crossroads.jl

### A Pluto.jl notebook ###
# v0.19.26

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 248bf010-7d15-4886-82e5-7fbbd7e0f7ec
using LinearAlgebra, RxInfer, Plots, PGFPlotsX, LogExpFunctions, PlutoUI

# ╔═╡ 90ef24e0-1fd9-11ee-2ed4-e947901d2a4c
md"""
# Crossroads
"""

# ╔═╡ 5123688d-a83f-4e09-a0f1-e03a1f583264
begin
	function draw_circle!(center, radius; kwargs...)
		θ = range(0, 2π, 100)
		plot!(center[1] .+ radius .* cos.(θ), center[2] .+ radius .* sin.(θ); kwargs...)
	end

	ReactiveMP.constrain_form(pmconstraint::RxInfer.PointMassFormConstraint, distribution::MultivariateNormalDistributionsFamily) = mean(distribution) 

	ReactiveMP.prod(::ProdAnalytical, left::Distribution, right::PointMass{Float64}) = right

	softmin(x; l=10) = -logsumexp(-l .* x)/l	

end;

# ╔═╡ fa3ebe3b-1ef9-4c1f-9849-72e1b4f3176c
md"Save figures $(@bind save_figures CheckBox(default=false))"

# ╔═╡ c4561368-15b9-49e4-a0ff-c5a85171a054
if save_figures
	mkpath("exports")
	nothing
end

# ╔═╡ f3b412ba-f0e6-4423-a44d-dcf04ad2b475
md"""
## Problem sketch
"""

# ╔═╡ 156d54ec-126b-4de1-a483-990b503c4a94
begin
	goals = hcat([
		# agent 1: start at (-15,5) with 0 velocity, end at (15,-5) with 0 velocity
		[
			[-15, 0, 5, 0],
			[15, 0, -5, 0]
		], 
		# agent 2: start at (-15,-5) with 0 velocity, end at (15,5) with 0 velocity
		[
			[-15, 0, -5, 0],
			[15, 0, 5, 0]
		],
		# agent 3: start at (-5,15) with 0 velocity, end at (5,-15) with 0 velocity
		[
			[-5, 0, 15, 0],
			[5, 0, -15, 0]
		],
		# agent 4: start at (5,15) with 0 velocity, end at (-5,-15) with 0 velocity
		[
			[5, 0, 15, 0],
			[-5, 0, -15, 0]
		]
	]...)
	radius1 = 2.5
	radius2 = 2.5
	radius3 = 2.5
	radius4 = 2.5
end;

# ╔═╡ ef868b3a-0616-495e-9bd0-de2edf1089db
begin
	plot(size = (600, 600))

	scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10)
	scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10)
	scatter!([goals[2,3][1]], [goals[2,3][3]], color="orange", label="", marker=:star5, markersize=10)
	scatter!([goals[2,4][1]], [goals[2,4][3]], color="green", label="", marker=:star5, markersize=10)
	
	draw_circle!([goals[1,1][1], goals[1,1][3]], radius1; color="red", label="")
	draw_circle!([goals[1,2][1], goals[1,2][3]], radius2; color="blue", label="")
	draw_circle!([goals[1,3][1], goals[1,3][3]], radius3; color="orange", label="")
	draw_circle!([goals[1,4][1], goals[1,4][3]], radius4; color="green", label="")

	xlims!(-20, 20)
	ylims!(-20, 20)
end

# ╔═╡ 452ea6ac-17ba-4bd5-8037-ef53b488e420
md"""
## Halfspace prior implementation
"""

# ╔═╡ 60dd5591-cfd1-41c5-a6ed-4c485fa27bb2
begin

	# node specification
	struct Halfspace end
	@node Halfspace Stochastic [out, a, σ2, γ]

	# rule specification
	@rule Halfspace(:out, Marginalisation) (q_a::PointMass, q_σ2::PointMass, q_γ::PointMass) = begin
		return NormalMeanVariance(mean(q_a) + mean(q_γ) * mean(q_σ2), mean(q_σ2))
	end

	@rule Halfspace(:σ2, Marginalisation) (q_out::UnivariateNormalDistributionsFamily, q_a::PointMass, q_γ::PointMass, ) = begin
		return PointMass( 1 / mean(q_γ) * sqrt(abs2(mean(q_out) - mean(q_a)) + var(q_out)))
	end
	
end

# ╔═╡ 9638259f-f1bb-4b6e-849d-4455db3a3447
md"""
## Model specification 
"""

# ╔═╡ b1eec7ac-9ced-4aac-9647-a15322b30fb5
function h(y1, y2, y3, y4; r1 = radius1, r2 = radius2, r3 = radius3, r4 = radius4)
	return softmin([
		norm(y1 - y2) - r1 - r2,
		norm(y1 - y3) - r1 - r3,
		norm(y1 - y4) - r1 - r4,
		norm(y2 - y3) - r2 - r3,
		norm(y2 - y4) - r2 - r4,
		norm(y3 - y4) - r3 - r4,
	])
end;

