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functions.jl
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functions.jl
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# Copyright (c) 2017: Miles Lubin and contributors
# Copyright (c) 2017: Google Inc.
#
# Use of this source code is governed by an MIT-style license that can be found
# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
module TestFunctions
using Test
import MathOptInterface as MOI
import MutableArithmetics as MA
function runtests()
for name in names(@__MODULE__; all = true)
if startswith("$(name)", "test_")
@testset "$(name)" begin
getfield(@__MODULE__, name)()
end
end
end
return
end
const w = MOI.VariableIndex(0)
const x = MOI.VariableIndex(1)
const y = MOI.VariableIndex(2)
const z = MOI.VariableIndex(3)
# Number-like but not subtype of `Number`
struct NonNumber
value::Int
end
Base.:*(a::NonNumber, b::NonNumber) = NonNumber(a.value * b.value)
Base.:+(a::NonNumber, b::NonNumber) = NonNumber(a.value + b.value)
Base.zero(::Type{NonNumber}) = NonNumber(0)
function Base.isapprox(a::NonNumber, b::NonNumber; kws...)
return isapprox(a.value, b.value; kws...)
end
function test_NonNumber()
two = NonNumber(2)
three = NonNumber(3)
six = NonNumber(6)
three_x = MOI.Utilities.operate(*, NonNumber, three, x)
six_x = MOI.Utilities.operate(*, NonNumber, six, x)
@test six_x ≈ two * three_x
@test six_x ≈ three_x * two
return
end
function test_Vectorization_vectorize()
g = MOI.VectorAffineFunction(
MOI.VectorAffineTerm.([3, 1], MOI.ScalarAffineTerm.([5, 2], [y, x])),
[3, 1, 4],
)
g1 = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(2, x)], 3)
g2 = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm{Int}[], 1)
g3 = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(5, y)], 4)
@test g ≈ MOI.Utilities.vectorize([g1, g2, g3])
vov = MOI.Utilities.vectorize(MOI.VariableIndex[])
@test MOI.output_dimension(vov) == 0
@test vov isa MOI.VectorOfVariables
aff = MOI.Utilities.vectorize(MOI.ScalarAffineFunction{Int}[])
@test MOI.output_dimension(aff) == 0
@test aff isa MOI.VectorAffineFunction{Int}
quad = MOI.Utilities.vectorize(MOI.ScalarQuadraticFunction{Int}[])
@test MOI.output_dimension(quad) == 0
@test quad isa MOI.VectorQuadraticFunction{Int}
return
end
function test_Vectorization_operate_vcat()
for T in [Int, Float64]
a = one(T)
b = zero(T)
c = 2a
x = [b, c]
@test MOI.Utilities.promote_operation(vcat, T, T, Vector{T}, T) ==
Vector{T}
@test MOI.Utilities.operate(vcat, T, a, x, b) == vcat(a, x, b)
@test MOI.Utilities.promote_operation(vcat, T, T) == Vector{T}
@test MOI.Utilities.operate(vcat, T, a) == [a]
@test MOI.Utilities.promote_operation(vcat, T, Vector{T}) == Vector{T}
@test MOI.Utilities.operate(vcat, T, x) == x
end
g = MOI.VectorAffineFunction(
MOI.VectorAffineTerm.([3, 1], MOI.ScalarAffineTerm.([5, 2], [y, x])),
[3, 1, 4],
)
v = MOI.VectorOfVariables([y, w])
for T in [Int, Float64]
@test MOI.VectorOfVariables == MOI.Utilities.promote_operation(
vcat,
T,
typeof(w),
typeof(v),
typeof(x),
)
vov = MOI.Utilities.operate(vcat, T, w, v, x)
@test vov.variables == [w, y, w, x]
@test MOI.VectorOfVariables == MOI.Utilities.promote_operation(
vcat,
T,
typeof(v),
typeof(w),
typeof(x),
)
vov = MOI.Utilities.operate(vcat, T, v, w, x)
@test vov.variables == [y, w, w, x]
@test MOI.VectorOfVariables == MOI.Utilities.promote_operation(
vcat,
T,
typeof(w),
typeof(x),
typeof(v),
)
vov = MOI.Utilities.operate(vcat, T, w, x, v)
@test vov.variables == [w, x, y, w]
end
f = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2, 4], [x, z]), 5)
g = MOI.VectorAffineFunction(
MOI.VectorAffineTerm.([3, 1], MOI.ScalarAffineTerm.([5, 2], [y, x])),
[3, 1, 4],
)
@test MOI.Utilities.promote_operation(
vcat,
Int,
typeof(w),
typeof(f),
typeof(v),
