bus_econ_hw.jl

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

using Markdown
using InteractiveUtils

# ╔═╡ ba28b0cc-b900-4bbb-8d40-6f628779bcb9
using Random, Pluto, Distributions, DataFrames, StatsBase, FreqTables, VegaLite, StatsPlots, Plots, PrettyTables

# ╔═╡ e80226ba-8932-47a0-b5bc-fec9a2e3e482
md"10000 individuals, J+1 = 9 products, set parameters"

# ╔═╡ 11280580-0b32-4b1d-9c29-814004a608e6
begin
	I = 10000
	J = 8
	β = 1
	α = 1
end

# ╔═╡ 1a26ca12-8e66-47d0-8b53-e404a4f91762
df = DataFrame(
    i = repeat(1:I, J+1), 
    j = repeat(0:J, I),
    ϵ = rand(GeneralizedExtremeValue(0,1,0), 90000),
    u = repeat(zeros(Float64,1), 90000),
    chosen1 = repeat(zeros(Float64, 1), 90000)
)

# ╔═╡ f917ad47-f5e6-43a8-be02-a7fa2433d4f0
# Define necessary functions

begin
	function price(j)
		if j == 9
			p = 10
		else
			p = 10 .- j/2
		end
    return p
	end


	function xi(j)
		if j == 9
	    	ξ = 8
		else
			ξ = j/5
		end
	    return ξ
	end

	function value(j)
		if j == 9
	    	x = 3
		else
			x = 10 .- j/10
		end
	    return x
	end

	function indicator(x,y)
    if x .≥ y .≥ 0
        dummy = 1
    else 
        dummy = 0
    end

    return dummy
	end

	function cs(df, utility, market_share,α=1)
    	surplus = df.utility / df.α * df.market_share ./ 100

    return surplus
	end

	function cond_utility(chosen, utility)
		cond_u = sum(chosen .* utility) ./ sum(chosen)
		return cond_u
	end
end

# ╔═╡ ca6f68da-cd56-43b8-b1a7-7006053cecf8
# Transform DF by adding price, x, and ξ
begin
transform!(df, :j => price => :p)
transform!(df, :j => xi => :ξ)
transform!(df, :j => value => :x)
end

# ╔═╡ fdb1cecb-36e1-410e-9c0f-4c3211d384eb
# utility
begin
	df.u = β .* df.x .- α .* df.p .+ df.ξ .+ df.ϵ
	df
end

# ╔═╡ f0e318ee-e814-45cb-8bb7-93eb3a673b7e
# Group by individual calculate maximumⱼ(uᵢⱼ)
transform!(groupby(df, :i), :u => maximum => :u_maximum)

# ╔═╡ 90f106bc-4e36-4e9e-9aa2-43aff3737ddf
# make chosen = 1 if uᵢⱼ = maximumⱼ(uᵢⱼ)
df.chosen1 = df.u .== df.u_maximum .≥ 0

# ╔═╡ 154f213b-c3e2-4578-88b0-0c5a6ced2310
# How many consumers choose each good j?
freqtable(df, :chosen1, :j)

# ╔═╡ 4aa87e62-a845-42c0-92f9-4bbd69c1fda5
md"""
***
Now let's look at how things change when α ~ LogNormal(0.3, √0.1)
"""

# ╔═╡ 153ac234-3659-45b7-9ebc-a44d4a51be6b
# initialize dataframe
params = DataFrame(
    i = repeat(1:I, J+1), 
    j = repeat(0:J, I),
    α = repeat(rand(LogNormal(0.3, sqrt(0.10)), I), J+1),
    new_u = repeat(zeros(Float64, 1), 90000)
)

# ╔═╡ ce64f43b-05a0-4818-bcb6-0b1c14127847
# Checking that α was correctly calculated; it should be the same for a given i
sort(params, order(:i))

# ╔═╡ e2fd7649-857b-4062-bbf9-977c1fe8a0b9
# form df for Q2 and rename chosen1 to chosen 2
q2_df = rename(select(leftjoin(df, params, on = [:i, :j]), Not([:u, :u_maximum])), :chosen1 => :chosen2)

# ╔═╡ d73b870a-7c83-46bd-a980-2b83fdfd4692
# Generate new_u
begin
	q2_df.new_u = β .* q2_df.x .- q2_df.α .* q2_df.p .+ q2_df.ξ .+ q2_df.ϵ
	q2_df
end

# ╔═╡ 51527d78-c1d7-4923-97ea-9bedbe147ee4
begin 
# we see that α and new_u are of type Float64?; change them to Float64
	q2_df[!, :α] = convert.(Float64, q2_df[:, :α])
	q2_df[!, :new_u] = convert.(Float64, q2_df[:, :new_u])
end

# ╔═╡ 35aad317-8a50-4d8a-8d3c-b76e94bfce6d
# Group by individual, calculate maximumⱼ(uᵢⱼ)
transform!(groupby(q2_df, :i), :new_u => maximum => :new_u_maximum)

# ╔═╡ 4d92cfed-6d18-440a-b141-dc35baffa5c5
# create chosen2 for q2_df
q2_df.chosen2 = q2_df.new_u .≥ q2_df.new_u_maximum .≥ 0

