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affexpr.jl
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affexpr.jl
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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/.
#############################################################################
# JuMP
# An algebraic modeling language for Julia
# See http://github.com/JuliaOpt/JuMP.jl
#############################################################################
# src/affexpr.jl
# Defines all types relating to affine expressions
# - GenericAffExpr ∑ aᵢ xᵢ + c
# - AffExpr Alias for (Float64, Variable)
# - AffExprConstraint AffExpr-in-set constraint
# Operator overloads in src/operators.jl
#############################################################################
#############################################################################
# GenericAffExpr
# ∑ aᵢ xᵢ + c
mutable struct GenericAffExpr{CoefType,VarType} <: AbstractJuMPScalar
vars::Vector{VarType}
coeffs::Vector{CoefType}
constant::CoefType
end
coeftype(::GenericAffExpr{C,V}) where {C,V} = C
Base.zero(::Type{GenericAffExpr{C,V}}) where {C,V} = GenericAffExpr{C,V}(V[],C[],zero(C))
Base.one(::Type{GenericAffExpr{C,V}}) where { C,V} = GenericAffExpr{C,V}(V[],C[], one(C))
Base.zero(a::GenericAffExpr) = zero(typeof(a))
Base.one( a::GenericAffExpr) = one(typeof(a))
Base.copy(a::GenericAffExpr) = GenericAffExpr(copy(a.vars),copy(a.coeffs),copy(a.constant))
"""
value(a::GenericAffExpr, map::Function)
Evaluate `a` given the value `map(v)` for each variable `v`.
"""
function value(a::GenericAffExpr{T, V}, map::Function) where {T, V}
S = Base.promote_op(map, V)
U = Base.promote_op(*, T, S)
ret = U(a.constant)
for it in eachindex(a.vars)
ret += a.coeffs[it] * map(a.vars[it])
end
ret
end
# Old iterator protocol - iterates over tuples (aᵢ,xᵢ)
struct LinearTermIterator{GAE<:GenericAffExpr}
aff::GAE
end
"""
linearterms(aff::GenericAffExpr)
Provides an iterator over the `(a_i::C,x_i::V)` terms in affine expression ``\\sum_i a_i x_i + b``.
"""
linearterms(aff::GenericAffExpr) = LinearTermIterator(aff)
Base.start(lti::LinearTermIterator) = 1
Base.done( lti::LinearTermIterator, state::Int) = state > length(lti.aff.vars)
Base.next( lti::LinearTermIterator, state::Int) = ((lti.aff.coeffs[state], lti.aff.vars[state]), state+1)
"""
Base.push!{C,V}(aff::GenericAffExpr{C,V}, new_coeff::C, new_var::V)
An efficient way to grow an affine expression by one term. For example, to add `5x` to an existing expression `aff`, use `push!(aff, 5.0, x)`. This is significantly more efficient than `aff += 5.0*x`.
"""
function Base.push!(aff::GenericAffExpr{C,V}, new_coeff::C, new_var::V) where {C,V}
push!(aff.coeffs, new_coeff)
push!(aff.vars, new_var)
aff
end
# Add an affine expression to an existing affine expression
"""
Base.append!{C,V}(aff::GenericAffExpr{C,V}, other::GenericAffExpr{C,V})
Efficiently append the terms of an affine expression to an existing affine expression. For example, given `aff = 5.0*x` and `other = 7.0*y + 3.0*z`, we can grow `aff` using `append!(aff, other)` which results in `aff` equaling `5x + 7y + 3z`. This is significantly more efficient than using `aff += other`.
"""
function Base.append!(aff::GenericAffExpr{C,V}, other::GenericAffExpr{C,V}) where {C,V}
append!(aff.vars, other.vars)
append!(aff.coeffs, other.coeffs)
aff.constant += other.constant
aff
end
# For consistency, allow appending constants and individual variables
Base.append!(aff::GenericAffExpr{C,C}, other::C) where {C} = error() # for ambiguity
function Base.append!(aff::GenericAffExpr{C,V}, other::C) where {C,V}
aff.constant += other
aff
end
function Base.append!(aff::GenericAffExpr{C,V}, other::Real) where {C,V}
aff.constant += other
aff
end
Base.append!(aff::GenericAffExpr{C,V}, other::V) where {C,V} = push!(aff,one(C),other)
function Base.isequal(aff::GenericAffExpr{C,V},other::GenericAffExpr{C,V}) where {C,V}
isequal(aff.constant, other.constant) || return false
length(aff.vars) == length(other.vars) || return false
for i in 1:length(aff.vars)
isequal(aff.vars[i], other.vars[i]) || return false
isequal(aff.coeffs[i], other.coeffs[i]) || return false
end
return true
end
# Check if two AffExprs are equal regardless of the order, and after merging duplicates
# Mostly useful for testing.
function isequal_canonical(aff::GenericAffExpr{C,V}, other::GenericAffExpr{C,V}) where {C,V}
function canonicalize(a)
d = Dict{V,C}()
@assert length(a.vars) == length(a.coeffs)
for k in 1:length(a.vars)
d[a.vars[k]] = a.coeffs[k] + get(d, a.vars[k], zero(C))
end
return d
end
d1 = canonicalize(aff)
d2 = canonicalize(other)
return isequal(d1,d1) && aff.constant == other.constant
end
# Alias for (Float64, Variable), the specific GenericAffExpr used by JuMP
const AffExpr = GenericAffExpr{Float64,Variable}
AffExpr() = zero(AffExpr)
Base.isempty(a::AffExpr) = (length(a.vars) == 0 && a.constant == 0.)
