<ahref="piecewise__linear__function_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aid="l00001"name="l00001"></a><spanclass="lineno"> 1</span><spanclass="comment">// Copyright 2010-2021 Google LLC</span></div>
<divclass="line"><aid="l00002"name="l00002"></a><spanclass="lineno"> 2</span><spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aid="l00003"name="l00003"></a><spanclass="lineno"> 3</span><spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aid="l00004"name="l00004"></a><spanclass="lineno"> 4</span><spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aid="l00008"name="l00008"></a><spanclass="lineno"> 8</span><spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aid="l00009"name="l00009"></a><spanclass="lineno"> 9</span><spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aid="l00010"name="l00010"></a><spanclass="lineno"> 10</span><spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aid="l00011"name="l00011"></a><spanclass="lineno"> 11</span><spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aid="l00012"name="l00012"></a><spanclass="lineno"> 12</span><spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aid="l00014"name="l00014"></a><spanclass="lineno"> 14</span><spanclass="comment">// This file implements piecewise linear functions over int64_t. It is built</span></div>
<divclass="line"><aid="l00015"name="l00015"></a><spanclass="lineno"> 15</span><spanclass="comment">// by inserting segments.</span></div>
<divclass="line"><aid="l00017"name="l00017"></a><spanclass="lineno"> 17</span><spanclass="comment">// This class maintains a minimal internal representation and checks for</span></div>
<divclass="line"><aid="l00035"name="l00035"></a><spanclass="lineno"> 35</span><spanclass="comment">// This structure stores one straight line. It contains the start point, the</span></div>
<divclass="line"><aid="l00036"name="l00036"></a><spanclass="lineno"> 36</span><spanclass="comment">// end point and the slope.</span></div>
<divclass="line"><aid="l00037"name="l00037"></a><spanclass="lineno"> 37</span><spanclass="comment">// It is defined for x values between start_x and end_x.</span></div>
<divclass="line"><aid="l00043"name="l00043"></a><spanclass="lineno"> 43</span><spanclass="comment">// Returns the value of the segment at point x.</span></div>
<divclass="line"><aid="l00045"name="l00045"></a><spanclass="lineno"> 45</span><spanclass="comment">// Returns the start of the segment's domain.</span></div>
<divclass="line"><aid="l00047"name="l00047"></a><spanclass="lineno"> 47</span><spanclass="comment">// Returns the end of the segment's domain.</span></div>
<divclass="line"><aid="l00049"name="l00049"></a><spanclass="lineno"> 49</span><spanclass="comment">// Returns the value at the start of the segment's domain.</span></div>
<divclass="line"><aid="l00051"name="l00051"></a><spanclass="lineno"> 51</span><spanclass="comment">// Returns the value at the end of the segment's domain.</span></div>
<divclass="line"><aid="l00055"name="l00055"></a><spanclass="lineno"> 55</span><spanclass="comment">// Returns the intersection of the segment's extension with the y axis.</span></div>
<divclass="line"><aid="l00058"name="l00058"></a><spanclass="lineno"> 58</span><spanclass="comment">// Comparison method useful for sorting a sequence of segments.</span></div>
<divclass="line"><aid="l00061"name="l00061"></a><spanclass="lineno"> 61</span><spanclass="comment">// Comparison method useful for finding in which segment a point belongs.</span></div>
<divclass="line"><aid="l00062"name="l00062"></a><spanclass="lineno"> 62</span><spanclass="keyword">static</span><spanclass="keywordtype">bool</span><aclass="code hl_function"href="classoperations__research_1_1_piecewise_segment.html#a77ce53a27b88c53f5fa438a08d00af34">FindComparator</a>(int64_t point, <spanclass="keyword">const</span><aclass="code hl_class"href="classoperations__research_1_1_piecewise_segment.html">PiecewiseSegment</a>& segment);</div>
<divclass="line"><aid="l00064"name="l00064"></a><spanclass="lineno"> 64</span><spanclass="comment">// Expands segment to the specified endpoint, if it is further</span></div>
<divclass="line"><aid="l00065"name="l00065"></a><spanclass="lineno"> 65</span><spanclass="comment">// than the current endpoint. The reference point of the segment</span></div>
