### A Pluto.jl notebook ###
# v0.17.2

using Markdown
using InteractiveUtils

# ╔═╡ d9015225-b635-42ad-ae96-fe7772a031b7
using Pkg, DrWatson

# ╔═╡ 727e041b-fe08-4f7d-ad19-e3c57772c967
begin
	using GLM
	using CSV
	using Random
	using StatsBase
	using DataFrames
	using Dagitty
	using Turing
	using StatsPlots
	using StatisticalRethinking
	using StatisticalRethinkingPlots
	using Logging
end

# ╔═╡ 5a128323-2c19-4efa-989f-ff345e6a9cb3
# Pkg.update()

# ╔═╡ 078fdb65-5bd6-4b0d-b672-617f5912480d
begin
	default(labels=false)
	Logging.disable_logging(Logging.Warn);
end;

# ╔═╡ 5141dfdf-490d-479e-ac58-63c929ae8fd1
md"## 7.1 The problem with parameters."

# ╔═╡ 611c3828-f01f-4721-830b-736b28620e7e
md"### Code 7.1"

# ╔═╡ ad511be2-fd88-4aba-a830-21e242d994f1
begin
	sppnames = ["afarensis", "africanus", "habilis", "boisei",
		"rudolfensis", "ergaster", "sapiens"]
	brainvolcc = [438, 452, 612, 521, 752, 871, 1350]
	masskg = [37.0, 35.5, 34.5, 41.5, 55.5, 61.0, 53.5]
	d = DataFrame(:species => sppnames, :brain => brainvolcc, :mass => masskg)
end;

# ╔═╡ 4ee38b80-aded-40af-93ac-11a4ac2b9378
md"### Code 7.2"

# ╔═╡ 5c7f1f26-02ac-4325-a06c-8c26c75e6cf4
begin
	d[!,:mass_std] = (d.mass .- mean(d.mass))./std(d.mass)
	d[!,:brain_std] = d.brain ./ maximum(d.brain)
	d
end

# ╔═╡ 5a2f79ca-2d3e-4cd4-9de9-7c7e283a5052
md"### Code 7.3"

# ╔═╡ 94b5539b-4374-40b8-9501-8d3df49f20c3
@model function model_m7_1(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ Normal(0, 10)
    μ = @. a + b*mass_std
    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ 2aafe78c-b1b1-4963-ad89-dbe09b546d96
begin
	m7_1_ch = sample(model_m7_1(d.mass_std, d.brain_std), NUTS(), 1000)
	m7_1 = DataFrame(m7_1_ch)
	PRECIS(m7_1)
end

# ╔═╡ 45122674-c5d2-4f61-af03-c74482618e90
md"### Code 7.4"

# ╔═╡ 3b7ca48f-078f-4eef-9d0c-fa8724e711d3
X = hcat(ones(length(d.mass_std)), d.mass_std)

# ╔═╡ 40c173f3-3dbb-4907-9188-632d34b3d7cf
m = lm(X, d.brain_std)

# ╔═╡ 39dc811c-2742-4977-a203-c9fdcb5b218d
md"### Code 7.5"

# ╔═╡ 85bb82da-efe7-4b34-8af5-cf60ae6e4757
Random.seed!(12);

# ╔═╡ 53806285-ea68-4f5c-b3fb-a382a894ec56
md"## Do explicit simulation due to log_σ."

# ╔═╡ 59b9a24b-6967-418b-a4f8-e67ceb0a5474
begin
	s = [
		rand(MvNormal((@. r.a + r.b * d.mass_std), exp(r.log_σ)))
		for r ∈ eachrow(m7_1)
	]
	s = vcat(s'...);

	r = mean.(eachcol(s)) .- d.brain_std;
	resid_var = var(r, corrected=false)
	outcome_var = var(d.brain_std, corrected=false)
	1 - resid_var/outcome_var
end

# ╔═╡ ed541621-2245-49f9-9672-31e20b9b7765
md"### Code 7.6"

# ╔═╡ 47d9566c-93ec-4f70-b7b6-5586193bcdef
md"#### Function is implemented in a generic way to support any amount of b[x] coefficients."

