overfitting-et-al.jl

### A Pluto.jl notebook ###
# v0.15.1

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 el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ c771792f-da93-4863-8d21-21933cc19c54
using LinearAlgebra, Plots, PlutoUI, Random, Statistics

# ╔═╡ 0ac1d752-e802-11eb-1457-edd0cfb36fe8
md"""
# Overfitting, underfitting e validação cruzada

Sabemos da física que soltando uma bolinha de borracha de uma altura $y$, a equação que relaciona o tempo $t$ que ela leva para chegar ao chão é

$y = \frac{1}{2}g t^2.$

Para este exercício, suponha que não sabemos disso.

Fazemos vários experimentos com um cronômetro de mão e várias alturas diferentes, obtendo.
"""

# ╔═╡ cf956436-0840-4051-85b9-f39ffb001971
begin
	Random.seed!(0)
	g = 9.8
	y = range(0, 2.0, length=15)
	n = length(y)
	t = sqrt.(2y .* (1 .+ randn(n) * 0.1 ) / g)
	scatter(y, t, leg=false, ms=2)
	yg = range(extrema(y)..., length=200)
	plot!(yg, sqrt.(2yg / g), c=:gray)
	xlabel!("y")
	ylabel!("t")
end

# ╔═╡ a616710d-08ea-4674-b3d6-6cd754d45083
md"""
p = $(@bind p Slider(1:n-1, show_value=true))
"""

# ╔═╡ c65c81f3-257a-4efd-b5ef-bc855d902841
begin
	Y = [y[i]^j for i = 1:n, j = 0:p]
	β̂ = Y \ t
	t̂ = Y * β̂
	scatter(y, t, leg=false, ms=2)
	plot!(yg, sqrt.(2yg / g), c=:gray)
	plot!(yg, β̂[1] .+ sum(β̂[j + 1] * yg.^j for j = 1:p), c=:red)
end

# ╔═╡ ca63c440-92c3-434a-a223-0ebb538dd4b6
let
	SQDados = Float64[]
	for p = 1:n-1
		Y = [y[i]^j for i = 1:n, j = 0:p]
		β̂ = Y \ t
		t̂ = Y * β̂
		push!(SQDados, norm(t - t̂)^2 / 2)
	end
	plot(SQDados, m=(3), xticks=1:n-1)
	xlabel!("grau")
	ylabel!("SQR")
end

# ╔═╡ 48aa56c7-076f-4711-bccf-0d8d4042b35c
md"""
- Quanto maior o grau, melhor o resultado.
- Na verdade não é o caso, porque sabemos o modelo original.
- Mas sem saber a verdade do modelo, poderíamos apenas fazer mais experimentos.
"""

# ╔═╡ 8754d253-a243-4e63-82ca-708624ec9236
begin
	Random.seed!(1)
	t2 = sqrt.(2y .* (1 .+ randn(n) * 0.1 ) / g)
	scatter(y, t, leg=false, ms=3)
	scatter!(y, t2, leg=false, ms=3, c=:red)
	plot!(yg, sqrt.(2yg / g), c=:gray)
	xlabel!("y")
	ylabel!("t")
end

# ╔═╡ 6ef45cb4-c7e1-4f38-a70c-333d42638fa4
md"""
p = $(@bind p2 Slider(1:n-1, show_value=true))
"""

# ╔═╡ b2b5af3e-f8f9-45b8-a051-e2528c25a841
begin
	Y2 = [y[i]^j for i = 1:n, j = 0:p2]
	β̂2 = Y2 \ t
	t̂2 = Y2 * β̂2
	scatter(y, t, leg=false, m=(3,:lightblue,stroke(1,:blue)), opacity=0.5)
	scatter!(y, t2, leg=false, ms=3, c=:red)
	plot!(yg, sqrt.(2yg / g), c=:gray, opacity=0.5)
	plot!(yg, β̂2[1] .+ sum(β̂2[j + 1] * yg.^j for j = 1:p2), c=:red)
end