<divclass="line"><aid="l00066"name="l00066"></a><spanclass="lineno"> 66</span><spanclass="comment">// doesn't change for overflow reasons.</span></div>
<divclass="line"><aid="l00068"name="l00068"></a><spanclass="lineno"> 68</span><spanclass="comment">// Adds 'constant' to the 'x' the segments.</span></div>
<divclass="line"><aid="l00070"name="l00070"></a><spanclass="lineno"> 70</span><spanclass="comment">// Adds 'constant' to the 'y' the segments.</span></div>
<divclass="line"><aid="l00076"name="l00076"></a><spanclass="lineno"> 76</span><spanclass="comment">// Computes the value of the segment at point x, taking care of possible</span></div>
<divclass="line"><aid="l00077"name="l00077"></a><spanclass="lineno"> 77</span><spanclass="comment">// overflows when the value x follow the x coordinate of the segment's</span></div>
<divclass="line"><aid="l00080"name="l00080"></a><spanclass="lineno"> 80</span><spanclass="comment">// Computes the value of the segment at point x, taking care of possible</span></div>
<divclass="line"><aid="l00081"name="l00081"></a><spanclass="lineno"> 81</span><spanclass="comment">// overflows when the value x follow the x coordinate of the segment's</span></div>
<divclass="line"><aid="l00085"name="l00085"></a><spanclass="lineno"> 85</span><spanclass="comment">// The x coordinate of the segment's left endpoint.</span></div>
<divclass="line"><aid="l00087"name="l00087"></a><spanclass="lineno"> 87</span><spanclass="comment">// The x coordinate of the segment's right endpoint.</span></div>
<divclass="line"><aid="l00091"name="l00091"></a><spanclass="lineno"> 91</span><spanclass="comment">// The x coordinate of the segment's finite reference point.</span></div>
<divclass="line"><aid="l00093"name="l00093"></a><spanclass="lineno"> 93</span><spanclass="comment">// The y coordinate of the segment's finite reference point.</span></div>
<divclass="line"><aid="l00095"name="l00095"></a><spanclass="lineno"> 95</span><spanclass="comment">// The intersection of the segment's extension with the y axis.</span></div>
<divclass="line"><aid="l00099"name="l00099"></a><spanclass="lineno"> 99</span><spanclass="comment">// In mathematics, a piecewise linear function is a function composed</span></div>
<divclass="line"><aid="l00100"name="l00100"></a><spanclass="lineno"> 100</span><spanclass="comment">// of straight-line, non overlapping sections.</span></div>
<divclass="line"><aid="l00105"name="l00105"></a><spanclass="lineno"> 105</span><spanclass="comment">// This API provides a factory for creating different families of Piecewise</span></div>
<divclass="line"><aid="l00106"name="l00106"></a><spanclass="lineno"> 106</span><spanclass="comment">// Linear Functions based on specific properties of each family. The</span></div>
<divclass="line"><aid="l00107"name="l00107"></a><spanclass="lineno"> 107</span><spanclass="comment">// PiecewiseLinearFunction is composed by a set of PiecwiseSegments and upon</span></div>
<divclass="line"><aid="l00108"name="l00108"></a><spanclass="lineno"> 108</span><spanclass="comment">// creation is not modifiable but with the provided function operations.</span></div>
<divclass="line"><aid="l00109"name="l00109"></a><spanclass="lineno"> 109</span><spanclass="comment">// The object returned by any of these builders in the factory is owned by</span></div>
<divclass="line"><aid="l00110"name="l00110"></a><spanclass="lineno"> 110</span><spanclass="comment">// the client code.</span></div>
<divclass="line"><aid="l00112"name="l00112"></a><spanclass="lineno"> 112</span><spanclass="comment">// Builds the most generic form of multiple-segment piecewise linear function</span></div>
<divclass="line"><aid="l00113"name="l00113"></a><spanclass="lineno"> 113</span><spanclass="comment">// supporting domain holes. For a fixed index i the elements in points_x[i]</span></div>
<divclass="line"><aid="l00114"name="l00114"></a><spanclass="lineno"> 114</span><spanclass="comment">// points_y[i], slopes[i], other_points_x[i] represent a segment.</span></div>
<divclass="line"><aid="l00115"name="l00115"></a><spanclass="lineno"> 115</span><spanclass="comment">// The point (points_x[i], points_y[i]) represents one of the endpoints of</span></div>
<divclass="line"><aid="l00116"name="l00116"></a><spanclass="lineno"> 116</span><spanclass="comment">// the segment and the other_points_x[i] represents the x coordinate of the</span></div>
