explicação/arvore.jl

### A Pluto.jl notebook ###
# v0.17.1

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

# ╔═╡ 0282427a-bb56-4de1-970c-9c31f1e20884
using LinearAlgebra, Plots, PlutoUI, Random

# ╔═╡ d1e17286-e8f0-11eb-391b-bdebef63dbc3
begin
	args = Dict(
		:C1 => (3,:pink,stroke(1,:red),:square),
		:C2 => (3,:lightblue,stroke(1,:blue),:circle),
		:C3 => (3,:lightgreen,stroke(1,:green),:diamond),
	)
	clr_range = Dict(
		:C1 => :pink,
		:C2 => :lightblue,
		:C3 => :lightgreen
	)
	nothing
end

# ╔═╡ d0785595-4dd4-4b1f-a3df-3d2157936954
md"""
# Árvore de decisão

- Uma estrutura de decisões aninhadas.
- Cada decisão corta o conjunto em dois.
- A classe majoritária dá a previsão no conjunto.
"""

# ╔═╡ 704ec9f9-2722-45fa-919c-43445eee60cb
md"""
- Usar uma árvore de decisão é só seguir as condições.
- Montar uma árvore envolve decidir qual variável e qual o valor do corte.
- Pra isso usamos uma medida de impureza.
- Sendo $p_k$ a proporção da classe $k$, temos
- Medida Gini:
$$\sum_{k} p_k (1 - p_k) = 1 - \sum_{k} p_k^2.$$
- Medida de entropia:
$$\sum_{k} -p_k \log_2 p_k.$$
- A impureza da divisão é a média ponderada das impurezas.
"""

# ╔═╡ 676bf827-44c1-4eb6-9b1a-f59a0375b54c
let
	plt = plot(layout=grid(2, 2), leg=false)
	plot!(
		plt[1,1],
		p -> 2p * (1 - p), 0, 1,
		xlabel="p₁",
		title="Medida Gini",
	)
	plot!(
		plt[1,2],
		p -> -p * log(p) - (1 - p) * log(1 - p), 0, 1,
		xlabel="p₁",
		title="Medida de entropia",
	)
	contour!(
		plt[2,1],
		range(0, 1, length=50),
		range(0, 1, length=50),
		(p₁, p₂) -> p₁ + p₂ ≤ 1 ? 1 - p₁^2 - p₂^2 - (1 - p₁ - p₂)^2 : NaN,
		xlabel="p₁",
		ylabel="p₂",
	)
	contour!(
		plt[2,2],
		range(0, 1, length=50),
		range(0, 1, length=50),
		(p₁, p₂) -> begin
			(p₁ + p₂ > 1) && return NaN
			p = [p₁; p₂; 1 - p₁ - p₂]
			-sum(p .* log.(p .+ 1e-8))
		end,
		xlabel="p₁",
		ylabel="p₂",
	)

end

# ╔═╡ 07aa9442-f783-44e3-a18b-8ac20559b470
md"""
- Corte separa $S$ em $S_\text{esq}$ e $S_\text{dir}$
- Medida $\text{imp}(S) = \dfrac{\text{imp}(S_\text{esq})|S_\text{esq}| + \text{imp}(S_\text{dir})|S_\text{dir}|}{|S|}$
"""

# ╔═╡ 5c0125c3-f88b-4ddf-a1a5-c68ef86abcb1
md"""
max\_depth = $(@bind max_depth_slider Slider(0:20, show_value=true))
"""

# ╔═╡ 65c38dd8-3dc0-487f-954f-683c133ab740
md"""
dataset = $(@bind dataset Slider(1:3))
"""

# ╔═╡ bb727704-d20c-4434-9009-a2cd4dc94796
begin
	mutable struct Arvore
		left
		right
		set
		idx
		valor
		y_values
		X
		y
	end
	
	function predict(arvore::Arvore, x)
		if x[arvore.idx] < arvore.valor
			if arvore.left isa Arvore
				return predict(arvore.left, x)
			else
				return set_value(arvore.left, arvore.y, arvore.y_values)
			end
		else
			if arvore.right isa Arvore
				return predict(arvore.right, x)
			else
				return set_value(arvore.right, arvore.y, arvore.y_values)
			end
		end
	end

