzero.end(), int64_t{0}),</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> .largest = MaxOrZero(local_max),</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> .smallest = MinOrZero(local_min),</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> .average = (num_elements > 0) ? local_sum.sum() / num_elements : NAN,</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> .l2_norm = (num_elements > 0) ? std::sqrt(local_sum_squared.sum()) : 0.0};</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span>}</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> </div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span>VectorInfo VariableBoundGapInfo(<span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>,</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">const</span> VectorXd& <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>,</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> VectorXd local_max(sharder.NumShards());</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> VectorXd local_min(sharder.NumShards());</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> VectorXd local_sum(sharder.NumShards());</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> std::vector<int64_t> local_num_finite(sharder.NumShards());</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> std::vector<int64_t> local_num_nonzero(sharder.NumShards());</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">const</span> <span class="keyword">auto</span> gap_shard = shard(<a class="code hl_variable" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>) - shard(<a class="code hl_variable" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>);</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = -<a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a>;</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a> = <a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a>;</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordtype">double</span> sum = 0.0;</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> int64_t <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a> = 0;</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> int64_t <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a4d37e0f041f757e75ba8ac17ded9cfbc">num_nonzero</a> = 0;</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">for</span> (int64_t i = 0; i < gap_shard.size(); ++i) {</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">if</span> (std::isfinite(gap_shard[i])) {</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>, gap_shard[i]);</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a>, gap_shard[i]);</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> sum += gap_shard[i];</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a> += 1;</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">if</span> (gap_shard[i] != 0) {</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a4d37e0f041f757e75ba8ac17ded9cfbc">num_nonzero</a> += 1;</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> }</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> }</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> local_max[shard.Index()] = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>;</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> local_min[shard.Index()] = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a>;</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> local_sum[shard.Index()] = sum;</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> local_num_finite[shard.Index()] = <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a>;</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> local_num_nonzero[shard.Index()] = <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a4d37e0f041f757e75ba8ac17ded9cfbc">num_nonzero</a>;</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> });</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// If an empty model was given, local_sum could be an empty vector,</span></div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// in which case calling .sum() directly would crash.</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keyword">const</span> int64_t <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a> = std::accumulate(</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> local_num_finite.begin(), local_num_finite.end(), int64_t{0});</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keywordflow">return</span> VectorInfo{</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> .num_finite = <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a>,</div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> .num_nonzero = std::accumulate(local_num_nonzero.begin(),</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> local_num_nonzero.end(), int64_t{0}),</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> .largest = MaxOrZero(local_max),</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> .smallest = MinOrZero(local_min),</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> .average = (<a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a> > 0) ? local_sum.sum() / <a class="code hl_variable" href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a> : NAN};</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span>}</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> </div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>VectorInfo MatrixAbsElementInfo(</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">const</span> SparseMatrix<double, ColMajor, int64_t>& matrix,</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keyword">const</span> Sharder& sharder) {</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> VectorXd local_max(sharder.NumShards());</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> VectorXd local_min(sharder.NumShards());</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> VectorXd local_sum(sharder.NumShards());</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">const</span> <span class="keyword">auto</span> matrix_shard = shard(matrix);</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = -<a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a>;</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a> = <a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a>;</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordtype">double</span> sum = 0.0;</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">for</span> (int64_t col_idx = 0; col_idx < matrix_shard.outerSize(); ++col_idx) {</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keywordflow">for</span> (<span class="keyword">decltype</span>(matrix_shard)::InnerIterator it(matrix_shard, col_idx); it;</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> ++it) {</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>, std::abs(it.value()));</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a>, std::abs(it.value()));</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> sum += std::abs(it.value());</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> }</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> }</div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> local_max[shard.Index()] = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>;</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> local_min[shard.Index()] = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a>;</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> local_sum[shard.Index()] = sum;</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> });</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keyword">const</span> int64_t num_nonzeros = matrix.nonZeros();</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="keywordflow">return</span> VectorInfo{</div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> .num_finite = num_nonzeros,</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> .largest = MaxOrZero(local_max),</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> .smallest = MinOrZero(local_min),</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> .average = (num_nonzeros > 0) ? local_sum.sum() / num_nonzeros : NAN};</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span>}</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> </div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span>VectorInfo CombinedBoundsInfo(<span class="keyword">const</span> VectorXd& rhs_upper_bounds,</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keyword">const</span> VectorXd& rhs_lower_bounds,</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keyword">const</span> Sharder& sharder,</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keyword">const</span> <span class="keywordtype">double</span> infinite_bound_threshold =</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> std::numeric_limits<double>::infinity()) {</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> VectorXd local_max(sharder.NumShards());</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> VectorXd local_min(sharder.NumShards());</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> VectorXd local_sum(sharder.NumShards());</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> VectorXd local_sum_squared(sharder.NumShards());</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keyword">const</span> <span class="keyword">auto</span> lb_shard = shard(rhs_lower_bounds);</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keyword">const</span> <span class="keyword">auto</span> ub_shard = shard(rhs_upper_bounds);</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = -<a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a>;</div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a> = <a class="code hl_variable" href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">kInfinity</a>;</div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keywordtype">double</span> sum = 0.0;</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="keywordtype">double</span> sum_squared = 0.0;</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="keywordflow">for</span> (int64_t i = 0; i < lb_shard.size(); ++i) {</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="keyword">const</span> <span class="keywordtype">double</span> combined =</div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> CombineBounds(ub_shard[i], lb_shard[i], infinite_bound_threshold);</div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>, combined);</div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a> = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(<a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a>, combined);</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> sum += combined;</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> sum_squared += combined * combined;</div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> }</div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> local_max[shard.Index()] = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a>;</div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> local_min[shard.Index()] = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a>;</div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> local_sum[shard.Index()] = sum;</div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> local_sum_squared[shard.Index()] = sum_squared;</div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> });</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_constraints = rhs_lower_bounds.size();</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keywordflow">return</span> VectorInfo{</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> .num_finite = num_constraints,</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> .largest = MaxOrZero(local_max),</div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> .smallest = MinOrZero(local_min),</div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> .average =</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> (num_constraints > 0) ? local_sum.sum() / num_constraints : NAN,</div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> .l2_norm =</div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> (num_constraints > 0) ? std::sqrt(local_sum_squared.sum()) : 0.0};</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>InfNormInfo ConstraintMatrixRowColInfo(</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keyword">const</span> SparseMatrix<double, ColMajor, int64_t>& constraint_matrix,</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keyword">const</span> SparseMatrix<double, ColMajor, int64_t>& constraint_matrix_transpose,</div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="keyword">const</span> Sharder& matrix_sharder, <span class="keyword">const</span> Sharder& matrix_transpose_sharder) {</div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> VectorXd col_norms = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">ScaledColLInfNorm</a>(</div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> constraint_matrix,</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="comment">/*row_scaling_vec=*/</span>VectorXd::Ones(constraint_matrix.rows()),</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="comment">/*col_scaling_vec=*/</span>VectorXd::Ones(constraint_matrix.cols()),</div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> matrix_sharder);</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> VectorXd row_norms =</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">ScaledColLInfNorm</a>(constraint_matrix_transpose,</div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> VectorXd::Ones(constraint_matrix_transpose.rows()),</div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> VectorXd::Ones(constraint_matrix_transpose.cols()),</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> matrix_transpose_sharder);</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">return</span> InfNormInfo{.max_col_norm = MaxOrZero(col_norms),</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> .min_col_norm = MinOrZero(col_norms),</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> .max_row_norm = MaxOrZero(row_norms),</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> .min_row_norm = MinOrZero(row_norms)};</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="comment">// namespace</span></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"><a class="line" href="namespaceoperations__research_1_1pdlp.html#ab315578d37cb2f5e1111b0176254cb84"> 303</a></span>QuadraticProgramStats <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#ab315578d37cb2f5e1111b0176254cb84">ComputeStats</a>(</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& qp,</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keyword">const</span> <span class="keywordtype">double</span> infinite_constraint_bound_threshold) {</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="comment">// Caution: if the constraint matrix is empty, elementwise operations</span></div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="comment">// (like .coeffs().maxCoeff() or .minCoeff()) will fail.