# ╔═╡ 1e5a39c0-6b5b-4d29-826e-e68c31c8f34e
function R2_is_bad(df; sigma=missing)
    degree = ncol(df[!,r"b"])
    # build mass_std*degree matrix, with each col exponentiated to col's index
    t = repeat(d.mass_std, 1, degree)
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    s = [
        begin
            # calculate product on coefficient's vector
            b = collect(r[r"b"])
            μ = r.a .+ t * b
            s = ismissing(sigma) ? exp(r.log_σ) : sigma
            rand(MvNormal(μ, s))
        end
        for r ∈ eachrow(df)
    ]
    s = vcat(s'...);

    r = mean.(eachcol(s)) .- d.brain_std;
    v1 = var(r, corrected=false)
    v2 = var(d.brain_std, corrected=false)
    1 - v1 / v2
end

# ╔═╡ e8f6166f-20e5-40a2-a8fc-692ea8704b6d
md"### Code 7.7"

# ╔═╡ f74d5bc3-747b-4b12-9fb2-7e4a19cfe2c1
@model function model_m7_2(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ MvNormal([0, 0], 10)
    μ = @. a + b[1]*mass_std + b[2]*mass_std^2
    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ fa9522ce-d91d-4cbd-9a1a-fe63fd2b7d15
begin
	m7_2_ch = sample(model_m7_2(d.mass_std, d.brain_std), NUTS(), 10000)
	m7_2 = DataFrame(m7_2_ch)
	PRECIS(m7_2)
end

# ╔═╡ 41fc983a-9209-4ff5-b9fa-5798c7d387af
md"### Code 7.8"

# ╔═╡ 0f8d2476-7379-4bec-8a6f-e6ef81066ebb
md"#### Implemented the sample in a general way."

# ╔═╡ 4632e385-2417-4683-9e31-72825cf5501c
@model function model_m7_n(mass_std, brain_std; degree::Int)
    a ~ Normal(0.5, 1)
    b ~ MvNormal(zeros(degree), 10)
    # build matrix n*degree
    t = repeat(mass_std, 1, degree)
    # exponent its columns
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    # calculate product on coefficient's vector
    μ = a .+ t * b

    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ bf763ccd-2c72-4529-b6ac-747f39f1b9cf
begin
	m7_3_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=3), NUTS(), 1000)
	m7_3 = DataFrame(m7_3_ch)
	PRECIS(m7_3)
end

# ╔═╡ ef2e821a-d947-40e1-9855-79819aec5dbb
begin
	m7_4_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=4), NUTS(), 1000)
	m7_4 = DataFrame(m7_4_ch)
	PRECIS(m7_4)
end

# ╔═╡ e1e48fb9-bb0f-4fe6-a34e-46ea2ced2510
begin
	m7_5_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=5), NUTS(), 1000)
	m7_5 = DataFrame(m7_5_ch)
	PRECIS(m7_5)
end

# ╔═╡ bff2a56e-e799-4d50-b97b-79983df86565
@model function model_m7_6(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ MvNormal(zeros(6), 10)
    μ = @. a + b[1]*mass_std + b[2]*mass_std^2 + b[3]*mass_std^3 +
               b[4]*mass_std^4 + b[5]*mass_std^5 + b[6]*mass_std^6
    brain_std ~ MvNormal(μ, 0.001)
end

# ╔═╡ 5c26fd02-6695-4f3d-8f17-37c9b2ada2e6
begin
	m7_6_ch = sample(model_m7_6(d.mass_std, d.brain_std), NUTS(), 1000)
	m7_6 = DataFrame(m7_6_ch)
	PRECIS(m7_6)
end

# ╔═╡ 941248e9-c1ec-4d6a-8a2a-dbdd9aee17d8
md"### Code 7.10"

# ╔═╡ 97a58b2a-a200-4249-acf3-c52d28ca6aea
mass_seq = range(extrema(d.mass_std)...; length=100)

# ╔═╡ 7174161a-6536-4ec7-a89e-2c385de7052c
begin
	l = [
    	@. r.a + r.b * mass_seq
    	for r ∈ eachrow(m7_1)
	]
	l = vcat(l'...)
	μ = mean.(eachcol(l))
end

# ╔═╡ f4955154-ea66-4523-aacd-1a4beef6d41b
begin
	ci = PI.(eachcol(l))
	ci = vcat(ci'...)
end

# ╔═╡ caa5e742-7606-43fa-8ae3-a1287ff24951
scatter(d.mass_std, d.brain_std; title="1: R² = $(round(R2_is_bad(m7_1); digits=3))")

