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<a href="sharder__test_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="sharder_8h.html">ortools/pdlp/sharder.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;algorithm&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include &lt;numeric&gt;</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;random&gt;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include &quot;Eigen/Core&quot;</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include &quot;Eigen/SparseCore&quot;</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &quot;absl/random/distributions.h&quot;</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &quot;gmock/gmock.h&quot;</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include &quot;gtest/gtest.h&quot;</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</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="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include &quot;<a class="code" href="mathutil_8h.html">ortools/base/mathutil.h</a>&quot;</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</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="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</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="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span>using ::Eigen::DiagonalMatrix;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span>using ::Eigen::VectorXd;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span>using ::testing::DoubleNear;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>using ::testing::ElementsAre;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span>using ::testing::Test;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="keyword">using</span> Shard = Sharder::Shard;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// Returns a sparse representation of the matrix</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// 7 -0.5 . .</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// 1 . 3 2</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// -1 . . 5</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span>Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; TestSparseMatrix() {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat(3, 4);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> mat.coeffRef(0, 0) = 7;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> mat.coeffRef(0, 1) = -0.5;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> mat.coeffRef(1, 0) = 1;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> mat.coeffRef(1, 2) = 3;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> mat.coeffRef(1, 3) = 2;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> mat.coeffRef(2, 0) = -1;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> mat.coeffRef(2, 3) = 5;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> mat.makeCompressed();</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">return</span> mat;</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><span class="comment">// A random matrix with a power law distribution of non-zeros per col.</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// Specifically col i has order n/(i+1) non-zeros in expectation.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; LargeSparseMatrix(</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">const</span> int64_t size) {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// Deterministic RNG.</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> std::mt19937 rand(48709241);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> std::vector&lt;Eigen::Triplet&lt;double, int64_t&gt;&gt; triplets;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</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; size; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> int64_t <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = -1;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">while</span> (<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> &lt; size) {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> += absl::Uniform(rand, 1, <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> + 2);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> &lt; size) {</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> = absl::Uniform(rand, 1, 10);</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> triplets.emplace_back(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> }</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat(size, size);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> mat.setFromTriplets(triplets.begin(), triplets.end());</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">return</span> mat;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span>}</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment">// Verify that the given sharder is consistent and has shards of reasonable</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment">// mass. Requires target_num_shards &gt; 0 and !element_masses.empty().</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="keywordtype">void</span> VerifySharder(<span class="keyword">const</span> Sharder&amp; sharder, <span class="keyword">const</span> <span class="keywordtype">int</span> target_num_shards,</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">const</span> std::vector&lt;int64_t&gt;&amp; element_masses) {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> int64_t num_elements = element_masses.size();</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordtype">int</span> num_shards = sharder.NumShards();</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> ASSERT_EQ(sharder.NumElements(), num_elements);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> ASSERT_GE(num_elements, 1);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> ASSERT_GE(num_shards, 1);</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> int64_t elements_so_far = 0;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> shard = 0; shard &lt; num_shards; ++shard) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> int64_t shard_start = sharder.ShardStart(shard);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> EXPECT_EQ(shard_start, elements_so_far) &lt;&lt; <span class="stringliteral">&quot; in shard: &quot;</span> &lt;&lt; shard;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> int64_t shard_mass = 0;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> EXPECT_GE(sharder.ShardSize(shard), 1) &lt;&lt; <span class="stringliteral">&quot; in shard: &quot;</span> &lt;&lt; shard;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> EXPECT_GE(sharder.ShardMass(shard), 1) &lt;&lt; <span class="stringliteral">&quot; in shard: &quot;</span> &lt;&lt; shard;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; sharder.ShardSize(shard); ++i) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> shard_mass += element_masses[shard_start + i];</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> EXPECT_EQ(shard_mass, sharder.ShardMass(shard)) &lt;&lt; <span class="stringliteral">&quot; in shard: &quot;</span> &lt;&lt; shard;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> elements_so_far += sharder.ShardSize(shard);</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> }</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> EXPECT_EQ(elements_so_far, num_elements);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> EXPECT_LE(num_shards, 2 * target_num_shards);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> ASSERT_GE(target_num_shards, 1);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">const</span> int64_t overall_mass =</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::accumulate(element_masses.begin(), element_masses.end(), int64_t{0});</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">const</span> int64_t max_element_mass =</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> *std::max_element(element_masses.begin(), element_masses.end());</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">const</span> int64_t upper_mass_limit = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> max_element_mass,</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_function" href="classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157">MathUtil::CeilOfRatio</a>(max_element_mass, int64_t{2}) +</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <a class="code hl_function" href="classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157">MathUtil::CeilOfRatio</a>(overall_mass, int64_t{target_num_shards}));</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keyword">const</span> int64_t lower_mass_limit =</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> overall_mass / target_num_shards -</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_function" href="classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157">MathUtil::CeilOfRatio</a>(max_element_mass, int64_t{2});</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> shard = 0; shard &lt; sharder.NumShards(); ++shard) {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> EXPECT_LE(sharder.ShardMass(shard), upper_mass_limit)</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> &lt;&lt; <span class="stringliteral">&quot; in shard: &quot;</span> &lt;&lt; shard;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">if</span> (shard + 1 &lt; sharder.NumShards()) {</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> EXPECT_GE(sharder.ShardMass(shard), lower_mass_limit)</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> &lt;&lt; <span class="stringliteral">&quot; in shard: &quot;</span> &lt;&lt; shard;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> }</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span>}</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, SharderFromMatrix) {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat =</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> TestSparseMatrix();</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> VerifySharder(sharder, 2, {4, 2, 2, 3});</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span>}</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharder) {</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>10, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> VerifySharder(sharder, 3, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1});</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><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharderFromOtherSharder) {</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> Sharder other_sharder(<span class="comment">/*num_elements=*/</span>5, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> Sharder sharder(other_sharder, <span class="comment">/*num_elements=*/</span>10);</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> VerifySharder(sharder, other_sharder.NumShards(),</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> {1, 1, 1, 1, 1, 1, 1, 1, 1, 1});</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span>}</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><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharderExcessiveShards) {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>5, <span class="comment">/*num_shards=*/</span>7, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> EXPECT_THAT(sharder.ShardStartsForTesting(), ElementsAre(0, 1, 2, 3, 4, 5));</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> VerifySharder(sharder, 7, {1, 1, 1, 1, 1});</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span>}</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharderOneShard) {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>5, <span class="comment">/*num_shards=*/</span>1, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> EXPECT_THAT(sharder.ShardStartsForTesting(), ElementsAre(0, 5));</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> VerifySharder(sharder, 1, {1, 1, 1, 1, 1});</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span>}</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharderOneElementVector) {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>1, <span class="comment">/*num_shards=*/</span>5, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> EXPECT_THAT(sharder.ShardStartsForTesting(), ElementsAre(0, 1));</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> VerifySharder(sharder, 5, {1});</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span>}</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharderZeroElementVector) {</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>0, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> EXPECT_THAT(sharder.ShardStartsForTesting(), ElementsAre(0));</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> EXPECT_EQ(sharder.NumShards(), 0);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> EXPECT_EQ(sharder.NumElements(), 0);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> sharder.ParallelForEachShard([](<span class="keyword">const</span> Shard&amp; <span class="comment">/*shard*/</span>) {</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#acdd38e3c9f22f127d7776920e3079eda">FATAL</a>) &lt;&lt; <span class="stringliteral">&quot;There are no shards so this shouldn&#39;t be called.