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Merge pull request #766 from JuliaReach/schillic/oa_TM
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Merge code for overapproximate of TaylorModelReachSet
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@schillic
schillic authored Jan 31, 2024
2 parents 2d7e7c1 + 6dee4f2 commit fb9601b
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Showing 2 changed files with 41 additions and 77 deletions.
116 changes: 40 additions & 76 deletions src/ReachSets/TaylorModelReachSet.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -256,13 +256,12 @@ function overapproximate(R::TaylorModelReachSet{N}, ::ZonotopeEnclosure) where {
end

# tdom defined in the methods below is the same as Δt - t0, but the domain inclusion check
# in TM.evauate may fail, so we unpack the domain again here; also note that
# in TM.evaluate may fail, so we unpack the domain again here; also note that
# by construction the TMs in time are centered at zero

# overapproximate taylor model reachset with one hyperrectangle
function _overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Hyperrectangle};
Δt::TimeInterval=tspan(R), dom=symBox(dim(R))) where {N}

# overapproximate Taylor model reachset with a set
function _overapproximate(R::TaylorModelReachSet, T::Type{<:LazySet};
Δt::TimeInterval=tspan(R), dom=symBox(dim(R)), kwargs...)
# dimension of the reachset
n = dim(R)

Expand All @@ -274,9 +273,6 @@ function _overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Hyperrectangle};
Δt ⊆ tspan(R) || throw(ArgumentError("the given time range $Δt does not belong to the " *
"reach-set's time span, $(tspan(R))"))

# normalized time domain
tdom = domain(R)

# evaluate the Taylor model in time
X = set(R)
tdom = Δt - tstart(R) # normalize time (to TM-internal time)
Expand All @@ -295,36 +291,54 @@ function _overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Hyperrectangle};
# fX̂ is a TaylorModelN whose coefficients are floats
fX̂ = fp_rpa.(X̂)

# evaluate the spatial variables in the given domain
X̂b = IntervalBox([evaluate(fX̂[i], dom) for i in 1:n]...)
H = convert(Hyperrectangle, X̂b)
return ReachSet(H, Δt)
# evaluate the spatial variables in the given domain and overapproximate
Y = _overapproximate_TM(fX̂, T; kwargs...)

return ReachSet(Y, Δt)
end

# overapproximate a Taylor model with a hyperrectangle
# TODO outsource to LazySets
function _overapproximate_TM(fX̂, ::Type{<:Hyperrectangle}; kwargs...)
B = IntervalBox([evaluate(fX̂[i], domain(p)) for (i, p) in enumerate(fX̂)]...)
return convert(Hyperrectangle, B)
end

LazySets.box_approximation(R::TaylorModelReachSet) = _overapproximate(R, Hyperrectangle)
# overapproximate a Taylor model with a zonotope using LazySets
function _overapproximate_TM(fX̂, ::Type{<:Zonotope}; kwargs...)
return overapproximate(fX̂, Zonotope; kwargs...)
end

function overapproximate(R::TaylorModelReachSet, T::Type{<:LazySet};
Δt::TimeInterval=tspan(R), dom=symBox(dim(R)), kwargs...)
return _overapproximate(R, T; Δt=Δt, dom=dom, kwargs...)
end

LazySets.box_approximation(R::TaylorModelReachSet) = overapproximate(R, Hyperrectangle)

# overapproximate taylor model reachset with several hyperrectangles,
# by splitting in time (ntdiv), and/or space (with either nsdiv for uniform partitions
# or by specifying a partition (vector of integers))
# e.g. if the partition is uniform for each dimension, the number of returned sets
# is nsdiv^D * ntdiv
# overapproximate TaylorModelReachSet with several hyperrectangles, by splitting
# in space (with either nsdiv for uniform partitions or by specifying a
# partition (vector of integers); the version not used should be set to
# `nothing`) and/or in time (ntdiv)
# e.g. if the partition is uniform for each dimension, the number of returned
# sets is nsdiv^D * ntdiv
function overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Hyperrectangle};
partition=nothing, nsdiv=nothing, ntdiv=1,
Δt::TimeInterval=tspan(R), dom=symBox(dim(R))) where {N}
Δt::TimeInterval=tspan(R), dom=symBox(dim(R)), kwargs...) where {N}
if !isnothing(partition) && !isnothing(nsdiv)
throw(ArgumentError("either `partition` or `nsdiv` should be specified, not both"))
end
if isnothing(partition) && isnothing(nsdiv)
nsdiv = 1
end

