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< h2 > C++ Reference< / h2 >
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< li > < a href = "../cpp_algorithms/annotated.html" > Algorithms< / a > < / li >
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< li > < a href = "../cpp_sat/annotated.html" > CP-SAT< / a > < / li >
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< li > < a href = "../cpp_linear/annotated.html" > Linear solver< / a > < / li >
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< h1 style = "color: #145A32;" > C++ Reference: Linear solver< / h1 >
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< a href = "#nested-classes" > Classes< / a > |
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< div class = "title" > linear_expr.h File Reference< / div > < / div >
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< a name = "details" id = "details" > < / a > < h2 class = "groupheader" > Detailed Description< / h2 >
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< div class = "textblock" > < p > This file allows you to write natural code (like a mathematical equation) to model optimization problems with MPSolver. < / p >
< p > It is syntatic sugar on top of the MPSolver API, it provides no additional functionality. Use of these APIs makes it much easier to write code that is both simple and big-O optimal for creating your model, at the cost of some additional constant factor overhead. If model creation is a bottleneck in your problem, consider using the MPSolver API directly instead.< / p >
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< p > This file contains two classes:< / p > < ol type = "1" >
< li > LinearExpr: models offset + sum_{i in S} a_i*x_i for decision var x_i,< / li >
< li > LinearRange: models lb < = sum_{i in S} a_i*x_i < = ub, and it provides various operator overloads to build up "LinearExpr"s and then convert them to "LinearRange"s.< / li >
< / ol >
< p > Recommended use (avoids dangerous code):< / p >
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< div class = "fragment" > < div class = "line" > MPSolver solver = ...;< / div >
< div class = "line" > < span class = "keyword" > const< / span > LinearExpr x = solver.MakeVar(...); * Note: implicit conversion< / div >
< div class = "line" > < span class = "keyword" > const< / span > LinearExpr y = solver.MakeVar(...);< / div >
< div class = "line" > < span class = "keyword" > const< / span > LinearExpr z = solver.MakeVar(...);< / div >
< div class = "line" > < span class = "keyword" > const< / span > LinearExpr e1 = x + y;< / div >
< div class = "line" > < span class = "keyword" > const< / span > LinearExpr e2 = (e1 + 7.0 + z)/3.0;< / div >
< div class = "line" > < span class = "keyword" > const< / span > LinearRange r = e1 < = e2;< / div >
< div class = "line" > solver.MakeRowConstraint(r);< / div >
< / div > <!-- fragment --> < p > < b > WARNING< / b > , AVOID THIS TRAP:< / p >
< div class = "fragment" > < div class = "line" > MPSolver solver = ...;< / div >
< div class = "line" > MPVariable* x = solver.MakeVar(...);< / div >
< div class = "line" > LinearExpr y = x + 5;< / div >
< / div > <!-- fragment --> < p > In evaluating "x+5" above, x is NOT converted to a LinearExpr before the addition, but rather is treated as a pointer, so x+5 gives a new pointer to garbage memory.< / p >
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< p > For this reason, when using LinearExpr, it is best practice to:< / p > < ol type = "1" >
< li > use double literals instead of ints (e.g. "x + 5.0", not "x + 5"),< / li >
< li > Immediately convert all MPVariable* to LinearExpr on creation, and only hold references to the "LinearExpr"s.< / li >
< / ol >
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< p > Likewise, the following code is NOT recommended: < / p > < div class = "fragment" > < div class = "line" > MPSolver solver = ...;< / div >
< div class = "line" > MPVariable* x = solver.MakeVar(...);< / div >
< div class = "line" > MPVariable* y = solver.MakeVar(...);< / div >
< div class = "line" > LinearExpr e1 = LinearExpr(x) + y + 5;< / div >
< / div > <!-- fragment --> < p > While it is correct, it violates the natural assumption that the + operator is associative. Thus you are setting a trap for future modifications of the code, as any of the following changes would lead to the above failure mode:< / p >
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< ul >
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< li > < div class = "fragment" > < div class = "line" > LinearExpr e1 = LinearExpr(x) + (y + 5); < / div >
< / div > <!-- fragment --> < / li >
< li > < div class = "fragment" > < div class = "line" > LinearExpr e1 = y + 5 + LinearExpr(x); < / div >
< / div > <!-- fragment --> < / li >
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< / ul >
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< p class = "definition" > Definition in file < a class = "el" href = "linear__expr_8h_source.html" > linear_expr.h< / a > .< / p >
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< p > < a href = "linear__expr_8h_source.html" > Go to the source code of this file.< / a > < / p >
< table class = "memberdecls" >
< tr class = "heading" > < td colspan = "2" > < h2 class = "groupheader" > < a name = "nested-classes" > < / a >
Classes< / h2 > < / td > < / tr >
