/
gram_matrix.jl
239 lines (230 loc) · 9.17 KB
/
gram_matrix.jl
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using LinearAlgebra, Test, SumOfSquares
@testset "GramMatrix tests" begin
@testset "GramMatrix" begin
@polyvar x y
P = GramMatrix{Int}((i, j) -> i + j, [x^2, x * y, y^2])
@test nvariables(P) == 2
@test variables(P) == [x, y]
Pp1 = 2x^4 + 6x^3 * y + 12x^2 * y^2 + 10x * y^3 + 6y^4 + 1
@test P + 1 == Pp1
@test P + 1.0 == Pp1
zP = zero(typeof(P))
@test isempty(zP.Q)
@test zP == 0
p = polynomial(P)
@test coefficients(p) == reverse([2, 6, 12, 10, 6])
@test monomial_type(p) == typeof(x * y)
@test monomial_type(typeof(p)) == typeof(x * y)
@test monomials(p) ==
monomial_vector([x^4, x^3 * y, x^2 * y^2, x * y^3, y^4])
for i in 1:3
for j in 1:3
@test P[i, j] == 8 - (i + j)
end
end
for P in (
GramMatrix{Int}((i, j) -> i * j, monomial_vector([x, y])),
GramMatrix{Int}((i, j) -> (3 - i) * (3 - j), [x, y]),
GramMatrix([1 2; 2 4], [y, x]),
GramMatrix([1 2; 2 4], monomial_vector([y, x])),
)
@test P.Q.Q == [1, 2, 4]
@test P.basis.monomials[1] == y
@test P.basis.monomials[2] == x
end
P = GramMatrix{Int}(
(i, j) -> ((i, j) == (1, 1) ? 2 : 0),
[x * y, x^2, y^2],
)
Q = GramMatrix([0 1; 1 0], [x^2, y^2])
@test P == Q
p = GramMatrix([2 3; 3 2], [x, y])
@test polynomial(p) isa AbstractPolynomial{Int}
@test polynomial(p, Float64) isa AbstractPolynomial{Float64}
@test -2 * x +
dot(-x - x^2, 0) +
GramMatrix{Int}((i, j) -> 1, [1, x]) == -(-x^2 - 1)
P = GramMatrix{Int}((i, j) -> i + j, [x^2, x * y, y^2])
p = polynomial(P)
@test !iszero(P)
@test iszero(P - P)
@test iszero(P - p)
@test iszero(p - P)
@test P + P == P + p
@test x * P == x * p
@test 2 * P == 2 * p
@test P * (2x) == (2x) * p
@test differentiate(GramMatrix{Int}((i, j) -> 1, [x]), y) == 0
@test differentiate(GramMatrix{Int}((i, j) -> 1, [x, y]), y, 1) ==
2x + 2y
#@inferred differentiate(GramMatrix{Int}((i,j)->1, [x, y]), y, 0) # FIXME failing at the moment
@test GramMatrix([2 3; 3 2], [x, y]) == 2x^2 + 2y^2 + 6x * y
mp = GramMatrix{Int}((i, j) -> i + j, [x])
@test norm(mp) == norm(mp, 2) == 2.0
@polyvar v[1:3]
P = [1 2 3; 2 4 5; 3 5 6]
p = GramMatrix(P, v)
#@inferred p(x => ones(3))
@test p(v => ones(3)) == 31
#@inferred subs(p, x => ones(3))
@test subs(p, v => ones(3)) == 31
@testset "Gram Operate" begin
p = GramMatrix([2 3; 3 2], [x, y])
q = GramMatrix(5 * ones(1, 1), [x])
r = @inferred gram_operate(/, q, 5)
@test r.Q == ones(1, 1)
@test r.basis.monomials == [x]
r = @inferred gram_operate(+, p, q)
@test r.Q == [2 3; 3 7]
@test r.basis.monomials == [x, y]
q = GramMatrix(5 * ones(1, 1), [y])
r = @inferred gram_operate(+, p, q)
@test r.Q == [7 3; 3 2]
@test r.basis.monomials == [x, y]
q = GramMatrix([5.0 7; 7 9], [x * y, 1])
r = @inferred gram_operate(+, p, q)
@test r.Q == [
9 0 0 7
0 2 3 0
0 3 2 0
7 0 0 5
]
@test r.basis.monomials == [x * y, x, y, 1]
end
@testset "With VariableIndex" begin
a = MOI.VariableIndex(1)
g = GramMatrix(SymMatrix([a, a, a], 2), [x, y])
U = MOI.ScalarAffineFunction{Float64}
@test coefficient_type(g) == U
@test g isa AbstractPolynomialLike{U}
@test polynomial_type(g) <: AbstractPolynomial{U}
@test polynomial_type(typeof(g)) <: AbstractPolynomial{U}
@test polynomial(g) isa AbstractPolynomial{U}
end
end
@testset "SOSDecomposition" begin
@polyvar x y
# @test isempty(SOSDecomposition(typeof(x)[]))
# ps = [1, x + y, x^2, x*y, 1 + x + x^2]
# P = GramMatrix(SOSDecomposition(ps))
# P.Q == [2 0 1 0 1; 0 1 0 0 0; 1 0 2 1 1; 0 0 1 1 0; 1 0 1 0 2]
# P.basis.monomials == [x^2, x*y, x, y, 1]
# @test P == P
# @test isapprox(GramMatrix(SOSDecomposition(P)), P)
P = GramMatrix{Int}((i, j) -> i + j, [x^2, x * y, y^2])
