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redundancy.jl
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redundancy.jl
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using Test
using StaticArrays
using Polyhedra
include("solvers.jl")
@testset "Redundancy removal" begin
@testset "LP-based" begin
@testset "HRepresentation with $(typeof(x))" for (x, y, z, w) in [
([1, 0], [0, 1], [1, 1], [0, 0]),
([1.0, 0.0], [0.0, 1.0], [1.0, 1.0], [0.0, 0.0]),
((@SVector [1, 0]), (@SVector [0, 1]), (@SVector [1, 1]), (@SVector [0, 0]))]
T = eltype(x)
AT = typeof(x)
d = Polyhedra.FullDim(x)
@testset "HAffineSpace" begin
for hr in [hrep(typeof(HyperPlane(x, one(T)))[]; d=d),
intersect(HyperPlane(w, zero(T)))]
@test dim(hr) == 2
for h in [detecthlinearity(hr, lp_solver),
removehredundancy(hr, lp_solver)]
@test dim(h) == 2
@test h isa HyperPlanesIntersection{T, AT}
@test !hashyperplanes(h)
@test !hashalfspaces(h)
end
end
hr = intersect(HyperPlane(x, one(T)))
@test dim(hr) == 1
for h in [detecthlinearity(hr, lp_solver),
removehredundancy(hr, lp_solver)]
@test dim(h) == 1
@test h isa HyperPlanesIntersection{T, AT}
@test nhyperplanes(h) == 1
@test !hashalfspaces(h)
end
hr = intersect(HyperPlane(w, one(T)))
@test dim(hr) == -1
for h in [detecthlinearity(hr, lp_solver),
removehredundancy(hr, lp_solver)]
@test dim(h) == -1
@test h isa HyperPlanesIntersection{T, AT}
@test nhyperplanes(h) == 3
@test !hashalfspaces(h)
end
end
@testset "Intersection" begin
for hr in [HalfSpace(z + x, 3) ∩ HalfSpace(-x, -one(T)) ∩ HalfSpace(-2y, -2),
HalfSpace(x, one(T)) ∩ HalfSpace(y, one(T)) ∩ HalfSpace(-z, -2)]
h = detecthlinearity(hr, lp_solver, verbose=2)
@test h isa Polyhedra.Intersection{T, AT}
@test nhyperplanes(h) == 2
@test !hashalfspaces(h)
end
for hr in [HalfSpace(z, zero(T)) ∩ HalfSpace(-z, -zero(T)),
HalfSpace(x, one(T)) ∩ HalfSpace(-x, -one(T))]
h = detecthlinearity(hr, lp_solver, verbose=2)
@test h isa Polyhedra.Intersection{T, AT}
@test nhyperplanes(h) == 1
@test !hashalfspaces(h)
end
for hr in [HalfSpace(-x, one(T)) ∩ HalfSpace(-y, one(T)) ∩ HalfSpace(x, one(T)) ∩ HalfSpace(y, one(T)) ∩ HalfSpace(-x, -9),
HalfSpace(x, zero(T)) ∩ HalfSpace(-x, -one(T))]
h = detecthlinearity(hr, lp_solver, verbose=2)
@test h isa Polyhedra.Intersection{T, AT}
@test nhyperplanes(h) == 3
@test !hashalfspaces(h)
end
end
end
@testset "VRepresentation with $(typeof(x))" for (x, y, z, w) in [
([1, 0], [0, 1], [1, 1], [0, 0]),
([1.0, 0.0], [0.0, 1.0], [1.0, 1.0], [0.0, 0.0]),
((@SVector [1, 0]), (@SVector [0, 1]), (@SVector [1, 1]), (@SVector [0, 0]))]
T = eltype(x)
AT = typeof(x)
d = Polyhedra.FullDim(x)
@testset "VLinearSpace" begin
for vr in [vrep(typeof(Line(x))[]; d=d),
convexhull(Line(w))]
for v in [detectvlinearity(vr, lp_solver),
removevredundancy(vr, lp_solver)]
@test v isa LinesHull{T, AT}
@test !haspoints(v)
@test !hasrays(v)
@test !haslines(v)
end
end
vr = convexhull(Line(x))
for v in [detectvlinearity(vr, lp_solver),
removevredundancy(vr, lp_solver)]
@test v isa LinesHull{T, AT}
@test npoints(v) == 1
@test !hasrays(v)
@test nlines(v) == 1
end
for vr in [convexhull(Line(x), Line(y)),
convexhull(Line(x), Line(y), Line(z)),
convexhull(Line(x), Line(z), Line(y)),
convexhull(Line(x), Line(z), Line(z))]
for v in [detectvlinearity(vr, lp_solver),
removevredundancy(vr, lp_solver)]
@test v isa LinesHull{T, AT}
@test npoints(v) == 1
@test !hasrays(v)
@test nlines(v) == 2
end
end
vrepm1 = Polyhedra.emptyspace(vr)
@test vrepm1 === @inferred removevredundancy(vrepm1, lp_solver)
end
@testset "Polyhedra.RaysHull" begin
vr = vrep(typeof(Line(x))[], typeof(Ray(x))[]; d=d)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test !haspoints(rm)