Int,
typeof(g),
typeof(x),
Int,
) == MOI.VectorAffineFunction{Int}
F = MOI.Utilities.operate(vcat, Int, w, f, v, 3, g, x, -4)
expected_terms =
MOI.VectorAffineTerm.(
[1, 2, 2, 3, 4, 8, 6, 9],
MOI.ScalarAffineTerm.(
[1, 2, 4, 1, 1, 5, 2, 1],
[w, x, z, y, w, y, x, x],
),
)
expected_constants = [0, 5, 0, 0, 3, 3, 1, 4, 0, -4]
F = MOI.Utilities.operate(vcat, Int, w, f, v, 3, g, x, -4)
@test F.terms == expected_terms
@test F.constants == expected_constants
return
end
function test_promote_operation_Quadratic()
@test MOI.Utilities.promote_operation(
vcat,
Int,
MOI.VectorQuadraticFunction{Int},
MOI.VariableIndex,
MOI.ScalarQuadraticFunction{Int},
MOI.VectorOfVariables,
Int,
MOI.ScalarQuadraticFunction{Int},
MOI.VectorQuadraticFunction{Int},
MOI.VariableIndex,
Int,
) == MOI.VectorQuadraticFunction{Int}
for T in (Float64, Int)
for TV in (MOI.ScalarAffineFunction{T}, MOI.ScalarQuadraticFunction{T})
@test promote_type(TV, MOI.VariableIndex) == TV
end
end
return
end
function test_MultirowChange_construction()
chg1 = MOI.MultirowChange(w, [(Int32(2), 2.0), (Int32(1), 3.0)])
chg2 = MOI.MultirowChange(w, [(Int64(2), 2.0), (Int64(1), 3.0)])
@test chg1.variable == chg2.variable
@test chg1.new_coefficients == chg2.new_coefficients
return
end
function test_VectorAffineTerm_VectorQuadraticTerm_construction()
scalaraffine = MOI.ScalarAffineTerm(2.0, z)
@test MOI.VectorAffineTerm(Int32(3), scalaraffine) ===
MOI.VectorAffineTerm(Int64(3), scalaraffine)
@test MOI.VectorAffineTerm{Float64}(Int32(3), scalaraffine) ===
MOI.VectorAffineTerm(Int64(3), scalaraffine)
scalarquad = MOI.ScalarQuadraticTerm(2.0, y, z)
@test MOI.VectorQuadraticTerm(Int32(3), scalarquad) ===
MOI.VectorQuadraticTerm(Int64(3), scalarquad)
@test MOI.VectorQuadraticTerm{Float64}(Int32(3), scalarquad) ===
MOI.VectorQuadraticTerm(Int64(3), scalarquad)
return
end
function test_eval_variables()
# We do tests twice to make sure the function is not modified
vals = Dict(w => 0, x => 3, y => 1, z => 5)
@test MOI.output_dimension(z) == 1
@test MOI.Utilities.eval_variables(vi -> vals[vi], z) ≈ 5
@test MOI.Utilities.eval_variables(vi -> vals[vi], z) ≈ 5
fvv = MOI.VectorOfVariables([x, z, y])
@test MOI.output_dimension(fvv) == 3
@test MOI.Utilities.eval_variables(vi -> vals[vi], fvv) ≈ [3, 5, 1]
@test MOI.Utilities.eval_variables(vi -> vals[vi], fvv) ≈ [3, 5, 1]
fsa = MOI.ScalarAffineFunction(
[
MOI.ScalarAffineTerm(1.0, x),
MOI.ScalarAffineTerm(3.0, z),
MOI.ScalarAffineTerm(2.0, y),
],
2.0,
)
@test MOI.output_dimension(fsa) == 1
@test MOI.Utilities.eval_variables(vi -> vals[vi], fsa) ≈ 22
@test MOI.Utilities.eval_variables(vi -> vals[vi], fsa) ≈ 22
fva = MOI.VectorAffineFunction(
MOI.VectorAffineTerm.(
[2, 1, 2],
MOI.ScalarAffineTerm.([1.0, 3.0, 2.0], [x, z, y]),
),
[-3.0, 2.0],
)
@test MOI.output_dimension(fva) == 2
@test MOI.Utilities.eval_variables(vi -> vals[vi], fva) ≈ [12, 7]
@test MOI.Utilities.eval_variables(vi -> vals[vi], fva) ≈ [12, 7]
fsq = MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.(1.0, [x, w, w], [z, z, y]),
MOI.ScalarAffineTerm.(1.0, [x, y]),
-3.0,
)
@test MOI.output_dimension(fsq) == 1
@test MOI.Utilities.eval_variables(vi -> vals[vi], fsq) ≈ 16
@test MOI.Utilities.eval_variables(vi -> vals[vi], fsq) ≈ 16
fvq = MOI.VectorQuadraticFunction(
MOI.VectorQuadraticTerm.(
[1, 2, 2],
MOI.ScalarQuadraticTerm.(1.0, [x, w, w], [z, z, y]),
),
MOI.VectorAffineTerm.([2, 1], MOI.ScalarAffineTerm.(1.0, [x, y])),
[-3.0, -2.0],
)
@test MOI.output_dimension(fvq) == 2
@test MOI.Utilities.eval_variables(vi -> vals[vi], fvq) ≈ [13, 1]
@test MOI.Utilities.eval_variables(vi -> vals[vi], fvq) ≈ [13, 1]
return
end
function test_substitute_variables()
# We do tests twice to make sure the function is not modified
subs = Dict(w => 1.0y + 1.0z, x => 2.0y + 1.0, y => 1.0y, z => -1.0w)