Base.convert(::Type{AffExpr}, v::Variable) = AffExpr([v], [1.], 0.)
Base.convert(::Type{AffExpr}, v::Real) = AffExpr(Variable[], Float64[], v)
# Check all coefficients are finite, i.e. not NaN, not Inf, not -Inf
function assert_isfinite(a::AffExpr)
coeffs = a.coeffs
for i in 1:length(a.vars)
isfinite(coeffs[i]) || error("Invalid coefficient $(coeffs[i]) on variable $(a.vars[i])")
end
end
"""
resultvalue(v::AffExpr)
Evaluate an `AffExpr` given the result returned by a solver.
Replaces `getvalue` for most use cases.
"""
resultvalue(a::AffExpr) = value(a, resultvalue)
# Note: No validation is performed that the variables in the AffExpr belong to
# the same model.
function MOI.ScalarAffineFunction(a::AffExpr)
return MOI.ScalarAffineFunction(index.(a.vars), a.coeffs, a.constant)
end
function AffExpr(m::Model, f::MOI.ScalarAffineFunction)
return AffExpr(Variable.(m,f.variables), f.coefficients, f.constant)
end
"""
_fillvaf!(outputindex, variables, coefficients, offset::Int, oi::Int, aff::AffExpr)
Fills the vectors outputindex, variables, coefficients at indices starting at `offset+1` with the terms of `aff`.
The output index for all terms is `oi`.
"""
function _fillvaf!(outputindex, variables, coefficients, offset::Int, oi::Int, aff::AffExpr)
for i in 1:length(aff.vars)
outputindex[offset+i] = oi
variables[offset+i] = index(aff.vars[i])
coefficients[offset+i] = aff.coeffs[i]
end
offset + length(aff.vars)
end
function MOI.VectorAffineFunction(affs::Vector{AffExpr})
len = sum(aff -> length(aff.vars), affs)
outputindex = Vector{Int}(len)
variables = Vector{MOIVAR}(len)
coefficients = Vector{Float64}(len)
constant = Vector{Float64}(length(affs))
offset = 0
for (i, aff) in enumerate(affs)
constant[i] = aff.constant
offset = _fillvaf!(outputindex, variables, coefficients, offset, i, aff)
end
MOI.VectorAffineFunction(outputindex, variables, coefficients, constant)
end
function setobjective(m::Model, sense::Symbol, a::AffExpr)
if sense == :Min
moisense = MOI.MinSense
else
@assert sense == :Max
moisense = MOI.MaxSense
end
MOI.set!(m.moibackend, MOI.ObjectiveSense(), moisense)
MOI.set!(m.moibackend, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(), MOI.ScalarAffineFunction(a))
nothing
end
"""
objectivefunction(m::Model, ::Type{AffExpr})
Return an `AffExpr` object representing the objective function.
Error if the objective is not linear.
"""
function objectivefunction(m::Model, ::Type{AffExpr})
f = MOI.get(m.moibackend, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}())::MOI.ScalarAffineFunction
return AffExpr(m, f)
end
# Copy an affine expression to a new model by converting all the
# variables to the new model's variables
function Base.copy(a::AffExpr, new_model::Model)
AffExpr(copy(a.vars, new_model), copy(a.coeffs), a.constant)
end
# TODO GenericAffExprConstraint
struct AffExprConstraint{S <: MOI.AbstractScalarSet} <: AbstractConstraint
func::AffExpr
set::S
end
moi_function_and_set(c::AffExprConstraint) = (MOI.ScalarAffineFunction(c.func), c.set)
# TODO: Find somewhere to put this error message.
#addconstraint(m::Model, c::Array{AffExprConstraint}) =
# error("The operators <=, >=, and == can only be used to specify scalar constraints. If you are trying to add a vectorized constraint, use the element-wise dot comparison operators (.<=, .>=, or .==) instead")
struct VectorAffExprConstraint{S <: MOI.AbstractVectorSet} <: AbstractConstraint
func::Vector{AffExpr}
set::S
end
moi_function_and_set(c::VectorAffExprConstraint) = (MOI.VectorAffineFunction(c.func), c.set)
function constraintobject(cr::ConstraintRef{Model}, ::Type{AffExpr}, ::Type{SetType}) where {SetType <: MOI.AbstractScalarSet}
f = MOI.get(cr.m, MOI.ConstraintFunction(), cr)::MOI.ScalarAffineFunction
s = MOI.get(cr.m, MOI.ConstraintSet(), cr)::SetType
return AffExprConstraint(AffExpr(cr.m, f), s)
end
function constraintobject(cr::ConstraintRef{Model}, ::Type{Vector{AffExpr}}, ::Type{SetType}) where {SetType <: MOI.AbstractVectorSet}
m = cr.m
f = MOI.get(m, MOI.ConstraintFunction(), cr)::MOI.VectorAffineFunction
s = MOI.get(m, MOI.ConstraintSet(), cr)::SetType
return VectorAffExprConstraint(map(f -> AffExpr(m, f), MOIU.eachscalar(f)), s)
end