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<h1 style="color: #145A32;">C++ Reference: Linear solver</h1>
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<a href="linear__expr_8h.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">#ifndef OR_TOOLS_LINEAR_SOLVER_LINEAR_EXPR_H_</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_LINEAR_SOLVER_LINEAR_EXPR_H_</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="preprocessor">#include &lt;ostream&gt;</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="preprocessor">#include &lt;string&gt;</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="preprocessor">#include &quot;absl/container/flat_hash_map.h&quot;</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html"> 84</a></span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// NOTE(user): forward declaration is necessary due to cyclic dependencies,</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">// MPVariable is defined in linear_solver.h, which depends on LinearExpr.</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_m_p_variable.html">MPVariable</a>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html"> 114</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> {</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a708e7b52aae1fa3c440ef7ced3f06cd9"> 116</a></span> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a708e7b52aae1fa3c440ef7ced3f06cd9">LinearExpr</a>();</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a7b163def8264a8ab405bb6069340d2c6"> 118</a></span> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a7b163def8264a8ab405bb6069340d2c6">LinearExpr</a>(<span class="keywordtype">double</span> constant); <span class="comment">// NOLINT</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"> 120</span><span class="comment"> /***</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment"> * Possible implicit conversions are intentional.</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment"> *</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment"> * Warning: var is not owned.</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment"> */</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#ab2ca0acd2e70df1dbf8ec0d516bc7fcc"> 125</a></span> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#ab2ca0acd2e70df1dbf8ec0d516bc7fcc">LinearExpr</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_m_p_variable.html">MPVariable</a>* var); <span class="comment">// NOLINT</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a11dac3cad352ecca7e70e1c82b93a419"> 134</a></span> <span class="keyword">static</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a11dac3cad352ecca7e70e1c82b93a419">NotVar</a>(<a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> var);</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> </div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a8bf5a8a9a39766ad2665df3918fa16f5"> 136</a></span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a8bf5a8a9a39766ad2665df3918fa16f5">operator+=</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a8e15a84c5f3a2689174372cc15e62848"> 137</a></span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a8e15a84c5f3a2689174372cc15e62848">operator-=</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a76cff2db2d37cf7bb3853edae5791536"> 138</a></span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a76cff2db2d37cf7bb3853edae5791536">operator*=</a>(<span class="keywordtype">double</span> rhs);</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a9e9625e3efbde1a73eaf5a49d11487fc"> 139</a></span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a9e9625e3efbde1a73eaf5a49d11487fc">operator/=</a>(<span class="keywordtype">double</span> rhs);</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a32985ab0882c48b374e1d26e0fdf9ce6"> 140</a></span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a32985ab0882c48b374e1d26e0fdf9ce6">operator-</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a96ffc785b7b2135c7980c985883ffdd3"> 142</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a96ffc785b7b2135c7980c985883ffdd3">offset</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> offset_; }</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#afb42f5cebaf659f1a302d5062a576af0"> 143</a></span> <span class="keyword">const</span> absl::flat_hash_map&lt;const MPVariable*, double&gt;&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#afb42f5cebaf659f1a302d5062a576af0">terms</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordflow">return</span> terms_;</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="l00152" name="l00152"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a1953d5ae154875095008836cd15ab348"> 152</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a1953d5ae154875095008836cd15ab348">SolutionValue</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_expr.html#a19c380b03cea21d7ac7325136a131ff0"> 158</a></span> std::string <a class="code hl_function" href="classoperations__research_1_1_linear_expr.html#a19c380b03cea21d7ac7325136a131ff0">ToString</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordtype">double</span> offset_;</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> absl::flat_hash_map&lt;const MPVariable*, double&gt; terms_;</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"><a class="line" href="namespaceoperations__research.html#a6dcd119b77400c438a8a316093d553f2"> 165</a></span>std::ostream&amp; <a class="code hl_function" href="namespaceoperations__research.html#a6dcd119b77400c438a8a316093d553f2">operator&lt;&lt;</a>(std::ostream&amp; stream, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; linear_expr);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="comment">// NOTE(user): in the ops below, the non-&quot;const LinearExpr&amp;&quot; are intentional.