&quot;</span>;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> });</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span>}</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SharderTest, UniformSharderFromOtherZeroElementSharder) {</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> Sharder empty_sharder(<span class="comment">/*num_elements=*/</span>0, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> EXPECT_THAT(empty_sharder.ShardStartsForTesting(), ElementsAre(0));</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> EXPECT_EQ(empty_sharder.NumShards(), 0);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> EXPECT_EQ(empty_sharder.NumElements(), 0);</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> Sharder sharder(empty_sharder, <span class="comment">/*num_elements=*/</span>5);</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> EXPECT_THAT(sharder.ShardStartsForTesting(), ElementsAre(0, 5));</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> VerifySharder(sharder, 1, {1, 1, 1, 1, 1});</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span>}</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> </div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelSumOverShards, SmallExample) {</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> VectorXd vec(3);</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> Sharder sharder(vec.size(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum = sharder.ParallelSumOverShards(</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> [&amp;vec](<span class="keyword">const</span> Shard&amp; shard) { <span class="keywordflow">return</span> shard(vec).sum(); });</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> EXPECT_EQ(sum, 6.0);</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span>}</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelSumOverShards, SmallExampleUsingVectorBlock) {</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> VectorXd vec(3);</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keyword">auto</span> vec_block = vec.segment(1, 2);</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> Sharder sharder(vec_block.size(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum = sharder.ParallelSumOverShards(</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> [&amp;vec_block](<span class="keyword">const</span> Shard&amp; shard) { <span class="keywordflow">return</span> shard(vec_block).sum(); });</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> EXPECT_EQ(sum, 5.0);</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>}</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelSumOverShards, SmallExampleUsingConstVectorBlock) {</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> VectorXd vec(3);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keyword">const</span> VectorXd&amp; const_vec = vec;</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keyword">auto</span> vec_block = const_vec.segment(1, 2);</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> Sharder sharder(vec_block.size(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum = sharder.ParallelSumOverShards(</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> [&amp;vec_block](<span class="keyword">const</span> Shard&amp; shard) { <span class="keywordflow">return</span> shard(vec_block).sum(); });</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> EXPECT_EQ(sum, 5.0);</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span>}</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelSumOverShards, SmallExampleUsingDiagonalMatrix) {</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> DiagonalMatrix&lt;double, Eigen::Dynamic&gt; diag{{1, 2, 3}};</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> Sharder sharder(diag.cols(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">const</span> <span class="keywordtype">double</span> sum = sharder.ParallelSumOverShards(</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> [&amp;diag](<span class="keyword">const</span> Shard&amp; shard) { <span class="keywordflow">return</span> shard(diag).diagonal().sum(); });</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> EXPECT_EQ(sum, 6.0);</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span>}</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> </div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelSumOverShards, SmallExampleUsingDiagonalMatrixMultiplication) {</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> DiagonalMatrix&lt;double, Eigen::Dynamic&gt; diag{{1, 2, 3}};</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> VectorXd vec{{1, 1, 1}};</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> VectorXd answer(3);</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> Sharder sharder(diag.cols(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> sharder.ParallelForEachShard(</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> [&amp;](<span class="keyword">const</span> Shard&amp; shard) { shard(answer) = shard(diag) * shard(vec); });</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> EXPECT_THAT(answer, ElementsAre(1.0, 2.0, 3.0));</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span>}</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelTrueForAllShards, SmallTrueExample) {</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> VectorXd vec(3);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> Sharder sharder(vec.size(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> result = sharder.ParallelTrueForAllShards(</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> [&amp;vec](<span class="keyword">const</span> Shard&amp; shard) { <span class="keywordflow">return</span> (shard(vec).array() &gt; 0.0).all(); });</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> EXPECT_TRUE(result);</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span>}</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ParallelTrueForAllShards, SmallFalseExample) {</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> VectorXd vec(3);</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> Sharder sharder(vec.size(), <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> result = sharder.ParallelTrueForAllShards(</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> [&amp;vec](<span class="keyword">const</span> Shard&amp; shard) { <span class="keywordflow">return</span> (shard(vec).array() &lt; 2.5).all(); });</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> EXPECT_FALSE(result);</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span>}</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> </div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(MatrixVectorProductTest, SmallExample) {</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat =</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> TestSparseMatrix();</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> VectorXd vec(3);</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> VectorXd ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">TransposedMatrixVectorProduct</a>(mat, vec, sharder);</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> EXPECT_THAT(ans, ElementsAre(6.0, -0.5, 