</span></div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> InfNormInfo cons_matrix_norm_info = ConstraintMatrixRowColInfo(</div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">constraint_matrix</a>, qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a1e0d1154156a56084d0ba5232819b134">TransposedConstraintMatrix</a>(),</div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ac9f7db642c1b4c4fc37f489f03d110a7">ConstraintMatrixSharder</a>(), qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a8bf92cdb63b602aba6f4d22b975e2f30">TransposedConstraintMatrixSharder</a>());</div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> VectorInfo cons_matrix_info = MatrixAbsElementInfo(</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">constraint_matrix</a>, qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ac9f7db642c1b4c4fc37f489f03d110a7">ConstraintMatrixSharder</a>());</div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> VectorInfo combined_bounds_info = CombinedBoundsInfo(</div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>, qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>,</div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">DualSharder</a>(), infinite_constraint_bound_threshold);</div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> VectorInfo obj_vec_info =</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> ComputeVectorInfo(qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#afdb3e07cd380793e1b265c1fded94edd">objective_vector</a>, qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>());</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> VectorInfo gaps_info =</div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> VariableBoundGapInfo(qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>,</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">variable_upper_bounds</a>, qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>());</div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> QuadraticProgramStats program_stats;</div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> program_stats.set_num_variables(qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">PrimalSize</a>());</div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> program_stats.set_num_constraints(qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">DualSize</a>());</div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> program_stats.set_constraint_matrix_col_min_l_inf_norm(</div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> cons_matrix_norm_info.min_col_norm);</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> program_stats.set_constraint_matrix_row_min_l_inf_norm(</div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> cons_matrix_norm_info.min_row_norm);</div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> program_stats.set_constraint_matrix_num_nonzeros(cons_matrix_info.num_finite);</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> program_stats.set_constraint_matrix_abs_max(cons_matrix_info.largest);</div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> program_stats.set_constraint_matrix_abs_min(cons_matrix_info.smallest);</div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> program_stats.set_constraint_matrix_abs_avg(cons_matrix_info.average);</div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> program_stats.set_combined_bounds_max(combined_bounds_info.largest);</div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> program_stats.set_combined_bounds_min(combined_bounds_info.smallest);</div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> program_stats.set_combined_bounds_avg(combined_bounds_info.average);</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> program_stats.set_combined_bounds_l2_norm(combined_bounds_info.l2_norm);</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> program_stats.set_variable_bound_gaps_num_finite(gaps_info.num_finite);</div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> program_stats.set_variable_bound_gaps_max(gaps_info.largest);</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> program_stats.set_variable_bound_gaps_min(gaps_info.smallest);</div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> program_stats.set_variable_bound_gaps_avg(gaps_info.average);</div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> program_stats.set_objective_vector_abs_max(obj_vec_info.largest);</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> program_stats.set_objective_vector_abs_min(obj_vec_info.smallest);</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> program_stats.set_objective_vector_abs_avg(obj_vec_info.average);</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> program_stats.set_objective_vector_l2_norm(obj_vec_info.l2_norm);</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a850865b3deabb2a623e130691df99f15">IsLinearProgram</a>(qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>())) {</div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> program_stats.set_objective_matrix_num_nonzeros(0);</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> program_stats.set_objective_matrix_abs_max(0);</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> program_stats.set_objective_matrix_abs_min(0);</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> program_stats.set_objective_matrix_abs_avg(NAN);</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> VectorInfo obj_matrix_info = ComputeVectorInfo(</div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae816a5fdb4bdd9b7af551cc7e88d2eb5">objective_matrix</a>->diagonal(), qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>());</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> program_stats.set_objective_matrix_num_nonzeros(</div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> obj_matrix_info.num_nonzero);</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> program_stats.set_objective_matrix_abs_max(obj_matrix_info.largest);</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> program_stats.set_objective_matrix_abs_min(obj_matrix_info.smallest);</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> program_stats.set_objective_matrix_abs_avg(obj_matrix_info.average);</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> }</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keywordflow">return</span> program_stats;</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</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">namespace </span>{</div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> </div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span><span class="keyword">enum class</span> ScalingNorm { kL2, kLInf };</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> </div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span><span class="comment">// Divides the vector (componentwise) by the square root of the divisor,</span></div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span><span class="comment">// updating the vector in-place. If a component of the divisor is equal to zero,</span></div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span><span class="comment">// leaves the component of the vector unchanged. The Sharder should have the</span></div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span><span class="comment">// same size as the vector. For best performance the Sharder should have been</span></div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span><span class="comment">// created with the Sharder(int64_t, int, ThreadPool*) constructor.</span></div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><span class="keywordtype">void</span> DivideBySquareRootOfDivisor(<span class="keyword">const</span> VectorXd& divisor,</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="keyword">const</span> Sharder& sharder, VectorXd& vector) {</div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="keyword">auto</span> vec_shard = shard(vector);</div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="keyword">auto</span> divisor_shard = shard(divisor);</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="keywordflow">for</span> (int64_t <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> = 0; <a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a> < vec_shard.size(); ++<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>) {</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="keywordflow">if</span> (divisor_shard[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>] != 0) {</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> vec_shard[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>] /= std::sqrt(divisor_shard[<a class="code hl_variable" href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>]);</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> }</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> }</div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</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> </div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span><span class="keywordtype">void</span> ApplyScalingIterationsForNorm(<span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp,</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_iterations,</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> <span class="keyword">const</span> ScalingNorm norm,</div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> VectorXd& row_scaling_vec,</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> VectorXd& col_scaling_vec) {</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="keyword">const</span> QuadraticProgram& qp = sharded_qp.Qp();</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="keyword">const</span> int64_t num_col = qp.constraint_matrix.cols();</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="keyword">const</span> int64_t num_row = qp.constraint_matrix.rows();</div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(num_col, col_scaling_vec.size());</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(num_row, row_scaling_vec.size());</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_iterations; ++i) {</div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> VectorXd col_norm;</div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> VectorXd row_norm;</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="keywordflow">switch</span> (norm) {</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="keywordflow">case</span> ScalingNorm::kL2: {</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> col_norm = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aa3c5dd95681fe94691be1407d6bb62aa">ScaledColL2Norm</a>(qp.constraint_matrix, row_scaling_vec,</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> col_scaling_vec,</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> sharded_qp.ConstraintMatrixSharder());</div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> row_norm = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aa3c5dd95681fe94691be1407d6bb62aa">ScaledColL2Norm</a>(</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> sharded_qp.TransposedConstraintMatrix(), col_scaling_vec,</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> row_scaling_vec, sharded_qp.TransposedConstraintMatrixSharder());</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> }</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="keywordflow">case</span> ScalingNorm::kLInf: {</div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> col_norm = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">ScaledColLInfNorm</a>(qp.constraint_matrix, row_scaling_vec,</div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> col_scaling_vec,</div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> sharded_qp.ConstraintMatrixSharder());</div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> row_norm = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">ScaledColLInfNorm</a>(</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> sharded_qp.TransposedConstraintMatrix(), col_scaling_vec,</div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> row_scaling_vec, sharded_qp.TransposedConstraintMatrixSharder());</div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</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> DivideBySquareRootOfDivisor(col_norm, sharded_qp.PrimalSharder(),</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> col_scaling_vec);</div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> DivideBySquareRootOfDivisor(row_norm, sharded_qp.DualSharder(),</div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> row_scaling_vec);</div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> }</div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span>}</div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> </div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> </div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a54ded6625965f8ddd342161a55263cce"> 425</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a54ded6625965f8ddd342161a55263cce">LInfRuizRescaling</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_iterations, VectorXd& row_scaling_vec,</div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> VectorXd& col_scaling_vec) {</div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> ApplyScalingIterationsForNorm(sharded_qp, num_iterations, ScalingNorm::kLInf,</div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> row_scaling_vec, col_scaling_vec);</div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span>}</div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> </div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a9dee2894b8028a57b7f7d2306b402e44"> 432</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a9dee2894b8028a57b7f7d2306b402e44">L2NormRescaling</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> VectorXd& row_scaling_vec, VectorXd& col_scaling_vec) {</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> ApplyScalingIterationsForNorm(sharded_qp, <span class="comment">/*num_iterations=*/</span>1,</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> ScalingNorm::kL2, row_scaling_vec,</div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> col_scaling_vec);</div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span>}</div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> </div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#aac68304831a1bc81557fb03623a619d6"> 439</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_scaling_vectors.html">ScalingVectors</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aac68304831a1bc81557fb03623a619d6">ApplyRescaling</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_rescaling_options.html">RescalingOptions</a>& rescaling_options,</div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp) {</div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_scaling_vectors.html">ScalingVectors</a> scaling{</div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> .<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_scaling_vectors.html#a5e823e9942e65836de2aa9ac368af52b">row_scaling_vec</a> = VectorXd::Ones(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">DualSize</a>()),</div>
