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<a href="glpk__computational__form_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 headers defines APIs that wrap GLPK APIs for indices of variables from</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// the computational form.</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">//</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// In GLPK (for details see glpk-5.0/doc/glpk.pdf available from</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// glpk-5.0.tar.gz) the general form of the problem is:</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">//</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// min (or max) z = c^T x_S + c_0</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// s.t. x_R = A x_S</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// l_R <= x_R <= u_R</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// l_S <= x_S <= u_S</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">//</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// where:</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// x_S are the structural variables</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// x_R are the auxiliary variables used to define constraints</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">//</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// This is this form that is used by most GLPK's APIs.</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">//</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// But to implement the simplex algorithms, GLPK uses the following</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// computational form:</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">//</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// min (or max) z = (0 | c)^T x + c_0</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// s.t. (I | -A) x = 0</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// l <= x <= u</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">//</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// where:</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// x = (x_R | x_S)</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">//</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// That is it merges the auxiliary and structural variables in a single set of</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// variables.</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">//</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// The dual of this problem is, when the primal is a minimization:</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">//</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// max Z = l^T λ_l + u^T λ_u</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// s.t. (I | -A)^T π + λ_l + λ_u = (O | c)^T</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// λ_l >= 0, λ_u <= 0</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">//</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// and if the primal is a maximization:</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">//</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// min Z = l^T λ_l + u^T λ_u</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// s.t. (I | -A)^T π + λ_l + λ_u = (O | c)^T</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// λ_l <= 0, λ_u >= 0</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">//</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// There is a reduced cost λ_k for each variable x_k:</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">//</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// λ = λ_l + λ_u</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">//</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// This header contains basic adapter functions that takes the index of a</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// variable x in the computational form and use the corresponding API for either</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">// x_R or x_S (a.k.a. primal values) and for the corresponding reduced costs λ</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// (a.k.a. dual values).</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">// This logic is usually necessary when using advanced APIs that deal with</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">// indices in the computational form.</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="preprocessor">#ifndef OR_TOOLS_GLPK_GLPK_COMPUTATIONAL_FORM_H_</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="preprocessor">#define OR_TOOLS_GLPK_GLPK_COMPUTATIONAL_FORM_H_</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="keyword">extern</span> <span class="stringliteral">"C"</span> {</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="preprocessor">#include <glpk.h></span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span>}</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// Returns the status of the variable k of the computational form by calling</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// either glp_get_row_stat() or glp_get_col_stat().</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">//</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">// Here k is an index in the joint set of indices of variables and constraints</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">// in the computational form (see the comment at the top of this header for</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment">// details):</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment">//</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">// - 1 <= k <= num_cstrs: index of the k-th auxiliary variable in the general</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment">// form (the variable associate with the k-th constraint).</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">//</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// - num_cstrs + 1 <= k <= num_cstrs + num_vars: index of the (k-num_cstrs)-th</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">// structural variable in the general form.</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19"> 88</a></span><span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code hl_function" href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19">ComputeFormVarStatus</a>(glp_prob* <span class="keyword">const</span> problem, <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs,</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keyword">const</span> <span class="keywordtype">int</span> k) {</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> k <= num_cstrs ? glp_get_row_stat(problem, k)</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> : glp_get_col_stat(problem, k - num_cstrs);</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// Returns the reduced cost of the variable k of the computational form by</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// calling either glp_get_row_dual() or glp_get_col_dual().