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

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

# ╔═╡ a22bf9fc-7b28-11eb-30c1-0fa6d84c74d1

begin
	#try
		using PlutoUI
		using Plots
		using Plots.PlotMeasures
		using LaTeXStrings
		using Markdown
		using Images
		#using LinearAlgebra
		#using SparseArrays
		#using SpecialFunctions
		#using StatsBase
		#using Random
		#using Distributions
		md""" 
		### Packages
		
		All needed Packages available :) """
	#=catch
		using Pkg;
		Pkg.activate(mktempdir())
		Pkg.add("PlutoUI")
		Pkg.add("Plots")
		Pkg.add("LaTeXStrings")
		Pkg.add("Markdown")
		Pkg.add("Images")
		#Pkg.add("LinearAlgebra")
		#Pkg.add("SparseArrays")
		#Pkg.add("SpecialFunctions")
		#Pkg.add("StatsBase")
		#Pkg.add("Distributions")
		using PlutoUI, Plots, LaTeXStrings, Markdown, Images, Plots.PlotMeasures
		#using LinearAlgebra
		#using SparseArrays
		#using StatsBase
		#using Random
		md""" 
		### Packages
		
		Some Package sources not added, this will take approx. 3 minutes"""
	end
	# TODO: make it more generally, so one understands how to compare rating
	# maybe make to diagrams next to each other to make them compareable
	=#
end

# ╔═╡ 9428fba4-67b3-4d2f-a09f-7dc5f28deadd
TableOfContents(aside=true)

# ╔═╡ 5210a326-7b34-11eb-0d14-67f67a882d68
md"""
# The starfish rating problem ⭐⭐⭐⭐⭐
## MaxEnt probabilities, given the true  mean 
 Here we use Maximum entropy to determine the rating probabilities given the normalization constraint and the instrinsic mean $\mu = \langle R \rangle$ with $R$ $\in$ $\{1,2,3,4,5\}$. 
"""

# ╔═╡ 852d6e36-7b31-11eb-0653-61bcf655249d
md"
choose intrinsic mean rating $\mu$  between 1 and 5:    $(@bind μ_r Slider(1.00:0.001:4.999, show_value=true,default=2.0)) 
"

# ╔═╡ 8240f678-7b35-11eb-1a68-bb2b66ce0d04
begin
	# images
	grey_starfish_url = "https://raw.githubusercontent.com/Captain-Bayes/images/main/starfish_grey_five.png"
	red_starfish_url = "https://raw.githubusercontent.com/Captain-Bayes/images/main/starfish_red_five.png"
	grey_starfish_local = download(grey_starfish_url)
	red_starfish_local = download(red_starfish_url)
	grey_starfish = load(grey_starfish_local)
	red_starfish = load(red_starfish_local)
	
	
	ir = Int64(round(μ_r))
	L_stars = ["⭐","⭐⭐","⭐⭐⭐","⭐⭐⭐⭐","⭐⭐⭐⭐⭐","★★★★★"]
md"""	
	$(L_stars[ir])
	"""
	
	[red_starfish[:,1:Int(ceil(μ_r/5*size(red_starfish,2)))] grey_starfish[:,(Int(ceil(μ_r/5*size(red_starfish,2)))):end]]
end

# ╔═╡ 0649912d-5164-4709-ad64-ca79b5256bf3
md"""
## Probability for the true mean, given the sample mean  of $\mathcal{N}$ votes
Here we use Bayesian probability theorem to determine the probability 
$P(\mu \mid \overline{\boldsymbol{R}},\mathcal{N})$ for the intrinsic mean $\mu$ given the average rating $\overline{\boldsymbol{R}}$  based on $\mathcal{N}$ votes.