vals = Dict(w => 0.0, x => 3.0, y => 1.0, z => 5.0)
subs_vals = Dict(w => 6.0, x => 3.0, y => 1.0, z => 0.0)
fsa = x + 3.0z + 2.0y + 2.0
subs_sa = -3.0w + 4.0y + 3.0
@test MOI.Utilities.eval_variables(vi -> subs_vals[vi], fsa) ==
MOI.Utilities.eval_variables(vi -> vals[vi], subs_sa)
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fsa) ≈ subs_sa
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fsa) ≈ subs_sa
fva = MOI.Utilities.operate(vcat, Float64, 3.0z - 3.0, x + 2.0y + 2.0)
subs_va = MOI.Utilities.operate(vcat, Float64, -3.0w - 3.0, 4.0y + 3.0)
@test MOI.Utilities.eval_variables(vi -> subs_vals[vi], fva) ==
MOI.Utilities.eval_variables(vi -> vals[vi], subs_va)
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fva) ≈ subs_va
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fva) ≈ subs_va
fsq = 1.0x + 1.0y + 1.0x * z + 1.0w * z + 1.0w * y + 2.0w * w - 3.0
# 2y + 1 + y - 2yw - w + (y + z) * (-w) + (y + z) * y + 2 (y + z) * (y + z) - 3
# 2y + y - 2yw - w - yw - zw + y^2 + zy + 2y^2 + 2z^2 + 4yz - 2
# 3y - w + 3y^2 + 2z^2 - 3yw - zw + 5yz - 2
subs_sq =
3.0y - 1.0w + 3.0y * y + 2.0z * z - 3.0y * w - 1.0z * w + 5.0y * z - 2.0
@test MOI.Utilities.eval_variables(vi -> subs_vals[vi], fsq) ==
MOI.Utilities.eval_variables(vi -> vals[vi], subs_sq)
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fsq) ≈ subs_sq
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fsq) ≈ subs_sq
fvq = MOI.Utilities.operate(
vcat,
Float64,
1.0y + 1.0x * z - 3.0,
1.0x + 1.0w * z + 1.0w * y - 2.0,
)
subs_vq = MOI.Utilities.operate(
vcat,
Float64,
1.0y - w - 2.0y * w - 3.0,
2.0y + 1.0y * y - 1.0w * y - 1.0w * z + 1.0y * z - 1.0,
)
@test MOI.Utilities.eval_variables(vi -> subs_vals[vi], fvq) ==
MOI.Utilities.eval_variables(vi -> vals[vi], subs_vq)
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fvq) ≈ subs_vq
@test MOI.Utilities.substitute_variables(vi -> subs[vi], fvq) ≈ subs_vq
complex_aff = 2.0im * y
# Test that variables can be substituted for `MOI.ScalarAffineFunction{S}`
# in a `MOI.ScalarAffineFunction{T}` where `S != T`.
@test MOI.Utilities.substitute_variables(vi -> 1.5x, complex_aff) ≈
3.0im * x
float_aff = 2.0 * y
@test MOI.Utilities.substitute_variables(vi -> 3x, float_aff) ≈ 6.0 * x
complex_quad = 1.5im * y * y
@test MOI.Utilities.substitute_variables(vi -> 2x, complex_quad) ≈
6.0im * x * x
int_quad = 3 * y * x
@test MOI.Utilities.substitute_variables(vi -> true * y, int_quad) ≈
3 * y * y
return
end
function test_map_indices()
fsq = MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.(1.0, [x, w, w], [z, z, y]),
MOI.ScalarAffineTerm.(1.0, [x, y]),
-3.0,
)
index_map = Dict(x => y, y => z, w => w, z => x)
gsq = MOI.Utilities.map_indices(index_map, fsq)
sats = MOI.ScalarAffineTerm.(1.0, [y, z])
sqts = MOI.ScalarQuadraticTerm.(1.0, [y, w, w], [x, x, z])
@test gsq.affine_terms == sats
@test gsq.quadratic_terms == sqts
@test gsq.constant == -3.0
fvq = MOI.VectorQuadraticFunction(
MOI.VectorQuadraticTerm.(
[1, 2, 2],
MOI.ScalarQuadraticTerm.(1.0, [x, w, w], [z, z, y]),
),
MOI.VectorAffineTerm.([2, 1], MOI.ScalarAffineTerm.(1.0, [x, y])),
[-3.0, -2.0],
)
gvq = MOI.Utilities.map_indices(index_map, fvq)
@test gvq.affine_terms == MOI.VectorAffineTerm.([2, 1], sats)
@test gvq.quadratic_terms == MOI.VectorQuadraticTerm.([1, 2, 2], sqts)
@test MOI.Utilities.constant_vector(gvq) == [-3.0, -2.0]
@test MOI.Utilities.map_indices(index_map, :s) == :s
@test MOI.Utilities.map_indices(index_map, [:a, :b]) == [:a, :b]
@test MOI.Utilities.map_indices(index_map, "s") == "s"
@test MOI.Utilities.map_indices(index_map, ["a", "b"]) == ["a", "b"]
return
end
function test_Conversion_VectorOfVariables_VectorAffineFunction()
f = MOI.VectorAffineFunction{Int}(MOI.VectorOfVariables([z, x, y]))