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<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> .col_scaling_vec = VectorXd::Ones(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">PrimalSize</a>())};</div>
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<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keywordtype">bool</span> do_rescale = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> <span class="keywordflow">if</span> (rescaling_options.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_rescaling_options.html#ad3f4c83145ae0a650089a980c4c7fe60">l_inf_ruiz_iterations</a> > 0) {</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> do_rescale = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a54ded6625965f8ddd342161a55263cce">LInfRuizRescaling</a>(sharded_qp, rescaling_options.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_rescaling_options.html#ad3f4c83145ae0a650089a980c4c7fe60">l_inf_ruiz_iterations</a>,</div>
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<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> scaling.row_scaling_vec, scaling.col_scaling_vec);</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> }</div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> <span class="keywordflow">if</span> (rescaling_options.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_rescaling_options.html#a74bba1825289ddbad8bf96e840ebfeab">l2_norm_rescaling</a>) {</div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> do_rescale = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a9dee2894b8028a57b7f7d2306b402e44">L2NormRescaling</a>(sharded_qp, scaling.row_scaling_vec,</div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> scaling.col_scaling_vec);</div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> }</div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="keywordflow">if</span> (do_rescale) {</div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a11d751c453d716f5462803d590adbe73">RescaleQuadraticProgram</a>(scaling.col_scaling_vec,</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> scaling.row_scaling_vec);</div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> }</div>
|
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> <span class="keywordflow">return</span> scaling;</div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span>}</div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> </div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a259d3f73717a2ababa9df2dd43914656"> 462</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html">LagrangianPart</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a259d3f73717a2ababa9df2dd43914656">ComputePrimalGradient</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="keyword">const</span> VectorXd& primal_solution,</div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keyword">const</span> VectorXd& dual_product) {</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html">LagrangianPart</a> result{.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html#a1cb87fb26e738040e82cbc0c02444be9">gradient</a> = VectorXd(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">PrimalSize</a>())};</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>();</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> VectorXd value_parts(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#aa6c18d04d5fcbe7a9343768b8b66be7f">NumShards</a>());</div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>(</div>
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<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> [&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a850865b3deabb2a623e130691df99f15">IsLinearProgram</a>(qp)) {</div>
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<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> shard(result.gradient) =</div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#afdb3e07cd380793e1b265c1fded94edd">objective_vector</a>) - shard(dual_product);</div>
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<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> value_parts[shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>()] =</div>
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<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> shard(primal_solution).dot(shard(result.gradient));</div>
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<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <span class="comment">// Note: using auto instead of VectorXd for the type of</span></div>
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<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> <span class="comment">// objective_product causes eigen to defer the matrix product until it</span></div>
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<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> <span class="comment">// is used (twice).</span></div>
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<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> <span class="keyword">const</span> VectorXd objective_product =</div>
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<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> shard(*qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae816a5fdb4bdd9b7af551cc7e88d2eb5">objective_matrix</a>) * shard(primal_solution);</div>
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<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> shard(result.gradient) = shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#afdb3e07cd380793e1b265c1fded94edd">objective_vector</a>) +</div>
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<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> objective_product - shard(dual_product);</div>
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<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> value_parts[shard.Index()] =</div>
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<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> shard(primal_solution)</div>
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<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> .dot(shard(result.gradient) - 0.5 * objective_product);</div>
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<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> }</div>
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<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> });</div>
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<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> result.value = value_parts.sum();</div>
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<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span>}</div>
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<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> </div>
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<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a6fe6fa17061fa3b8610cce9cf707574f"> 492</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a6fe6fa17061fa3b8610cce9cf707574f">DualSubgradientCoefficient</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> constraint_lower_bound,</div>
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<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> <span class="keyword">const</span> <span class="keywordtype">double</span> constraint_upper_bound,</div>
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<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dual,</div>
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<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_product) {</div>
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<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> <span class="keywordflow">if</span> (dual < 0.0) {</div>
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<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> <span class="keywordflow">return</span> constraint_upper_bound;</div>
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<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (dual > 0.0) {</div>
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<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> <span class="keywordflow">return</span> constraint_lower_bound;</div>
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<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::isfinite(constraint_lower_bound) &&</div>
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<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> std::isfinite(constraint_upper_bound)) {</div>
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<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> <span class="keywordflow">if</span> (primal_product < constraint_lower_bound) {</div>
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<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> <span class="keywordflow">return</span> constraint_lower_bound;</div>
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<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (primal_product > constraint_upper_bound) {</div>
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<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> <span class="keywordflow">return</span> constraint_upper_bound;</div>
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<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> <span class="keywordflow">return</span> primal_product;</div>
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<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> }</div>
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<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::isfinite(constraint_lower_bound)) {</div>
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<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> <span class="keywordflow">return</span> constraint_lower_bound;</div>
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<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::isfinite(constraint_upper_bound)) {</div>
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<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> <span class="keywordflow">return</span> constraint_upper_bound;</div>
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<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keywordflow">return</span> 0.0;</div>
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<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> }</div>
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<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span>}</div>
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<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> </div>
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<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a608ed26a4c7ff3bdcb22d25ff890f47d"> 518</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html">LagrangianPart</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a608ed26a4c7ff3bdcb22d25ff890f47d">ComputeDualGradient</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> <span class="keyword">const</span> Eigen::VectorXd& dual_solution,</div>
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<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> <span class="keyword">const</span> Eigen::VectorXd& primal_product) {</div>
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<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html">LagrangianPart</a> result{.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html#a1cb87fb26e738040e82cbc0c02444be9">gradient</a> = VectorXd(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">DualSize</a>())};</div>
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<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>();</div>
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<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> VectorXd value_parts(sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">DualSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#aa6c18d04d5fcbe7a9343768b8b66be7f">NumShards</a>());</div>
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<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">DualSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>(</div>
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<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> [&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> <span class="keyword">auto</span> constraint_lower_bounds = shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>);</div>