"""

# ╔═╡ f1646630-8507-4967-beab-a61c2f26bd17
md"""
### Bayesian theory  

Eager to see the theory ? 🤓🧐😋😃👏  _click here_ 👉$(@bind show_Bayes CheckBox())


"""

# ╔═╡ d22311d9-c2c5-4dbd-be38-a377c6b19c37
if show_Bayes
md"""
- we seek: $P(\mu \mid \mathcal{\boldsymbol{R}}, \mathcal{N})$, where $\mathcal{\boldsymbol{R}}$ is the sum of the $ \mathcal{N}$ votes

- Bayes' theorem gives: $P(\mu\mid \mathcal{\boldsymbol{R}}, \mathcal{N}) \propto P(\mathcal{\boldsymbol{R}}\mid \mu , \mathcal{N}) \; P(\mu)$

- We marginalize over the unknown ratings $\boldsymbol{R}_{\nu}$ of the $\mathcal{N}$ voters
$P(\mathcal{\boldsymbol{R}}\mid \mu , \mathcal{N})  = \sum_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}=1}^{5}  
P(\mathcal{\boldsymbol{R}}\mid  \boldsymbol{R},\mu , \mathcal{N})\;  \prod_{\nu}  P(R = \boldsymbol{R}_{\nu}\mid \mu)$ 

- the terms $P(R_{i}\mid \mu)$ have been computed in the MaxEnt section

- the remaining probability for the total rating $\boldsymbol{\mathcal{R}}$ given the individual ratings is
$P(\boldsymbol{\mathcal{R}}\mid \boldsymbol{R})
=
\begin{cases}
	1 & \text{if }\sum_{\nu} \boldsymbol{R}_{\nu} = \boldsymbol{\mathcal{R}}\\
	0 & \text{otherwise}
\end{cases}$

- which simply leads to a restricted sum  
$P(\mu\mid \mathcal{\boldsymbol{R}},\mathcal{N}) \propto
\sum^{\sum_{\nu}\boldsymbol{R}_\nu = \boldsymbol{\mathcal{R}}}_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}}\;
\prod_{\nu}\frac{e^{\lambda(\mu) \boldsymbol{R}_{\nu}}}{Z(\mu)}
\propto
\sum^{\sum_{\nu}\boldsymbol{R}_\nu = \boldsymbol{\mathcal{R}}}_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}}  \;
\; \frac{e^{\lambda(\mu) \sum_{\nu}\boldsymbol{R}_{\nu}}}{(Z(\mu))^{\mathcal{N}}}
\propto
\bigg[\sum^{\sum_{\nu}\boldsymbol{R}_\nu = \boldsymbol{\mathcal{R}}}_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}} 1\bigg] \;
\frac{e^{\lambda(\mu) \mathcal{\boldsymbol{R}}}}{(Z(\mu))^{\mathcal{N}}}$

- final result:
$P(\mu\mid \overline{\boldsymbol{R}},\mathcal{N})  =\frac{1}{Z}
\frac{e^{\lambda(\mu) \mathcal{\boldsymbol{R}}}}{(Z(\mu))^{\mathcal{N}}}\;P(\mu)$


"""
end

# ╔═╡ f6a34d0c-2591-45f9-baac-f58fd5eace8b
md"""
### Prior
"""

# ╔═╡ 74a7a904-f043-4a69-93ea-2483d9eb0826
begin
	
	image_claire = "https://raw.githubusercontent.com/Captain-Bayes/images/main/claire_100px.gif"
	tin_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Tin_pot.png"
	iron_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Iron_pot.png"
	brass_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Brass_pot.png"
	copper_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Copper_pot.png"
	
	
	md"""
	The pot ratings of Claire's pottery store
	 were the following:
	
	- Tin pot: ``\overline{\boldsymbol{R}} = 3.9,\, \mathcal{N} = 250``
	- Brass pot: ``\overline{\boldsymbol{R}} = 4.2,\, \mathcal{N} = 80``
	- Iron pot: ``\overline{\boldsymbol{R}} = 5,\, \mathcal{N} = 2``
	- Copper pot: ``\overline{\boldsymbol{R}} = 4.5,\, \mathcal{N} = 15``
	$(Resource(image_claire, :width=> 200))
	$(Resource(tin_pot, :width=> 80)) 
	$(Resource(brass_pot, :width=> 100)) 
	$(Resource(iron_pot, :width=> 130)) 
	$(Resource(copper_pot, :width=> 100))
	"""
end