# ╔═╡ 3e45e374-6fe0-4523-bfbd-e3656ba2b38f
let
	sqr_tr = Float64[]
	sqr_te = Float64[]
	for p = 1:n-1
		Y = [y[i]^j for i = 1:n, j = 0:p]
		β̂ = Y \ t
		t̂ = Y * β̂
		push!(sqr_tr, norm(t - t̂)^2 / 2)
		push!(sqr_te, norm(t2 - t̂)^2 / 2)
	end
	plot(sqr_tr, m=(3), xticks=1:n, leg=false)
	plot!(sqr_te, m=(3,:red))
	xlabel!("grau")
end

# ╔═╡ 281d46fc-ed79-43e0-80c9-654baf953e82
md"""
- No segundo conjunto de dados, o modelo encontrando mostra a realidade.
- Neste caso, o modelo de grau 6 é relativamente bom.
- Quanto maior o grau, pior o modelo nos casos extras.
- Podemos repetir várias vezes:
"""

# ╔═╡ 523fdcfa-f717-4a85-8380-eded0597b860
md"""
seeds = $(@bind seeds Slider(10:10:100, show_value=true))
"""

# ╔═╡ 611fa8c1-d4f6-4743-a9d2-7ff874d6630c
let
	SQDados = Float64[]
	for p = 1:n-1
		Y = [y[i]^j for i = 1:n, j = 0:p]
		β̂ = Y \ t
		t̂ = Y * β̂
		push!(SQDados, norm(t - t̂)^2 / 2)
	end
	plot(SQDados, m=(3), leg=false)

	SQmedia = zeros(length(SQDados))
	for s = 1:seeds
		Random.seed!(s)
		SQ2 = Float64[]
		for p = 1:n-1
			Y = [y[i]^j for i = 1:n, j = 0:p]
			β̂ = Y \ t
			t̂ = Y * β̂
			t2 = sqrt.(max.(2y .* (1 .+ randn(n) * 0.1 ) / g, 0))
			push!(SQ2, norm(t2 - t̂)^2 / 2)
		end
		SQmedia .+= SQ2
		plot!(SQ2, c=:red, opacity=0.1)
	end
	SQmedia /= seeds
	plot!(SQmedia, m=(3,:magenta), c=:magenta, lw=2)
	ylims!(0, 0.02)
end

# ╔═╡ 4c1f34fd-89d6-4710-b0d4-121940d5c6a0
md"""
## Validação Cruzada

- Não podemos fazer novos experimentos, o que fazer?

### Separação em treino e teste (train-test split ou holdout)

- Fingir que parte do conjunto é de um experimento diferente
- A parte que usamos para calcular $\beta$ é chamado de conjunto de treino
- A outra parte é o conjunto de teste
- Às vezes o nome validação é usada no lugar de teste
"""

# ╔═╡ db54f761-a928-4d2c-a463-9ac1996e9faa
md"""
splitseed = $(@bind splitseed Slider(-2:10, show_value=true, default=0))

splitperc = $(@bind splitperc Slider(0.25:0.25:0.75, show_value=true, default=0.5))
"""

# ╔═╡ 9e371bd9-48ef-48e3-9784-08b6a50cb088
let
	Random.seed!(max(splitseed, 0))
	m = round(Int, splitperc * n)
	I = if splitseed ≥ 0
		shuffle(1:n)
	elseif splitseed == -1
		1:n
	else
		n:-1:1
	end
	Itr = I[1:m]
	Ite = setdiff(I, Itr)
	
	plt = plot(layout=grid(1, 2), size=(800,300))
	
	SQDados = Float64[]
	SQ2 = Float64[]
	for p = 1:6
		Y = [y[i]^j for i = 1:n, j = 0:p]
		β̂ = Y[Itr,:] \ t[Itr]
		t̂ = Y * β̂
		push!(SQDados, norm(t[Itr] - t̂[Itr])^2 / length(Itr))
		push!(SQ2, norm(t[Ite] - t̂[Ite])^2 / length(Ite))
	end
	plot!(plt[2], SQDados, m=(3), leg=false)
	plot!(plt[2], SQ2, m=(3,:red))
	
	p = argmin(SQ2)		
	Y = [y[i]^j for i = Itr, j = 0:p]
	β̂ = Y \ t[Itr]
	
	scatter!(plt[1], y[Itr], t[Itr], leg=false, m=(3,:lightblue,stroke(1,:blue)), opacity=0.5)
	scatter!(plt[1], y[Ite], t[Ite], leg=false, ms=3, c=:red)
	plot!(plt[1], yg, β̂[1] .+ sum(β̂[j + 1] * yg.^j for j = 1:p), c=:red)
	title!(plt[1], "Melhor: p = $p")
end