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<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="keyword">auto</span> constraint_upper_bounds = shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>);</div>
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<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> <span class="keyword">auto</span> dual_solution_shard = shard(dual_solution);</div>
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<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> <span class="keyword">auto</span> dual_gradient_shard = shard(result.gradient);</div>
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<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="keyword">auto</span> primal_product_shard = shard(primal_product);</div>
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<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> <span class="keywordtype">double</span> value_sum = 0.0;</div>
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<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> <span class="keywordflow">for</span> (int64_t i = 0; i < dual_gradient_shard.size(); ++i) {</div>
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<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> dual_gradient_shard[i] = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a6fe6fa17061fa3b8610cce9cf707574f">DualSubgradientCoefficient</a>(</div>
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<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> constraint_lower_bounds[i], constraint_upper_bounds[i],</div>
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<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> dual_solution_shard[i], primal_product_shard[i]);</div>
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<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> value_sum += dual_gradient_shard[i] * dual_solution_shard[i];</div>
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<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> }</div>
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<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> value_parts[shard.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">Index</a>()] = value_sum;</div>
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<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> dual_gradient_shard -= primal_product_shard;</div>
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<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> });</div>
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<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> result.value = value_parts.sum();</div>
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<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span>}</div>
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<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> </div>
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<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> </div>
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<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span>using ::Eigen::ColMajor;</div>
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<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span>using ::Eigen::SparseMatrix;</div>
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<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> </div>
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<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span><span class="comment">// Scales a vector (in-place) to have norm 1, unless it has norm 0 (in which</span></div>
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<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span><span class="comment">// case it is left unscaled). Returns the norm of the input vector.</span></div>
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<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span><span class="keywordtype">double</span> NormalizeVector(<span class="keyword">const</span> Sharder& sharder, VectorXd& vector) {</div>
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<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> <span class="keyword">const</span> <span class="keywordtype">double</span> norm = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#ade56a0bd875b06000c45e1730398e5a8">Norm</a>(vector, sharder);</div>
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<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> <span class="keywordflow">if</span> (norm != 0.0) {</div>
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<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> sharder.ParallelForEachShard(</div>
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<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> [&](<span class="keyword">const</span> Sharder::Shard& shard) { shard(vector) /= norm; });</div>
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<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> }</div>
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<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> <span class="keywordflow">return</span> norm;</div>
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<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span>}</div>
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<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> </div>
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<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span><span class="comment">// Estimates the probability that the power method, after k iterations, has</span></div>
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<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span><span class="comment">// relative error > epsilon. This is based on Theorem 4.1(a) (on page 13) from</span></div>
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<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span><span class="comment">// "Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a</span></div>
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<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span><span class="comment">// Random Start"</span></div>
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<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span><span class="comment">// https://pdfs.semanticscholar.org/2b2e/a941e55e5fa2ee9d8f4ff393c14482051143.pdf</span></div>
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<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span><span class="keywordtype">double</span> PowerMethodFailureProbability(int64_t dimension, <span class="keywordtype">double</span> epsilon, <span class="keywordtype">int</span> k) {</div>
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<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> <span class="keywordflow">if</span> (k < 2 || epsilon <= 0.0) {</div>
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<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> <span class="comment">// The theorem requires epsilon > 0 and k >= 2.</span></div>
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<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> }</div>
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<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(0.824, 0.354 / (epsilon * (k - 1))) * std::sqrt(dimension) *</div>
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<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> std::pow(1.0 - epsilon, k - 0.5);</div>
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<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span>}</div>
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<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> </div>
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<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span>SingularValueAndIterations EstimateMaximumSingularValue(</div>
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<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> <span class="keyword">const</span> SparseMatrix<double, ColMajor, int64_t>& matrix,</div>
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<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> <span class="keyword">const</span> SparseMatrix<double, ColMajor, int64_t>& matrix_transpose,</div>
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<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> <span class="keyword">const</span> absl::optional<VectorXd>& active_set_indicator,</div>
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<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> <span class="keyword">const</span> absl::optional<VectorXd>& transpose_active_set_indicator,</div>
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<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> <span class="keyword">const</span> Sharder& matrix_sharder, <span class="keyword">const</span> Sharder& matrix_transpose_sharder,</div>
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<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> <span class="keyword">const</span> Sharder& primal_vector_sharder, <span class="keyword">const</span> Sharder& dual_vector_sharder,</div>
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<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> <span class="keyword">const</span> <span class="keywordtype">double</span> desired_relative_error, <span class="keyword">const</span> <span class="keywordtype">double</span> failure_probability,</div>
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<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> std::mt19937& mt_generator) {</div>
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<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <span class="comment">// Easy case: matrix is diagonal.</span></div>
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<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>(matrix, matrix_sharder)) {</div>
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<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> VectorXd local_max(matrix_sharder.NumShards());</div>
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<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> matrix_sharder.ParallelForEachShard([&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> <span class="keyword">const</span> <span class="keyword">auto</span> matrix_shard = shard(matrix);</div>
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<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> local_max[shard.Index()] =</div>
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<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> (matrix_shard *</div>
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<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> VectorXd::Ones(matrix_sharder.ShardSize(shard.Index())))</div>
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<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> .lpNorm<Eigen::Infinity>();</div>
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<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> });</div>
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<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> <span class="keywordflow">return</span> {.singular_value = local_max.lpNorm<Eigen::Infinity>(),</div>
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<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> .num_iterations = 0,</div>
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<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> .estimated_relative_error = 0.0};</div>
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<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> }</div>
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<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> <span class="keyword">const</span> int64_t dimension = matrix.cols();</div>
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<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> VectorXd eigenvector(dimension);</div>
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<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> <span class="comment">// Even though it will be slower, we initialize eigenvector sequentially so</span></div>
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<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> <span class="comment">// that the result doesn't depend on the number of threads.</span></div>
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<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> <span class="keywordflow">for</span> (<span class="keywordtype">double</span>& entry : eigenvector) {</div>
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<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> entry = absl::Gaussian<double>(mt_generator);</div>
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<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> }</div>
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<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> <span class="keywordflow">if</span> (active_set_indicator.has_value()) {</div>
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<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a920005e41b36a7a0c7f4ad148ad7069d">CoefficientWiseProductInPlace</a>(*active_set_indicator, primal_vector_sharder,</div>
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<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> eigenvector);</div>
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<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> }</div>
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<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> NormalizeVector(primal_vector_sharder, eigenvector);</div>
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<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span> <span class="keywordtype">double</span> eigenvalue_estimate = 0.0;</div>
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<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> </div>
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<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span> <span class="keywordtype">int</span> num_iterations = 0;</div>
