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Use LazySets plot recipes #933

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4e628ca
use LazySets plot recipes
schillic Sep 5, 2025
ac85187
use same color for flowpipe recipes
schillic Sep 5, 2025
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2 changes: 2 additions & 0 deletions docs/Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -9,6 +9,7 @@ LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
LazySets = "b4f0291d-fe17-52bc-9479-3d1a343d9043"
Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
MathematicalSystems = "d14a8603-c872-5ed3-9ece-53e0e82e39da"
Optim = "429524aa-4258-5aef-a3af-852621145aeb"
OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
ReachabilityBase = "379f33d0-9447-4353-bd03-d664070e549f"
Expand All @@ -25,6 +26,7 @@ LaTeXStrings = "1"
LazySets = "2.14, 3, 4, 5"
Literate = "2"
MathematicalSystems = "0.14.1"
Optim = "0.15 - 0.22, 1"
OrdinaryDiffEq = "6"
Plots = "1"
ReachabilityBase = "0.2.3 - 0.3"
Expand Down
2 changes: 1 addition & 1 deletion docs/make.jl
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@@ -1,7 +1,7 @@
using Documenter, ReachabilityAnalysis, DocumenterCitations

# load optional packages for complete documentation
import ExponentialUtilities
import ExponentialUtilities, Optim

DocMeta.setdocmeta!(ReachabilityAnalysis, :DocTestSetup,
:(using ReachabilityAnalysis); recursive=true)
Expand Down
1 change: 1 addition & 0 deletions docs/src/tutorials/linear_methods/discrete_time.md
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Expand Up @@ -26,6 +26,7 @@ To gain some intuition, let's build the matrix and apply it to some points.
```@example discrete_propagation
using ReachabilityAnalysis, Plots
using ReachabilityAnalysis: center
import Optim

# initial set
X0 = BallInf(ones(2), 0.2)
Expand Down
184 changes: 34 additions & 150 deletions src/Flowpipes/recipes.jl
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Expand Up @@ -21,6 +21,8 @@ using LazySets: plot_recipe,
isapproxzero,
_plot_singleton_list

DEFAULT_COLOR_FLOWPIPE = :blue

# heuristics for projecting a reach-set either concretely or lazily to the space
# spanned by vars; the returned set is concrete when the exact projection can be done
# efficiently; in all other cases a lazy set is returned
Expand Down Expand Up @@ -65,7 +67,7 @@ end

function _project_reachset(::Type{<:LazySet}, R, vars)
πR = Projection(R, vars) # lazy projection
return X = set(πR)
return set(πR)
end

# ---------------------------------------
Expand Down Expand Up @@ -128,9 +130,6 @@ end
vars=nothing,
ε=N(PLOT_PRECISION)) where {N}
_check_vars(vars)
X = _project_reachset(R, vars)

dim(X) == 1 && return plot_recipe(X, ε)

label --> DEFAULT_LABEL
grid --> DEFAULT_GRID
Expand All @@ -140,121 +139,20 @@ end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR

# extract limits and extrema of already plotted sets
p = plotattributes[:plot_object]
lims = _extract_limits(p, plotattributes)
extr = _extract_extrema(p)

if !isbounded(X)
_set_auto_limits_to_extrema!(lims, extr)
X = intersection(X, _bounding_hyperrectangle(lims, eltype(X)))

elseif length(p) > 0
# if there is already a plotted set and the limits are fixed,
# automatically adjust the axis limits (e.g. after plotting a unbounded set)
_update_plot_limits!(lims, X)
end

xlims --> lims[:x]
ylims --> lims[:y]

x, y = plot_recipe(X, ε)
if !isempty(x)
m = length(x)
if m == 1
seriestype := :scatter
elseif m == 2 && isapproxzero((x[1] - x[2])^2 + (y[1] - y[2])^2)
seriestype := :scatter
else
seriestype := :shape
end
end
return (x, y)
end

# TODO use LazySets._plot_singleton_list_1D if the reach-sets are stored as a struct
# array. Otherwise, we could use pass the list through x -> set(x)
function _plot_singleton_list_1D(list::Union{Flowpipe{N},AbstractVector{<:AbstractReachSet{N}}}) where {N}
m = length(list)

x = Vector{N}(undef, m)
y = zeros(N, m)

@inbounds for (i, Xi) in enumerate(list)
p = element(set(Xi))
x[i] = p[1]
end
return x, y
end

function _plot_singleton_list_2D(list::Union{Flowpipe{N},AbstractVector{<:AbstractReachSet{N}}}) where {N}
m = length(list)
x = Vector{N}(undef, m)
y = Vector{N}(undef, m)

@inbounds for (i, Xi) in enumerate(list)
p = element(set(Xi))
x[i] = p[1]
y[i] = p[2]
end
return x, y
X = _project_reachset(R, vars)
return X
end

function _plot_reachset_list(list, N, vars, ε, Nφ)
first = true
x = Vector{N}()
y = Vector{N}()