	function Base.length(arvore::Arvore)
		d = 1
		if arvore.left isa Arvore
			d = max(d, length(arvore.left) + 1)
		end
		if arvore.right isa Arvore
			d = max(d, length(arvore.right) + 1)
		end
		return d
	end
	
	function set_value(set, y, yvalues)
		D = Dict(yi => count(yi .== y[set]) for yi in yvalues)
		yi = argmax(D)
		return yi
	end

	function plot_noh!(plt, set, y, uy, posx, posy, depth)
		Δx = 1.0
		Δy = 1.0
		δ = 0.3
		T = Dict(yi => count(yi .== y[set]) for yi in uy)
		this = argmax(T)
		perc = count(this .== y[set]) / length(set)
		c = clr_range[this]
		Tann = join(["$k:$v" for (k, v) in T] |> sort, ",")
		plot!(
			plt,
			posx .+ 2δ * [-1, 1, 1, -1, -1] * depth,
			posy .+ δ * [-1, -1, 1, 1, -1] * 2,
			c=c,
			fill=true,
			ann=(posx, posy, text("$this\n$(round(Int, 100 * perc))%", 10))
		)
	end
	
	function plot_arvore!(plt, arvore, x=0.0, y=0.0, depth=length(arvore))
		δx = 2^length(arvore)
		plot!(plt, [x, x - δx], [y, y - 2], c=:black, l=:arrow, lw=2)
		plot!(plt, [x, x + δx], [y, y - 2], c=:black, l=:arrow, lw=2)
		v = round(arvore.valor, digits=2)
		annotate!(plt, [
			(x - δx, y - 1, text("x$(arvore.idx) < $v", 10)),
			# (x + δx, y - 1, "x$(arvore.idx) ≥ $v"),
		])
		plot_noh!(plt, arvore.set, arvore.y, arvore.y_values, x, y, depth)
		if arvore.left isa Arvore
			plot_arvore!(plt, arvore.left, x - δx, y - 2, depth)
		else
			plot_noh!(plt, arvore.left, arvore.y, arvore.y_values, x - δx, y - 2, depth)
		end
		if arvore.right isa Arvore
			plot_arvore!(plt, arvore.right, x + δx, y - 2, depth)
		else
			plot_noh!(plt, arvore.right, arvore.y, arvore.y_values, x + δx, y - 2, depth)
		end
	end
end

# ╔═╡ 0d5b7ab6-df45-4ec8-8ce0-d00593e687d6
begin
	function plot_regions!(
		plt,
		arvore::Arvore,
		lower=minimum(arvore.X[arvore.set,:], dims=1),
		upper=maximum(arvore.X[arvore.set,:], dims=1)
	)
		lower_left = copy(lower)
		lower_right = copy(lower)
		upper_left = copy(upper)
		upper_right = copy(upper)
		lower_right[arvore.idx] = arvore.valor
		upper_left[arvore.idx] = arvore.valor
		if arvore.idx == 1
			plot!(plt, fill(arvore.valor, 2), [lower[2], upper[2]], c=:black)
		else
			plot!(plt, [lower[1], upper[1]], fill(arvore.valor, 2), c=:black)
		end
		if arvore.left isa Arvore
			plot_regions!(plt, arvore.left, lower_left, upper_left)
		else
			set = arvore.left
			if length(set) > 0
				plot_regions!(
					plt,
					arvore.y[set], 
					lower_left,
					upper_left,
				)
			end
		end
		if arvore.right isa Arvore
			plot_regions!(plt, arvore.right, lower_right, upper_right)
		else
			set = arvore.right
			if length(set) > 0
				plot_regions!(
					plt,
					arvore.y[set],
					lower_right,
					upper_right,
				)
			end
		end
	end

	function plot_regions!(
		plt,
		y::Vector,
		lower,
		upper
	)
		if length(y) == 0
			return
		end
		uy = unique(y)
		counts = Dict(yi => count(yi .== y) for yi in unique(y))
		plot!(plt,
			[lower[1], upper[1], upper[1], lower[1], lower[1]],
			[lower[2], lower[2], upper[2], upper[2], lower[2]],
			fill=true,
			c=clr_range[argmax(counts)],
			opacity=0.3,
		)
	end
end