6.0, 19));</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span>}</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(AddScaledVectorTest, SmallExample) {</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> Sharder sharder(3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> VectorXd vec1(3), vec2(3);</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> vec1 &lt;&lt; 4, 5, 20;</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> vec2 &lt;&lt; 1, 7, 3;</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a904cea6c14ac90eea354da5d70ec1719">AddScaledVector</a>(2.0, vec2, sharder, <span class="comment">/*dest=*/</span>vec1);</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> EXPECT_THAT(vec1, ElementsAre(6, 19, 26));</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span>}</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(AssignVectorTest, SmallExample) {</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> VectorXd vec1, vec2(3);</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> vec2 &lt;&lt; 1, 7, 3;</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#afca8f74da7e8301c8aee45f33c93896c">AssignVector</a>(vec2, sharder, <span class="comment">/*dest=*/</span>vec1);</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> EXPECT_THAT(vec1, ElementsAre(1, 7, 3));</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span>}</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> </div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(CloneVectorTest, SmallExample) {</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> VectorXd vec(3);</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> vec &lt;&lt; 1, 7, 3;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> EXPECT_THAT(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aaa4a3bad4a7c95a6d68387ba8ae8c104">CloneVector</a>(vec, sharder), ElementsAre(1, 7, 3));</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span>}</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> </div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(CoefficientWiseProductInPlaceTest, SmallExample) {</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> VectorXd vec1(3), vec2(3);</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> vec1 &lt;&lt; 4, 5, 20;</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> vec2 &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a920005e41b36a7a0c7f4ad148ad7069d">CoefficientWiseProductInPlace</a>(<span class="comment">/*scale=*/</span>vec2, sharder,</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="comment">/*dest=*/</span>vec1);</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> EXPECT_THAT(vec1, ElementsAre(4, 10, 60));</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span>}</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> </div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(CoefficientWiseQuotientInPlaceTest, SmallExample) {</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> VectorXd vec1(3), vec2(3);</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> vec1 &lt;&lt; 4, 6, 20;</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> vec2 &lt;&lt; 1, 2, 5;</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a92c8ca6bf2bb288c322e1d8fbd6ea2bc">CoefficientWiseQuotientInPlace</a>(<span class="comment">/*scale=*/</span>vec2, sharder,</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="comment">/*dest=*/</span>vec1);</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> EXPECT_THAT(vec1, ElementsAre(4, 3, 4));</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span>}</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> </div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(DotTest, SmallExample) {</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> VectorXd vec1(3), vec2(3);</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> vec1 &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> vec2 &lt;&lt; 4, 5, 6;</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a11831586b99d28a708bc103bce1a945e">Dot</a>(vec1, vec2, sharder);</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> EXPECT_THAT(ans, DoubleNear(4 + 10 + 18, 1.0e-13));</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span>}</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(LInfNormTest, SmallExample) {</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> VectorXd vec(3);</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> vec &lt;&lt; -1, 2, -3;</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a33a42241df5501b0165ee77c3de54d7f">LInfNorm</a>(vec, sharder);</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> EXPECT_EQ(ans, 3);</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span>}</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(LInfNormTest, EmptyExample) {</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>0, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> VectorXd vec(0);</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a33a42241df5501b0165ee77c3de54d7f">LInfNorm</a>(vec, sharder);</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> EXPECT_EQ(ans, 0);</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span>}</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(L1NormTest, SmallExample) {</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> VectorXd vec(3);</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> vec &lt;&lt; -1, 2, -3;</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aa577696ad9121b3f002cd37de6f86989">L1Norm</a>(vec, sharder);</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> EXPECT_EQ(ans, 6);</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span>}</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> </div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(L1NormTest, EmptyExample) {</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>0, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> VectorXd vec(0);</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aa577696ad9121b3f002cd37de6f86989">L1Norm</a>(vec, sharder);</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> EXPECT_EQ(ans, 0);</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span>}</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SquaredNormTest, SmallExample) {</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> VectorXd vec(3);</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a051e8994e91729e038b6cab678ef5f89">SquaredNorm</a>(vec, sharder);</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> EXPECT_THAT(ans, DoubleNear(1 + 4 + 9, 1.0e-13));</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span>}</div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> </div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(NormTest, SmallExample) {</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> VectorXd