# ╔═╡ 2f524064-abcc-40a1-a21e-99a0a4636545
plot!(mass_seq, [μ μ]; fillrange=ci, c=:black, fillalpha=0.3)

# ╔═╡ 0f92b3fa-1b99-45f4-8a8e-5b7ea33a464d
md"### Reimplemented the brain_plot function to check my results."

# ╔═╡ cb2d9bdf-3cf3-48f2-a984-5440dba08ad9
function brain_plot(df; sigma=missing)
    degree = ncol(df[!,r"b"])
    # build mass_seq*degree matrix, with each col exponentiated to col's index
    t = repeat(mass_seq, 1, degree)
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    l = [
        r.a .+ t * collect(r[r"b"])
        for r ∈ eachrow(df)
    ]
    l = vcat(l'...)
    μ = mean.(eachcol(l))
    ci = PI.(eachcol(l))
    ci = vcat(ci'...)

    r2 = round(R2_is_bad(df, sigma=sigma); digits=3)
    scatter(d.mass_std, d.brain_std; title="$degree: R² = $r2")
    plot!(mass_seq, [μ μ]; fillrange=ci, c=:black, fillalpha=0.3)
end;

# ╔═╡ 29f7fc44-1d5c-4912-a0b0-07a7e97cfe26
plot(
    brain_plot(m7_1),
    brain_plot(m7_2),
    brain_plot(m7_3),
    brain_plot(m7_4),
    brain_plot(m7_5),
    brain_plot(m7_6, sigma=0.001);
    size=(1000, 600)
)

# ╔═╡ bb21db38-31cf-4e88-86d2-922d62533769
md"### Code 7.11"

# ╔═╡ 4f7bfda2-297d-432d-83c9-c931f5f62868
i = 3;

# ╔═╡ 90d5c3e8-a045-4d96-aebc-2ec99609e10b
d_minus_i = d[setdiff(1:end,i),:];

# ╔═╡ 3babf620-dd01-45ae-b21c-e46e136057f6
function brain_loo_plot(model, data; title::String)
    (a, b) = extrema(data.brain_std)
    p = scatter(data.mass_std, data.brain_std; title=title, ylim=(a-0.1, b+0.1))
    mass_seq = range(extrema(data.mass_std)...; length=100)

    for i ∈ 1:nrow(data)
        d_minus_i = data[setdiff(1:end,i),:]
        df = DataFrame(sample(
				model(d_minus_i.mass_std, d_minus_i.brain_std),
				NUTS(),
				1000))

        degree = ncol(df[!,r"b"])

        # build mass_seq*degree matrix, with each col exponentiated to col's index

        t = repeat(mass_seq, 1, degree)
        t = hcat(map(.^, eachcol(t), 1:degree)...)
        l = [
            r.a .+ t * collect(r[r"b"])
            for r ∈ eachrow(df)
        ]
        l = vcat(l'...)
        μ = mean.(eachcol(l))
        plot!(mass_seq, μ; c=:black)
    end
    p
end

# ╔═╡ 9a5d927d-e816-4f5f-a460-c89a507ce1ae
model_m7_4 = (mass, brain) -> model_m7_n(mass, brain, degree=4)

# ╔═╡ b3778ab5-03b7-4ba5-9501-3e6bb643e4d5
plot(
    brain_loo_plot(model_m7_1, d, title="m7.1"),
    brain_loo_plot(model_m7_4, d, title="m7.4");
    size=(800, 400)
)

# ╔═╡ b55cffd3-d5ce-41db-968d-0b54b1b872a7
md"## 7.2 Entropy and accuracy."

# ╔═╡ e8765238-eec6-41c0-9c8c-148c9e51aad9
md"### Code 7.12"

# ╔═╡ fd1f8ae2-6839-4f7e-9141-66824490df72
p = [0.3, 0.7];

# ╔═╡ 3a3537ec-039a-434d-a7d4-15ab41eb97d8
-sum(p .* log.(p))

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
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StatisticalRethinking = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
StatisticalRethinkingPlots = "e1a513d0-d9d9-49ff-a6dd-9d2e9db473da"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
CSV = "~0.8.5"
Dagitty = "~0.0.1"
DataFrames = "~1.2.2"
DrWatson = "~2.4.1"
GLM = "~1.5.1"
StatisticalRethinking = "~4.0.4"
StatisticalRethinkingPlots = "~0.3.0"
StatsBase = "~0.33.10"
StatsPlots = "~0.14.26"
Turing = "~0.18.0"
"""

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

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[[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"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

[[VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "5239606cf3552aff43d79ecc75b1af1ce4625109"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.21"

[[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"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "80661f59d28714632132c73779f8becc19a113f2"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.4"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[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"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[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"

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

[[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 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

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

[[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"
"""

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