# ╔═╡ 44ea4b68-20d0-4f67-95d6-4228c9174c2b
md"""
## Some nice large plots
"""

# ╔═╡ 8102cbf7-e2ad-4492-9756-278fb8d072e7
begin
	Q = [0.000001;0.01:0.01:1]
	ll = -Q.*log.(Q)
	
	plot(Q, ll, 
	size = (600,400),
	xlabel = latexstring("Q_i"),
	ylabel = latexstring("S(Q_i)"),
	labelfontsize = 20,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,
	linewidth = 3,
	label = :none,
		title= "Entropy",
	titlefontsize = 20,	
	#foreground_color_grid = :black,
	#foreground_color_xticks = :black,
	background_color = :transparent,
	#foreground_color_axis = :black,
	#foreground_color_text = :black,
	#foreground_color_border = :black,
	foreground_color = :black,
	fontfamily="Computer Modern"
	)
	
	#	savefig("C://Lehre//Bayes MOOC//Lesson 6//Images//entropy")
	
	
end

# ╔═╡ 9345ab4c-69f9-47b2-a1a4-388adeb4f74c
begin
	Rat = 1:5
	lam = -5:0.01:5
	
	normierung = sum(exp.(lam'.*Rat),dims=1)
	mean_value = sum(Rat.*exp.(lam'.*Rat)./normierung, dims = 1)
	
	plot(lam, mean_value', 
	size = (600,400),
	xlabel = latexstring("\\lambda"),
	ylabel = latexstring("\\mu(\\lambda)"),
	labelfontsize = 20,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,
	linewidth = 3,
	label = :none,
	titlefontsize = 20,	
		title = "Lagrange paramter and mean value",
	#foreground_color_grid = :black,
	#foreground_color_xticks = :black,
	background_color = :transparent,
	#foreground_color_axis = :black,
	#foreground_color_text = :black,
	#foreground_color_border = :black,
	foreground_color = :black,
	fontfamily="Computer Modern"
	)
	
	#	savefig("C://Lehre//Bayes MOOC//Lesson 6//Images//lagrange")
	
	
end

# ╔═╡ 033db041-4b66-4a4f-a063-1b7d310c232c
md"""
## Program code
"""

# ╔═╡ 248a131d-49c7-45cd-8e30-527386e317f5
begin
	L_r = [1:5;]
	
	function Newton(L_r,μ_r; max_iter = 10000, ε = 1.e-8)
		#=
			for given true mean μ_r compute 
			Z(μ_r) und λ(μ_r) of Maxent solution for
			probability q_r = P(r| μ_r)   = exp(λ r)/Z
		=#

		λ = 0.0
		Z = 0.0
		q_r = zeros(size(L_r))
		for i_step = 1: max_iter
			𝜌_r = exp.(λ .* L_r)
			Z   = sum(𝜌_r)
			q_r = 𝜌_r ./ Z
			avg_r = sum(L_r .* q_r)
			var_r = sum(L_r.^2 .* q_r) - avg_r^2
			𝛷 = avg_r - μ_r
			𝛥𝜆 = 𝛷 / var_r
			λ  = λ - 𝛥𝜆 
			if abs(𝛥𝜆) < ε
				break
			end
		end

		return Z,λ,q_r
	end
	md" ### Newton Raphson"
end

# ╔═╡ b033b45c-7b28-11eb-1216-5703dc0e7792
begin	
	aux1,𝜆_ME,q_r = Newton(L_r,μ_r; max_iter = 10000, ε = 1.e-3)

	txt2 = latexstring("\\mathrm{MaxEnt\\, probability\\,  for\\, given \\, true\\, mean\\, \\mu }")
	col_pal = palette(:default) # color palette
	
	plot(L_r,q_r,
		line= (0.0 , 2.0 , :bar),
		bar_width = 0.05,
		title = txt2,
		ylim = (0.0, 1.1),
		xlabel = latexstring("R"),
		ylabel = latexstring("P\\,(R\\,|\\mu)"),		
		label = false
	)
	plot!(L_r,q_r,size=[500,300],
		line = ( 1, 0., :path),
		marker = (5, 1., :o),
		markerstrokewidth = 1.,
    	color = col_pal[1],
		label = false
	)

end


# ╔═╡ a0e51c0c-7b2f-11eb-2c1c-a77cfaf645f7
md"
 **The corresponding Lagrange parameter is**: $\lambda$ = $(round(𝜆_ME,digits=4))
"