<divclass="line"><aid="l00117"name="l00117"></a><spanclass="lineno"> 117</span><spanclass="comment">// other endpoint which may precede, follow or coincide with points_x[i].</span></div>
<divclass="line"><aid="l00118"name="l00118"></a><spanclass="lineno"> 118</span><spanclass="comment">// The segments represented by these vectors should not be overlapping.</span></div>
<divclass="line"><aid="l00119"name="l00119"></a><spanclass="lineno"> 119</span><spanclass="comment">// Common endpoints are allowed.</span></div>
<divclass="line"><aid="l00124"name="l00124"></a><spanclass="lineno"> 124</span><spanclass="comment">// Builds a multiple-segment step function with continuous or non continuous</span></div>
<divclass="line"><aid="l00125"name="l00125"></a><spanclass="lineno"> 125</span><spanclass="comment">// domain. The arguments have the same semantics with the generic builder of</span></div>
<divclass="line"><aid="l00126"name="l00126"></a><spanclass="lineno"> 126</span><spanclass="comment">// the piecewise linear function. In the step function all the slopes are 0.</span></div>
<divclass="line"><aid="l00131"name="l00131"></a><spanclass="lineno"> 131</span><spanclass="comment">// Builds a multiple-segment piecewise linear function with domain from</span></div>
<divclass="line"><aid="l00132"name="l00132"></a><spanclass="lineno"> 132</span><spanclass="comment">// from kint64min to kint64max with n points and n+1 slopes. Each slope</span></div>
<divclass="line"><aid="l00133"name="l00133"></a><spanclass="lineno"> 133</span><spanclass="comment">// stops at the point with the corresponding index apart from the last one</span></div>
<divclass="line"><aid="l00134"name="l00134"></a><spanclass="lineno"> 134</span><spanclass="comment">// which stops at kint64max. The first slope stops at the first point at</span></div>
<divclass="line"><aid="l00135"name="l00135"></a><spanclass="lineno"> 135</span><spanclass="comment">// the level specified.</span></div>
<divclass="line"><aid="l00140"name="l00140"></a><spanclass="lineno"> 140</span><spanclass="comment">// Builds a function consisting of one segment.</span></div>
<divclass="line"><aid="l00144"name="l00144"></a><spanclass="lineno"> 144</span><spanclass="comment">// Builds a function consisting of one ray starting at the specified</span></div>
<divclass="line"><aid="l00145"name="l00145"></a><spanclass="lineno"> 145</span><spanclass="comment">// x and y coordinates with the specified slope.</span></div>
<divclass="line"><aid="l00150"name="l00150"></a><spanclass="lineno"> 150</span><spanclass="comment">// Builds a function consisting of one ray starting at the specified</span></div>
<divclass="line"><aid="l00151"name="l00151"></a><spanclass="lineno"> 151</span><spanclass="comment">// x and y coordinates with the specified slope.</span></div>
<divclass="line"><aid="l00156"name="l00156"></a><spanclass="lineno"> 156</span><spanclass="comment">// Builds a two-segment fixed charge piecewise linear cost function. For</span></div>
<divclass="line"><aid="l00157"name="l00157"></a><spanclass="lineno"> 157</span><spanclass="comment">// values less than zero, the cost is zero. For values greater than zero,</span></div>
<divclass="line"><aid="l00158"name="l00158"></a><spanclass="lineno"> 158</span><spanclass="comment">// cost follows the line specified by the slope and the value given as</span></div>
<divclass="line"><aid="l00159"name="l00159"></a><spanclass="lineno"> 159</span><spanclass="comment">// arguments. The slope and value are positive.</span></div>
<divclass="line"><aid="l00163"name="l00163"></a><spanclass="lineno"> 163</span><spanclass="comment">// Builds an earliness-tardiness two-segment piecewise linear cost function.</span></div>
<divclass="line"><aid="l00164"name="l00164"></a><spanclass="lineno"> 164</span><spanclass="comment">// The reference specifies the point where the cost is zero. Before the</span></div>
<divclass="line"><aid="l00165"name="l00165"></a><spanclass="lineno"> 165</span><spanclass="comment">// reference, the cost increases with the earliness slope and after the</span></div>
<divclass="line"><aid="l00166"name="l00166"></a><spanclass="lineno"> 166</span><spanclass="comment">// reference, it increases with the tardiness slope. The absolute values of</span></div>