# ╔═╡ b06b8936-bbff-4203-8a9d-e65ff3f13c91
md"""
**Problemas:**

- Menos treino = mais variância
- Aleatoriedade pode dar uma escolha ruim
"""

# ╔═╡ 5440f214-4bd0-44f3-ac8e-bb77273be11d
md"""
### Validação deixando um de fora (leave-one-out validation)

- Todos os dados são usados pra validação
- n _fits_ são feitos e usa-se a média
- Um _fit_ por dado, com o dado sendo o conjunto de teste e o resto o de treino
"""

# ╔═╡ c8025145-bfcc-47e9-b9d0-eca0d67565d6
md"""
dado usado = $(@bind loo_dado Slider(1:n, show_value=true))
"""

# ╔═╡ 31ac68b0-6bd3-4439-9e20-4638f73e40bf
let
	Ite = [loo_dado]
	Itr = setdiff(1:n, Ite)
	
	plt = plot(layout=grid(1, 2), size=(800,300))
	
	SQDados = Float64[]
	SQ2 = Float64[]
	for p = 1:6
		Y = [y[i]^j for i = 1:n, j = 0:p]
		β̂ = Y[Itr,:] \ t[Itr]
		t̂ = Y * β̂
		push!(SQDados, norm(t[Itr] - t̂[Itr])^2 / length(Itr))
		push!(SQ2, (t[loo_dado] - t̂[loo_dado])^2)
	end
	plot!(plt[2], SQDados, m=(3), leg=false)
	plot!(plt[2], SQ2, m=(3,:red))
	
	p = argmin(SQ2)		
	Y = [y[i]^j for i = Itr, j = 0:p]
	β̂ = Y \ t[Itr]
	
	scatter!(plt[1], y[Itr], t[Itr], leg=false, m=(3,:lightblue,stroke(1,:blue)), opacity=0.5)
	scatter!(plt[1], y[Ite], t[Ite], leg=false, ms=3, c=:red)
	plot!(plt[1], yg, β̂[1] .+ sum(β̂[j + 1] * yg.^j for j = 1:p), c=:red)
	title!(plt[1], "Melhor: p = $p")
end

# ╔═╡ 29b09242-1f4f-4ce3-a62a-ef5ffbfdb67b
let
	SQDados = zeros(n, 6)
	SQ2 = zeros(n, 6)
	
	for p = 1:6
		Y = [y[i]^j for i = 1:n, j = 0:p]
		for i = 1:n
			Itr = setdiff(1:n, [i])
			β̂ = Y[Itr,:] \ t[Itr]
			t̂ = Y * β̂
			SQDados[i,p] = norm(t[Itr] - t̂[Itr])^2 / length(Itr)
			SQ2[i,p] = (t[i] - t̂[i])^2
		end
	end
	
	plt = plot(leg=false)
	for i = 1:n
		plot!(SQDados[i,:], c=:blue, m=(1,:blue), opacity=0.2)
		plot!(SQ2[i,:], c=:red, m=(1,:red), opacity=0.2)
	end
	
	sqr_tr = sum(SQDados, dims=1)[:] / n
	sqr_te = sum(SQ2, dims=1)[:] / n
	plot!(sqr_tr, c=:blue, m=(3,:blue))
	plot!(sqr_te, c=:red, m=(3,:red))
	ylims!(0, maximum(sqr_te) * 1.1)
end

# ╔═╡ 6472d1a1-be3a-45f4-ae1e-d8b78f291030
md"""
- O "resta-um" é muito bom pra minimizar a variância. A maior parte dos treinos foi bem parecida.
- Além disso, como olha todos os dados individualmente, faz uma validação boa.
- No entanto, é caro pois precisa fazer um fit por dado.
"""