@test polynomial_type(SOSDecomposition(P)) <: AbstractPolynomialLike
@test sprint(show, SOSDecomposition([x + y, x - y])) ==
"(y + x)^2 + (-y + x)^2"
@test polynomial(SOSDecomposition([x + y, x - y])) ==
(x + y)^2 + (x - y)^2
@test polynomial(SOSDecomposition([x + y, x - y]), Float64) ==
(x + y)^2 + (x - y)^2
@testset "SOSDecomposition equality" begin
@polyvar x y
@test !isapprox(
SOSDecomposition([x + y, x - y]),
SOSDecomposition([x + y]),
)
@test !isapprox(
SOSDecomposition([x + y, x - y]),
SOSDecomposition([x + y, x + y]),
)
@test isapprox(
SOSDecomposition([x + y, x - y]),
SOSDecomposition([x + y, x - y]),
)
@test isapprox(
SOSDecomposition([x + y, x - y]),
SOSDecomposition([x - y, x + y + 1e-8]),
ztol = 1e-7,
)
end
@testset "With VariableIndex" begin
a = MOI.VariableIndex(1)
p = polynomial([a], [x])
q = polynomial([a], [y])
s = SOSDecomposition([p, q])
U = MOI.ScalarQuadraticFunction{Float64}
@test coefficient_type(s) == U
@test s isa AbstractPolynomialLike{U}
@test polynomial_type(s) <: AbstractPolynomial{U}
@test polynomial_type(typeof(s)) <: AbstractPolynomial{U}
end
end
@testset "SOSDecompositionWithDomain" begin
@polyvar x y
K = @set 1 - x^2 >= 0 && 1 - y^2 >= 0
ps = SOSDecomposition([x + y, x - y])
ps1 = SOSDecomposition([x])
ps2 = SOSDecomposition([y])
@test [ps, ps1] isa Vector{
SOSDecomposition{Int,T,Int},
} where {T<:AbstractPolynomialLike}
@test sprint(show, SOSDecompositionWithDomain(ps, [ps1, ps2], K)) ==
"(y + x)^2 + (-y + x)^2 + (x)^2 * (1 - x^2) + (y)^2 * (1 - y^2)"
@testset "SOSDecompositionWithDomain equality" begin
@polyvar x y
K = @set 1 - x^2 >= 0 && 1 - y^2 >= 0
B = @set 1 - x >= 0 && 1 - y >= 0
ps = SOSDecomposition([x + y, x - y])
ps1 = SOSDecomposition([x + y, x^2 - y])
ps2 = SOSDecomposition([x + y, y^2 - x])
sosdec = SOSDecompositionWithDomain(ps, [ps1, ps2], K)
@test typeof(polynomial(sosdec)) <: AbstractPolynomialLike
@test isapprox(sosdec, sosdec)
@test !isapprox(
sosdec,
SOSDecompositionWithDomain(ps, [ps1, ps2], B),
)
@test !isapprox(
SOSDecompositionWithDomain(ps, [ps1, ps1], K),
sosdec,
)
end
end
@testset "build_gram_matrix" begin
v = MOI.VariableIndex.(1:3)
w = MOI.VariableIndex.(1:4)
@polyvar x y
basis = MonomialBasis(monomials([x, y], 1))
@testset "$T" for T in [Float64, Int, BigFloat]
#@test_throws DimensionMismatch SumOfSquares.build_gram_matrix(w, basis, T, MOI.PositiveSemidefiniteConeTriangle)
g = SumOfSquares.build_gram_matrix(
v,
basis,
MOI.PositiveSemidefiniteConeTriangle,
T,
)
@test g isa GramMatrix{
MOI.VariableIndex,
typeof(basis),
MOI.ScalarAffineFunction{T},
}
@test g.Q[1, 2] == v[2]
p = polynomial(g)
@test p isa AbstractPolynomial{MOI.ScalarAffineFunction{T}}
@test typeof(p) == polynomial_type(g)
#@test_throws DimensionMismatch SumOfSquares.build_gram_matrix(v, basis, T, MOI.HermitianPositiveSemidefiniteConeTriangle)
h = SumOfSquares.build_gram_matrix(
w,
basis,
MOI.HermitianPositiveSemidefiniteConeTriangle,
T,
)
@test h isa GramMatrix{
MOI.ScalarAffineFunction{Complex{T}},
typeof(basis),
MOI.ScalarAffineFunction{Complex{T}},
SumOfSquares.MultivariateMoments.VectorizedHermitianMatrix{
MOI.VariableIndex,
T,
MOI.ScalarAffineFunction{Complex{T}},
},
}
@test h.Q[1, 2] ≈ w[2] + im * w[4]
q = polynomial(h)
@test q isa AbstractPolynomial{MOI.ScalarAffineFunction{Complex{T}}}
@test typeof(q) == polynomial_type(h)
end
end
end