# ╔═╡ 3bcf9ac2-213d-44fe-b8b5-8b54695c3029
begin
	N_iter_max = 10000
	eps_lagr = 1.e-8
	μ_Delta = 0.01
	L_μ = [1.01:μ_Delta:4.99;]
	L_𝜆 = zeros(length(L_μ))
	L_Z = zeros(length(L_μ))

	for (i,μ_r) in enumerate(L_μ)
		Z,λ,aux2  = Newton(L_r,μ_r; max_iter = 10000, ε = 1.e-8)
		L_𝜆[i]   = λ
		L_Z[i]   = Z	
	end
	
	md"""
	 ### determine auxiliary Maxent functions 
	 $\lambda(\mu)$  and $Z(\mu)$
	"""
end


# ╔═╡ 4c48af3c-dac8-43d4-9a57-7fed5052300a
begin
	slider_α = @bind 	α 	Scrubbable(0:.1:5, default=2.0)
	slider_β = @bind 	β   Scrubbable(0:.1:5, default=3.0)
	md"### sliders "
end

# ╔═╡ cdf3d720-bc21-44f5-976e-87fb5d8ed64b
md"""
  We still need to choose the prior probability $P(\mu)$ that encode our prior knowledge/ expectation about the true rating-mean $\mu$

We seek a function of $\mu \in [1,5]$, that (depending on some paramerters) is flexble enough to cover all conceivable shapes a prior probability  distribution my have.


Such a function is given by an adjusted Beta distribution

$P(\mu) \propto (\mu-1)^{\alpha-1}  (5-\mu)^{\beta-1}$ 

which depends only on two parameters.

---------------
_Choose the paramters_ $\alpha$ and $\beta$ and try to match your prior expectations

🔊 **to change the values, click and pull the numbers**

α:    $slider_α     
β:    $slider_β
"""

# ╔═╡ 53365c4a-b00a-4bdf-8314-9ab9dbd19db6
begin
	Prior = (L_μ .- 1).^(α-1)  .* (5 .- L_μ).^(β-1)
	Prior = Prior ./ (sum(Prior)*(L_μ[2]-L_μ[1]))
	
	plot1 = plot(L_μ,Prior,
	xlim = (1,5), ylim = (0, 1),
	label = false,
	xlabel = latexstring("\\mu"),
	ylabel = latexstring("P\\,(\\mu)"),		
	title = "Prior probabilities"
	)
	plot!(size=(400,200))
end

# ╔═╡ 4b6c15b2-7ac8-42cf-8c6b-070ae19405bd
md"""
### Posterior
_now you can study how the posterior probability_ $P(\mu\;| \overline{\boldsymbol{R}}, \mathcal{N} )$
depends on the sample rating-mean $\overline{\boldsymbol{R}}$, the sample size (# of votes) $\mathcal{N}$
and your prior choice
(_remember_  $\boldsymbol{\mathcal{R}} = \mathcal{N}\overline{\boldsymbol{R}}$)

-------------


rating $\overline{\boldsymbol{R}}$:    $(@bind 	mean_r Scrubbable(1.0:0.05:5, default=4.5)) 


number of votes $\mathcal{N}$: $(@bind 	N Slider(1:250, show_value=true,default=80)) 


Parameters for prior probability (flat prior: ``\alpha = \beta = 1``):

 ``\alpha``:    $slider_α     
 ``\beta``:    $slider_β     
      (_to change the values, click and pull the numbers_) 
"""

# ╔═╡ 1b9848f0-7a4a-4916-b7df-ffcd61c39415
begin
	# compute posterior 
	R       = N * mean_r
	L_ln_P 	= R * L_𝜆 .- N * log.(L_Z) .- log.(Prior)
	L_ln_P  = L_ln_P .- maximum(L_ln_P)
	L_P     = exp.(L_ln_P)
	L_P     = L_P/(sum(L_P)*μ_Delta)
    md"### compute posterior "
end