@test f isa MOI.VectorAffineFunction{Int}
@test f.terms ==
MOI.VectorAffineTerm.(
1:3,
MOI.ScalarAffineTerm.(ones(Int, 3), [z, x, y]),
)
@test all(iszero.(MOI.Utilities.constant_vector(f)))
f = MOI.VectorAffineFunction{Float64}(MOI.VectorOfVariables([x, w]))
@test f isa MOI.VectorAffineFunction{Float64}
@test f.terms ==
MOI.VectorAffineTerm.(1:2, MOI.ScalarAffineTerm.(1.0, [x, w]))
@test all(iszero.(MOI.Utilities.constant_vector(f)))
return
end
function test_iteration_and_indexing_on_VectorOfVariables()
f = MOI.VectorOfVariables([z, w, x, y])
it = MOI.Utilities.eachscalar(f)
@test length(it) == 4
@test eltype(it) == MOI.VariableIndex
@test collect(it) == [z, w, x, y]
@test it[2] == w
@test it[end] == y
return
end
function test_indexing_on_VectorAffineFunction()
f = MOI.VectorAffineFunction(
MOI.VectorAffineTerm.(
[2, 1, 3, 2, 2, 1, 3, 1, 2],
MOI.ScalarAffineTerm.(
[1, 7, 2, 9, 3, 1, 6, 4, 1],
[x, y, z, z, y, z, x, x, y],
),
),
[2, 7, 5],
)
it = MOI.Utilities.eachscalar(f)
@test length(it) == 3
@test eltype(it) == MOI.ScalarAffineFunction{Int}
g = it[2]
@test g isa MOI.ScalarAffineFunction
@test g.terms == MOI.ScalarAffineTerm.([1, 9, 3, 1], [x, z, y, y])
@test g.constant == 7
g = it[1]
@test g isa MOI.ScalarAffineFunction
@test g.terms == MOI.ScalarAffineTerm.([7, 1, 4], [y, z, x])
@test g.constant == 2
g = it[end]
@test g isa MOI.ScalarAffineFunction
@test g.terms == MOI.ScalarAffineTerm.([2, 6], [z, x])
@test g.constant == 5
h = it[[3, 1]]
@test h isa MOI.VectorAffineFunction
@test sort(h.terms, by = t -> t.output_index) ==
MOI.VectorAffineTerm.(
[1, 1, 2, 2, 2],
MOI.ScalarAffineTerm.([2, 6, 7, 1, 4], [z, x, y, z, x]),
)
@test MOI.Utilities.constant_vector(h) == [5, 2]
F = MOI.Utilities.operate(vcat, Int, it[[1, 2]], it[3])
@test F isa MOI.VectorAffineFunction{Int}
@test sort(F.terms, by = t -> t.output_index) ==
MOI.VectorAffineTerm.(
[1, 1, 1, 2, 2, 2, 2, 3, 3],
MOI.ScalarAffineTerm.(
[7, 1, 4, 1, 9, 3, 1, 2, 6],
[y, z, x, x, z, y, y, z, x],
),
)
@test MOI.Utilities.constant_vector(F) == MOI.Utilities.constant_vector(f)
return
end
function test_indexing_on_VectorQuadraticFunction()
f = MOI.VectorQuadraticFunction(
MOI.VectorQuadraticTerm.(
[2, 3, 1, 2],
MOI.ScalarQuadraticTerm.([1, 6, 4, 3], [z, x, x, y], [y, z, z, y]),
),
MOI.VectorAffineTerm.(
[2, 1, 3, 2, 2],
MOI.ScalarAffineTerm.([1, 7, 2, 9, 3], [x, y, z, z, y]),
),
[2, 7, 5],
)
it = MOI.Utilities.eachscalar(f)
@test length(it) == 3
@test eltype(it) == MOI.ScalarQuadraticFunction{Int}
g = it[2]
@test g isa MOI.ScalarQuadraticFunction
@test g.affine_terms == MOI.ScalarAffineTerm.([1, 9, 3], [x, z, y])
@test g.quadratic_terms == MOI.ScalarQuadraticTerm.([1, 3], [z, y], [y, y])
@test g.constant == 7
g = it[end]
@test g isa MOI.ScalarQuadraticFunction
@test g.affine_terms == MOI.ScalarAffineTerm.([2], [z])
@test g.quadratic_terms == MOI.ScalarQuadraticTerm.([6], [x], [z])
@test g.constant == 5
return
end
function test_Scalar_Variable_isone()
f = MOI.VariableIndex(0)
g = MOI.VariableIndex(1)
@test !isone(f)
@test !isone(g)
return
end
function test_Scalar_Variable_iszero()
f = MOI.VariableIndex(0)
g = MOI.VariableIndex(1)
@test !iszero(f)
@test !iszero(g)
@test f + 1 ≈ 1 + f
@test (f + 1.0) - 1.0 ≈ (2.0f) / 2.0
@test (f - 1.0) + 1.0 ≈ (2.0f) / 2.0
@test (1.0 + f) - 1.0 ≈ (f * 2.0) / 2.0
@test 1.0 - (1.0 - f) ≈ (f / 2.0) * 2.0
return
end
function test_Scalar_Variable_complex()
f = MOI.VariableIndex(0)
@test real(f) === f
@test MA.promote_operation(real, typeof(f)) == typeof(f)
for T in [Int, Int32, Float64]
z = MOI.Utilities.operate(imag, T, f)
@test z isa MOI.ScalarAffineFunction{T}
@test iszero(z)
@test MOI.Utilities.promote_operation(imag, T, typeof(f)) == typeof(z)
end
@test conj(f) === f
@test MA.promote_operation(conj, typeof(f)) == typeof(f)
