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<a href="rays_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>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// This header defines primal/dual unboundness ray computation functions for</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// GLPK solver. They use the index space of the computation form of the model as</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// defined in operations_research/glpk/glpk_computational_form.h.</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#ifndef OR_TOOLS_MATH_OPT_SOLVERS_GLPK_RAYS_H_</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#define OR_TOOLS_MATH_OPT_SOLVERS_GLPK_RAYS_H_</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <optional></span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "absl/status/statusor.h"</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">extern</span> <span class="stringliteral">"C"</span> {</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include <glpk.h></span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a> {</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// The type of the GlpkRay.</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7"> 33</a></span><span class="keyword">enum</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7">GlpkRayType</a> {</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// A primal ray.</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// If x (vector of variables) is a primal feasible solution to a primal</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// unbounded problem and r is the ray, then x' = x + t r is also a primal</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// feasible solution for all t >= 0.</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e"> 39</a></span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e">kPrimal</a>,</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// A dual ray.</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// If λ (vector of reduced costs) is a dual feasible solution to a dual</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// unbounded problem and r is the ray, then λ' = λ + t r is also a dual</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// feasible solution for all t >= 0.</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91"> 46</a></span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91">kDual</a>,</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span>};</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// A primal or dual unbound ray for the model in computational form.</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">//</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// See the top comment of operations_research/glpk/glpk_computational_form.h to</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// understand that the computational form is. This structure uses the word</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// "variable" to mean a variable in the joint set of structural and auxiliary</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// variables.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html"> 55</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html">GlpkRay</a> {</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd"> 56</a></span> <span class="keyword">using</span> <a class="code hl_typedef" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">SparseVector</a> = std::vector<std::pair<int, double>>;</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a488c6f810ff77a3759d6900693105bdd">GlpkRay</a>(<a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7">GlpkRayType</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ae4d99fbf696707096e05ce6d9a6643d1">type</a>, <a class="code hl_typedef" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">SparseVector</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a382af1531c239d3063ffcbcd2787368c">non_zero_components</a>);</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// The type of ray, primal or dual.</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ae4d99fbf696707096e05ce6d9a6643d1"> 61</a></span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7">GlpkRayType</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ae4d99fbf696707096e05ce6d9a6643d1">type</a>;</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// The non zero components of the vector, in no particular order.</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// The first member of the pair is the index of the variable (or of its</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// corresponding reduced cost) and the second is the component's value.</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// A given index can only appear once.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// The indices in GLPK are one-based. Here the indices are defined by:</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// - if 1 <= k <= m: k is the index of the k-th auxiliary variable</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// (a.k.a. row, a.k.a. constraint)</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// - if m + 1 <= k <= m + n: k is the index of the (k-m)-th structural</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// variable (a.k.a. column)</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// Note that the value k = 0 is not used.</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a382af1531c239d3063ffcbcd2787368c"> 76</a></span> <a class="code hl_typedef" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">SparseVector</a> <a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a382af1531c239d3063ffcbcd2787368c">non_zero_components</a>;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>};</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">// Returns the primal or dual ray if one is identified by</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">// glp_get_unbnd_ray(). Returns an error status if an internal error occurs.</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>absl::StatusOr<std::optional<GlpkRay>> <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#aa3bcd3f312f5746e50d53bd5a8dedd2a">GlpkComputeUnboundRay</a>(glp_prob* problem);</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>} <span class="comment">// namespace operations_research::math_opt</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_MATH_OPT_SOLVERS_GLPK_RAYS_H_</span></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a></div><div class="ttdef"><b>Definition:</b> <a href="arrow__operator__proxy_8h_source.html#l00020">arrow_operator_proxy.h:20</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_aa3bcd3f312f5746e50d53bd5a8dedd2a"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#aa3bcd3f312f5746e50d53bd5a8dedd2a">operations_research::math_opt::GlpkComputeUnboundRay</a></div><div class="ttdeci">absl::StatusOr< std::optional< GlpkRay > > GlpkComputeUnboundRay(glp_prob *const problem)</div><div class="ttdef"><b>Definition:</b> <a href="rays_8cc_source.html#l00351">rays.cc:351</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad6ffe3747921431333fa443d04f0dcd7"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7">operations_research::math_opt::GlpkRayType</a></div><div class="ttdeci">GlpkRayType</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00033">rays.h:33</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a168c8e12a7f30e09240e40ae392f3c1e">operations_research::math_opt::kPrimal</a></div><div class="ttdeci">@ kPrimal</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00039">rays.h:39</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad6ffe3747921431333fa443d04f0dcd7a853ead83f7e75b38bba794318254dc91">operations_research::math_opt::kDual</a></div><div class="ttdeci">@ kDual</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00046">rays.h:46</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html">operations_research::math_opt::GlpkRay</a></div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00055">rays.h:55</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html_a382af1531c239d3063ffcbcd2787368c"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a382af1531c239d3063ffcbcd2787368c">operations_research::math_opt::GlpkRay::non_zero_components</a></div><div class="ttdeci">SparseVector non_zero_components</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00076">rays.h:76</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html_a488c6f810ff77a3759d6900693105bdd"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#a488c6f810ff77a3759d6900693105bdd">operations_research::math_opt::GlpkRay::GlpkRay</a></div><div class="ttdeci">GlpkRay(GlpkRayType type, SparseVector non_zero_components)</div><div class="ttdef"><b>Definition:</b> <a href="rays_8cc_source.html#l00348">rays.cc:348</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html_ab6e7a7fab6fd3cfc7263644c7ede57bd"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ab6e7a7fab6fd3cfc7263644c7ede57bd">operations_research::math_opt::GlpkRay::SparseVector</a></div><div class="ttdeci">std::vector< std::pair< int, double > > SparseVector</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00056">rays.h:56</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_glpk_ray_html_ae4d99fbf696707096e05ce6d9a6643d1"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_glpk_ray.html#ae4d99fbf696707096e05ce6d9a6643d1">operations_research::math_opt::GlpkRay::type</a></div><div class="ttdeci">GlpkRayType type</div><div class="ttdef"><b>Definition:</b> <a href="rays_8h_source.html#l00061">rays.h:61</a></div></div>
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