# ╔═╡ fe9df76f-9df5-46f7-8161-353ddbf94c09
@model function crossroads_model(nr_steps; γ=10, ΔT=1)

	# controls
	u = randomvar(4, nr_steps)

	# hidden state
	x = randomvar(4, nr_steps + 1)

	# observations
	y = randomvar(4, nr_steps)
	goals = datavar(Vector{Int64}, (2, 4))
	
	# distance variable
	d = randomvar(nr_steps)
	σ2 = randomvar(nr_steps)

	# transition model
	A = constvar([1 ΔT 0 0; 0 1 0 0; 0 0 1 ΔT; 0 0 0 1])
	B = constvar([0 0; ΔT 0; 0 0; 0 ΔT])
	C = constvar([1 0 0 0; 0 0 1 0])

	# single agent models
	for k in 1:4

		# prior on state
		x[k,1] ~ MvNormalMeanCovariance(zeros(4), 1e2I)
	
		for t in 1:nr_steps
			
			# prior on controls
			u[k,t] ~ MvNormalMeanCovariance(zeros(2), 1e-2I)
	
			# state transition
			x[k,t+1] ~ A * x[k,t] + B * u[k,t]
	
			# observation model
			y[k,t] ~ C * x[k,t+1]

		end

		# goal priors (indexing reverse due to definition)
		goals[1,k] ~ MvNormalMeanCovariance(x[k,1], 1e-5I)
		goals[2,k] ~ MvNormalMeanCovariance(x[k,end], 1e-5I)
		
	end

	# multi-agent models
	for t = 1:nr_steps

		# observation constraint
		σ2[t] ~ GammaShapeRate(3/2, γ^2/2)
		d[t] ~ h(y[1,t], y[2,t], y[3,t], y[4,t])
		d[t] ~ Halfspace(0, σ2[t], γ)
		
	end
	
end;

# ╔═╡ 6792be47-148c-414b-9f21-d7ae11807bd9
md"""
## Constraint specification
"""

# ╔═╡ 1e2ba3eb-b073-40cc-8b56-633e18d041d9
@constraints function crossroads_constraints() 
	q(d, σ2) = q(d)q(σ2)
end;

# ╔═╡ e6d347ee-835b-4077-968b-0e7b11540056
md"""
## Probabilistic inference
"""

# ╔═╡ daa54871-05cb-4987-a81c-16f7895da90f
crossroads_meta = @meta begin 
    h() -> Linearization()
end;

# ╔═╡ 12677bf1-5cae-405b-baf0-b3b741ed1770
nr_steps = 50

# ╔═╡ 5dba141f-a4ff-4439-91bc-c7d6d5a3f18e
nr_iterations = 5000

# ╔═╡ ead11ddb-2c4d-47a7-9cf5-483cb40598a0
results = inference(
	model 			= crossroads_model(nr_steps),
	data  			= ( goals = goals, ),
	constraints 	= crossroads_constraints(),
	meta 			= crossroads_meta,
	iterations 		= nr_iterations,
	returnvars 		= KeepLast(), 
	initmarginals 	= ( 
		σ2 = repeat([PointMass(1)], nr_steps),
		u  = repeat([PointMass(0)], nr_steps)
	),
	initmessages = (
		x = MvNormalMeanCovariance(randn(4), 100I),
	),
	options = ( limit_stack_depth = 300, )
)

# ╔═╡ 8e994302-4316-4d23-87e2-020883800e65
md"""
## Results
"""

# ╔═╡ 9512a92b-32df-4d9b-8e02-870ade5ef1ba
begin
	if save_figures
		animation = @animate for t in 1:nr_steps
			plot(size = (600, 600), legend=false)
	
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][1,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][1,1:t]);
				color="red", linestyle=:dash
			)
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][2,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][2,1:t]);
				color="blue", linestyle=:dash
			)
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][3,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][3,1:t]);
				color="orange", linestyle=:dash
			)
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][4,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][4,1:t]);
				color="green", linestyle=:dash
			)
		
			draw_circle!(mean(results.posteriors[:x][1,t])[[1,3]], radius1; color="red", label="")
			draw_circle!(mean(results.posteriors[:y][2,t]), radius2; color="blue", label="")
			draw_circle!(mean(results.posteriors[:x][3,t])[[1,3]], radius3; color="orange", label="")
			draw_circle!(mean(results.posteriors[:y][4,t]), radius4; color="green", label="")
		
			scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10)
			scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10)
			scatter!([goals[2,3][1]], [goals[2,3][3]], color="orange", label="", marker=:star5, markersize=10)
			scatter!([goals[2,4][1]], [goals[2,4][3]], color="green", label="", marker=:star5, markersize=10)
			
			xlims!(-20, 20)
			ylims!(-20, 20)
			
		end
	
		gif(animation, "exports/crossroads.gif", fps = 15)

	else

		@gif for t in 1:nr_steps
			plot(size = (600, 600), legend=false)
	