return
end
function test_Scalar_Affine_zero()
f = @inferred MOI.Utilities.zero(MOI.ScalarAffineFunction{Float64})
@test iszero(f)
@test MOI.Utilities.isapprox_zero(f, 1e-16)
return
end
function test_Scalar_Affine_complex()
x = MOI.VariableIndex(1)
y = MOI.VariableIndex(2)
r = 3x + 4y
c = 2x + 5y
f = (1 + 0im) * r + c * im
@test real(f) ≈ r
@test MOI.Utilities.operate(imag, Int, f) ≈ c
@test imag(f) ≈ c
@test conj(f) ≈ (1 + 0im) * r - c * im
@test MA.promote_operation(real, typeof(f)) == typeof(r)
@test MA.promote_operation(imag, typeof(f)) == typeof(c)
@test MA.promote_operation(conj, typeof(f)) == typeof(f)
return
end
function test_Scalar_Affine_promote_operation()
@test MOI.Utilities.promote_operation(-, Int, MOI.VariableIndex) ==
MOI.ScalarAffineFunction{Int}
@test MOI.Utilities.promote_operation(
-,
Int,
MOI.ScalarAffineFunction{Int},
) == MOI.ScalarAffineFunction{Int}
@test MOI.Utilities.promote_operation(
+,
Float64,
MOI.VariableIndex,
MOI.VariableIndex,
) == MOI.ScalarAffineFunction{Float64}
@test MOI.Utilities.promote_operation(
+,
Float64,
MOI.ScalarAffineFunction{Float64},
Float64,
) == MOI.ScalarAffineFunction{Float64}
@test MOI.Utilities.promote_operation(
+,
Int,
MOI.ScalarAffineFunction{Int},
MOI.ScalarAffineFunction{Int},
) == MOI.ScalarAffineFunction{Int}
return
end
function test_Scalar_Affine_comparison()
@test MOI.Utilities.operate(+, Float64, x, z) + 1.0 ≈
MOI.ScalarAffineFunction(
MOI.ScalarAffineTerm.([1, 1e-7, 1], [x, y, z]),
1.0,
) atol = 1e-6
f1 = MOI.ScalarAffineFunction(
[MOI.ScalarAffineTerm(1.0, x), MOI.ScalarAffineTerm(1e-7, y)],
1.0,
)
f2 = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 1.0)
@test f1 ≈ f2 atol = 1e-6
fdiff = f1 - f2
@test !iszero(fdiff)
@test iszero(f1 - f1)
@test iszero(f2 - f2)
MOI.Utilities.canonicalize!(fdiff)
@test !MOI.Utilities.isapprox_zero(fdiff, 1e-8)
@test MOI.Utilities.isapprox_zero(fdiff, 1e-6)
return
end
function test_Scalar_Affine_canonical()
f = MOI.Utilities.canonical(
MOI.ScalarAffineFunction(
MOI.ScalarAffineTerm.([2, 1, 3, -2, -3], [y, x, z, x, z]),
5,
),
)
@test MOI.output_dimension(f) == 1
@test f.terms == MOI.ScalarAffineTerm.([-1, 2], [x, y])
@test f.constant == 5
f = MOI.Utilities.canonical(
MOI.ScalarAffineFunction(
MOI.ScalarAffineTerm.([1, 3, 1, 2, -3, 2], [w, y, w, x, x, z]),
2,
) + MOI.ScalarAffineFunction(
MOI.ScalarAffineTerm.([-1, -2, -2, 3, 2], [y, z, w, x, y]),
3,
),
)
@test f.terms == MOI.ScalarAffineTerm.([2, 4], [x, y])
@test f.constant == 5
end
function test_Scalar_Affine_convert()
f = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1.0, 0.5], [x, y]), 0.5)
@test_throws InexactError convert(MOI.VariableIndex, f)
@test_throws InexactError MOI.Utilities.convert_approx(MOI.VariableIndex, f)
@test MOI.Utilities.convert_approx(MOI.VariableIndex, f, tol = 0.5) == x
@test convert(typeof(f), f) === f
quad_f = MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm{Float64}[],
f.terms,
f.constant,
)
@test convert(MOI.ScalarQuadraticFunction{Float64}, f) ≈ quad_f
for g in [
convert(MOI.ScalarAffineFunction{Float64}, x),
convert(MOI.ScalarAffineFunction{Float64}, 1x),
]
@test g isa MOI.ScalarAffineFunction{Float64}
@test convert(MOI.VariableIndex, g) == x
@test MOI.Utilities.convert_approx(MOI.VariableIndex, g) == x
end
return
end
function test_Scalar_Affine_operate_with_Float_coefficient()
f = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1.0, 4.0], [x, y]), 5.0)
@test f ≈ 2.0f / 2.0
return
end
function test_Scalar_Affine_operate_with_Int_coefficient()
f = MOI.Utilities.canonical(
MOI.ScalarAffineFunction(
MOI.ScalarAffineTerm.([1, 3, 1, 2, -3, 2], [w, y, w, x, x, z]),
2,
) + MOI.ScalarAffineFunction(
MOI.ScalarAffineTerm.([-1, -2, -2, 3, 2], [y, z, w, x, y]),
3,
),
)