# ╔═╡ 7cde88e1-a4c0-4541-aa8d-61845b479192
begin
    # plot posterior	
	txt    = "Posterior probability "
	plot2  = plot(L_μ,L_P,
	label  = false,
	xlabel = latexstring("\\mu"),
	ylabel = latexstring("P\\, (\\mu |  \\textbf{R}, \\mathcal{N})"),
	title  = txt,
	ylim   = (0, 6)
	)
	plot(plot1,plot2,layout = (1, 2))
		plot!(size=[600,300])
end

# ╔═╡ 9096d5fe-ee6b-4842-ac4b-0fd8a421db32
begin
	mean_rating = sum(L_μ.*L_P)
	stdeviation = sqrt(sum((L_μ .-mean_rating).^2 .*L_P))
	string(round(mean_rating, digits=3))*"±"*string(round(stdeviation,digits=2))
	md"### mean rating"
end

# ╔═╡ eb0a9de2-48b4-4220-abfc-433ce87c879c
function sr(variable, dig = 2)
	# string and round - converts a variable into a string with the predifined precission - to be extended to scientific and other formats
	if dig == 0
		return string(round(Int, variable))
	else
		return string(round(variable, digits = dig))
	end
end

# ╔═╡ 43389709-7d95-4d06-a284-a532b3d23dee
begin
	
	#plotting for video
	title_mu_plots = latexstring("\\overline{\\boldsymbol{R}} = " * string(round(mean_r,digits=2)) * ",\\, \\mathcal{N} = "*string(round(Int,N)))
	
	plot(plot2,size=(600,400), 
	xlabel = latexstring("\\mu_{\\textrm{copper}}"),
	labelfontsize = 20,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,
		linewidth = 3,
	#title = title_mu_plots,
	titlefontsize = 20,
	background_color = :transparent,
	fontfamily="Computer Modern",
		ylim = [0,2],
		label=latexstring("\\overline{\\mathbf{R}} = "* sr(mean_r,2) * ", \\mathcal{N} = "* sr(N,0) ),
		legendfontsize = 15,
		leg = :topleft,

		
		
	)
	#savefig("C://Lehre//Bayes MOOC//Lesson 6//Images//posterior_copper")
	
	# copper: 
	
end

# ╔═╡ f1586893-5fe6-4202-801b-80fda48511bc
begin
bind_prior = @bind rr Slider(1.00:0.001:4.999, default=2.0)
	nothing
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

[compat]
Images = "~0.25.0"
LaTeXStrings = "~1.3.0"
Plots = "~1.24.0"
PlutoUI = "~0.7.20"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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version = "0.13.4"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.3"

[[InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.2"

[[IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"

[[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"

[[JLD2]]
deps = ["DataStructures", "FileIO", "MacroTools", "Mmap", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
git-tree-sha1 = "46b7834ec8165c541b0b5d1c8ba63ec940723ffb"
uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
version = "0.4.15"

[[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 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[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 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.9"

[[LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"

[[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"

[[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"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.5"

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

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "5455aef09b40e5020e1520f551fa3135040d4ed0"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+2"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.9"

[[MappedArrays]]
git-tree-sha1 = "e8b359ef06ec72e8c030463fe02efe5527ee5142"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.1"

[[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"

[[MetaGraphs]]
deps = ["Graphs", "JLD2", "Random"]
git-tree-sha1 = "2af69ff3c024d13bde52b34a2a7d6887d4e7b438"
uuid = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
version = "0.7.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

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

[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.3"

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

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

[[NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "16baacfdc8758bc374882566c9187e785e85c2f0"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.9"

[[Netpbm]]
deps = ["FileIO", "ImageCore"]
git-tree-sha1 = "18efc06f6ec36a8b801b23f076e3c6ac7c3bf153"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.0.2"

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

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "043017e0bdeff61cfbb7afeb558ab29536bbb5ed"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.8"

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

[[OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
version = "0.3.2"

[[OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "923319661e9a22712f24596ce81c54fc0366f304"
uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
version = "3.1.1+0"

[[OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"

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

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+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"

[[PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "6d105d40e30b635cfed9d52ec29cf456e27d38f8"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
version = "0.3.12"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "646eed6f6a5d8df6708f15ea7e02a7a2c4fe4800"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.10"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.3"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.1.2"

[[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"

[[PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
version = "0.1.1"