@test !hasrays(rm)
@test !haslines(rm)
vr = convexhull(Ray(x))
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 1
@test !haslines(rm)
vr = convexhull(Ray(x), Ray(y))
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 2
@test !haslines(rm)
for vr in [convexhull(Ray(x), Ray(y), Ray(z)),
convexhull(Ray(x), Ray(z), Ray(y)),
convexhull(Ray(z), Ray(x), Ray(y))]
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 2
rs = collect(rays(rm))
@test rs[1] == Ray(x)
@test rs[2] == Ray(y)
@test !haslines(rm)
end
vr = convexhull(Ray(x), Ray(y), Ray(-z))
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 3
@test !haslines(rm)
vr = convexhull(Ray(x), Ray(y), Line(z))
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 2
@test nlines(rm) == 1
vr = convexhull(Ray(x), Ray(-y), Line(z))
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 1
@test nlines(rm) == 1
vr = conichull(Ray(x), Ray(y), Ray(-z))
rm = detectvlinearity(vr, lp_solver)
@test rm isa Polyhedra.RaysHull{T, AT}
@test npoints(rm) == 1
@test nrays(rm) == 0
@test nlines(rm) == 2
end
@testset "Polyhedra.PointsHull" begin
vr = vrep(typeof(x)[]; d=d)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.PointsHull{T, AT}
@test !haspoints(rm)
@test !hasrays(rm)
@test !haslines(rm)
vr = convexhull(x)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.PointsHull{T, AT}
@test npoints(rm) == 1
@test !hasrays(rm)
@test !haslines(rm)
vr = convexhull(x, y)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.PointsHull{T, AT}
@test npoints(rm) == 2
@test !hasrays(rm)
@test !haslines(rm)
for vr in [convexhull(2x, 2y, z),
convexhull(2x, z, 2y),
convexhull(z, 2x, 2y)]
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.PointsHull{T, AT}
@test npoints(rm) == 2
ps = collect(points(rm))
@test ps[1] == 2x
@test ps[2] == 2y
@test !hasrays(rm)
@test !haslines(rm)
end
vr = convexhull(x, y, z)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.PointsHull{T, AT}
@test npoints(rm) == 3
@test !hasrays(rm)
@test !haslines(rm)
vr = convexhull(x, y, -z)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.PointsHull{T, AT}
@test npoints(rm) == 3
@test !hasrays(rm)
@test !haslines(rm)
vr = convexhull(x, y) + Ray(z)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.Hull{T, AT}
@test npoints(rm) == 2
@test nrays(rm) == 1
@test !haslines(rm)
vr = convexhull(x, y) + Line(z)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.Hull{T, AT}
@test npoints(rm) == 2
@test !hasrays(rm)
@test nlines(rm) == 1
vr = convexhull(x, -y) + Ray(z)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.Hull{T, AT}
@test npoints(rm) == 1
@test first(points(rm)) == -y
@test nrays(rm) == 1
@test !haslines(rm)
vr = convexhull(x, -y) + Line(z)
rm = removevredundancy(vr, lp_solver)
@test rm isa Polyhedra.Hull{T, AT}
@test npoints(rm) == 1
@test !hasrays(rm)
@test nlines(rm) == 1
end
end
end
@testset "Representation-based" begin
@testset "isredundant" begin
@test isredundant(HyperPlane([0, 1], 0) ∩ HalfSpace([1, 1], 1), [0, 0], nl=0)
@test !isredundant(HalfSpace([1, 1], 1) ∩ HyperPlane([0, 1], 0) ∩ HalfSpace([-1, -1], 1), [1, 0], nl=0)
#@test !ishredundant(convexhull(SymPoint([1, 0])), HyperPlane([0, 1], 0), d=1)
#@test isredundant(convexhull(SymPoint([1, 0])), HalfSpace([0, 1], 1), d=1)
@test isredundant(HalfSpace([1, 1], 2) ∩ HalfSpace([-1, 0], 0) ∩ HalfSpace([0, -1], 0), [1, 1], nl=0)
@test !isredundant(HalfSpace([1, 1], 2) ∩ HalfSpace([-1, 0], 0) ∩ HalfSpace([0, -1], 0), [1, 1], nl=0, strongly=true)
end