<divclass="line"><aid="l00167"name="l00167"></a><spanclass="lineno"> 167</span><spanclass="comment">// the slopes are given.</span></div>
<divclass="line"><aid="l00171"name="l00171"></a><spanclass="lineno"> 171</span><spanclass="comment">// Builds an earliness-tardiness three-segment piecewise linear cost function</span></div>
<divclass="line"><aid="l00172"name="l00172"></a><spanclass="lineno"> 172</span><spanclass="comment">// with a slack period around the due date. The early slack is the point</span></div>
<divclass="line"><aid="l00173"name="l00173"></a><spanclass="lineno"> 173</span><spanclass="comment">// before which the cost increases with the ealiness slope specified. The</span></div>
<divclass="line"><aid="l00174"name="l00174"></a><spanclass="lineno"> 174</span><spanclass="comment">// late slack is the point after which the cost increases with the late slope</span></div>
<divclass="line"><aid="l00175"name="l00175"></a><spanclass="lineno"> 175</span><spanclass="comment">// specified. Between the early and the late slack point, the cost is zero.</span></div>
<divclass="line"><aid="l00176"name="l00176"></a><spanclass="lineno"> 176</span><spanclass="comment">// The absolute values of the slopes are given.</span></div>
<divclass="line"><aid="l00181"name="l00181"></a><spanclass="lineno"> 181</span><spanclass="comment">// Returns if x is in the domain of the function.</span></div>
<divclass="line"><aid="l00183"name="l00183"></a><spanclass="lineno"> 183</span><spanclass="comment">// Determines whether the piecewise linear function is convex or non-convex</span></div>
<divclass="line"><aid="l00184"name="l00184"></a><spanclass="lineno"> 184</span><spanclass="comment">// and returns true when the function is convex.</span></div>
<divclass="line"><aid="l00186"name="l00186"></a><spanclass="lineno"> 186</span><spanclass="comment">// Returns true if the piecewise linear function is non-decreasing.</span></div>
<divclass="line"><aid="l00188"name="l00188"></a><spanclass="lineno"> 188</span><spanclass="comment">// Returns true if the piecewise linear function is non-increasing.</span></div>
<divclass="line"><aid="l00190"name="l00190"></a><spanclass="lineno"> 190</span><spanclass="comment">// Returns the value of the piecewise linear function for x.</span></div>
<divclass="line"><aid="l00192"name="l00192"></a><spanclass="lineno"> 192</span><spanclass="comment">// Returns the maximum value of all the segments in the function.</span></div>
<divclass="line"><aid="l00194"name="l00194"></a><spanclass="lineno"> 194</span><spanclass="comment">// Returns the minimum value of all the segments in the function.</span></div>
<divclass="line"><aid="l00196"name="l00196"></a><spanclass="lineno"> 196</span><spanclass="comment">// Returns the maximum endpoint value of the segments in the specified</span></div>
<divclass="line"><aid="l00197"name="l00197"></a><spanclass="lineno"> 197</span><spanclass="comment">// range. If the range is disjoint from the segments in the function, it</span></div>
<divclass="line"><aid="l00200"name="l00200"></a><spanclass="lineno"> 200</span><spanclass="comment">// Returns the minimum endpoint value of the segments in the specified</span></div>
<divclass="line"><aid="l00201"name="l00201"></a><spanclass="lineno"> 201</span><spanclass="comment">// range. If the range is disjoint from the segments in the function, it</span></div>
<divclass="line"><aid="l00204"name="l00204"></a><spanclass="lineno"> 204</span><spanclass="comment">// Returns the smallest range within a given range containing all values</span></div>
<divclass="line"><aid="l00205"name="l00205"></a><spanclass="lineno"> 205</span><spanclass="comment">// greater than a given value.</span></div>
<divclass="line"><aid="l00208"name="l00208"></a><spanclass="lineno"> 208</span><spanclass="comment">// Returns the smallest range within a given range containing all values</span></div>
<divclass="line"><aid="l00209"name="l00209"></a><spanclass="lineno"> 209</span><spanclass="comment">// less than a given value.</span></div>
<divclass="line"><aid="l00212"name="l00212"></a><spanclass="lineno"> 212</span><spanclass="comment">// Returns the smallest range within a given range containing all values</span></div>
<divclass="line"><aid="l00213"name="l00213"></a><spanclass="lineno"> 213</span><spanclass="comment">// greater than value_min and less than value_max.</span></div>