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][1,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][1,1:t]);
				color="red", linestyle=:dash
			)
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][2,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][2,1:t]);
				color="blue", linestyle=:dash
			)
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][3,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][3,1:t]);
				color="orange", linestyle=:dash
			)
			plot!(
				map(x -> mean(x)[1], results.posteriors[:y][4,1:t]),
				map(x -> mean(x)[2], results.posteriors[:y][4,1:t]);
				color="green", linestyle=:dash
			)
		
			draw_circle!(mean(results.posteriors[:x][1,t])[[1,3]], radius1; color="red", label="")
			draw_circle!(mean(results.posteriors[:y][2,t]), radius2; color="blue", label="")
			draw_circle!(mean(results.posteriors[:x][3,t])[[1,3]], radius3; color="orange", label="")
			draw_circle!(mean(results.posteriors[:y][4,t]), radius4; color="green", label="")
		
			scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10)
			scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10)
			scatter!([goals[2,3][1]], [goals[2,3][3]], color="orange", label="", marker=:star5, markersize=10)
			scatter!([goals[2,4][1]], [goals[2,4][3]], color="green", label="", marker=:star5, markersize=10)
			
			xlims!(-20, 20)
			ylims!(-20, 20)
			
		end
	end
end

# ╔═╡ a7eebc8c-e3ec-4962-9088-af61b17af122
begin
	θ = range(0, 2π, 100)
	
	fig = @pgf GroupPlot(

	    # group plot options
	    {
	        group_style = {
	            group_size = "8 by 1",
	            vertical_sep = "0cm",
				horizontal_sep = "0cm"
	        },
			ticks = "none",
			ymin = -20,
			ymax = 20,
			xmin = -20,
			xmax = 20,
			width = "4cm",
			height = "4cm",
			grid = "major",
			scale_only_axis = true
	    },
	)

	@pgf for k in 1:8
		push!(
			fig, 
			{},
			Plot(
				{
					"red",
					"dashed",
					line_width = 1.5
				},
				Table(
					map(x -> mean(x)[1], results.posteriors[:y][1,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
					map(x -> mean(x)[2], results.posteriors[:y][1,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
				)
			),
			Plot(
				{
					"blue",
					"dashed",
					line_width = 1.5
				},
				Table(
					map(x -> mean(x)[1], results.posteriors[:y][2,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
					map(x -> mean(x)[2], results.posteriors[:y][2,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
				)
			),
			Plot(
				{
					"orange",
					"dashed",
					line_width = 1.5
				},
				Table(
					map(x -> mean(x)[1], results.posteriors[:y][3,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
					map(x -> mean(x)[2], results.posteriors[:y][3,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
				)
			),
			Plot(
				{
					"green",
					"dashed",
					line_width = 1.5
				},
				Table(
					map(x -> mean(x)[1], results.posteriors[:y][4,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
					map(x -> mean(x)[2], results.posteriors[:y][4,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]),
				)
			),
			Plot(
				{
					"red",
					line_width = 1.5
				},
				Table(
					mean(results.posteriors[:y][1,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius1 .* cos.(θ),
					mean(results.posteriors[:y][1,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius1 .* sin.(θ)
				)
			),
			Plot(
				{
					"blue",
					line_width = 1.5
				},
				Table(
					mean(results.posteriors[:y][2,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius2 .* cos.(θ),
					mean(results.posteriors[:y][2,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius2 .* sin.(θ)
				)
			),
			Plot(
				{
					"orange",
					line_width = 1.5
				},
				Table(
					mean(results.posteriors[:y][3,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius1 .* cos.(θ),
					mean(results.posteriors[:y][3,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius1 .* sin.(θ)
				)
			),
			Plot(
				{
					"green",
					line_width = 1.5
				},
				Table(
					mean(results.posteriors[:y][4,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius2 .* cos.(θ),
					mean(results.posteriors[:y][4,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius2 .* sin.(θ)
				)
			),
			Plot(
				{
					"only marks",
					mark = "triangle*",
					mark_size = 5,
					"red",
				},
				Table([goals[2,1][1]],[goals[2,1][3]])
			),
			Plot(
				{
					"only marks",
					mark = "triangle*",
					mark_size = 5,
					"blue",
				},
				Table([goals[2,2][1]],[goals[2,2][3]])
			),
			Plot(
				{
					"only marks",
					mark = "triangle*",
					mark_size = 5,
					"orange",
				},
				Table([goals[2,3][1]],[goals[2,3][3]])
			),
			Plot(
				{
					"only marks",
					mark = "triangle*",
					mark_size = 5,
					"green",
				},
				Table([goals[2,4][1]],[goals[2,4][3]])
			)
		)
	end;
	if save_figures
		pgfsave("exports/crossroads.pdf", fig)
		pgfsave("exports/crossroads.tikz", fig)
	end
	fig

end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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RxInfer = "86711068-29c9-4ff7-b620-ae75d7495b3d"

[compat]
LogExpFunctions = "~0.3.24"
PGFPlotsX = "~1.6.0"
Plots = "~1.38.16"
PlutoUI = "~0.7.51"
RxInfer = "~2.11.1"
"""

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[[deps.Xorg_libXrandr_jll]]
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git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.15.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+0"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

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