D = dim(R)
S = symBox(D)

# no splitting
if isnothing(partition) && nsdiv == 1 && ntdiv == 1
return _overapproximate(R, Hyperrectangle; Δt, dom)
return _overapproximate(R, Hyperrectangle; Δt=Δt, dom=dom, kwargs...)
end

D = dim(R)
S = symBox(D)
@assert Δt == tspan(R) "time subdomain not implemented"
@assert dom == S "spatial subdomain not implemented"

Expand Down Expand Up @@ -378,44 +392,6 @@ function overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Hyperrectangle};
return R̂out
end

# overapproximate taylor model reachset with one zonotope
function overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Zonotope};
Δt::TimeInterval=tspan(R), dom=symBox(dim(R))) where {N}

# consistency checks
dim(R) == dim(dom) ||
throw(ArgumentError("the dimension of the reach-set should match the dimension of the domain, " *
"but they are $(dim(R)) and $(dim(dom)) respectively"))
dom ⊆ symBox(dim(R)) || throw(ArgumentError("`dom` must be a subset of [-1, 1]^n"))
Δt ⊆ tspan(R) || throw(ArgumentError("the given time range $Δt does not belong to the " *
"reach-set's time span, $(tspan(R))"))

# dimension of the reachset
n = dim(R)

# evaluate the Taylor model in time
X = set(R)
tdom = Δt - tstart(R) # normalize time (to TM-internal time)
tdom = tdom ∩ domain(R) # intersection handles round-off errors
# X_Δt is a vector of TaylorN (spatial variables) whose coefficients are intervals
X_Δt = evaluate(X, tdom)

# transform the domain if needed
X_Δt = _taylor_shift(X_Δt, dom)

# builds the associated taylor model for each coordinate j = 1...n
# X̂ is a TaylorModelN whose coefficients are intervals
X̂ = [TaylorModelN(X_Δt[j], zeroI, zeroBox(n), symBox(n)) for j in 1:n]

# compute floating point rigorous polynomial approximation
# fX̂ is a TaylorModelN whose coefficients are floats
fX̂ = fp_rpa.(X̂)

# overapproximate the Taylor model with a zonotope using LazySets
Z = overapproximate(fX̂, Zonotope)
return ReachSet(Z, Δt)
end

# overapproximate taylor model reachset with several zonotopes given the partition,
# that specifies the way in which the symmetric box [-1, 1]^n is split:
#
Expand Down Expand Up @@ -448,21 +424,9 @@ function overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Zonotope},
return ReachSet(ConvexHullArray(Z), Δt)
end

# evaluate at a given time and overapproximate the resulting set with a zonotope
function overapproximate(R::TaylorModelReachSet{N}, ::Type{<:Zonotope}, t::AbstractFloat;
remove_zero_generators=true) where {N}
@assert t ∈ tspan(R) "the given time point $t does not belong to the reach-set's time span, $(tspan(R))"

X = set(R)
tn = t - tstart(R) # normalize time (to TM-internal time)
tn = interval(tn) ∩ domain(R) # intersection handles round-off errors
X_Δt = evaluate(X, tn)
n = dim(R)
X̂ = [TaylorModelN(X_Δt[j], zeroI, zeroBox(n), symBox(n)) for j in 1:n]
fX̂ = fp_rpa.(X̂)
Zi = overapproximate(fX̂, Zonotope; remove_zero_generators=remove_zero_generators)
Δt = TimeInterval(t, t)
return ReachSet(Zi, Δt)
# evaluate at a given time point and overapproximate the resulting set
function overapproximate(R::TaylorModelReachSet, T::Type{<:LazySet}, t::AbstractFloat; kwargs...)
return overapproximate(R, T, TimeInterval(t, t); kwargs...)
end

# convert a hyperrectangular set to a taylor model reachset
Expand Down
2 changes: 1 addition & 1 deletion test/reachsets/reachsets.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -157,7 +157,7 @@ end
@test isequivalent(ConvexHullArray(set.(Z)), set(Z0))
end

@testset "Overapproximation of a Taylor model reach-sets II" begin
@testset "Overapproximation of Taylor model reach-sets II" begin

# Two dimensional
# ------------------
Expand Down

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