@test f === +f
@test f ≈
x + MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1, 4], [x, y]), 5)
@test f ≈ f * 1
@test f ≈
MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1, 2], [x, y]), 2) *
2 + 1
@test f ≈
x -
MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([-1, -4], [x, y]), -5)
@test f ≈
MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([3, 4], [x, y]), 5) - x
return
end
function test_Scalar_Affine_modification()
f = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2, 4], [x, y]), 0)
f = MOI.Utilities.modify_function(f, MOI.ScalarConstantChange(6))
@test f.constant == 6
g = deepcopy(f)
@test g ≈ f
f = MOI.Utilities.modify_function(f, MOI.ScalarCoefficientChange(y, 3))
@test !(g ≈ f)
@test g.terms == MOI.ScalarAffineTerm.([2, 4], [x, y])
@test f.terms == MOI.ScalarAffineTerm.([2, 3], [x, y])
f = MOI.Utilities.modify_function(f, MOI.ScalarCoefficientChange(x, 0))
@test f.terms == MOI.ScalarAffineTerm.([3], [y])
return
end
function test_Scalar_Quadratic_zero()
f = @inferred MOI.Utilities.zero(MOI.ScalarQuadraticFunction{Float64})
@test MOI.Utilities.isapprox_zero(f, 1e-16)
return
end
function test_Scalar_Quadratic_promote_operation()
@test MOI.Utilities.promote_operation(
-,
Int,
MOI.ScalarQuadraticFunction{Int},
) == MOI.ScalarQuadraticFunction{Int}
@test MOI.Utilities.promote_operation(
+,
Int,
MOI.ScalarQuadraticFunction{Int},
MOI.ScalarQuadraticFunction{Int},
) == MOI.ScalarQuadraticFunction{Int}
@test MOI.Utilities.promote_operation(
+,
Int,
MOI.ScalarQuadraticFunction{Int},
MOI.ScalarAffineFunction{Int},
) == MOI.ScalarQuadraticFunction{Int}
@test MOI.Utilities.promote_operation(
+,
Int,
MOI.ScalarAffineFunction{Int},
MOI.ScalarQuadraticFunction{Int},
) == MOI.ScalarQuadraticFunction{Int}
@test MOI.Utilities.promote_operation(
*,
Int,
MOI.VariableIndex,
MOI.VariableIndex,
) == MOI.ScalarQuadraticFunction{Int}
@test MOI.Utilities.promote_operation(
*,
Float64,
MOI.VariableIndex,
MOI.ScalarAffineFunction{Float64},
) == MOI.ScalarQuadraticFunction{Float64}
@test MOI.Utilities.promote_operation(
*,
Int,
MOI.ScalarAffineFunction{Int},
MOI.VariableIndex,
) == MOI.ScalarQuadraticFunction{Int}
@test MOI.Utilities.promote_operation(
*,
Float64,
MOI.ScalarAffineFunction{Float64},
MOI.ScalarAffineFunction{Float64},
) == MOI.ScalarQuadraticFunction{Float64}
@test MOI.Utilities.promote_operation(
/,
Float64,
MOI.ScalarQuadraticFunction{Float64},
Float64,
) == MOI.ScalarQuadraticFunction{Float64}
return
end
function test_Scalar_Quadratic_Comparison_With_iszero()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
MOI.Utilities.canonicalize!(f)
@test !iszero(f)
@test iszero(0 * f)
@test iszero(f - f)
return
end
function test_Scalar_Quadratic_Comparison_With_tolerance()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
MOI.Utilities.canonicalize!(f)
@test !MOI.Utilities.isapprox_zero(f, 1e-8)
# Test isapprox_zero with zero terms
@test MOI.Utilities.isapprox_zero(0 * f, 1e-8)
g = 1.0x * y - (1 + 1e-6) * y * x
MOI.Utilities.canonicalize!(g)
@test MOI.Utilities.isapprox_zero(g, 1e-5)
@test !MOI.Utilities.isapprox_zero(g, 1e-7)
return
end
function test_Scalar_Quadratic_convert()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
MOI.Utilities.canonicalize!(f)
@test_throws InexactError convert(MOI.VariableIndex, f)
@test_throws InexactError convert(MOI.ScalarAffineFunction{Int}, f)
g = convert(MOI.ScalarQuadraticFunction{Float64}, x)
@test convert(MOI.VariableIndex, g) == x
return
end
function test_Scalar_Quadratic_Power_Affine()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
aff = 1x + 2 + y
@test isone(@inferred aff^0)
@test convert(typeof(f), aff) ≈ @inferred aff^1
@test aff * aff ≈ @inferred aff^2
err = ArgumentError("Cannot take $(typeof(aff)) to the power 3.")