</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="comment">// We need to create a new LinearExpr for the result, so we lose nothing by</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment">// passing one argument by value, mutating it, and then returning it. In</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment">// particular, this allows (with move semantics and RVO) an optimized</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment">// evaluation of expressions such as</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="comment">// a + b + c + d</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="comment">// (see http://en.cppreference.com/w/cpp/language/operators).</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a97f9b83239285f5fdfcac1b8e8b4f162"> 174</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="namespaceoperations__research.html#a97f9b83239285f5fdfcac1b8e8b4f162">operator+</a>(<a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> lhs, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a515cdaf4f9c4000bb3482a0c450e23c3"> 175</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="namespaceoperations__research.html#a515cdaf4f9c4000bb3482a0c450e23c3">operator-</a>(<a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> lhs, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a138bb0f103cd9d68e4d13fa773901186"> 176</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="namespaceoperations__research.html#a138bb0f103cd9d68e4d13fa773901186">operator*</a>(<a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> lhs, <span class="keywordtype">double</span> rhs);</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#abebdd7f40e90df8dc7d557b6e26da942"> 177</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="namespaceoperations__research.html#abebdd7f40e90df8dc7d557b6e26da942">operator/</a>(<a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> lhs, <span class="keywordtype">double</span> rhs);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a62b131d2829f1cdacd2414d2d7bc6c7c"> 178</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> <a class="code hl_function" href="namespaceoperations__research.html#a138bb0f103cd9d68e4d13fa773901186">operator*</a>(<span class="keywordtype">double</span> lhs, <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> rhs);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_range.html"> 192</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_linear_range.html">LinearRange</a> {</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_range.html#a32ea297f2577df1857c480c965f0b6b7"> 194</a></span> <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a32ea297f2577df1857c480c965f0b6b7">LinearRange</a>() : lower_bound_(0), upper_bound_(0) {}</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_range.html#ac594ef42ae702537dd3fcd7dee8742a2"> 202</a></span> <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#ac594ef42ae702537dd3fcd7dee8742a2">LinearRange</a>(<span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a9748ce3280b2d4c16a2cd38a480b9c7c">lower_bound</a>, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a4b3f32be654fc87e926e6c1cb2167fc0">linear_expr</a>,</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a5158072d27a176fc38524893183d6527">upper_bound</a>);</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_range.html#a9748ce3280b2d4c16a2cd38a480b9c7c"> 205</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a9748ce3280b2d4c16a2cd38a480b9c7c">lower_bound</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> lower_bound_; }</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_range.html#a4b3f32be654fc87e926e6c1cb2167fc0"> 206</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a4b3f32be654fc87e926e6c1cb2167fc0">linear_expr</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> linear_expr_; }</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_linear_range.html#a5158072d27a176fc38524893183d6527"> 207</a></span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1_linear_range.html#a5158072d27a176fc38524893183d6527">upper_bound</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> upper_bound_; }</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> </div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordtype">double</span> lower_bound_;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="comment">// invariant: linear_expr_.offset() == 0.