for Ri in list
Xi = _project_reachset(Ri, vars)

if Xi isa Intersection
xcoords, ycoords = plot_recipe(Xi, ε, Nφ)

else
Pi = isoperation(Xi) ? overapproximate(Xi, ε) : Xi
vlist = convex_hull(vertices_list(Pi))
m = length(vlist)
if m == 0
@warn "overapproximation during plotting was empty"
continue
end
xcoords = Vector{N}(undef, m)
ycoords = Vector{N}(undef, m)
@inbounds for (i, v) in enumerate(vlist)
xcoords[i] = v[1]
ycoords[i] = v[2]
end
if m > 1
# add first vertex to "close" the polygon
push!(xcoords, xcoords[1])
push!(ycoords, ycoords[1])
end
end
isempty(xcoords) && continue

x_new = xcoords
y_new = ycoords

if first
first = false
else
push!(x, N(NaN))
push!(y, N(NaN))
end
append!(x, x_new)
append!(y, y_new)
end
return x, y
function _plot_reachset_list(list, vars)
return [_project_reachset(Ri, vars) for Ri in list]
end

# ========================
# Flowpipe plot recipes
# ========================

@recipe function plot_list(list::Union{Flowpipe{N},AbstractVector{<:AbstractReachSet{N}}};
vars=nothing,
ε=N(PLOT_PRECISION),
Nφ=PLOT_POLAR_DIRECTIONS) where {N}
vars=nothing) where {N}
_check_vars(vars)

label --> DEFAULT_LABEL
Expand All @@ -263,22 +161,20 @@ end
aspect_ratio --> DEFAULT_ASPECT_RATIO
end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR
seriescolor --> DEFAULT_COLOR_FLOWPIPE

if !(0 ∈ vars) && (setrep(list) <: AbstractSingleton)
@series if !(0 ∈ vars) && (setrep(list) <: AbstractSingleton)
seriestype --> :scatter
_plot_singleton_list(list)
else
seriestype --> :shape
_plot_reachset_list(list, N, vars, ε, Nφ)
_plot_reachset_list(list, vars)
end
end

# composite flowpipes
@recipe function plot_list(fp::Union{<:HybridFlowpipe{N},<:MixedFlowpipe{N}};
vars=nothing,
ε=Float64(PLOT_PRECISION),
Nφ=PLOT_POLAR_DIRECTIONS) where {N}
vars=nothing) where {N}
_check_vars(vars)

label --> DEFAULT_LABEL
Expand All @@ -287,30 +183,24 @@ end
aspect_ratio --> DEFAULT_ASPECT_RATIO
end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR
seriescolor --> DEFAULT_COLOR_FLOWPIPE
seriestype --> :shape

x = Vector{N}()
y = Vector{N}()

for F in fp
x_new, y_new = _plot_reachset_list(F, N, vars, ε, Nφ)
append!(x, x_new)
append!(y, y_new)
push!(x, N(NaN))
push!(y, N(NaN))
@series begin
Xs = LazySet{N}[]
for F in fp
append!(Xs, _plot_reachset_list(F, vars))
end
Xs
end
return x, y
end

# ========================
# Solution plot recipes
# ========================

@recipe function plot_list(sol::ReachSolution{<:Flowpipe{N}};
vars=nothing,
ε=Float64(PLOT_PRECISION),
Nφ=PLOT_POLAR_DIRECTIONS) where {N}
vars=nothing) where {N}
_check_vars(vars)

label --> DEFAULT_LABEL
Expand All @@ -319,24 +209,22 @@ end
aspect_ratio --> DEFAULT_ASPECT_RATIO
end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR
seriescolor --> DEFAULT_COLOR_FLOWPIPE

fp = flowpipe(sol)
if !(0 ∈ vars) && (setrep(fp) <: AbstractSingleton)
@series if !(0 ∈ vars) && (setrep(fp) <: AbstractSingleton)
seriestype --> :scatter
_plot_singleton_list(fp)
else
seriestype --> :shape
_plot_reachset_list(fp, N, vars, ε, Nφ)
_plot_reachset_list(fp, vars)
end
end

# compound solution flowpipes
@recipe function plot_list(sol::Union{ReachSolution{<:MixedFlowpipe{N}},
ReachSolution{<:HybridFlowpipe{N}}};
vars=nothing,
ε=Float64(PLOT_PRECISION),
Nφ=PLOT_POLAR_DIRECTIONS) where {N}
vars=nothing) where {N}
_check_vars(vars)

label --> DEFAULT_LABEL
Expand All @@ -345,21 +233,17 @@ end
aspect_ratio --> DEFAULT_ASPECT_RATIO
end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR
seriescolor --> DEFAULT_COLOR_FLOWPIPE
seriestype --> :shape

x = Vector{N}()
y = Vector{N}()

fp = flowpipe(sol)
for F in fp
x_new, y_new = _plot_reachset_list(F, N, vars, ε, Nφ)
append!(x, x_new)
append!(y, y_new)
push!(x, N(NaN))
push!(y, N(NaN))
@series begin
fp = flowpipe(sol)
Xs = LazySet{N}[]
for F in fp
append!(Xs, _plot_reachset_list(F, vars))
end
Xs
end
return x, y
end

# TODO new plot recipe to dispatch on ShiftedFlowpipe
Expand All @@ -379,7 +263,7 @@ end
aspect_ratio --> DEFAULT_ASPECT_RATIO
end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR
seriescolor --> DEFAULT_COLOR_FLOWPIPE
seriestype --> :shape

first = true
Expand Down Expand Up @@ -450,7 +334,7 @@ end
aspect_ratio --> DEFAULT_ASPECT_RATIO
end
seriesalpha --> DEFAULT_ALPHA
seriescolor --> DEFAULT_COLOR
seriescolor --> DEFAULT_COLOR_FLOWPIPE
seriestype --> :scatter
markershape --> :circle

Expand Down
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