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<a href="sharded__quadratic__program_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &quot;<a class="code" href="sharded__quadratic__program_8h.html">ortools/pdlp/sharded_quadratic_program.h</a>&quot;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;memory&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &quot;Eigen/Core&quot;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &quot;Eigen/SparseCore&quot;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include &quot;absl/memory/memory.h&quot;</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include &quot;absl/strings/string_view.h&quot;</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include &quot;<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>&quot;</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &quot;<a class="code" href="threadpool_8h.html">ortools/base/threadpool.h</a>&quot;</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &quot;<a class="code" href="quadratic__program_8h.html">ortools/pdlp/quadratic_program.h</a>&quot;</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include &quot;<a class="code" href="sharder_8h.html">ortools/pdlp/sharder.h</a>&quot;</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research_1_1pdlp.html">operations_research::pdlp</a> {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// Logs a warning if the given matrix has more than density_limit non-zeros in</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// a single column.</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="keywordtype">void</span> WarnIfMatrixUnbalanced(</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">const</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt;&amp; matrix,</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> absl::string_view matrix_name, int64_t density_limit) {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> (matrix.cols() == 0) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> int64_t worst_column = 0;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">for</span> (int64_t <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = 0; <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> &lt; matrix.cols(); ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">if</span> (matrix.col(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).nonZeros() &gt; matrix.col(worst_column).nonZeros()) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> worst_column = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> }</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">if</span> (matrix.col(worst_column).nonZeros() &gt; density_limit) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// TODO(user): fix this automatically in presolve instead of asking the</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// user to do it.</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#a50e5762f38854b37ee3e2851bc1bb0e7">WARNING</a>)</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> &lt;&lt; <span class="stringliteral">&quot;The &quot;</span> &lt;&lt; matrix_name &lt;&lt; <span class="stringliteral">&quot; has &quot;</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> &lt;&lt; matrix.col(worst_column).nonZeros() &lt;&lt; <span class="stringliteral">&quot; non-zeros in its &quot;</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> &lt;&lt; worst_column</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> &lt;&lt; <span class="stringliteral">&quot;th column. For best parallelization all rows and columns should &quot;</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="stringliteral">&quot;have at most order &quot;</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> &lt;&lt; density_limit</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> &lt;&lt; <span class="stringliteral">&quot; non-zeros. Consider rewriting the QP to split the corresponding &quot;</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="stringliteral">&quot;variable or constraint.&quot;</span>;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>}</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span>} <span class="comment">// namespace</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a2b0ac472da1c6933805c1f9e1a67d750"> 62</a></span><a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a2b0ac472da1c6933805c1f9e1a67d750">ShardedQuadraticProgram::ShardedQuadraticProgram</a>(<a class="code hl_struct" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html">QuadraticProgram</a> qp,</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_threads,</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_shards)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> : qp_(<a class="code hl_namespace" href="namespacestd.html">std</a>::move(qp)),</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> transposed_constraint_matrix_(qp_.constraint_matrix.transpose()),</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> thread_pool_(num_threads == 1</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> ? nullptr</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> : <a class="code hl_namespace" href="namespaceabsl.html">absl</a>::make_unique&lt;<a class="code hl_class" href="classoperations__research_1_1_thread_pool.html">ThreadPool</a>&gt;(<span class="stringliteral">&quot;PDLP&quot;</span>, num_threads)),</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> constraint_matrix_sharder_(qp_.constraint_matrix, num_shards,</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> thread_pool_.get()),</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> transposed_constraint_matrix_sharder_(transposed_constraint_matrix_,</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> num_shards, thread_pool_.get()),</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> primal_sharder_(qp_.