[[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 = "b084324b4af5a438cd63619fd006614b3b20b87b"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.15"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
git-tree-sha1 = "02a083caba3f73e42decb810b2e0740783022978"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.24.0"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "1e0cb51e0ccef0afc01aab41dc51a3e7f781e8cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.20"

[[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"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.1"

[[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"

[[RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.2"

[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.4.1"

[[Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[RegionTrees]]
deps = ["IterTools", "LinearAlgebra", "StaticArrays"]
git-tree-sha1 = "4618ed0da7a251c7f92e869ae1a19c74a7d2a7f9"
uuid = "dee08c22-ab7f-5625-9660-a9af2021b33f"
version = "0.3.2"

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

[[Rotations]]
deps = ["LinearAlgebra", "Random", "StaticArrays", "Statistics"]
git-tree-sha1 = "6a23472b6b097d66da87785b61137142ac104f94"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.4"

[[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"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[SimpleWeightedGraphs]]
deps = ["Graphs", "LinearAlgebra", "Markdown", "SparseArrays", "Test"]
git-tree-sha1 = "a6f404cc44d3d3b28c793ec0eb59af709d827e4e"
uuid = "47aef6b3-ad0c-573a-a1e2-d07658019622"
version = "1.2.1"

[[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"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "e08890d19787ec25029113e88c34ec20cac1c91e"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.0.0"

[[StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
version = "0.1.1"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.4.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.13"

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

[[StatsAPI]]
git-tree-sha1 = "0f2aa8e32d511f758a2ce49208181f7733a0936a"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.1.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.13"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.3"

[[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 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

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

[[TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

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

[[TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "c342ae2abf4902d65a0b0bf59b28506a6e17078a"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.5.2"

[[TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "5683455224ba92ef59db72d10690690f4a8dc297"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
version = "0.3.1"

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[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"

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[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"

[[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"

[[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"
"""

# ╔═╡ Cell order:
# ╟─9428fba4-67b3-4d2f-a09f-7dc5f28deadd
# ╟─5210a326-7b34-11eb-0d14-67f67a882d68
# ╟─8240f678-7b35-11eb-1a68-bb2b66ce0d04
# ╟─852d6e36-7b31-11eb-0653-61bcf655249d
# ╟─b033b45c-7b28-11eb-1216-5703dc0e7792
# ╟─a0e51c0c-7b2f-11eb-2c1c-a77cfaf645f7
# ╟─0649912d-5164-4709-ad64-ca79b5256bf3
# ╟─f1646630-8507-4967-beab-a61c2f26bd17
# ╟─d22311d9-c2c5-4dbd-be38-a377c6b19c37
# ╟─f6a34d0c-2591-45f9-baac-f58fd5eace8b
# ╟─cdf3d720-bc21-44f5-976e-87fb5d8ed64b
# ╟─53365c4a-b00a-4bdf-8314-9ab9dbd19db6
# ╟─4b6c15b2-7ac8-42cf-8c6b-070ae19405bd
# ╟─7cde88e1-a4c0-4541-aa8d-61845b479192
# ╟─74a7a904-f043-4a69-93ea-2483d9eb0826
# ╟─44ea4b68-20d0-4f67-95d6-4228c9174c2b
# ╟─43389709-7d95-4d06-a284-a532b3d23dee
# ╟─8102cbf7-e2ad-4492-9756-278fb8d072e7
# ╟─9345ab4c-69f9-47b2-a1a4-388adeb4f74c
# ╟─033db041-4b66-4a4f-a063-1b7d310c232c
# ╟─3bcf9ac2-213d-44fe-b8b5-8b54695c3029
# ╟─1b9848f0-7a4a-4916-b7df-ffcd61c39415
# ╟─9096d5fe-ee6b-4842-ac4b-0fd8a421db32
# ╟─248a131d-49c7-45cd-8e30-527386e317f5
# ╟─a22bf9fc-7b28-11eb-30c1-0fa6d84c74d1
# ╟─4c48af3c-dac8-43d4-9a57-7fed5052300a
# ╟─eb0a9de2-48b4-4220-abfc-433ce87c879c
# ╟─f1586893-5fe6-4202-801b-80fda48511bc
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