# ╔═╡ 883f6af6-b764-4a8c-bdc7-02b7549c6a3b
md"""
### K-Fold

- O K-Fold é o meio termo, generaliza o resta-um.
- No lugar de olhar cada dado, olhamos um conjunto de dados.
- Separamos o conjunto inteiro em $k$ conjuntos disjuntos.
- Fazemos $k$ fits, um pra cada conjunto.
- O conjunto da vez é o teste da vez, e o resto do conjunto é o treino.
"""

# ╔═╡ 3dcea0c2-09bc-4f53-a061-e02295be6369
let
	I = shuffle(1:n)
	m = ceil(Int, n / 5)
	plot(leg=false, size=(n * 15, 5 * 20), xticks=[], yticks=[])
	δ = 0.4
	for k = 1:5
		idx = ((k-1) * m + 1):min(n, k*m)
		Ite = I[idx]
		Itr = setdiff(I, Ite)
		scatter!(Itr, k * ones(length(Itr)), c=:blue, ms=4)
		scatter!(Ite, k * ones(length(Ite)), c=:red, ms=4)
		plot!([1-δ, n+δ, n+δ, 1-δ, 1-δ], [k-δ, k-δ, k+δ, k+δ, k-δ], c=:gray)
	end
	xlabel!("Dados")
	ylabel!("Folds")
	xlims!(0, n+1)
	ylims!(0, 6)
end

# ╔═╡ 3fe3bebf-e785-4adc-b173-ad12a3d8955b
md"""
kfoldseed = $(@bind kfoldseed Slider(0:10))
kfoldset = $(@bind kfoldset Slider(1:5))
"""

# ╔═╡ cd8b12ea-9c98-4089-9f9e-f830d9707a03
let
	Random.seed!(max(kfoldseed, 0))
	I = shuffle(1:n)
	m = ceil(Int, n / 5)
	idx = ((kfoldset-1) * m + 1):min(n, kfoldset*m)
	Ite = I[idx]
	Itr = setdiff(I, Ite)
	
	plt = plot(layout=grid(1, 2), size=(800,300))
	
	SQDados = Float64[]
	SQ2 = Float64[]
	for p = 1:6
		Y = [y[i]^j for i = 1:n, j = 0:p]
		β̂ = Y[Itr,:] \ t[Itr]
		t̂ = Y * β̂
		push!(SQDados, norm(t[Itr] - t̂[Itr])^2 / length(Itr))
		push!(SQ2, norm(t[Ite] - t̂[Ite])^2 / length(Ite))
	end
	plot!(plt[2], SQDados, m=(3), leg=false)
	plot!(plt[2], SQ2, m=(3,:red))
	
	p = argmin(SQ2)		
	Y = [y[i]^j for i = Itr, j = 0:p]
	β̂ = Y \ t[Itr]
	
	scatter!(plt[1], y[Itr], t[Itr], leg=false, m=(3,:lightblue,stroke(1,:blue)), opacity=0.5)
	scatter!(plt[1], y[Ite], t[Ite], leg=false, ms=3, c=:red)
	plot!(plt[1], yg, β̂[1] .+ sum(β̂[j + 1] * yg.^j for j = 1:p), c=:red)
	title!(plt[1], "Melhor: p = $p")
end

# ╔═╡ 7422bd22-3224-4e97-830f-649db2380667
let
	Random.seed!(0)
	kfoldnfolds = 5
	I = shuffle(1:n)
	m = ceil(Int, n / kfoldnfolds)
	
	SQDados = zeros(kfoldnfolds, 6)
	SQ2 = zeros(kfoldnfolds, 6)
	for p = 1:6
		Y = [y[i]^j for i = 1:n, j = 0:p]
		for k = 1:kfoldnfolds
			idx = ((k-1) * m + 1):min(n, k*m)
			Ite = I[idx]
			Itr = setdiff(I, Ite)
			β̂ = Y[Itr,:] \ t[Itr]
			t̂ = Y * β̂
			SQDados[k,p] = norm(t[Itr] - t̂[Itr])^2 / length(Itr)
			SQ2[k,p] = norm(t[Ite] - t̂[Ite])^2 / length(Ite)
		end
	end
	