<divclass="line"><aid="l00218"name="l00218"></a><spanclass="lineno"> 218</span><spanclass="comment">// Adds 'constant' to the 'x' of all segments. If the argument is positive,</span></div>
<divclass="line"><aid="l00219"name="l00219"></a><spanclass="lineno"> 219</span><spanclass="comment">// the translation is to the right and when it's negative, to the left. The</span></div>
<divclass="line"><aid="l00220"name="l00220"></a><spanclass="lineno"> 220</span><spanclass="comment">// overflows and the underflows are sticky.</span></div>
<divclass="line"><aid="l00222"name="l00222"></a><spanclass="lineno"> 222</span><spanclass="comment">// Adds 'constant' to the 'y' of all segments. If the argument is positive,</span></div>
<divclass="line"><aid="l00223"name="l00223"></a><spanclass="lineno"> 223</span><spanclass="comment">// the translation is up and when it's negative, down. The overflows and the</span></div>
<divclass="line"><aid="l00224"name="l00224"></a><spanclass="lineno"> 224</span><spanclass="comment">// underflows are sticky.</span></div>
<divclass="line"><aid="l00226"name="l00226"></a><spanclass="lineno"> 226</span><spanclass="comment">// Adds the function to the existing one. The domain of the resulting</span></div>
<divclass="line"><aid="l00227"name="l00227"></a><spanclass="lineno"> 227</span><spanclass="comment">// function is the intersection of the two domains. The overflows and</span></div>
<divclass="line"><aid="l00228"name="l00228"></a><spanclass="lineno"> 228</span><spanclass="comment">// the underflows are sticky.</span></div>
<divclass="line"><aid="l00230"name="l00230"></a><spanclass="lineno"> 230</span><spanclass="comment">// Subtracts the function to the existing one. The domain of the</span></div>
<divclass="line"><aid="l00231"name="l00231"></a><spanclass="lineno"> 231</span><spanclass="comment">// resulting function is the intersection of the two domains. The</span></div>
<divclass="line"><aid="l00232"name="l00232"></a><spanclass="lineno"> 232</span><spanclass="comment">// overflows and the underflows are sticky.</span></div>
<divclass="line"><aid="l00234"name="l00234"></a><spanclass="lineno"> 234</span><spanclass="comment">// Decomposes the piecewise linear function in a set of convex piecewise</span></div>
<divclass="line"><aid="l00235"name="l00235"></a><spanclass="lineno"> 235</span><spanclass="comment">// linear functions. The objects in the vector are owned by the client code.</span></div>
<divclass="line"><aid="l00243"name="l00243"></a><spanclass="lineno"> 243</span><spanclass="comment">// Takes the sequence of segments, sorts them on increasing start and inserts</span></div>
<divclass="line"><aid="l00244"name="l00244"></a><spanclass="lineno"> 244</span><spanclass="comment">// them in the piecewise linear function.</span></div>
<divclass="line"><aid="l00248"name="l00248"></a><spanclass="lineno"> 248</span><spanclass="comment">// Operation between two functions. In any operation between two functions the</span></div>
<divclass="line"><aid="l00249"name="l00249"></a><spanclass="lineno"> 249</span><spanclass="comment">// final domain is the intersection between the two domains.</span></div>
<divclass="line"><aid="l00252"name="l00252"></a><spanclass="lineno"> 252</span><spanclass="comment">// Finds start and end segment indices from a range; returns false if the</span></div>
<divclass="line"><aid="l00253"name="l00253"></a><spanclass="lineno"> 253</span><spanclass="comment">// range is outside the domain of the function.</span></div>
<divclass="line"><aid="l00268"name="l00268"></a><spanclass="lineno"> 268</span><spanclass="comment">// The vector of segments in the function, sorted in ascending order of start</span></div>
<divclass="ttc"id="aclassoperations__research_1_1_piecewise_linear_function_html_a5b390931557183bd4a55afe4cbf4e2ae"><divclass="ttname"><ahref="classoperations__research_1_1_piecewise_linear_function.html#a5b390931557183bd4a55afe4cbf4e2ae">operations_research::PiecewiseLinearFunction::kNotFound</a></div><divclass="ttdeci">static const int kNotFound</div><divclass="ttdef"><b>Definition:</b><ahref="piecewise__linear__function_8h_source.html#l00103">piecewise_linear_function.h:103</a></div></div>
<divclass="ttc"id="anamespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><divclass="ttdef"><b>Definition:</b><ahref="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