vec(3);</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> vec &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#ade56a0bd875b06000c45e1730398e5a8">Norm</a>(vec, sharder);</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> EXPECT_THAT(ans, DoubleNear(std::sqrt(1 + 4 + 9), 1.0e-13));</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span>}</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> </div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(SquaredDistanceTest, SmallExample) {</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> VectorXd vec1(3);</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> VectorXd vec2(3);</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> vec1 &lt;&lt; 1, 1, 1;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> vec2 &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a32389515e696df20cec86493cf9852e6">SquaredDistance</a>(vec1, vec2, sharder);</div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> EXPECT_THAT(ans, DoubleNear(5, 1.0e-13));</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span>}</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(DistanceTest, SmallExample) {</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> VectorXd vec1(3);</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> VectorXd vec2(3);</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> vec1 &lt;&lt; 1, 1, 1;</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> vec2 &lt;&lt; 1, 2, 3;</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a3e28f45b9c1ccdec8d926b4034d3679b">Distance</a>(vec1, vec2, sharder);</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> EXPECT_THAT(ans, DoubleNear(std::sqrt(5), 1.0e-13));</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span>}</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> </div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ScaledLInfNormTest, SmallExample) {</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> VectorXd vec(3);</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> VectorXd scale(3);</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> vec &lt;&lt; -1, 2, -3;</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> scale &lt;&lt; 4, 6, 1;</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a55b8c43a5adfafddb030074c75aeef70">ScaledLInfNorm</a>(vec, scale, sharder);</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> EXPECT_EQ(ans, 12);</div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span>}</div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> </div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ScaledSquaredNormTest, SmallExample) {</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> VectorXd vec(3);</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> VectorXd scale(3);</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> vec &lt;&lt; -1, 2, -3;</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> scale &lt;&lt; 4, 6, 1;</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a65f71a53d7766ac4c753d2218887cf98">ScaledSquaredNorm</a>(vec, scale, sharder);</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> EXPECT_EQ(ans, 169);</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span>}</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> </div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(ScaledNormTest, SmallExample) {</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> Sharder sharder(<span class="comment">/*num_elements=*/</span>3, <span class="comment">/*num_shards=*/</span>2, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> VectorXd vec(3);</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> VectorXd scale(3);</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> vec &lt;&lt; -1, 2, -3;</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> scale &lt;&lt; 4, 6, 1;</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="keywordtype">double</span> ans = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a0b812156619599417e29521a41b7a734">ScaledNorm</a>(vec, scale, sharder);</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> EXPECT_EQ(ans, std::sqrt(169));</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span>}</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> </div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">ScaledColLInfNorm</a>, SmallExample) {</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat =</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> TestSparseMatrix();</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> VectorXd row_scaling_vec(3);</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> VectorXd col_scaling_vec(4);</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> row_scaling_vec &lt;&lt; 1, -2, 1;</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> col_scaling_vec &lt;&lt; 1, 2, -1, -1;</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> VectorXd answer =</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a69a3cf251337531692721a574033a9df">ScaledColLInfNorm</a>(mat, row_scaling_vec, col_scaling_vec, sharder);</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> EXPECT_THAT(answer, ElementsAre(7, 1, 6, 5));</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span>}</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> </div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aa3c5dd95681fe94691be1407d6bb62aa">ScaledColL2Norm</a>, SmallExample) {</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat =</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> TestSparseMatrix();</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> VectorXd row_scaling_vec(3);</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> VectorXd col_scaling_vec(4);</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> row_scaling_vec &lt;&lt; 1, -2, 1;</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> col_scaling_vec &lt;&lt; 1, 2, -1, -1;</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> VectorXd answer =</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aa3c5dd95681fe94691be1407d6bb62aa">ScaledColL2Norm</a>(mat, row_scaling_vec, col_scaling_vec, sharder);</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> EXPECT_THAT(answer, ElementsAre(std::sqrt(54), 1.0, 6.0, std::sqrt(41)));</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span>}</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> </div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>, DiagonalSquareMatrix) {</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat(4, 4);</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> std::vector&lt;Eigen::Triplet&lt;double, int64_t&gt;&gt; matrix_triplets = {</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> {0, 0, 1.0}, {1, 1, 2.5}, {3, 