</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">//</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// See ComputeFormVarStatus() for details about k.</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a78b479e166142f91a81aa29b32f3f2bd"> 98</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research.html#a78b479e166142f91a81aa29b32f3f2bd">ComputeFormVarReducedCost</a>(glp_prob* <span class="keyword">const</span> problem,</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs, <span class="keyword">const</span> <span class="keywordtype">int</span> k) {</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">return</span> k <= num_cstrs ? glp_get_row_dual(problem, k)</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> : glp_get_col_dual(problem, k - num_cstrs);</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>}</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// Returns the primal value of the variable k of the computational form by</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// calling either glp_get_row_prim() or glp_get_col_prim().</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">//</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// See ComputeFormVarStatus() for details about k.</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a08778ed3d6825737a554d34700015bde"> 108</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research.html#a08778ed3d6825737a554d34700015bde">ComputeFormVarPrimalValue</a>(glp_prob* <span class="keyword">const</span> problem,</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs, <span class="keyword">const</span> <span class="keywordtype">int</span> k) {</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">return</span> k <= num_cstrs ? glp_get_row_prim(problem, k)</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> : glp_get_col_prim(problem, k - num_cstrs);</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span>}</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment">// Returns the lower bound of the variable k of the computational form by</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span><span class="comment">// calling either glp_get_row_lb() or glp_get_col_lb().</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment">//</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">// See ComputeFormVarStatus() for details about k.</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ab1175b5bb75d496f60b63e49399e1818"> 118</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research.html#ab1175b5bb75d496f60b63e49399e1818">ComputeFormVarLowerBound</a>(glp_prob* <span class="keyword">const</span> problem,</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs, <span class="keyword">const</span> <span class="keywordtype">int</span> k) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">return</span> k <= num_cstrs ? glp_get_row_lb(problem, k)</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> : glp_get_col_lb(problem, k - num_cstrs);</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span>}</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment">// Returns the upper bound of the variable k of the computational form by</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="comment">// calling either glp_get_row_ub() or glp_get_col_ub().</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="comment">//</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment">// See ComputeFormVarStatus() for details about k.</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ae8092de2472a0ac3308c39609792e6fb"> 128</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research.html#ae8092de2472a0ac3308c39609792e6fb">ComputeFormVarUpperBound</a>(glp_prob* <span class="keyword">const</span> problem,</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cstrs, <span class="keyword">const</span> <span class="keywordtype">int</span> k) {</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">return</span> k <= num_cstrs ? glp_get_row_ub(problem, k)</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> : glp_get_col_ub(problem, k - num_cstrs);</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>}</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> </div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_GLPK_GLPK_COMPUTATIONAL_FORM_H_</span></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a08778ed3d6825737a554d34700015bde"><div class="ttname"><a href="namespaceoperations__research.html#a08778ed3d6825737a554d34700015bde">operations_research::ComputeFormVarPrimalValue</a></div><div class="ttdeci">double ComputeFormVarPrimalValue(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00108">glpk_computational_form.h:108</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a3017e52db1c2688aa77b569b9f7a7b19"><div class="ttname"><a href="namespaceoperations__research.html#a3017e52db1c2688aa77b569b9f7a7b19">operations_research::ComputeFormVarStatus</a></div><div class="ttdeci">int ComputeFormVarStatus(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00088">glpk_computational_form.h:88</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a78b479e166142f91a81aa29b32f3f2bd"><div class="ttname"><a href="namespaceoperations__research.html#a78b479e166142f91a81aa29b32f3f2bd">operations_research::ComputeFormVarReducedCost</a></div><div class="ttdeci">double ComputeFormVarReducedCost(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00098">glpk_computational_form.h:98</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ab1175b5bb75d496f60b63e49399e1818"><div class="ttname"><a href="namespaceoperations__research.html#ab1175b5bb75d496f60b63e49399e1818">operations_research::ComputeFormVarLowerBound</a></div><div class="ttdeci">double ComputeFormVarLowerBound(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00118">glpk_computational_form.h:118</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ae8092de2472a0ac3308c39609792e6fb"><div class="ttname"><a href="namespaceoperations__research.html#ae8092de2472a0ac3308c39609792e6fb">operations_research::ComputeFormVarUpperBound</a></div><div class="ttdeci">double ComputeFormVarUpperBound(glp_prob *const problem, const int num_cstrs, const int k)</div><div class="ttdef"><b>Definition:</b> <a href="glpk__computational__form_8h_source.html#l00128">glpk_computational_form.h:128</a></div></div>
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