	plt = plot(leg=false)
	for i = 1:kfoldnfolds
		plot!(SQDados[i,:], c=:blue, m=(1,:blue), opacity=0.2)
		plot!(SQ2[i,:], c=:red, m=(1,:red), opacity=0.2)
	end
	
	sqr_tr = sum(SQDados, dims=1)[:] / kfoldnfolds
	sqr_te = sum(SQ2, dims=1)[:] / kfoldnfolds
	plot!(sqr_tr, c=:blue, m=(3,:blue))
	plot!(sqr_te, c=:red, m=(3,:red))
end

# ╔═╡ 41eafea5-24c3-45e5-a927-50831333ea1d
md"""
- K-Fold equilibra o trabalho com a variância.
- Para conjuntos razoáveis, é o mais usado.
- Para conjuntos pequenos, o resta-um pode ser necessário.
- Para conjuntos grandes, o holdout pode ser suficiente.
"""

# ╔═╡ 21da2012-484e-40f2-b3d3-75322d7c8e77
md"""
## Exemplo com outros modelos

- Overfitting - só o treino importa.
- Underfitting - nem o treino está sendo satisfeito.
- O overfitting acontece com a complexidade do modelo.
- A validação pode ser usada para qualquer comparação entre modelos.
- Também vale para classificação.
"""

# ╔═╡ 97090575-74ec-40ad-ac57-b5aee7a08b42
begin
	Random.seed!(0)
	nclf = 100
	Xclf = rand(nclf, 2) * 2 .- 1
	yclf = Int[
		Xclf[i,1]^2 - abs(Xclf[i,2] .+ 1) > -0.7 + randn() * 0.4 for i = 1:nclf
	]
	
	function knn(X, y, x, k)
		n = size(X, 1)
		D = [norm(x - X[i,:]) for i = 1:n]
		I = sortperm(D)
		round(Int, sum(y[I[1:k]]) / k)
	end
	
	plot(leg=false)
	I = findall(yclf .== 0)
	scatter!(Xclf[I,1], Xclf[I,2], m=(:lightblue,stroke(1,:blue),3,:circle))
	I = findall(yclf .== 1)
	scatter!(Xclf[I,1], Xclf[I,2], m=(:pink,stroke(1,:red),3,:square))
end

# ╔═╡ d8d28251-0a1f-438d-883f-4956eacc17ac
md"""
num vizinhos = $(@bind n_viz Slider(1:2:nclf, show_value=true))
"""

# ╔═╡ 4a1caa14-19dc-4299-b6fd-b60138b554ce
let
	xg = range(-1, 1, length=100)
	yg = range(-1, 1, length=100)
	zg = [knn(Xclf, yclf, [xi; yi], n_viz) for xi in xg, yi in yg]
	contourf(xg, yg, zg', c=cgrad([:lightblue,:pink]), leg=false)
	I = findall(yclf .== 0)
	scatter!(Xclf[I,1], Xclf[I,2], m=(:lightblue,stroke(1,:blue),3,:circle))
	I = findall(yclf .== 1)
	scatter!(Xclf[I,1], Xclf[I,2], m=(:pink,stroke(1,:red),3,:square))
end

# ╔═╡ 81327d54-5d71-40c4-82bf-1d27d91d1e6f
let
	Random.seed!(0)
	kfoldnfolds = 10
	I = shuffle(1:nclf)
	m = ceil(Int, nclf / kfoldnfolds)
	vizset = 1:2:div(nclf,2)
	
	acc_tr = zeros(kfoldnfolds, length(vizset))
	acc_te = zeros(kfoldnfolds, length(vizset))
	for (nvizi,nviz) in enumerate(vizset)
		for k = 1:kfoldnfolds
			idx = ((k-1) * m + 1):min(nclf, k*m)
			Ite = I[idx]
			Itr = setdiff(I, Ite)
			