3, -3}};</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> mat.setFromTriplets(matrix_triplets.begin(), matrix_triplets.end());</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> EXPECT_TRUE(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>(mat, sharder));</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span>}</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> </div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>, DiagonalRectangularMatrix) {</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat(3, 5);</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> std::vector&lt;Eigen::Triplet&lt;double, int64_t&gt;&gt; matrix_triplets = {</div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> {0, 0, 2}, {1, 1, -1}, {2, 2, 3}};</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> mat.setFromTriplets(matrix_triplets.begin(), matrix_triplets.end());</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> EXPECT_TRUE(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>(mat, sharder));</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span>}</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> </div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span><a class="code hl_function" href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">TEST</a>(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>, NonDiagonalSquareMatrix) {</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat(3, 3);</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> std::vector&lt;Eigen::Triplet&lt;double, int64_t&gt;&gt; matrix_triplets = {</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> {0, 0, 2}, {0, 1, -1}, {1, 0, -1}, {2, 2, 1}};</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> mat.setFromTriplets(matrix_triplets.begin(), matrix_triplets.end());</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> Sharder sharder(mat, <span class="comment">/*num_shards=*/</span>3, <span class="keyword">nullptr</span>);</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> EXPECT_FALSE(<a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#aba946188cad9bee97f5f8206e15496e5">IsDiagonal</a>(mat, sharder));</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span>}</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> </div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span><span class="keyword">class </span>VariousSizesTest : <span class="keyword">public</span> testing::TestWithParam&lt;int64_t&gt; {};</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> </div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span>TEST_P(VariousSizesTest, LargeMatVec) {</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="keyword">const</span> int64_t size = GetParam();</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> Eigen::SparseMatrix&lt;double, Eigen::ColMajor, int64_t&gt; mat =</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> LargeSparseMatrix(size);</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_threads = 5;</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keyword">const</span> <span class="keywordtype">int</span> shards_per_thread = 3;</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> ThreadPool pool(<span class="stringliteral">&quot;MatrixVectorProductTest&quot;</span>, num_threads);</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> pool.StartWorkers();</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> Sharder sharder(mat, shards_per_thread * num_threads, &amp;pool);</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> VectorXd rhs = VectorXd::Random(size);</div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> VectorXd direct = mat.transpose() * rhs;</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> VectorXd threaded = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a463586ded0a114d3ca4b97a048d37d8a">TransposedMatrixVectorProduct</a>(mat, rhs, sharder);</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> EXPECT_LE((direct - threaded).norm(), 1.0e-8);</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span>}</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> </div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span>TEST_P(VariousSizesTest, LargeVectors) {</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="keyword">const</span> int64_t size = GetParam();</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_threads = 5;</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> ThreadPool pool(<span class="stringliteral">&quot;SquaredNormTest&quot;</span>, num_threads);</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> pool.StartWorkers();</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> Sharder sharder(size, num_threads, &amp;pool);</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> VectorXd vec = VectorXd::Random(size);</div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> <span class="keyword">const</span> <span class="keywordtype">double</span> direct = vec.squaredNorm();</div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> <span class="keyword">const</span> <span class="keywordtype">double</span> threaded = <a class="code hl_function" href="namespaceoperations__research_1_1pdlp.html#a051e8994e91729e038b6cab678ef5f89">SquaredNorm</a>(vec, sharder);</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> EXPECT_THAT(threaded, DoubleNear(direct, size * 1.0e-14));</div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span>}</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> </div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span>INSTANTIATE_TEST_SUITE_P(VariousSizesTestInstantiation, VariousSizesTest,</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> testing::Values(10, 1000, 100 * 1000));</div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> </div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span>} <span class="comment">// namespace</span></div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span>} <span class="comment">// namespace operations_research::pdlp</span></div>
<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>
<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_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_math_util_html_a0cfaf8b139304c54e3403d4ffbd60157"><div class="ttname"><a href="classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157">operations_research::MathUtil::CeilOfRatio</a></div><div class="ttdeci">static IntegralType CeilOfRatio(IntegralType numerator, IntegralType denominator)</div><div class="ttdef"><b>Definition:</b> <a href="mathutil_8h_source.html#l00039">mathutil.h:39</a></div></div>
<div class="ttc" id="ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
<div class="ttc" id="alog__severity_8h_html_acdd38e3c9f22f127d7776920e3079eda"><div class="ttname"><a href="log__severity_8h.html#acdd38e3c9f22f127d7776920e3079eda">FATAL</a></div><div class="ttdeci">const int FATAL</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00032">log_severity.h:32</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="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