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< tr class = "memitem:" > < td class = "memItemLeft" align = "right" valign = "top" > class   < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "classoperations__research_1_1_linear_expr.html" > LinearExpr< / a > < / td > < / tr >
< tr class = "memdesc:" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > < a class = "el" href = "classoperations__research_1_1_linear_expr.html" title = "LinearExpr models a quantity that is linear in the decision variables (MPVariable) of an optimization..." > LinearExpr< / a > models a quantity that is linear in the decision variables (< a class = "el" href = "classoperations__research_1_1_m_p_variable.html" title = "The class for variables of a Mathematical Programming (MP) model." > MPVariable< / a > ) of an optimization problem, i.e. < a href = "classoperations__research_1_1_linear_expr.html#details" > More...< / a > < br / > < / td > < / tr >
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< tr class = "memitem:" > < td class = "memItemLeft" align = "right" valign = "top" > class   < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "classoperations__research_1_1_linear_range.html" > LinearRange< / a > < / td > < / tr >
< tr class = "memdesc:" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > An expression of the form: < a href = "classoperations__research_1_1_linear_range.html#details" > More...< / a > < br / > < / td > < / tr >
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< tr class = "memitem:namespaceoperations__research" > < td class = "memItemLeft" align = "right" valign = "top" >   < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html" > operations_research< / a > < / td > < / tr >
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Functions< / h2 > < / td > < / tr >
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< tr class = "memitem:ad3390eca60a1042a3d81452cea3863aa" > < td class = "memItemLeft" align = "right" valign = "top" > std::ostream &   < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#ad3390eca60a1042a3d81452cea3863aa" > operator< < < / a > (std::ostream & stream, const LinearExpr & linear_expr)< / td > < / tr >
< tr class = "separator:ad3390eca60a1042a3d81452cea3863aa" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:a97f9b83239285f5fdfcac1b8e8b4f162" > < td class = "memItemLeft" align = "right" valign = "top" > LinearExpr  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#a97f9b83239285f5fdfcac1b8e8b4f162" > operator+< / a > (LinearExpr lhs, const LinearExpr & rhs)< / td > < / tr >
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< tr class = "separator:a97f9b83239285f5fdfcac1b8e8b4f162" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a515cdaf4f9c4000bb3482a0c450e23c3" > < td class = "memItemLeft" align = "right" valign = "top" > LinearExpr  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#a515cdaf4f9c4000bb3482a0c450e23c3" > operator-< / a > (LinearExpr lhs, const LinearExpr & rhs)< / td > < / tr >
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< tr class = "memitem:a138bb0f103cd9d68e4d13fa773901186" > < td class = "memItemLeft" align = "right" valign = "top" > LinearExpr  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#a138bb0f103cd9d68e4d13fa773901186" > operator*< / a > (LinearExpr lhs, double rhs)< / td > < / tr >
< tr class = "separator:a138bb0f103cd9d68e4d13fa773901186" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:abebdd7f40e90df8dc7d557b6e26da942" > < td class = "memItemLeft" align = "right" valign = "top" > LinearExpr  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#abebdd7f40e90df8dc7d557b6e26da942" > operator/< / a > (LinearExpr lhs, double rhs)< / td > < / tr >
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< tr class = "separator:abebdd7f40e90df8dc7d557b6e26da942" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a62b131d2829f1cdacd2414d2d7bc6c7c" > < td class = "memItemLeft" align = "right" valign = "top" > LinearExpr  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#a62b131d2829f1cdacd2414d2d7bc6c7c" > operator*< / a > (double lhs, LinearExpr rhs)< / td > < / tr >
< tr class = "separator:a62b131d2829f1cdacd2414d2d7bc6c7c" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a6d1fa20f9c9faf7027c0b16f97139e80" > < td class = "memItemLeft" align = "right" valign = "top" > LinearRange  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#a6d1fa20f9c9faf7027c0b16f97139e80" > operator< =< / a > (const LinearExpr & lhs, const LinearExpr & rhs)< / td > < / tr >
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< tr class = "separator:a6d1fa20f9c9faf7027c0b16f97139e80" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a08146f196bd9c3f492ee108732449ced" > < td class = "memItemLeft" align = "right" valign = "top" > LinearRange  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#a08146f196bd9c3f492ee108732449ced" > operator==< / a > (const LinearExpr & lhs, const LinearExpr & rhs)< / td > < / tr >
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< tr class = "separator:a08146f196bd9c3f492ee108732449ced" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:ac4052f92af6a7fbb1d45e17befcb68e0" > < td class = "memItemLeft" align = "right" valign = "top" > LinearRange  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "namespaceoperations__research.html#ac4052f92af6a7fbb1d45e17befcb68e0" > operator> =< / a > (const LinearExpr & lhs, const LinearExpr & rhs)< / td > < / tr >
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