# ╔═╡ 7f0cf3c9-653e-40e5-b0b3-59b4ac5b2ed1
begin
	Random.seed!(0)
	n = 400
	X = [range(-1, 1, length=n) shuffle(range(-1, 1, length=n))]
	global y
	if dataset == 1
		y = [X[i,1]^2+log(1 .+X[i,2].^2)*X[i,1] > 0.2 + randn()*0.1 ? :C1 : :C2 for i = 1:n]
		y[findall(X[:,1] + 0.5X[:,2] + randn(n) * 0.4 .> 0.3)] .= :C3
	elseif dataset == 2
		y = Symbol.("C" .* string.([
			floor(Int, (atan(X[i,2], X[i,1]) + π) * 3 / 2π + 1)
			for i = 1:n
		]))
	elseif dataset == 3
		y = Symbol.("C" .* string.([
			floor(Int, 1 .+ 3*exp(2 * (-X[i,1]^2 - X[i,2]^2))) for i = 1:n
		]))
	end
	uy = sort(unique(y))
	nuy = length(uy)

	function plot_dataset!(plt)
		for (i,yi) in enumerate(uy)
			I = findall(y .== yi)
			scatter!(plt, X[I,1], X[I,2], m=args[yi])
		end
		plt
	end
	plot_dataset!(plot(leg=false, size=(800,600)))
end

# ╔═╡ 96cc5ea8-9575-4f12-b399-cf19797e0084
let
	subset = findall(X[:,1] .≥ -0.5)
	arvore = Arvore(
		findall(X[:,1] .< -0.5),
		Arvore(
			findall(X[:,2] .< 0.3) ∩ subset,
			findall(X[:,2] .≥ 0.3) ∩ subset,
			findall(X[:,1] .≥ -0.5),
			2,
			0.3,
			unique(y),
			X,
			y,
		),
		1:n,
		1,
		-0.5,
		sort(unique(y)),
		X,
		y,
	)
	
	plt = plot(layout=grid(2, 1), leg=false, size=(800,1200))
	plot_arvore!(plt[1], arvore)
	plot_dataset!(plt[2])
	plot_regions!(plt[2], arvore)
	plt
end

# ╔═╡ 86cd42d0-14b1-4367-a67b-2599d4d5b4ba
begin
	function entropy(set, y, y_values)
		if length(set) == 1
			return 1.0
		end
		sum(
			begin
				p = sum(y[set] .== yi) / length(set)
				p == 0 ? 0.0 : -p * log(p)
			end for yi in y_values
		)
	end
			
	function entropy(arvore)
		left_ent = if arvore.left isa Arvore
			entropy(arvore.left)
		else
			entropy(arvore.left, arvore.y, arvore.y_values)
		end
		right_ent = if arvore.right isa Arvore
			entropy(arvore.right)
		else
			entropy(arvore.right, arvore.y, arvore.y_values)
		end
		n = length(arvore.set)
		m = count(arvore.X[arvore.idx,:] .< arvore.valor)
		return (left_ent * m + right_ent * (n - m)) / n
	end
	
	function split(set, X, y, y_values)
		length(set) == 0 && error("Empty set")
		V = []
		ρ0 = entropy(set, y, y_values)
		t_opt, j_opt, ρ_opt = 0, 0, 1.0
		for j = 1:size(X, 2)
			v = sort(unique(X[set,j]))
			v = [(v[i] + v[i+1]) / 2 for i = 1:length(v)-1]
			for t in v
				left = set[findall(X[set,j] .< t)]
				right = setdiff(set, left)
				(length(left) == 0 || length(right) == 0) && continue
				ρ = (entropy(left, y, y_values) * length(left) +
					entropy(right, y, y_values) * length(right)) / length(set)
				if ρ ≤ ρ_opt
					t_opt, j_opt, ρ_opt = t, j, ρ
				end
				push!(V, (t, j, ρ0, ρ, ρ_opt, left, right))
			end
		end
		if j_opt == 0
			error("set = $set, V = $V")
		end
		