<a class="code hl_variable" href="trust__region__test_8cc.html#a16346c4c462dec8f0cf38493c5e0358c">variable_lower_bounds</a>.size(), num_shards,</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> thread_pool_.get()),</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> dual_sharder_(qp_.constraint_lower_bounds.size(), num_shards,</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> thread_pool_.get()) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(num_threads, 1);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(num_shards, num_threads);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">if</span> (num_threads &gt; 1) {</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> thread_pool_-&gt;StartWorkers();</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">const</span> int64_t work_per_iteration = qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">constraint_matrix</a>.nonZeros() +</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>.size() +</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>.size();</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">const</span> int64_t column_density_limit = work_per_iteration / num_threads;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> WarnIfMatrixUnbalanced(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae7a462ef3035095eff6c883ae0078d02">constraint_matrix</a>, <span class="stringliteral">&quot;constraint matrix&quot;</span>,</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> column_density_limit);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> WarnIfMatrixUnbalanced(transposed_constraint_matrix_,</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="stringliteral">&quot;transposed constraint matrix&quot;</span>,</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> column_density_limit);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> }</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// Multiply each entry of the matrix by the corresponding element of</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// row_scaling_vec and col_scaling_vec, i.e., matrix[i,j] *= row_scaling_vec[i]</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// * col_scaling_vec[j].</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="keywordtype">void</span> ScaleMatrix(</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">const</span> Eigen::VectorXd&amp; col_scaling_vec,</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">const</span> Eigen::VectorXd&amp; row_scaling_vec, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1pdlp_1_1_sharder.html">Sharder</a>&amp; sharder,</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt;&amp; matrix) {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(matrix.cols(), col_scaling_vec.size());</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(matrix.rows(), row_scaling_vec.size());</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> sharder.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>([&amp;](<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>&amp; shard) {</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">auto</span> matrix_shard = shard(matrix);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">auto</span> col_scaling_vec_shard = shard(col_scaling_vec);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">for</span> (int64_t col_num = 0; col_num &lt; shard(matrix).outerSize(); ++col_num) {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">for</span> (<span class="keyword">decltype</span>(matrix_shard)::InnerIterator it(matrix_shard, col_num); it;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> ++it) {</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> it.valueRef() *=</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> row_scaling_vec[it.row()] * col_scaling_vec_shard[it.col()];</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> }</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> });</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span>}</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span>} <span class="comment">// namespace</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"><a class="line" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a11d751c453d716f5462803d590adbe73"> 120</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a11d751c453d716f5462803d590adbe73">ShardedQuadraticProgram::RescaleQuadraticProgram</a>(</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">const</span> Eigen::VectorXd&amp; col_scaling_vec,</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keyword">const</span> Eigen::VectorXd&amp; row_scaling_vec) {</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#ab945b88f1937277a896d4c7c7935d605">PrimalSize</a>(), col_scaling_vec.size());</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#afcafa95b1a351212291c7a030deec52a">DualSize</a>(), row_scaling_vec.size());</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> primal_sharder_.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>([&amp;](<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>&amp; shard) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>((shard(col_scaling_vec).array() &gt; 0.0).all());</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#afdb3e07cd380793e1b265c1fded94edd">objective_vector</a>) =</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#afdb3e07cd380793e1b265c1fded94edd">objective_vector</a>).cwiseProduct(shard(col_scaling_vec));</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>) =</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a0f72e7b49f91d0b980f5a54a18c06964">variable_lower_bounds</a>).cwiseQuotient(shard(col_scaling_vec));</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">variable_upper_bounds</a>) =</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a097d329b7af662bea9b5a8e310a22726">variable_upper_bounds</a>).cwiseQuotient(shard(col_scaling_vec));</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a850865b3deabb2a623e130691df99f15">IsLinearProgram</a>(qp_)) {</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae816a5fdb4bdd9b7af551cc7e88d2eb5">objective_matrix</a>-&gt;diagonal()) =</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#ae816a5fdb4bdd9b7af551cc7e88d2eb5">objective_matrix</a>-&gt;diagonal())</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> .cwiseProduct(</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> shard(col_scaling_vec).cwiseProduct(shard(col_scaling_vec)));</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> }</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> });</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> dual_sharder_.