@test_throws err aff^3
return
end
function test_Scalar_Quadratic_Power_Quadratic()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
@test isone(@inferred f^0)
@test f ≈ @inferred f^1
err = ArgumentError("Cannot take $(typeof(f)) to the power 2.")
@test_throws err f^2
return
end
function test_Scalar_Quadratic_no_zero_affine_term()
# Test that no affine 0y term is created when multiplying 1x by y
for xy in [1x * y, x * 1y]
@test isempty(xy.affine_terms)
@test length(xy.quadratic_terms) == 1
@test xy.quadratic_terms[1] == MOI.ScalarQuadraticTerm(1, x, y) ||
xy.quadratic_terms[1] == MOI.ScalarQuadraticTerm(1, y, x)
end
for xx in [1x * x, x * 1x]
@test isempty(xx.affine_terms)
@test length(xx.quadratic_terms) == 1
@test xx.quadratic_terms[1] == MOI.ScalarQuadraticTerm(2, x, x)
end
return
end
function test_Scalar_Quadratic_operate!()
q = 1.0x + 1.0y + (1.0x) * z + (1.0w) * z
@test q ≈ 1.0x + 1.0y + (1.0w) * z + (1.0x) * z
# This calls
aff = 1.0x + 1.0y
# which tries to mutate `aff`, gets a quadratic expression
# and mutate it with the remaining term
@test MOI.Utilities.operate!(+, Float64, aff, (1.0x) * z, (1.0w) * z) ≈ q
return
end
function test_Scalar_Quadratic_operate()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
@test f ≈ 7 + (x + 2y) * (1x + y) + 3x
@test f ≈ -(-7 - 3x) + (x + 2y) * (1x + y)
@test f ≈ -((x + 2y) * (MOI.Utilities.operate(-, Int, x) - y)) + 3x + 7
@test f ≈ 7 + MOI.Utilities.operate(*, Int, x, x) + 3x * (y + 1) + 2y * y
@test f ≈ (x + 2) * (x + 1) + (y + 1) * (2y + 3x) + (5 - 3x - 2y)
@test f ≈ begin
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2], [x], [x]),
[MOI.ScalarAffineTerm(3, x)],
4,
) + MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([4, 3], [y, x], [y, y]),
MOI.ScalarAffineTerm{Int}[],
3,
)
end
@test f ≈ begin
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2], [x], [x]),
[MOI.ScalarAffineTerm(3, x)],
10,
) - MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([-4, -3], [y, x], [y, y]),
MOI.ScalarAffineTerm{Int}[],
3,
)
end
@test f ≈ begin
MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(3, x)], 5) +
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2, 4, 3], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm{Int}[],
2,
)
end
@test f ≈ begin
MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(3, x)], 5) -
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([-2, -4, -3], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm{Int}[],
-2,
)
end
@test f ≈ begin
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2, 4, 3], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm{Int}[],
2,
) + MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(3, x)], 5)
end
@test f ≈ begin
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2, 4, 3], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm{Int}[],
12,
) - MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(-3, x)], 5)
end
@test f ≈ begin
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2, 4, 3], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm.([2], [x]),
7,
) + x
end
@test f ≈
MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2, 4, 3], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm.([3], [x]),
10,
) - 3
@test f ≈
2.0 * MOI.ScalarQuadraticFunction(
MOI.ScalarQuadraticTerm.([2.0, 4.0, 3.0], [x, y, x], [x, y, y]),
MOI.ScalarAffineTerm.([3.0], [x]),
7.0,
) / 2.0
return
end
function test_Scalar_Quadratic_modification()
f = 7 + 3x + 1x * x + 2y * y + 3x * y