			ŷ = [knn(Xclf[Itr,:], yclf[Itr], Xclf[i,:], nviz) for i = 1:nclf]
			
			acc_tr[k,nvizi] = sum(yclf[Itr] .== ŷ[Itr]) / length(Itr)
			acc_te[k,nvizi] = sum(yclf[Ite] .== ŷ[Ite]) / length(Ite)
		end
	end
	
	plt = plot(leg=false)
	for i = 1:kfoldnfolds
		plot!(acc_tr[i,:], c=:blue, opacity=0.2)
		plot!(acc_te[i,:], c=:red, opacity=0.2)
	end
	
	acc_tr_avg = sum(acc_tr, dims=1)[:] / kfoldnfolds
	acc_te_avg = sum(acc_te, dims=1)[:] / kfoldnfolds
	plot!(acc_tr_avg, c=:blue, m=(3,:blue))
	plot!(acc_te_avg, c=:red, m=(3,:red))
	xticks!(1:length(vizset), string.(vizset))
	xlabel!("Número de vizinhos")
	ylabel!("Acurácia")
end

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PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

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Plots = "~1.19.2"
PlutoUI = "~0.7.9"
"""

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[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.0+6"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
git-tree-sha1 = "ed268efe58512df8c7e224d2e170afd76dd6a417"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.13.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.31.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[DataAPI]]
git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.7.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.9"

[[DataValueInterfaces]]
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 = "dba1e8614e98949abfa60480b13653813d8f0157"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+0"

[[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 = "761a393aeccd6aa92ec3515e428c26bf99575b3b"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+0"

[[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"]
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"

[[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 = ["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"

[[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:
# ╟─c771792f-da93-4863-8d21-21933cc19c54
# ╟─0ac1d752-e802-11eb-1457-edd0cfb36fe8
# ╟─cf956436-0840-4051-85b9-f39ffb001971
# ╟─a616710d-08ea-4674-b3d6-6cd754d45083
# ╟─c65c81f3-257a-4efd-b5ef-bc855d902841
# ╟─ca63c440-92c3-434a-a223-0ebb538dd4b6
# ╟─48aa56c7-076f-4711-bccf-0d8d4042b35c
# ╟─8754d253-a243-4e63-82ca-708624ec9236
# ╟─6ef45cb4-c7e1-4f38-a70c-333d42638fa4
# ╟─b2b5af3e-f8f9-45b8-a051-e2528c25a841
# ╟─3e45e374-6fe0-4523-bfbd-e3656ba2b38f
# ╟─281d46fc-ed79-43e0-80c9-654baf953e82
# ╟─523fdcfa-f717-4a85-8380-eded0597b860
# ╟─611fa8c1-d4f6-4743-a9d2-7ff874d6630c
# ╟─4c1f34fd-89d6-4710-b0d4-121940d5c6a0
# ╟─db54f761-a928-4d2c-a463-9ac1996e9faa
# ╟─9e371bd9-48ef-48e3-9784-08b6a50cb088
# ╟─b06b8936-bbff-4203-8a9d-e65ff3f13c91
# ╟─5440f214-4bd0-44f3-ac8e-bb77273be11d
# ╟─c8025145-bfcc-47e9-b9d0-eca0d67565d6
# ╟─31ac68b0-6bd3-4439-9e20-4638f73e40bf
# ╟─29b09242-1f4f-4ce3-a62a-ef5ffbfdb67b
# ╟─6472d1a1-be3a-45f4-ae1e-d8b78f291030
# ╟─883f6af6-b764-4a8c-bdc7-02b7549c6a3b
# ╟─3dcea0c2-09bc-4f53-a061-e02295be6369
# ╟─3fe3bebf-e785-4adc-b173-ad12a3d8955b
# ╟─cd8b12ea-9c98-4089-9f9e-f830d9707a03
# ╟─7422bd22-3224-4e97-830f-649db2380667
# ╟─41eafea5-24c3-45e5-a927-50831333ea1d
# ╟─21da2012-484e-40f2-b3d3-75322d7c8e77
# ╟─97090575-74ec-40ad-ac57-b5aee7a08b42
# ╟─d8d28251-0a1f-438d-883f-4956eacc17ac
# ╟─4a1caa14-19dc-4299-b6fd-b60138b554ce
# ╟─81327d54-5d71-40c4-82bf-1d27d91d1e6f
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002