# @testset "Non-redundant SymPoint" begin
# vr = convexhull(SymPoint([-1, 0]), SymPoint([0, 1]))
# hr = HalfSpace([-1, -1], 1) ∩ HalfSpace([1, -1], 1) ∩ HalfSpace([1, 1], 1) ∩ HalfSpace([-1, 1], 1)
# vr = @inferred Polyhedra.removevredundancy(vr, hr)
# @test vr isa Polyhedra.PointsHull{2,Int,Vector{Int}}
# @test collect(sympoints(vr)) == [SymPoint([-1, 0]), SymPoint([0, 1])]
# @test !haspoints(vr)
# @test !hasallrays(vr)
# end
@testset "Point" begin
# x - y ≤ 1
# x + y ≥ -1
hr = HalfSpace([-1, -1], 1) ∩ HalfSpace([1, -1], 1)
# [-1, 0] is weakly redundant as it belongs to the facet x + y = -1
@test isredundant(hr, [-1, 0], nl=0)
@test !isredundant(hr, [-1, 0], strongly=true, nl=0)
# [0, -1] is not redundant as it is an extreme point
@test !isredundant(hr, [0, -1], nl=0)
@test !isredundant(hr, [0, -1], strongly=true, nl=0)
# [0, 0] is strongly redundant as it is in the relative interior
@test isredundant(hr, [0, 0], nl=0)
@test isredundant(hr, [0, 0], strongly=true, nl=0)
vr = convexhull([-1, 0], [0, -1], [0, 0]) + conichull([1, 1], [-1, 1])
@test collect(removevredundancy(points(vr), hr, nl=0)) == [[0, -1]]
@test collect(removevredundancy(points(vr), hr, strongly=true, nl=0)) == [[-1, 0], [0, -1]]
vrr = Polyhedra.removevredundancy(vr, hr)
@test collect(points(vrr)) == [[0, -1]]
@test !haslines(vrr)
@test collect(rays(vrr)) == [Ray([1, 1]), Ray([-1, 1])]
vrr = Polyhedra.removevredundancy(vr, hr, strongly=true)
@test collect(points(vrr)) == [[-1, 0], [0, -1]]
@test !haslines(vrr)
@test collect(rays(vrr)) == [Ray([1, 1]), Ray([-1, 1])]
p = polyhedron(vr, DefaultLibrary{Rational{BigInt}}(Polyhedra.OppositeMockOptimizer))
Polyhedra.computehrep!(p)
removevredundancy!(p, strongly=true)
@test collect(points(p)) == [[-1, 0], [0, -1]]
@test !haslines(p)
@test collect(rays(p)) == [Ray([1, 1]), Ray([-1, 1])]
removevredundancy!(p, planar=false)
@test collect(points(p)) == [[0, -1]]
@test !haslines(p)
@test collect(rays(p)) == [Ray([1, 1]), Ray([-1, 1])]
end
# @testset "Split SymPoint" begin
# vr = convexhull(SymPoint([-1, 0]), SymPoint([0, 1])) + conichull([1, 1], [-1, 1])
# hr = HalfSpace([-1, -1], 1) ∩ HalfSpace([1, -1], 1)
# vr = Polyhedra.removevredundancy(vr, hr)
# @test !hassympoints(vr)
# @test collect(points(vr)) == [[0, -1]]
# @test !haslines(vr)
# @test collect(rays(vr)) == [Ray([1, 1]), Ray([-1, 1])]
#
# vr = convexhull(SymPoint([1, 0]), SymPoint([0, 1])) + conichull([-1, 1])
# hr = HalfSpace([-1, -1], 1) ∩ HalfSpace([1, -1], 1) ∩ HalfSpace([1, 1], 1)
# vr = Polyhedra.removevredundancy(vr, hr)
# @test !hassympoints(vr)
# @test collect(points(vr)) == [[1, 0], [0, -1]]
# @test !haslines(vr)
# @test collect(rays(vr)) == [Ray([-1, 1])]
# end
end
end
@testset "Duplicate removal" begin
h = removeduplicates(hrep([1 1; -1 -1; 1 0; 0 -1], [1, -1, 1, 0]))
@test nhyperplanes(h) == 1
@test first(hyperplanes(h)) == HyperPlane([1, 1], 1)
@test first(hyperplanes(h)) == HyperPlane([-1, -1], -1)
@test nhalfspaces(h) == 1
h = removeduplicates(hrep([1 1; -1 -1], [2, -1]))
@test !hashyperplanes(h)
@test nhalfspaces(h) == 2
# v = removeduplicates(convexhull([1, 2], SymPoint([1, 2]), [-1, 1]))
# @test typeof(v) == Polyhedra.PointsHull{2,Int,Vector{Int}}
# @test collect(sympoints(v)) == [SymPoint([1, 2])]
# @test collect(points(v)) == [[-1, 1]]
# @test !hasallrays(v)
for v in (#removeduplicates(convexhull([1, 2], [2, 1], SymPoint([1, 2]), [-1, 1]) + Line([0, 1])),
#removeduplicates(Line([0, 1]) + convexhull([1, 2], [2, 1], SymPoint([1, 2]), [-1, 1])),
removeduplicates(Line([0, 1]) + convexhull([-1, -2], [2, 1], [1, 2], [-1, 1], [-1, -2])),)
@test typeof(v) == Polyhedra.Hull{Int, Vector{Int}, Int}
#@test collect(sympoints(v)) == [SymPoint([1, 2])]
@test collect(points(v)) == [[-1, -2], [2, 1], [1, 2]]
@test !hasrays(v)
@test collect(lines(v)) == [Line([0, 1])]
end
end