</span></div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a> linear_expr_;</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keywordtype">double</span> upper_bound_;</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> </div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a6d1fa20f9c9faf7027c0b16f97139e80"> 216</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_range.html">LinearRange</a> <a class="code hl_function" href="namespaceoperations__research.html#a6d1fa20f9c9faf7027c0b16f97139e80">operator&lt;=</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; lhs, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a08146f196bd9c3f492ee108732449ced"> 217</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_range.html">LinearRange</a> <a class="code hl_function" href="namespaceoperations__research.html#a08146f196bd9c3f492ee108732449ced">operator==</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; lhs, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ac4052f92af6a7fbb1d45e17befcb68e0"> 218</a></span><a class="code hl_class" href="classoperations__research_1_1_linear_range.html">LinearRange</a> <a class="code hl_function" href="namespaceoperations__research.html#ac4052f92af6a7fbb1d45e17befcb68e0">operator&gt;=</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; lhs, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_linear_expr.html">LinearExpr</a>&amp; rhs);</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span><span class="comment">// TODO(user): explore defining more overloads to support:</span></div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span><span class="comment">// solver.AddRowConstraint(0.0 &lt;= x + y + z &lt;= 1.0);</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>} <span class="comment">// namespace operations_research</span></div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_LINEAR_SOLVER_LINEAR_EXPR_H_</span></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html">operations_research::LinearExpr</a></div><div class="ttdoc">LinearExpr models a quantity that is linear in the decision variables (MPVariable) of an optimization...</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00114">linear_expr.h:114</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a11dac3cad352ecca7e70e1c82b93a419"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a11dac3cad352ecca7e70e1c82b93a419">operations_research::LinearExpr::NotVar</a></div><div class="ttdeci">static LinearExpr NotVar(LinearExpr var)</div><div class="ttdoc">Returns 1-var.</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a1953d5ae154875095008836cd15ab348"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a1953d5ae154875095008836cd15ab348">operations_research::LinearExpr::SolutionValue</a></div><div class="ttdeci">double SolutionValue() const</div><div class="ttdoc">Evaluates the value of this expression at the solution found.</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a19c380b03cea21d7ac7325136a131ff0"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a19c380b03cea21d7ac7325136a131ff0">operations_research::LinearExpr::ToString</a></div><div class="ttdeci">std::string ToString() const</div><div class="ttdoc">A human readable representation of this.</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a32985ab0882c48b374e1d26e0fdf9ce6"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a32985ab0882c48b374e1d26e0fdf9ce6">operations_research::LinearExpr::operator-</a></div><div class="ttdeci">LinearExpr operator-() const</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a708e7b52aae1fa3c440ef7ced3f06cd9"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a708e7b52aae1fa3c440ef7ced3f06cd9">operations_research::LinearExpr::LinearExpr</a></div><div class="ttdeci">LinearExpr()</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a76cff2db2d37cf7bb3853edae5791536"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a76cff2db2d37cf7bb3853edae5791536">operations_research::LinearExpr::operator*=</a></div><div class="ttdeci">LinearExpr &amp; operator*=(double rhs)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a7b163def8264a8ab405bb6069340d2c6"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a7b163def8264a8ab405bb6069340d2c6">operations_research::LinearExpr::LinearExpr</a></div><div class="ttdeci">LinearExpr(double constant)</div><div class="ttdoc">Possible implicit conversions are intentional.</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a8bf5a8a9a39766ad2665df3918fa16f5"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a8bf5a8a9a39766ad2665df3918fa16f5">operations_research::LinearExpr::operator+=</a></div><div class="ttdeci">LinearExpr &amp; operator+=(const LinearExpr &amp;rhs)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a8e15a84c5f3a2689174372cc15e62848"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a8e15a84c5f3a2689174372cc15e62848">operations_research::LinearExpr::operator-=</a></div><div class="ttdeci">LinearExpr &amp; operator-=(const LinearExpr &amp;rhs)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a96ffc785b7b2135c7980c985883ffdd3"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a96ffc785b7b2135c7980c985883ffdd3">operations_research::LinearExpr::offset</a></div><div class="ttdeci">double offset() const</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00142">linear_expr.h:142</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_a9e9625e3efbde1a73eaf5a49d11487fc"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#a9e9625e3efbde1a73eaf5a49d11487fc">operations_research::LinearExpr::operator/=</a></div><div class="ttdeci">LinearExpr &amp; operator/=(double rhs)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_ab2ca0acd2e70df1dbf8ec0d516bc7fcc"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#ab2ca0acd2e70df1dbf8ec0d516bc7fcc">operations_research::LinearExpr::LinearExpr</a></div><div class="ttdeci">LinearExpr(const MPVariable *var)</div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_expr_html_afb42f5cebaf659f1a302d5062a576af0"><div class="ttname"><a href="classoperations__research_1_1_linear_expr.html#afb42f5cebaf659f1a302d5062a576af0">operations_research::LinearExpr::terms</a></div><div class="ttdeci">const absl::flat_hash_map&lt; const MPVariable *, double &gt; &amp; terms() const</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00143">linear_expr.h:143</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_range_html"><div class="ttname"><a href="classoperations__research_1_1_linear_range.html">operations_research::LinearRange</a></div><div class="ttdoc">An expression of the form:</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00192">linear_expr.h:192</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_range_html_a32ea297f2577df1857c480c965f0b6b7"><div class="ttname"><a href="classoperations__research_1_1_linear_range.html#a32ea297f2577df1857c480c965f0b6b7">operations_research::LinearRange::LinearRange</a></div><div class="ttdeci">LinearRange()</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00194">linear_expr.h:194</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_range_html_a4b3f32be654fc87e926e6c1cb2167fc0"><div class="ttname"><a href="classoperations__research_1_1_linear_range.html#a4b3f32be654fc87e926e6c1cb2167fc0">operations_research::LinearRange::linear_expr</a></div><div class="ttdeci">const LinearExpr &amp; linear_expr() const</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00206">linear_expr.h:206</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_range_html_a5158072d27a176fc38524893183d6527"><div class="ttname"><a href="classoperations__research_1_1_linear_range.html#a5158072d27a176fc38524893183d6527">operations_research::LinearRange::upper_bound</a></div><div class="ttdeci">double upper_bound() const</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00207">linear_expr.h:207</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_range_html_a9748ce3280b2d4c16a2cd38a480b9c7c"><div class="ttname"><a href="classoperations__research_1_1_linear_range.html#a9748ce3280b2d4c16a2cd38a480b9c7c">operations_research::LinearRange::lower_bound</a></div><div class="ttdeci">double lower_bound() const</div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00205">linear_expr.h:205</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1_linear_range_html_ac594ef42ae702537dd3fcd7dee8742a2"><div class="ttname"><a href="classoperations__research_1_1_linear_range.html#ac594ef42ae702537dd3fcd7dee8742a2">operations_research::LinearRange::LinearRange</a></div><div class="ttdeci">LinearRange(double lower_bound, const LinearExpr &amp;linear_expr, double upper_bound)</div><div class="ttdoc">The bounds of the linear range are updated so that they include the offset from &quot;linear_expr&quot;,...</div></div>
<div class="ttc" id="aclassoperations__research_1_1_m_p_variable_html"><div class="ttname"><a href="classoperations__research_1_1_m_p_variable.html">operations_research::MPVariable</a></div><div class="ttdoc">The class for variables of a Mathematical Programming (MP) model.</div><div class="ttdef"><b>Definition:</b> <a href="linear__solver_8h_source.html#l01093">linear_solver.h:1093</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__expr_8h_source.html#l00084">linear_expr.h:84</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html_a08146f196bd9c3f492ee108732449ced"><div class="ttname"><a href="namespaceoperations__research.html#a08146f196bd9c3f492ee108732449ced">operations_research::operator==</a></div><div class="ttdeci">LinearRange operator==(const LinearExpr &amp;lhs, const LinearExpr &amp;rhs)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_a138bb0f103cd9d68e4d13fa773901186"><div class="ttname"><a href="namespaceoperations__research.html#a138bb0f103cd9d68e4d13fa773901186">operations_research::operator*</a></div><div class="ttdeci">LinearExpr operator*(LinearExpr lhs, double rhs)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_a515cdaf4f9c4000bb3482a0c450e23c3"><div class="ttname"><a href="namespaceoperations__research.html#a515cdaf4f9c4000bb3482a0c450e23c3">operations_research::operator-</a></div><div class="ttdeci">LinearExpr operator-(LinearExpr lhs, const LinearExpr &amp;rhs)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_a6d1fa20f9c9faf7027c0b16f97139e80"><div class="ttname"><a href="namespaceoperations__research.html#a6d1fa20f9c9faf7027c0b16f97139e80">operations_research::operator&lt;=</a></div><div class="ttdeci">LinearRange operator&lt;=(const LinearExpr &amp;lhs, const LinearExpr &amp;rhs)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_a6dcd119b77400c438a8a316093d553f2"><div class="ttname"><a href="namespaceoperations__research.html#a6dcd119b77400c438a8a316093d553f2">operations_research::operator&lt;&lt;</a></div><div class="ttdeci">std::ostream &amp; operator&lt;&lt;(std::ostream &amp;stream, const LinearExpr &amp;linear_expr)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_a97f9b83239285f5fdfcac1b8e8b4f162"><div class="ttname"><a href="namespaceoperations__research.html#a97f9b83239285f5fdfcac1b8e8b4f162">operations_research::operator+</a></div><div class="ttdeci">LinearExpr operator+(LinearExpr lhs, const LinearExpr &amp;rhs)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_abebdd7f40e90df8dc7d557b6e26da942"><div class="ttname"><a href="namespaceoperations__research.html#abebdd7f40e90df8dc7d557b6e26da942">operations_research::operator/</a></div><div class="ttdeci">LinearExpr operator/(LinearExpr lhs, double rhs)</div></div>
<div class="ttc" id="anamespaceoperations__research_html_ac4052f92af6a7fbb1d45e17befcb68e0"><div class="ttname"><a href="namespaceoperations__research.html#ac4052f92af6a7fbb1d45e17befcb68e0">operations_research::operator&gt;=</a></div><div class="ttdeci">LinearRange operator&gt;=(const LinearExpr &amp;lhs, const LinearExpr &amp;rhs)</div></div>
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