		left = set[findall(X[set,j_opt] .< t_opt)]
		right = setdiff(set, left)
		Arvore(left, right, set, j_opt, t_opt, y_values, X, y)
	end
	
	function cria_arvore(X, y; max_depth=Inf)
		@assert max_depth > 0
		y_values = unique(y)
		arvore = split(1:n, X, y, y_values)
		next = [(arvore, 1)]
		while length(next) != 0
			(noh, this_depth) = popfirst!(next)
			if this_depth == max_depth
				continue
			end
			if length(unique(y[noh.left])) > 1
				noh.left = split(noh.left, X, y, y_values)
				push!(next, (noh.left, this_depth + 1))
			end
			if length(unique(y[noh.right])) > 1
				noh.right = split(noh.right, X, y, y_values)
				push!(next, (noh.right, this_depth + 1))
			end
		end
		return arvore
	end

	# function cria_arvore(X, y; max_num_nodes=Inf)
	# 	y_values = unique(y)
	# 	num_nodes = 2
	# 	arvore = split(1:n, X, y, y_values)
	# 	next = [arvore]
	# 	while length(next) != 0 && num_nodes ≤ max_num_nodes
	# 		noh = popfirst!(next)
	# 		if length(unique(y[noh.left])) > 1
	# 			noh.left = split(noh.left, X, y, y_values)
	# 			num_nodes += 1
	# 			push!(next, noh.left)
	# 		end
	# 		if length(unique(y[noh.right])) > 1
	# 			noh.right = split(noh.right, X, y, y_values)
	# 			num_nodes += 1
	# 			push!(next, noh.right)
	# 		end
	# 	end
	# 	return arvore
	# end
end

# ╔═╡ c36853d4-86f3-43dd-a405-88d7c0767ceb
let
	if dataset > 1
		nothing
	else
		τ = range(-1, 1, length=100)
		anim = Animation()
		for limiar = τ
			arvore = Arvore(
				findall(X[:,1] .< limiar),
				findall(X[:,1] .≥ limiar),
				1:n,
				1,
				limiar,
				sort(unique(y)),
				X,
				y,
			)
	
			plt = plot(layout=grid(2, 1, heights=[0.2, 0.8]), leg=false, size=(800,800))
		
			E(lim) = begin
				left = findall(X[:,1] .< lim)
				right = setdiff(1:n, left)
				uy = unique(y)
				(entropy(left, y, uy) * length(left) + entropy(right, y, uy) * length(right)) / n
			end
			plot!(plt[1], τ, E)
			scatter!(plt[1], [limiar], [E(limiar)], c=:black, ms=3)
			plot_dataset!(plt[2])
			plot_regions!(plt[2], arvore)
			frame(anim)
		end
		gif(anim, fps=10)
	end
end

# ╔═╡ 8f6db78e-cbb3-44b5-a3fa-47686809482f
let
	plt = plot(leg=false, size=(800,700))
	if max_depth_slider == 0
		ŷ = argmax(Dict(yi => count(y .== yi) for yi in uy))
		plot!(plt, [-1, 1, 1, -1, -1], [-1, -1, 1, 1, -1], c=clr_range[ŷ], fill=true, opacity=0.3)
		plot_dataset!(plt)
		acc = round(100 * sum(y .== ŷ) / n, digits=2)
		imp = round(entropy(1:n, y, uy), digits=2)
		title!("Acurácia = $acc%, impureza = $imp")
	else
		arvore = cria_arvore(X, y, max_depth=max_depth_slider)
		plot_regions!(plt, arvore)
		plot_dataset!(plt)
		ŷ = [predict(arvore, X[i,:]) for i = 1:n]
		acc = round(100 * sum(y .== ŷ) / n, digits=2)
		imp = round(entropy(arvore), digits=2)
		title!("Acurácia = $acc%, impureza = $imp")
	end
	plt
end

