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| # Copyright 2017, Iain Dunning, Joey Huchette, Miles Lubin, and contributors | ||
| # This Source Code Form is subject to the terms of the Mozilla Public | ||
| # License, v. 2.0. If a copy of the MPL was not distributed with this | ||
| # file, You can obtain one at http://mozilla.org/MPL/2.0/. | ||
|
|
||
| """ | ||
| LPMatrixData{T} | ||
| The struct returned by [`lp_matrix_data`](@ref). See [`lp_matrix_data`](@ref) | ||
| for a description of the public fields. | ||
| """ | ||
| struct LPMatrixData{T} | ||
| A::SparseArrays.SparseMatrixCSC{T,Int} | ||
| b_lower::Vector{T} | ||
| b_upper::Vector{T} | ||
| x_lower::Vector{T} | ||
| x_upper::Vector{T} | ||
| c::Vector{T} | ||
| c_offset::T | ||
| sense::MOI.OptimizationSense | ||
| variables::Vector{GenericVariableRef{T}} | ||
| affine_constraints::Vector{ConstraintRef} | ||
| variable_constraints::Vector{ConstraintRef} | ||
| end | ||
|
|
||
| """ | ||
| lp_matrix_data(model::GenericModel{T}) | ||
| Given a JuMP model of a linear program, return an [`LPMatrixData{T}`](@ref) | ||
| struct storing data for an equivalent linear program in the form: | ||
| ```math | ||
| \\begin{aligned} | ||
| \\min & c^\\top x + c_0\\ | ||
| & b_l \\le A x \\le b_u \\ | ||
| & x_l \\le x \\le x_u | ||
| \\end{aligned} | ||
| ``` | ||
| ## Fields | ||
| The struct returned by [`lp_matrix_data`](@ref) has the fields: | ||
| * `A::SparseArrays.SparseMatrixCSC{T,Int}`: the constraint matrix in sparse | ||
| matrix form. | ||
| * `b_lower::Vector{T}`: the dense vector of row lower bounds. If missing, the | ||
| value of `typemin(T)` is used. | ||
| * `b_upper::Vector{T}`: the dense vector of row upper bounds. If missing, the | ||
| value of `typemax(T)` is used. | ||
| * `x_lower::Vector{T}`: the dense vector of variable lower bounds. If missing, | ||
| the value of `typemin(T)` is used. | ||
| * `x_upper::Vector{T}`: the dense vector of variable upper bounds. If missing, | ||
| the value of `typemax(T)` is used. | ||
| * `c::Vector{T}`: the dense vector of linear objective coefficiennts | ||
| * `c_offset::T`: the constant term in the objective function. | ||
| * `sense::MOI.OptimizationSense`: the objective sense of the model. | ||
| * `variables::Vector{GenericVariableRef{T}}`: a vector of [`GenericVariableRef`](@ref), | ||
| corresponding to order of the columns in the matrix form. | ||
| * `affine_constraints::Vector{ConstraintRef}`: a vector of [`ConstraintRef`](@ref), | ||
| corresponding to the order of rows in the matrix form. | ||
| ## Limitations | ||
| The models supported by [`lp_matrix_data`](@ref) are intentionally limited | ||
| to linear programs. | ||
| If your model has integrality, use [`relax_integrality`](@ref) to remove integer | ||
| restrictions before calling [`lp_matrix_data`](@ref). | ||
| """ | ||
| function lp_matrix_data(model::GenericModel{T}) where {T} | ||
| variables = all_variables(model) | ||
| columns = Dict(var => i for (i, var) in enumerate(variables)) | ||
| n = length(columns) | ||
| cache = (; | ||
| x_l = fill(typemin(T), n), | ||
| x_u = fill(typemax(T), n), | ||
| c = zeros(T, n), | ||
| c_offset = Ref{T}(zero(T)), | ||
| b_l = T[], | ||
| b_u = T[], | ||
| I = Int[], | ||
| J = Int[], | ||
| V = T[], | ||
| variable_to_column = columns, | ||
| bound_constraints = ConstraintRef[], | ||