<a class="code hl_function" href="classoperations__research_1_1pdlp_1_1_sharder.html#a5bbfc4ed3da7a0815ba5f6c7ddee320b">ParallelForEachShard</a>([&amp;](<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>&amp; shard) {</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>((shard(row_scaling_vec).array() &gt; 0.0).all());</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>) =</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#a61349a88b7e83784a92be3d231cfa638">constraint_lower_bounds</a>).cwiseProduct(shard(row_scaling_vec));</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>) =</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> shard(qp_.<a class="code hl_variable" href="structoperations__research_1_1pdlp_1_1_quadratic_program.html#af2acc3fce9196f0cd70ed7505923234c">constraint_upper_bounds</a>).cwiseProduct(shard(row_scaling_vec));</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> });</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> ScaleMatrix(col_scaling_vec, row_scaling_vec, constraint_matrix_sharder_,</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> qp_.<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="l00150" name="l00150"></a><span class="lineno"> 150</span> ScaleMatrix(row_scaling_vec, col_scaling_vec,</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> transposed_constraint_matrix_sharder_,</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> transposed_constraint_matrix_);</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span>}</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span>} <span class="comment">// namespace operations_research::pdlp</span></div>
<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_a3e1cfef60e774a81f30eaddf26a3a274"><div class="ttname"><a href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a></div><div class="ttdeci">#define CHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00495">base/logging.h:495</a></div></div>
<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>
<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>
<div class="ttc" id="abase_2logging_8h_html_accad43a85d781d53381cd53a9894b6ae"><div class="ttname"><a href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a></div><div class="ttdeci">#define LOG(severity)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00420">base/logging.h:420</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_thread_pool_html"><div class="ttname"><a href="classoperations__research_1_1_thread_pool.html">operations_research::ThreadPool</a></div><div class="ttdef"><b>Definition:</b> <a href="threadpool_8h_source.html#l00026">threadpool.h:26</a></div></div>
<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 &amp;col_scaling_vec, const Eigen::VectorXd &amp;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>
<div class="ttc" id="aclassoperations__research_1_1pdlp_1_1_sharded_quadratic_program_html_a2b0ac472da1c6933805c1f9e1a67d750"><div class="ttname"><a href="classoperations__research_1_1pdlp_1_1_sharded_quadratic_program.html#a2b0ac472da1c6933805c1f9e1a67d750">operations_research::pdlp::ShardedQuadraticProgram::ShardedQuadraticProgram</a></div><div class="ttdeci">ShardedQuadraticProgram(QuadraticProgram qp, int num_threads, int num_shards)</div><div class="ttdef"><b>Definition:</b> <a href="sharded__quadratic__program_8cc_source.html#l00062">sharded_quadratic_program.cc:62</a></div></div>
<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>
<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>
<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>
<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>
<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&lt; void(const Shard &amp;)&gt; &amp;func) const</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00097">sharder.cc:97</a></div></div>
<div class="ttc" id="alog__severity_8h_html_a50e5762f38854b37ee3e2851bc1bb0e7"><div class="ttname"><a href="log__severity_8h.html#a50e5762f38854b37ee3e2851bc1bb0e7">WARNING</a></div><div class="ttdeci">const int WARNING</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00031">log_severity.h:31</a></div></div>
<div class="ttc" id="amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
<div class="ttc" id="anamespaceabsl_html"><div class="ttname"><a href="namespaceabsl.html">absl</a></div><div class="ttdef"><b>Definition:</b> <a href="cleanup_8h_source.html#l00022">cleanup.h:22</a></div></div>
<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>
<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 &amp;qp)</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00150">quadratic_program.h:150</a></div></div>
<div class="ttc" id="anamespacestd_html"><div class="ttname"><a href="namespacestd.html">std</a></div><div class="ttdoc">STL namespace.</div></div>
<div class="ttc" id="aquadratic__program_8h_html"><div class="ttname"><a href="quadratic__program_8h.html">quadratic_program.h</a></div></div>
<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>
<div class="ttc" id="asharder_8h_html"><div class="ttname"><a href="sharder_8h.html">sharder.h</a></div></div>
<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>
<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>
<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>
<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>
<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&lt; double, Eigen::ColMajor, int64_t &gt; constraint_matrix</div><div class="ttdef"><b>Definition:</b> <a href="quadratic__program_8h_source.html#l00131">quadratic_program.h:131</a></div></div>
<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&lt; Eigen::DiagonalMatrix&lt; double, Eigen::Dynamic &gt; &gt; 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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