# ╔═╡ 84545d26-f552-408f-b9b6-fb260f787bf0
begin
	if max_depth_slider > 0
		plt = plot(leg=false)
		arvore = cria_arvore(X, y, max_depth=max_depth_slider)
		plot_arvore!(plt, arvore)
	end
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[compat]
Plots = "~1.19.2"
PlutoUI = "~0.7.9"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
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[[ColorSchemes]]
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[[Compat]]
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[[DataStructures]]
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git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.1.5+1"

[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.2.10+0"

[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "3cc57ad0a213808473eafef4845a74766242e05f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.3.1+4"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "35895cf184ceaab11fd778b4590144034a167a2f"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.1+14"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.1+5"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+1"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "9f473cdf6e2eb360c576f9822e7c765dd9d26dbc"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.58.0"

[[GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "eaf96e05a880f3db5ded5a5a8a7817ecba3c7392"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.58.0+0"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "15ff9a14b9e1218958d3530cc288cf31465d9ae2"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.3.13"

[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "47ce50b742921377301e15005c96e979574e130b"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.1+0"

[[Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "c6a1fff2fd4b1da29d3dccaffb1e1001244d844e"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.12"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.1"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[LaTeXStrings]]
git-tree-sha1 = "c7f1c695e06c01b95a67f0cd1d34994f3e7db104"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.2.1"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a4b12a1bd2ebade87891ab7e36fdbce582301a92"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.6"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[LibVPX_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "12ee7e23fa4d18361e7c2cde8f8337d4c3101bc7"
uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a"
version = "1.10.0+0"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

[[LinearAlgebra]]
deps = ["Libdl", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.6"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.0"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+0"

[[OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.10+0"

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "c8abc88faa3f7a3950832ac5d6e690881590d6dc"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "1.1.0"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "501c20a63a34ac1d015d5304da0e645f42d91c9f"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.11"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"]
git-tree-sha1 = "f3d4d35b8cb87adc844c05c722f505776ac29988"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.19.2"

[[PlutoUI]]
deps = ["Base64", "Dates", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "Suppressor"]
git-tree-sha1 = "44e225d5837e2a2345e69a1d1e01ac2443ff9fcb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.9"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+0"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RecipesBase]]
git-tree-sha1 = "b3fb709f3c97bfc6e948be68beeecb55a0b340ae"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.1.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "2a7a2469ed5d94a98dea0e85c46fa653d76be0cd"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.3.4"

[[Reexport]]
git-tree-sha1 = "5f6c21241f0f655da3952fd60aa18477cf96c220"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.1.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "1b9a0f17ee0adde9e538227de093467348992397"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.7"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2f6792d523d7448bbe2fec99eca9218f06cc746d"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.8"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.0"

[[Suppressor]]
git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787"
uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
version = "0.2.0"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "8ed4a3ea724dac32670b062be3ef1c1de6773ae8"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.4.4"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[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"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[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"

[[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"

[[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"

[[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"

[[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"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+4"

[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+4"

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

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
# ╟─0282427a-bb56-4de1-970c-9c31f1e20884
# ╠═0d5b7ab6-df45-4ec8-8ce0-d00593e687d6
# ╠═d1e17286-e8f0-11eb-391b-bdebef63dbc3
# ╟─d0785595-4dd4-4b1f-a3df-3d2157936954
# ╠═7f0cf3c9-653e-40e5-b0b3-59b4ac5b2ed1
# ╠═96cc5ea8-9575-4f12-b399-cf19797e0084
# ╟─704ec9f9-2722-45fa-919c-43445eee60cb
# ╟─676bf827-44c1-4eb6-9b1a-f59a0375b54c
# ╟─c36853d4-86f3-43dd-a405-88d7c0767ceb
# ╟─07aa9442-f783-44e3-a18b-8ac20559b470
# ╟─5c0125c3-f88b-4ddf-a1a5-c68ef86abcb1
# ╟─65c38dd8-3dc0-487f-954f-683c133ab740
# ╠═8f6db78e-cbb3-44b5-a3fa-47686809482f
# ╟─84545d26-f552-408f-b9b6-fb260f787bf0
# ╟─86cd42d0-14b1-4367-a67b-2599d4d5b4ba
# ╟─bb727704-d20c-4434-9009-a2cd4dc94796
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002