| affine_constraints = ConstraintRef[], | ||
| ) | ||
| for (F, S) in list_of_constraint_types(model) | ||
| _fill_standard_form(model, F, S, cache) | ||
| end | ||
| _fill_standard_form(model, objective_function_type(model), cache) | ||
| return LPMatrixData( | ||
| SparseArrays.sparse(cache.I, cache.J, cache.V, length(cache.b_l), n), | ||
| cache.b_l, | ||
| cache.b_u, | ||
| cache.x_l, | ||
| cache.x_u, | ||
| cache.c, | ||
| cache.c_offset[], | ||
| MOI.get(model, MOI.ObjectiveSense()), | ||
| variables, | ||
| cache.affine_constraints, | ||
| cache.bound_constraints, | ||
| ) | ||
| end | ||
|
|
||
| _bounds(s::MOI.LessThan{T}) where {T} = (typemin(T), s.upper) | ||
| _bounds(s::MOI.GreaterThan{T}) where {T} = (s.lower, typemax(T)) | ||
| _bounds(s::MOI.EqualTo{T}) where {T} = (s.value, s.value) | ||
| _bounds(s::MOI.Interval{T}) where {T} = (s.lower, s.upper) | ||
|
|
||
| function _fill_standard_form( | ||
| model::GenericModel{T}, | ||
| ::Type{GenericVariableRef{T}}, | ||
| ::Type{S}, | ||
| cache::Any, | ||
| ) where { | ||
| T, | ||
| S<:Union{MOI.LessThan{T},MOI.GreaterThan{T},MOI.EqualTo{T},MOI.Interval{T}}, | ||
| } | ||
| for c in all_constraints(model, GenericVariableRef{T}, S) | ||
| push!(cache.bound_constraints, c) | ||
| c_obj = constraint_object(c) | ||
| i = cache.variable_to_column[c_obj.func] | ||
| l, u = _bounds(c_obj.set) | ||
| cache.x_l[i] = max(cache.x_l[i], l) | ||
| cache.x_u[i] = min(cache.x_u[i], u) | ||
| end | ||
| return | ||
| end | ||
|
|
||
| function _fill_standard_form( | ||
| model::GenericModel{T}, | ||
| ::Type{F}, | ||
| ::Type{S}, | ||
| cache::Any, | ||
| ) where { | ||
| T, | ||
| F<:GenericAffExpr{T,GenericVariableRef{T}}, | ||
| S<:Union{MOI.LessThan{T},MOI.GreaterThan{T},MOI.EqualTo{T},MOI.Interval{T}}, | ||
| } | ||
| for c in all_constraints(model, F, S) | ||
| push!(cache.affine_constraints, c) | ||
| c_obj = constraint_object(c) | ||
| @assert iszero(c_obj.func.constant) | ||
| row = length(cache.b_l) + 1 | ||
| l, u = _bounds(c_obj.set) | ||
| push!(cache.b_l, l) | ||
| push!(cache.b_u, u) | ||
| for (x, coef) in c_obj.func.terms | ||
| push!(cache.I, row) | ||
| push!(cache.J, cache.variable_to_column[x]) | ||
| push!(cache.V, coef) | ||
| end | ||
| end | ||
| return | ||
| end | ||
|
|
||
| function _fill_standard_form( | ||
| ::GenericModel{T}, | ||
| ::Type{F}, | ||
| ::Type{S}, | ||
| ::Any, | ||
| ) where {T,F,S} | ||
| return error("Unsupported constraint type in `lp_matrix_data`: $F -in- $S") | ||
| end | ||
|
|
||
| function _fill_standard_form( | ||
| model::GenericModel{T}, | ||
| ::Type{GenericVariableRef{T}}, | ||
| cache::Any, | ||
| ) where {T} | ||
| cache.c[cache.variable_to_column[objective_function(model)]] = one(T) | ||
| cache.c_offset[] = zero(T) | ||
| return | ||
| end | ||
|
|
||
| function _fill_standard_form( | ||
| model::GenericModel{T}, | ||
| ::Type{GenericAffExpr{T,GenericVariableRef{T}}}, | ||
| cache::Any, | ||
| ) where {T} | ||
| f = objective_function(model) | ||
| for (k, v) in f.terms | ||
| cache.c[cache.variable_to_column[k]] += v | ||
| end | ||
| cache.c_offset[] = f.constant | ||
| return | ||
| end | ||
|
|
||
| function _fill_standard_form(::GenericModel{T}, ::Type{F}, ::Any) where {T,F} | ||
| return error("Unsupported objective type in `lp_matrix_data`: $F") | ||
| end |
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