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<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span> <span class="comment">// The maximum singular value of A is the square root of the maximum</span></div>
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<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span> <span class="comment">// eigenvalue of A^T A. epsilon is the relative error needed for the maximum</span></div>
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<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> <span class="comment">// eigenvalue of A^T A that gives desired_relative_error for the maximum</span></div>
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<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> <span class="comment">// singular value of A.</span></div>
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<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">const</span> <span class="keywordtype">double</span> epsilon = 1.0 - <a class="code hl_function" href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">MathUtil::Square</a>(1.0 - desired_relative_error);</div>
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<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="keywordflow">while</span> (PowerMethodFailureProbability(dimension, epsilon, num_iterations) ></div>
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<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> failure_probability) {</div>
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<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> VectorXd dual_eigenvector = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">TransposedMatrixVectorProduct</a>(</div>
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<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> matrix_transpose, eigenvector, matrix_transpose_sharder);</div>
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<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> <span class="keywordflow">if</span> (transpose_active_set_indicator.has_value()) {</div>
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<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a920005e41b36a7a0c7f4ad148ad7069d">CoefficientWiseProductInPlace</a>(*transpose_active_set_indicator,</div>
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<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> dual_vector_sharder, dual_eigenvector);</div>
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<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> }</div>
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<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span> VectorXd next_eigenvector =</div>
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<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">TransposedMatrixVectorProduct</a>(matrix, dual_eigenvector, matrix_sharder);</div>
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<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> <span class="keywordflow">if</span> (active_set_indicator.has_value()) {</div>
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<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a920005e41b36a7a0c7f4ad148ad7069d">CoefficientWiseProductInPlace</a>(*active_set_indicator,</div>
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<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> primal_vector_sharder, next_eigenvector);</div>
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<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> }</div>
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<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> eigenvalue_estimate =</div>
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<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a11831586b99d28a708bc103bce1a945e">Dot</a>(eigenvector, next_eigenvector, primal_vector_sharder);</div>
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<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> eigenvector = std::move(next_eigenvector);</div>
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<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> ++num_iterations;</div>
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<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> <span class="keyword">const</span> <span class="keywordtype">double</span> primal_norm =</div>
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<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> NormalizeVector(primal_vector_sharder, eigenvector);</div>
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<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> </div>
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<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Iteration "</span> << num_iterations << <span class="stringliteral">" singular value estimate "</span></div>
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<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> << std::sqrt(eigenvalue_estimate) << <span class="stringliteral">" primal norm "</span> << primal_norm;</div>
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<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> }</div>
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<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> <span class="keywordflow">return</span> SingularValueAndIterations{</div>
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<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> .singular_value = std::sqrt(eigenvalue_estimate),</div>
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<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> .num_iterations = num_iterations,</div>
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<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> .estimated_relative_error = desired_relative_error};</div>
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<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span>}</div>
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<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> </div>
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<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span><span class="comment">// Given a primal solution, compute a {0, 1}-valued vector that is nonzero in</span></div>
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<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span><span class="comment">// all the coordinates that are not saturating the primal variable bounds.</span></div>
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<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span>VectorXd ComputePrimalActiveSetIndicator(</div>
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<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> <span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp,</div>
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<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span> <span class="keyword">const</span> VectorXd& primal_solution) {</div>
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<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> VectorXd indicator(sharded_qp.PrimalSize());</div>
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<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> sharded_qp.PrimalSharder().ParallelForEachShard(</div>
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<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> [&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
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|
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> <span class="keyword">const</span> <span class="keyword">auto</span> lower_bound_shard =</div>
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<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> shard(sharded_qp.Qp().variable_lower_bounds);</div>
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|
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> <span class="keyword">const</span> <span class="keyword">auto</span> upper_bound_shard =</div>
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<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> shard(sharded_qp.Qp().variable_upper_bounds);</div>
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<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> <span class="keyword">const</span> <span class="keyword">auto</span> primal_solution_shard = shard(primal_solution);</div>
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<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> <span class="keyword">auto</span> indicator_shard = shard(indicator);</div>
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|
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="keyword">const</span> int64_t shard_size =</div>
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|
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> sharded_qp.PrimalSharder().ShardSize(shard.Index());</div>
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|
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> <span class="keywordflow">for</span> (int64_t i = 0; i < shard_size; ++i) {</div>
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<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> <span class="keywordflow">if</span> ((primal_solution_shard[i] == lower_bound_shard[i]) ||</div>
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|
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> (primal_solution_shard[i] == upper_bound_shard[i])) {</div>
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<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> indicator_shard[i] = 0.0;</div>
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|
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> } <span class="keywordflow">else</span> {</div>
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|
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> indicator_shard[i] = 1.0;</div>
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|
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> }</div>
|
|
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> }</div>
|
|
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> });</div>
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|
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> <span class="keywordflow">return</span> indicator;</div>
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|
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span>}</div>
|
|
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> </div>
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|
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span><span class="comment">// Like ComputePrimalActiveSetIndicator(sharded_qp, primal_solution), but this</span></div>
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|
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span><span class="comment">// time using the implicit bounds on the dual variable.</span></div>
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|
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span>VectorXd ComputeDualActiveSetIndicator(</div>
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|
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> <span class="keyword">const</span> ShardedQuadraticProgram& sharded_qp, <span class="keyword">const</span> VectorXd& dual_solution) {</div>
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|
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> VectorXd indicator(sharded_qp.DualSize());</div>
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|
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> sharded_qp.DualSharder().ParallelForEachShard(</div>
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|
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> [&](<span class="keyword">const</span> Sharder::Shard& shard) {</div>
|
|
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> <span class="keyword">const</span> <span class="keyword">auto</span> lower_bound_shard =</div>
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|
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> shard(sharded_qp.Qp().constraint_lower_bounds);</div>
|
|
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> <span class="keyword">const</span> <span class="keyword">auto</span> upper_bound_shard =</div>
|
|
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> shard(sharded_qp.Qp().constraint_upper_bounds);</div>
|
|
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span> <span class="keyword">const</span> <span class="keyword">auto</span> dual_solution_shard = shard(dual_solution);</div>
|
|
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> <span class="keyword">auto</span> indicator_shard = shard(indicator);</div>
|
|
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> <span class="keyword">const</span> int64_t shard_size =</div>
|
|
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> sharded_qp.DualSharder().ShardSize(shard.Index());</div>
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|
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> <span class="keywordflow">for</span> (int64_t i = 0; i < shard_size; ++i) {</div>
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|
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> <span class="keywordflow">if</span> (dual_solution_shard[i] == 0.0 &&</div>
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|
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> (std::isinf(lower_bound_shard[i]) ||</div>
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|
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> std::isinf(upper_bound_shard[i]))) {</div>
|
|
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> indicator_shard[i] = 0.0;</div>
|
|
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> indicator_shard[i] = 1.0;</div>
|
|
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span> }</div>
|
|
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> }</div>
|
|
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span> });</div>
|
|
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span> <span class="keywordflow">return</span> indicator;</div>
|
|