<div class="ttc" id="amathutil_8h_html"><div class="ttname"><a href="mathutil_8h.html">mathutil.h</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_a051e8994e91729e038b6cab678ef5f89"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a051e8994e91729e038b6cab678ef5f89">operations_research::pdlp::SquaredNorm</a></div><div class="ttdeci">double SquaredNorm(const VectorXd &amp;vector, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00215">sharder.cc:215</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a0b812156619599417e29521a41b7a734"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a0b812156619599417e29521a41b7a734">operations_research::pdlp::ScaledNorm</a></div><div class="ttdeci">double ScaledNorm(const VectorXd &amp;vector, const VectorXd &amp;scale, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00253">sharder.cc:253</a></div></div>
<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 &amp;v1, const VectorXd &amp;v2, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00197">sharder.cc:197</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a32389515e696df20cec86493cf9852e6"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a32389515e696df20cec86493cf9852e6">operations_research::pdlp::SquaredDistance</a></div><div class="ttdeci">double SquaredDistance(const VectorXd &amp;vector1, const VectorXd &amp;vector2, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00224">sharder.cc:224</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a33a42241df5501b0165ee77c3de54d7f"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a33a42241df5501b0165ee77c3de54d7f">operations_research::pdlp::LInfNorm</a></div><div class="ttdeci">double LInfNorm(const VectorXd &amp;vector, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00202">sharder.cc:202</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a3e28f45b9c1ccdec8d926b4034d3679b"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a3e28f45b9c1ccdec8d926b4034d3679b">operations_research::pdlp::Distance</a></div><div class="ttdeci">double Distance(const VectorXd &amp;vector1, const VectorXd &amp;vector2, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00231">sharder.cc:231</a></div></div>
<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&lt; double, Eigen::ColMajor, int64_t &gt; &amp;matrix, const VectorXd &amp;vector, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00151">sharder.cc:151</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a55b8c43a5adfafddb030074c75aeef70"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a55b8c43a5adfafddb030074c75aeef70">operations_research::pdlp::ScaledLInfNorm</a></div><div class="ttdeci">double ScaledLInfNorm(const VectorXd &amp;vector, const VectorXd &amp;scale, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00236">sharder.cc:236</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a65f71a53d7766ac4c753d2218887cf98"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a65f71a53d7766ac4c753d2218887cf98">operations_research::pdlp::ScaledSquaredNorm</a></div><div class="ttdeci">double ScaledSquaredNorm(const VectorXd &amp;vector, const VectorXd &amp;scale, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00246">sharder.cc:246</a></div></div>
<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&lt; double, Eigen::ColMajor, int64_t &gt; &amp;matrix, const VectorXd &amp;row_scaling_vec, const VectorXd &amp;col_scaling_vec, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00258">sharder.cc:258</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a904cea6c14ac90eea354da5d70ec1719"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a904cea6c14ac90eea354da5d70ec1719">operations_research::pdlp::AddScaledVector</a></div><div class="ttdeci">void AddScaledVector(const double scale, const VectorXd &amp;increment, const Sharder &amp;sharder, VectorXd &amp;dest)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00162">sharder.cc:162</a></div></div>
<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 &amp;scale, const Sharder &amp;sharder, VectorXd &amp;dest)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00182">sharder.cc:182</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_a92c8ca6bf2bb288c322e1d8fbd6ea2bc"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#a92c8ca6bf2bb288c322e1d8fbd6ea2bc">operations_research::pdlp::CoefficientWiseQuotientInPlace</a></div><div class="ttdeci">void CoefficientWiseQuotientInPlace(const VectorXd &amp;scale, const Sharder &amp;sharder, VectorXd &amp;dest)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00190">sharder.cc:190</a></div></div>
<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&lt; double, Eigen::ColMajor, int64_t &gt; &amp;matrix, const VectorXd &amp;row_scaling_vec, const VectorXd &amp;col_scaling_vec, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00280">sharder.cc:280</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_aa577696ad9121b3f002cd37de6f86989"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#aa577696ad9121b3f002cd37de6f86989">operations_research::pdlp::L1Norm</a></div><div class="ttdeci">double L1Norm(const VectorXd &amp;vector, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00210">sharder.cc:210</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1pdlp_html_aaa4a3bad4a7c95a6d68387ba8ae8c104"><div class="ttname"><a href="namespaceoperations__research_1_1pdlp.html#aaa4a3bad4a7c95a6d68387ba8ae8c104">operations_research::pdlp::CloneVector</a></div><div class="ttdeci">VectorXd CloneVector(const VectorXd &amp;vec, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00175">sharder.cc:175</a></div></div>
<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&lt; double, Eigen::ColMajor, int64_t &gt; &amp;matrix, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00304">sharder.cc:304</a></div></div>
<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 &amp;vector, const Sharder &amp;sharder)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00220">sharder.cc:220</a></div></div>
<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 &amp;vec, const Sharder &amp;sharder, VectorXd &amp;dest)</div><div class="ttdef"><b>Definition:</b> <a href="sharder_8cc_source.html#l00169">sharder.cc:169</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_a817553ad64738460e5c339f24fe5ea13"><div class="ttname"><a href="namespaceoperations__research.html#a817553ad64738460e5c339f24fe5ea13">operations_research::TEST</a></div><div class="ttdeci">TEST(LinearAssignmentTest, NullMatrix)</div><div class="ttdef"><b>Definition:</b> <a href="hungarian__test_8cc_source.html#l00074">hungarian_test.cc:74</a></div></div>
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