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intersection of CartesianProduct with polyhedron #3361

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Aug 18, 2023
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intersection of CartesianProduct with polyhedron #3361

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2 changes: 1 addition & 1 deletion docs/src/lib/binary_functions.md
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Original file line number Diff line number Diff line change
Expand Up @@ -86,7 +86,7 @@ intersection(::Universe, ::LazySet)
intersection(::AbstractPolyhedron, ::ResetMap)
intersection(::CartesianProductArray, ::CartesianProductArray)
intersection(::LinearMap, ::LazySet)
intersection(::CartesianProductArray, ::AbstractPolyhedron)
intersection(::Union{CartesianProduct,CartesianProductArray}, ::AbstractPolyhedron)
intersection(::LineSegment, ::Line2D)
intersection(::LineSegment, ::LineSegment)
intersection(::AbstractZonotope{N}, ::HalfSpace{N}) where {N}
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22 changes: 11 additions & 11 deletions src/ConcreteOperations/intersection.jl
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Expand Up @@ -905,7 +905,7 @@ intersection(U::Universe, ::Universe) = U
@commutative intersection(U::Universe, S::AbstractSingleton) = S
@commutative intersection(U::Universe, X::Interval) = X
@commutative intersection(U::Universe, L::LinearMap) = L
@commutative intersection(U::Universe, X::CartesianProductArray) = X
@commutative intersection(U::Universe, X::Union{CartesianProduct,CartesianProductArray}) = X
@commutative intersection(U::Universe, cup::UnionSet) = cup
@commutative intersection(U::Universe, cup::UnionSetArray) = cup

Expand Down Expand Up @@ -979,7 +979,8 @@ function intersection(X::CartesianProductArray, Y::CartesianProductArray)
end

"""
intersection(cpa::CartesianProductArray, P::AbstractPolyhedron)
intersection(cpa::Union{CartesianProduct,CartesianProductArray},
P::AbstractPolyhedron)

Compute the intersection of a Cartesian product of a finite number of polyhedral
sets with a polyhedron.
Expand Down Expand Up @@ -1036,7 +1037,7 @@ minimal dimension.
Finally, we convert ``Y`` to a polyhedron and intersect it with a suitable
projection of `P`.
"""
@commutative function intersection(cpa::CartesianProductArray,
@commutative function intersection(cpa::Union{CartesianProduct,CartesianProductArray},
P::AbstractPolyhedron)
# search for the indices of the block trisection into
# "unconstrained | constrained | unconstrained" (the first and third section
Expand All @@ -1048,12 +1049,11 @@ projection of `P`.
minimal = minimum(constrained_dims)
maximal = maximum(constrained_dims)
lower_bound = 1
blocks = array(cpa)
cb_start = 0
cb_end = length(blocks)
cb_end = length(cpa)
dim_start = 0
dim_end = dim(P)
for (i, block) in enumerate(blocks)
for (i, block) in enumerate(cpa)
dim_block = dim(block)
upper_bound = lower_bound + dim_block - 1
interval = lower_bound:upper_bound
Expand All @@ -1069,13 +1069,13 @@ projection of `P`.
lower_bound = upper_bound + 1
end
# compute intersection with constrained blocks
cap = _intersection_polyhedron_constrained(CartesianProductArray(blocks[cb_start:cb_end]), P,
cap = _intersection_polyhedron_constrained(CartesianProductArray(cpa[cb_start:cb_end]), P,
dim_start:dim_end)

# construct result
result_array = vcat(blocks[1:(cb_start - 1)], # unconstrained
result_array = vcat(cpa[1:(cb_start - 1)], # unconstrained
[cap], # constrained, intersected
blocks[(cb_end + 1):length(blocks)]) # unconstrained
cpa[(cb_end + 1):end]) # unconstrained
return CartesianProductArray(result_array)
end

Expand All @@ -1087,10 +1087,10 @@ function _intersection_polyhedron_constrained(X::LazySet, P::AbstractPolyhedron,
end

# disambiguation
@commutative function intersection(S::AbstractSingleton, cpa::CartesianProductArray)
@commutative function intersection(cpa::Union{CartesianProduct,CartesianProductArray}, S::AbstractSingleton)
return _intersection_singleton(S, cpa)
end
@commutative intersection(cpa::CartesianProductArray, X::Interval) = _intersection_interval(X, cpa)
@commutative intersection(cpa::Union{CartesianProduct,CartesianProductArray}, X::Interval) = _intersection_interval(X, cpa)

"""
intersection(Z::AbstractZonotope{N}, H::HalfSpace{N};
Expand Down
8 changes: 8 additions & 0 deletions test/LazyOperations/CartesianProduct.jl
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Expand Up @@ -234,6 +234,14 @@ for N in [Float64, Float32, Rational{Int}]
S2 = Singleton(N[4, 5, 6])
@test convert(Singleton, S1 × S2) == Singleton(N[1, 2, 3, 4, 5, 6])

# concrete intersection
S1 = BallInf(zeros(N, 2), N(1))
S2 = BallInf(ones(N, 2), N(1))
P = BallInf(fill(N(1/2), 2), N(3/2))
cp = S1 × S2
cpa = intersection(cp, P)
@test isequivalent(concretize(cpa), cp)

# =====================
# CartesianProductArray
# =====================
Expand Down