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span>}</div>
|
|
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> </div>
|
|
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span>} <span class="comment">// namespace</span></div>
|
|
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> </div>
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<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a880902cb3a98b7205fa57be9e16a82c7"> 706</a></span><a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_singular_value_and_iterations.html">SingularValueAndIterations</a> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a880902cb3a98b7205fa57be9e16a82c7">EstimateMaximumSingularValueOfConstraintMatrix</a>(</div>
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<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> <span class="keyword">const</span> absl::optional<VectorXd>& primal_solution,</div>
|
|
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> <span class="keyword">const</span> absl::optional<VectorXd>& dual_solution,</div>
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|
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> <span class="keyword">const</span> <span class="keywordtype">double</span> desired_relative_error, <span class="keyword">const</span> <span class="keywordtype">double</span> failure_probability,</div>
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|
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> std::mt19937& mt_generator) {</div>
|
|
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> absl::optional<VectorXd> primal_active_set_indicator;</div>
|
|
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> absl::optional<VectorXd> dual_active_set_indicator;</div>
|
|
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> <span class="keywordflow">if</span> (primal_solution.has_value()) {</div>
|
|
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> primal_active_set_indicator =</div>
|
|
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> ComputePrimalActiveSetIndicator(sharded_qp, *primal_solution);</div>
|
|
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> }</div>
|
|
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> <span class="keywordflow">if</span> (dual_solution.has_value()) {</div>
|
|
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> dual_active_set_indicator =</div>
|
|
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> ComputeDualActiveSetIndicator(sharded_qp, *dual_solution);</div>
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|
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> }</div>
|
|
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> <span class="keywordflow">return</span> EstimateMaximumSingularValue(</div>
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|
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>().<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">constraint_matrix</a>,</div>
|
|
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a1e0d1154156a56084d0ba5232819b134">TransposedConstraintMatrix</a>(), primal_active_set_indicator,</div>
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|
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> dual_active_set_indicator, sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ac9f7db642c1b4c4fc37f489f03d110a7">ConstraintMatrixSharder</a>(),</div>
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|
<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a8bf92cdb63b602aba6f4d22b975e2f30">TransposedConstraintMatrixSharder</a>(),</div>
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<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>(), sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">DualSharder</a>(),</div>
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|
<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> desired_relative_error, failure_probability, mt_generator);</div>
|
|
<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span>}</div>
|
|
<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> </div>
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<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a5482747bc024e4a57be9c9200d329fad"> 731</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a77dbe245ed9fb597ad836b27ac989f26">HasValidBounds</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp) {</div>
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|
<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>();</div>
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|
<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> constraint_bounds_valid =</div>
|
|
<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">DualSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a9761cf0a21e5b7efe9126765eec48a3a">ParallelTrueForAllShards</a>(</div>
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<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> [&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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|
<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> <span class="keywordflow">return</span> (shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>).array() <=</div>
|
|
<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>).array())</div>
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<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> .all();</div>
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<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span> });</div>
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<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> variable_bounds_valid =</div>
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<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"> 741</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a9761cf0a21e5b7efe9126765eec48a3a">ParallelTrueForAllShards</a>(</div>
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<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span> [&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span> <span class="keywordflow">return</span> (shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>).array() <=</div>
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<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">variable_upper_bounds</a>).array())</div>
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<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span> .all();</div>
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<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> });</div>
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<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> </div>
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<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span> <span class="keywordflow">return</span> constraint_bounds_valid && variable_bounds_valid;</div>
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<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span>}</div>
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<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span> </div>
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<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#acb7f29f435d6c9fc53148ee403c7049e"> 751</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#acb7f29f435d6c9fc53148ee403c7049e">ProjectToPrimalVariableBounds</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00752" name="l00752"></a><span class="lineno"> 752</span> VectorXd& primal) {</div>
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<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">PrimalSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>(</div>
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<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"> 754</span> [&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>();</div>
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<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span> shard(primal) = shard(primal)</div>
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<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> .cwiseMin(shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">variable_upper_bounds</a>))</div>
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<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span> .cwiseMax(shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>));</div>
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<div class="line"><a id="l00759" name="l00759"></a><span class="lineno"> 759</span> });</div>
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<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span>}</div>
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<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span> </div>
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<div class="line"><a id="l00762" name="l00762"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1pdlp.html#a898c0c776a5736cf1931036d0d370724"> 762</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a898c0c776a5736cf1931036d0d370724">ProjectToDualVariableBounds</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">ShardedQuadraticProgram</a>& sharded_qp,</div>
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<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span> VectorXd& dual) {</div>
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<div class="line"><a id="l00764" name="l00764"></a><span class="lineno"> 764</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a>& qp = sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">Qp</a>();</div>
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<div class="line"><a id="l00765" name="l00765"></a><span class="lineno"> 765</span> sharded_qp.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">DualSharder</a>().<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>(</div>
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<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span> [&](<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">Sharder::Shard</a>& shard) {</div>
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<div class="line"><a id="l00767" name="l00767"></a><span class="lineno"> 767</span> <span class="keyword">const</span> <span class="keyword">auto</span> lower_bound_shard = shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>);</div>
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<div class="line"><a id="l00768" name="l00768"></a><span class="lineno"> 768</span> <span class="keyword">const</span> <span class="keyword">auto</span> upper_bound_shard = shard(qp.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>);</div>
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<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"> 769</span> <span class="keyword">auto</span> dual_shard = shard(dual);</div>
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<div class="line"><a id="l00770" name="l00770"></a><span class="lineno"> 770</span> </div>
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<div class="line"><a id="l00771" name="l00771"></a><span class="lineno"> 771</span> <span class="keywordflow">for</span> (int64_t i = 0; i < dual_shard.size(); ++i) {</div>
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<div class="line"><a id="l00772" name="l00772"></a><span class="lineno"> 772</span> <span class="keywordflow">if</span> (!std::isfinite(upper_bound_shard[i])) {</div>
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<div class="line"><a id="l00773" name="l00773"></a><span class="lineno"> 773</span> dual_shard[i] = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(dual_shard[i], 0.0);</div>
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<div class="line"><a id="l00774" name="l00774"></a><span class="lineno"> 774</span> }</div>
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<div class="line"><a id="l00775" name="l00775"></a><span class="lineno"> 775</span> <span class="keywordflow">if</span> (!std::isfinite(lower_bound_shard[i])) {</div>
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<div class="line"><a id="l00776" name="l00776"></a><span class="lineno"> 776</span> dual_shard[i] = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(dual_shard[i], 0.0);</div>
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<div class="line"><a id="l00777" name="l00777"></a><span class="lineno"> 777</span> }</div>
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<div class="line"><a id="l00778" name="l00778"></a><span class="lineno"> 778</span> }</div>
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<div class="line"><a id="l00779" name="l00779"></a><span class="lineno"> 779</span> });</div>
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<div class="line"><a id="l00780" name="l00780"></a><span class="lineno"> 780</span>}</div>
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<div class="line"><a id="l00781" name="l00781"></a><span class="lineno"> 781</span> </div>