f = MOI.Utilities.modify_function(f, MOI.ScalarConstantChange(9))
@test f.constant == 9
f = MOI.Utilities.modify_function(f, MOI.ScalarCoefficientChange(y, 0))
@test f.affine_terms == MOI.ScalarAffineTerm.([3], [x])
g = deepcopy(f)
@test f ≈ g
f = MOI.Utilities.modify_function(f, MOI.ScalarCoefficientChange(y, 2))
@test !(f ≈ g)
@test g.affine_terms == MOI.ScalarAffineTerm.([3], [x])
@test f.affine_terms == MOI.ScalarAffineTerm.([3, 2], [x, y])
return
end
function test_Vector_Variable()
f = MOI.VectorOfVariables([MOI.VariableIndex(1), MOI.VariableIndex(2)])
@test real(f) === f
@test MA.promote_operation(real, typeof(f)) == typeof(f)
for T in [Int, Int32, Float64]
z = MOI.Utilities.operate(imag, T, f)
@test z isa MOI.VectorAffineFunction{T}
@test isempty(z.terms)
@test all(iszero, z.constants)
@test MOI.output_dimension(z) == MOI.output_dimension(f)
@test MOI.Utilities.promote_operation(imag, T, typeof(f)) == typeof(z)
end
@test conj(f) === f
@test MA.promote_operation(conj, typeof(f)) == typeof(f)
end
function test_Vector_Affine_complex()
x = MOI.VectorOfVariables([MOI.VariableIndex(1)])
y = MOI.VectorOfVariables([MOI.VariableIndex(2)])
r = 3x + 4y
c = 2x + 5y
f = (1 + 0im) * r + c * im
@test real(f) ≈ r
@test MOI.Utilities.operate(imag, Int, f) ≈ c
@test imag(f) ≈ c
@test conj(f) ≈ (1 + 0im) * r - c * im
@test MA.promote_operation(real, typeof(f)) == typeof(r)
@test MA.promote_operation(imag, typeof(f)) == typeof(c)
@test MA.promote_operation(conj, typeof(f)) == typeof(f)
return
end
function test_Vector_Affine()
f = MOI.Utilities.canonical(
MOI.VectorAffineFunction(
MOI.VectorAffineTerm.(
[2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2],
MOI.ScalarAffineTerm.(
[3, 2, 3, -3, -1, -2, 3, -2, 1, 3, 5, -2, 0, -1],
[x, x, z, y, y, x, y, z, x, y, y, x, x, z],
),
),
[5, 7],
),
)
@test MOI.output_dimension(f) == 2
@test f.terms ==
MOI.VectorAffineTerm.(
[1, 1, 2],
MOI.ScalarAffineTerm.([2, 4, 3], [x, y, y]),
)
@test MOI.Utilities.constant_vector(f) == [5, 7]
f = MOI.Utilities.modify_function(f, MOI.VectorConstantChange([6, 8]))
@test MOI.Utilities.constant_vector(f) == [6, 8]
g = deepcopy(f)
@test f ≈ g
f = MOI.Utilities.modify_function(f, MOI.MultirowChange(y, [(2, 9)]))
@test !(f ≈ g)
@test f.terms ==
MOI.VectorAffineTerm.(
[1, 1, 2],
MOI.ScalarAffineTerm.([2, 4, 9], [x, y, y]),
)
@test g.terms ==
MOI.VectorAffineTerm.(
[1, 1, 2],
MOI.ScalarAffineTerm.([2, 4, 3], [x, y, y]),
)
f = MOI.Utilities.modify_function(f, MOI.MultirowChange(y, [(1, 0)]))
@test f.terms ==
MOI.VectorAffineTerm.([1, 2], MOI.ScalarAffineTerm.([2, 9], [x, y]))
return
end
function test_Vector_Quadratic()
f = MOI.VectorQuadraticFunction(
MOI.VectorQuadraticTerm.(
[1, 1, 2],
MOI.ScalarQuadraticTerm.([1, 2, 3], [x, y, x], [x, y, y]),
),
MOI.VectorAffineTerm.(
[1, 2, 2],
MOI.ScalarAffineTerm.([3, 1, 2], [x, x, y]),
),
[7, 3, 4],
)
@test MOI.output_dimension(f) == 3
f = MOI.Utilities.modify_function(f, MOI.VectorConstantChange([10, 11, 12]))
@test MOI.Utilities.constant_vector(f) == [10, 11, 12]
f = MOI.Utilities.modify_function(
f,
MOI.MultirowChange(y, [(2, 0), (1, 1)]),
)
@test f.affine_terms ==
MOI.VectorAffineTerm.(
[1, 2, 1],
MOI.ScalarAffineTerm.([3, 1, 1], [x, x, y]),
)
g = deepcopy(f)
f = MOI.Utilities.modify_function(
f,
MOI.MultirowChange(x, [(1, 0), (3, 4)]),
)
@test f.affine_terms ==
MOI.VectorAffineTerm.(
[2, 1, 3],
MOI.ScalarAffineTerm.([1, 1, 4], [x, y, x]),
)
@test g.affine_terms ==
MOI.VectorAffineTerm.(
[1, 2, 1],
MOI.ScalarAffineTerm.([3, 1, 1], [x, x, y]),
)
return
end