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<div class="line"><a id="l00782" name="l00782"></a><span class="lineno"> 782</span>} <span class="comment">// namespace operations_research::pdlp</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_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00703">base/logging.h:703</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00707">base/logging.h:707</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#l00984">base/logging.h:984</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_math_util_html_aac72849250cdf23aefdd991eb0fc0385"><div class="ttname"><a href="classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385">operations_research::MathUtil::Square</a></div><div class="ttdeci">static T Square(const T x)</div><div class="ttdef"><b>Definition:</b> <a href="mathutil_8h_source.html#l00101">mathutil.h:101</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html">operations_research::pdlp::ShardedQuadraticProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00033">sharded_quadratic_program.h:33</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a101ca40b60dd25bbf6271bef1370e8d1"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a101ca40b60dd25bbf6271bef1370e8d1">operations_research::pdlp::ShardedQuadraticProgram::DualSharder</a></div><div class="ttdeci">const Sharder & DualSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00064">sharded_quadratic_program.h:64</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a11d751c453d716f5462803d590adbe73"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a11d751c453d716f5462803d590adbe73">operations_research::pdlp::ShardedQuadraticProgram::RescaleQuadraticProgram</a></div><div class="ttdeci">void RescaleQuadraticProgram(const Eigen::VectorXd &col_scaling_vec, const Eigen::VectorXd &row_scaling_vec)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8cc_source.html#l00120">sharded_quadratic_program.cc:120</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a1e0d1154156a56084d0ba5232819b134"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a1e0d1154156a56084d0ba5232819b134">operations_research::pdlp::ShardedQuadraticProgram::TransposedConstraintMatrix</a></div><div class="ttdeci">const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > & TransposedConstraintMatrix() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00049">sharded_quadratic_program.h:49</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a8bf92cdb63b602aba6f4d22b975e2f30"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a8bf92cdb63b602aba6f4d22b975e2f30">operations_research::pdlp::ShardedQuadraticProgram::TransposedConstraintMatrixSharder</a></div><div class="ttdeci">const Sharder & TransposedConstraintMatrixSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00058">sharded_quadratic_program.h:58</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_ab7ab55f549e3f9c1a1c8c8d2b766f75b"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab7ab55f549e3f9c1a1c8c8d2b766f75b">operations_research::pdlp::ShardedQuadraticProgram::PrimalSharder</a></div><div class="ttdeci">const Sharder & PrimalSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00062">sharded_quadratic_program.h:62</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_ab945b88f1937277a896d4c7c7935d605"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">operations_research::pdlp::ShardedQuadraticProgram::PrimalSize</a></div><div class="ttdeci">int64_t PrimalSize() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00066">sharded_quadratic_program.h:66</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_abfdc79e4b2325ff283b7d2333d40fffe"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#abfdc79e4b2325ff283b7d2333d40fffe">operations_research::pdlp::ShardedQuadraticProgram::Qp</a></div><div class="ttdeci">const QuadraticProgram & Qp() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00045">sharded_quadratic_program.h:45</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_ac9f7db642c1b4c4fc37f489f03d110a7"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ac9f7db642c1b4c4fc37f489f03d110a7">operations_research::pdlp::ShardedQuadraticProgram::ConstraintMatrixSharder</a></div><div class="ttdeci">const Sharder & ConstraintMatrixSharder() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00054">sharded_quadratic_program.h:54</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_afcafa95b1a351212291c7a030deec52a"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">operations_research::pdlp::ShardedQuadraticProgram::DualSize</a></div><div class="ttdeci">int64_t DualSize() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8h_source.html#l00067">sharded_quadratic_program.h:67</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_weighted_average_html_a1e57e9610f2a8aef08167fe8f0501eb8"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#a1e57e9610f2a8aef08167fe8f0501eb8">operations_research::pdlp::ShardedWeightedAverage::ShardedWeightedAverage</a></div><div class="ttdeci">ShardedWeightedAverage(const Sharder *sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00045">sharded_optimization_utils.cc:45</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_weighted_average_html_a67840b47c5130550899905f06eba16da"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#a67840b47c5130550899905f06eba16da">operations_research::pdlp::ShardedWeightedAverage::Add</a></div><div class="ttdeci">void Add(const Eigen::VectorXd &datapoint, double weight)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00056">sharded_optimization_utils.cc:56</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_weighted_average_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::pdlp::ShardedWeightedAverage::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00067">sharded_optimization_utils.cc:67</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_weighted_average_html_ab1e40710c900002a2cf0af3e6c490bde"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_weighted_average.html#ab1e40710c900002a2cf0af3e6c490bde">operations_research::pdlp::ShardedWeightedAverage::ComputeAverage</a></div><div class="ttdeci">Eigen::VectorXd ComputeAverage() const</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00075">sharded_optimization_utils.cc:75</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_1_1_shard_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html">operations_research::pdlp::Sharder::Shard</a></div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00055">sharder.h:55</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_1_1_shard_html_a8ef12397d1682615bc3108c397734179"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder_1_1_shard.html#a8ef12397d1682615bc3108c397734179">operations_research::pdlp::Sharder::Shard::Index</a></div><div class="ttdeci">int Index() const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00127">sharder.h:127</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html">operations_research::pdlp::Sharder</a></div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00034">sharder.h:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_a5bbfc4ed3da7a0815ba5f6c7ddee320b"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">operations_research::pdlp::Sharder::ParallelForEachShard</a></div><div class="ttdeci">void ParallelForEachShard(const std::function< void(const Shard &)> &func) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00097">sharder.cc:97</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_a9761cf0a21e5b7efe9126765eec48a3a"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#a9761cf0a21e5b7efe9126765eec48a3a">operations_research::pdlp::Sharder::ParallelTrueForAllShards</a></div><div class="ttdeci">bool ParallelTrueForAllShards(const std::function< bool(const Shard &)> &func) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00140">sharder.cc:140</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_aa6c18d04d5fcbe7a9343768b8b66be7f"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#aa6c18d04d5fcbe7a9343768b8b66be7f">operations_research::pdlp::Sharder::NumShards</a></div><div class="ttdeci">int NumShards() const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00181">sharder.h:181</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharder_html_ada07b6c423e2d359a22b11df7c9fef0a"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharder.html#ada07b6c423e2d359a22b11df7c9fef0a">operations_research::pdlp::Sharder::NumElements</a></div><div class="ttdeci">int64_t NumElements() const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8h_source.html#l00184">sharder.h:184</a></div></div>
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<div class="ttc" id="alocal__search_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="local__search_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="local__search_8cc_source.html#l02750">local_search.cc:2750</a></div></div>
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<div class="ttc" id="amathutil_8h_html"><div class="ttname"><a href="mathutil_8h.html">mathutil.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html">operations_research::pdlp</a></div><div class="ttdef"><b>Definition:</b> <a href="iteration__stats_8cc_source.html#l00040">iteration_stats.cc:40</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a11831586b99d28a708bc103bce1a945e"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a11831586b99d28a708bc103bce1a945e">operations_research::pdlp::Dot</a></div><div class="ttdeci">double Dot(const VectorXd &v1, const VectorXd &v2, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00197">sharder.cc:197</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a259d3f73717a2ababa9df2dd43914656"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a259d3f73717a2ababa9df2dd43914656">operations_research::pdlp::ComputePrimalGradient</a></div><div class="ttdeci">LagrangianPart ComputePrimalGradient(const ShardedQuadraticProgram &sharded_qp, const VectorXd &primal_solution, const VectorXd &dual_product)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00462">sharded_optimization_utils.cc:462</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a463586ded0a114d3ca4b97a048d37d8a"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">operations_research::pdlp::TransposedMatrixVectorProduct</a></div><div class="ttdeci">VectorXd TransposedMatrixVectorProduct(const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > &matrix, const VectorXd &vector, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00151">sharder.cc:151</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a54ded6625965f8ddd342161a55263cce"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a54ded6625965f8ddd342161a55263cce">operations_research::pdlp::LInfRuizRescaling</a></div><div class="ttdeci">void LInfRuizRescaling(const ShardedQuadraticProgram &sharded_qp, const int num_iterations, VectorXd &row_scaling_vec, VectorXd &col_scaling_vec)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00425">sharded_optimization_utils.cc:425</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a608ed26a4c7ff3bdcb22d25ff890f47d"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a608ed26a4c7ff3bdcb22d25ff890f47d">operations_research::pdlp::ComputeDualGradient</a></div><div class="ttdeci">LagrangianPart ComputeDualGradient(const ShardedQuadraticProgram &sharded_qp, const Eigen::VectorXd &dual_solution, const Eigen::VectorXd &primal_product)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00518">sharded_optimization_utils.cc:518</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a649a0e24412692f36d1d6c1301caf1d1"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a649a0e24412692f36d1d6c1301caf1d1">operations_research::pdlp::kInfinity</a></div><div class="ttdeci">constexpr double kInfinity</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00039">sharded_optimization_utils.cc:39</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a69a3cf251337531692721a574033a9df"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">operations_research::pdlp::ScaledColLInfNorm</a></div><div class="ttdeci">VectorXd ScaledColLInfNorm(const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > &matrix, const VectorXd &row_scaling_vec, const VectorXd &col_scaling_vec, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00258">sharder.cc:258</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a6fe6fa17061fa3b8610cce9cf707574f"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a6fe6fa17061fa3b8610cce9cf707574f">operations_research::pdlp::DualSubgradientCoefficient</a></div><div class="ttdeci">double DualSubgradientCoefficient(const double constraint_lower_bound, const double constraint_upper_bound, const double dual, const double primal_product)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00492">sharded_optimization_utils.cc:492</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a77dbe245ed9fb597ad836b27ac989f26"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a77dbe245ed9fb597ad836b27ac989f26">operations_research::pdlp::HasValidBounds</a></div><div class="ttdeci">bool HasValidBounds(const QuadraticProgram &qp)</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8cc_source.html#l00084">quadratic_program.cc:84</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a850865b3deabb2a623e130691df99f15"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a850865b3deabb2a623e130691df99f15">operations_research::pdlp::IsLinearProgram</a></div><div class="ttdeci">bool IsLinearProgram(const QuadraticProgram &qp)</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00150">quadratic_program.h:150</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a880902cb3a98b7205fa57be9e16a82c7"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a880902cb3a98b7205fa57be9e16a82c7">operations_research::pdlp::EstimateMaximumSingularValueOfConstraintMatrix</a></div><div class="ttdeci">SingularValueAndIterations EstimateMaximumSingularValueOfConstraintMatrix(const ShardedQuadraticProgram &sharded_qp, const absl::optional< VectorXd > &primal_solution, const absl::optional< VectorXd > &dual_solution, const double desired_relative_error, const double failure_probability, std::mt19937 &mt_generator)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00706">sharded_optimization_utils.cc:706</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a898c0c776a5736cf1931036d0d370724"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a898c0c776a5736cf1931036d0d370724">operations_research::pdlp::ProjectToDualVariableBounds</a></div><div class="ttdeci">void ProjectToDualVariableBounds(const ShardedQuadraticProgram &sharded_qp, VectorXd &dual)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00762">sharded_optimization_utils.cc:762</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a920005e41b36a7a0c7f4ad148ad7069d"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a920005e41b36a7a0c7f4ad148ad7069d">operations_research::pdlp::CoefficientWiseProductInPlace</a></div><div class="ttdeci">void CoefficientWiseProductInPlace(const VectorXd &scale, const Sharder &sharder, VectorXd &dest)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00182">sharder.cc:182</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a9dee2894b8028a57b7f7d2306b402e44"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a9dee2894b8028a57b7f7d2306b402e44">operations_research::pdlp::L2NormRescaling</a></div><div class="ttdeci">void L2NormRescaling(const ShardedQuadraticProgram &sharded_qp, VectorXd &row_scaling_vec, VectorXd &col_scaling_vec)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00432">sharded_optimization_utils.cc:432</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_aa3c5dd95681fe94691be1407d6bb62aa"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#aa3c5dd95681fe94691be1407d6bb62aa">operations_research::pdlp::ScaledColL2Norm</a></div><div class="ttdeci">VectorXd ScaledColL2Norm(const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > &matrix, const VectorXd &row_scaling_vec, const VectorXd &col_scaling_vec, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00280">sharder.cc:280</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_aac68304831a1bc81557fb03623a619d6"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#aac68304831a1bc81557fb03623a619d6">operations_research::pdlp::ApplyRescaling</a></div><div class="ttdeci">ScalingVectors ApplyRescaling(const RescalingOptions &rescaling_options, ShardedQuadraticProgram &sharded_qp)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00439">sharded_optimization_utils.cc:439</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_ab315578d37cb2f5e1111b0176254cb84"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#ab315578d37cb2f5e1111b0176254cb84">operations_research::pdlp::ComputeStats</a></div><div class="ttdeci">QuadraticProgramStats ComputeStats(const ShardedQuadraticProgram &qp, const double infinite_constraint_bound_threshold)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00303">sharded_optimization_utils.cc:303</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_aba946188cad9bee97f5f8206e15496e5"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">operations_research::pdlp::IsDiagonal</a></div><div class="ttdeci">bool IsDiagonal(const Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > &matrix, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00304">sharder.cc:304</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_acb7f29f435d6c9fc53148ee403c7049e"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#acb7f29f435d6c9fc53148ee403c7049e">operations_research::pdlp::ProjectToPrimalVariableBounds</a></div><div class="ttdeci">void ProjectToPrimalVariableBounds(const ShardedQuadraticProgram &sharded_qp, VectorXd &primal)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00751">sharded_optimization_utils.cc:751</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_ade56a0bd875b06000c45e1730398e5a8"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#ade56a0bd875b06000c45e1730398e5a8">operations_research::pdlp::Norm</a></div><div class="ttdeci">double Norm(const VectorXd &vector, const Sharder &sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00220">sharder.cc:220</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_afca8f74da7e8301c8aee45f33c93896c"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#afca8f74da7e8301c8aee45f33c93896c">operations_research::pdlp::AssignVector</a></div><div class="ttdeci">void AssignVector(const VectorXd &vec, const Sharder &sharder, VectorXd &dest)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00169">sharder.cc:169</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a5a9881f8a07b166ef2cbde572cea27b6"><div class="ttname"><a href="namespaceoperations__research.html#a5a9881f8a07b166ef2cbde572cea27b6">operations_research::Zero</a></div><div class="ttdeci">int64_t Zero()</div><div class="ttdoc">NOLINT.</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_8h_source.html#l03161">constraint_solver.h:3161</a></div></div>
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<div class="ttc" id="apack_8cc_html_a4255f714cea26cdd64f6a0ee72d34a8c"><div class="ttname"><a href="pack_8cc.html#a4255f714cea26cdd64f6a0ee72d34a8c">weight</a></div><div class="ttdeci">int64_t weight</div><div class="ttdef"><b>Definition:</b> <a href="pack_8cc_source.html#l00510">pack.cc:510</a></div></div>
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<div class="ttc" id="aquadratic__program_8h_html"><div class="ttname"><a href="quadratic__program_8h.html">quadratic_program.h</a></div></div>
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<div class="ttc" id="asat_2lp__utils_8cc_html_a561d7bf12fc7674b3fe0ad2ba2e175a0"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a></div><div class="ttdeci">std::vector< double > lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00606">sat/lp_utils.cc:606</a></div></div>
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<div class="ttc" id="asat_2lp__utils_8cc_html_a88215c8581662c40eec0fb8621c44af3"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a></div><div class="ttdeci">std::vector< double > upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00607">sat/lp_utils.cc:607</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a229a2d9c49444ad43e50c4efddb3b607"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a229a2d9c49444ad43e50c4efddb3b607">smallest</a></div><div class="ttdeci">double smallest</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00100">sharded_optimization_utils.cc:100</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a2a897122b37c5a906205687aecdb627b"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a2a897122b37c5a906205687aecdb627b">l2_norm</a></div><div class="ttdeci">double l2_norm</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00102">sharded_optimization_utils.cc:102</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a2bc5760472b765b9ccbba08b19a93ac1"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a2bc5760472b765b9ccbba08b19a93ac1">min_row_norm</a></div><div class="ttdeci">double min_row_norm</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00109">sharded_optimization_utils.cc:109</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a2e50537b138c27e2e30e8d3a568fbee0"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a2e50537b138c27e2e30e8d3a568fbee0">average</a></div><div class="ttdeci">double average</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00101">sharded_optimization_utils.cc:101</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a4d37e0f041f757e75ba8ac17ded9cfbc"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a4d37e0f041f757e75ba8ac17ded9cfbc">num_nonzero</a></div><div class="ttdeci">int64_t num_nonzero</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00098">sharded_optimization_utils.cc:98</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a50b61c289d15248d14d7e2560242f08c"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a50b61c289d15248d14d7e2560242f08c">max_row_norm</a></div><div class="ttdeci">double max_row_norm</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00108">sharded_optimization_utils.cc:108</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a7c25263f41ff0baff82a0faaf3630ce4"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a7c25263f41ff0baff82a0faaf3630ce4">num_finite</a></div><div class="ttdeci">int64_t num_finite</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00097">sharded_optimization_utils.cc:97</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_a90a377dabbff2504d9c2c3a51030d216"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#a90a377dabbff2504d9c2c3a51030d216">largest</a></div><div class="ttdeci">double largest</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00099">sharded_optimization_utils.cc:99</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_aa2e8644f5973aaf5614f7694ef29281d"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#aa2e8644f5973aaf5614f7694ef29281d">max_col_norm</a></div><div class="ttdeci">double max_col_norm</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00106">sharded_optimization_utils.cc:106</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8cc_html_aed33cfe7d4d1bcda205ef2b972014b69"><div class="ttname"><a href="sharded__optimization__utils_8cc.html#aed33cfe7d4d1bcda205ef2b972014b69">min_col_norm</a></div><div class="ttdeci">double min_col_norm</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8cc_source.html#l00107">sharded_optimization_utils.cc:107</a></div></div>
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<div class="ttc" id="asharded__optimization__utils_8h_html"><div class="ttname"><a href="sharded__optimization__utils_8h.html">sharded_optimization_utils.h</a></div></div>
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<div class="ttc" id="asharded__quadratic__program_8h_html"><div class="ttname"><a href="sharded__quadratic__program_8h.html">sharded_quadratic_program.h</a></div></div>
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<div class="ttc" id="asharder_8h_html"><div class="ttname"><a href="sharder_8h.html">sharder.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_lagrangian_part_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html">operations_research::pdlp::LagrangianPart</a></div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00125">sharded_optimization_utils.h:125</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_lagrangian_part_html_a1cb87fb26e738040e82cbc0c02444be9"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_lagrangian_part.html#a1cb87fb26e738040e82cbc0c02444be9">operations_research::pdlp::LagrangianPart::gradient</a></div><div class="ttdeci">Eigen::VectorXd gradient</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00127">sharded_optimization_utils.h:127</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">operations_research::pdlp::QuadraticProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00054">quadratic_program.h:54</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_a097d329b7af662bea9b5a8e310a22726"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">operations_research::pdlp::QuadraticProgram::variable_upper_bounds</a></div><div class="ttdeci">Eigen::VectorXd variable_upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00133">quadratic_program.h:133</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_a0f72e7b49f91d0b980f5a54a18c06964"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">operations_research::pdlp::QuadraticProgram::variable_lower_bounds</a></div><div class="ttdeci">Eigen::VectorXd variable_lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00133">quadratic_program.h:133</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_a61349a88b7e83784a92be3d231cfa638"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">operations_research::pdlp::QuadraticProgram::constraint_lower_bounds</a></div><div class="ttdeci">Eigen::VectorXd constraint_lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00132">quadratic_program.h:132</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_ae7a462ef3035095eff6c883ae0078d02"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">operations_research::pdlp::QuadraticProgram::constraint_matrix</a></div><div class="ttdeci">Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t > constraint_matrix</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00131">quadratic_program.h:131</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_ae816a5fdb4bdd9b7af551cc7e88d2eb5"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae816a5fdb4bdd9b7af551cc7e88d2eb5">operations_research::pdlp::QuadraticProgram::objective_matrix</a></div><div class="ttdeci">std::optional< Eigen::DiagonalMatrix< double, Eigen::Dynamic > > objective_matrix</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00130">quadratic_program.h:130</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_af2acc3fce9196f0cd70ed7505923234c"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">operations_research::pdlp::QuadraticProgram::constraint_upper_bounds</a></div><div class="ttdeci">Eigen::VectorXd constraint_upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00132">quadratic_program.h:132</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_quadratic_program_html_afdb3e07cd380793e1b265c1fded94edd"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#afdb3e07cd380793e1b265c1fded94edd">operations_research::pdlp::QuadraticProgram::objective_vector</a></div><div class="ttdeci">Eigen::VectorXd objective_vector</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00127">quadratic_program.h:127</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_rescaling_options_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_rescaling_options.html">operations_research::pdlp::RescalingOptions</a></div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00110">sharded_optimization_utils.h:110</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_rescaling_options_html_a74bba1825289ddbad8bf96e840ebfeab"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_rescaling_options.html#a74bba1825289ddbad8bf96e840ebfeab">operations_research::pdlp::RescalingOptions::l2_norm_rescaling</a></div><div class="ttdeci">bool l2_norm_rescaling</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00112">sharded_optimization_utils.h:112</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_rescaling_options_html_ad3f4c83145ae0a650089a980c4c7fe60"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_rescaling_options.html#ad3f4c83145ae0a650089a980c4c7fe60">operations_research::pdlp::RescalingOptions::l_inf_ruiz_iterations</a></div><div class="ttdeci">int l_inf_ruiz_iterations</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00111">sharded_optimization_utils.h:111</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_scaling_vectors_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_scaling_vectors.html">operations_research::pdlp::ScalingVectors</a></div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00115">sharded_optimization_utils.h:115</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_scaling_vectors_html_a5e823e9942e65836de2aa9ac368af52b"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_scaling_vectors.html#a5e823e9942e65836de2aa9ac368af52b">operations_research::pdlp::ScalingVectors::row_scaling_vec</a></div><div class="ttdeci">Eigen::VectorXd row_scaling_vec</div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00116">sharded_optimization_utils.h:116</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1pdlp_1_1_singular_value_and_iterations_html"><div class="ttname"><a href="structoperations__research_1_1pdlp_1_1_singular_value_and_iterations.html">operations_research::pdlp::SingularValueAndIterations</a></div><div class="ttdef"><b>Definition:</b> <a href="sharded__optimization__utils_8h_source.html#l00168">sharded_optimization_utils.h:168</a></div></div>
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