# ╔═╡ 2867033b-4fa5-4a98-a4d0-f87e21c12fa7
md"Let's compare the product choices"

# ╔═╡ 53b5ed1d-4fd2-4589-802c-b137b20d9aba
begin
	q1_choices = combine(groupby(filter(row -> row.chosen1 .== true, df), [:j]), nrow => :purchases)
	pretty_table(q1_choices)
end

# ╔═╡ 621933bd-651e-44b7-99e5-bf1ac197261c
begin
	q2_choices = combine(groupby(filter(row -> row.chosen2 .== true, q2_df), [:j]), nrow => :purchases)
	pretty_table(q2_choices)
end

# ╔═╡ 7911e666-77a0-40ac-bb20-4a74b90e8905
# Calculate utility: = 0 if no purchase, otherwise equals the utility conditonal on purchasing
transform!(q2_df, [:chosen2, :new_u] => ((x,y) -> x .* y) => :new_u_given_purchase)

# ╔═╡ 939a1ce2-262b-48e5-be5f-b94867ff3d39
transform!(df, [:chosen1, :u] => ((x,y) -> x .* y) => :u_given_purchase)

# ╔═╡ e0ae73b2-edf5-4ef1-afad-e6711ebac405
# Filter so that only rows where chosen ==1 
begin
df_purchased = filter(row -> row.chosen1 ==true, df)
q2_df_purchased = filter(row -> row.chosen2 ==true, q2_df)
end

# ╔═╡ eda75465-c037-4590-a03e-8166b23e6e3c
simulated_utility_lnormal = histogram(q2_df_purchased.new_u_given_purchase, label = "αᵢ ~ LogNormal(0.3, √(0.1)", xlabel = "Simulated Utility, Conditional on Purchasing", normalize = true)

# ╔═╡ 34264042-3536-45cb-a5cd-cce9df948590
simulated_utility_both = histogram!(df_purchased.u_given_purchase, label = "α = 1", normalize = true, fillalpha = 0.8)

# ╔═╡ c54a5928-04c9-4c72-afc5-b29250b59ff9
# Combine df and q2_df, group by j and find the total number of customers who purchase
begin
	df_summary = combine(groupby(df_purchased, :j), :chosen1 => sum, :u_given_purchase => mean, :p => mean)
	
	q2_df_summary = combine(groupby(q2_df_purchased, :j), :chosen2 => sum, :α => mean, :new_u_given_purchase => mean, :p => mean)

	summary = leftjoin(df_summary, q2_df_summary, on = [:j, :p_mean])
end

# ╔═╡ 939f556f-c2ca-4caf-8da0-8948d265e270
# Calculate market shares (note the market is *not* covered with the LogNormal α)
begin
	transform!(summary, :chosen1_sum => (x -> 100x / sum(x)) => :market_share1)
	transform!(summary, :chosen2_sum => (x -> 100x / sum(x)) => :market_share2)
	summary.cum_market_share1 = cumsum(summary.market_share1)
	summary.cum_market_share2 = cumsum(summary.market_share2)
	summary.cum_chosen1 = cumsum(summary.chosen1_sum)
	summary.cum_chosen2 = cumsum(summary.chosen2_sum)
	summary.market_share2 = round.(summary.market_share2, digits = 2)
	summary.market_share1 = round.(summary.market_share1, digits = 2)
end

# ╔═╡ 4d6039df-91fe-40b4-9481-ace40a0e1e61
# check that market shares add to 100
sum(summary.market_share1)

# ╔═╡ 687bd8e4-45c5-4cd9-909a-22a18f12c918
sum(summary.market_share2) #checks out

# ╔═╡ 27480f11-e7c1-470b-8bb2-f0f30b406f2a
md"""
But some consumers under scenario 2 are not purchasing any good!

Let's see how many actually choose to purchase:
"""

# ╔═╡ 10fa4fcb-ce99-47cb-8cc9-164e39f30563
sum(summary.chosen2_sum)

# ╔═╡ d7c1ab26-1ba9-41b0-9a15-438bd5b6a568
begin
	α_histogram = histogram(q2_df.α, xaxis = "α", label = "Simulated α", normalize = true)
	# Fit α to a Log Normal Distribution
	fitted_α = fit(LogNormal, q2_df.α)
	distr_α = Distributions.params(fitted_α)
	plot!(LogNormal(distr_α[1], distr_α[2]), label = "True Log Normal Density", normalize = true, fill = true, alpha = 0.5)
end

# ╔═╡ ae51fc4d-e866-4d17-b799-916b65d35b92
md"What happens if we assume that utility is normally distributed?"

# ╔═╡ 1f9eed48-c129-4761-bc0d-1228d2d357cf
begin
	fitted_new_u_given_purchase = fit(Normal, q2_df_purchased.new_u_given_purchase)
	distr_new_u_given_purchase = Distributions.params(fitted_new_u_given_purchase)

	fitted_u_given_purchase = fit(Normal, df_purchased.u_given_purchase)
	distr_u_given_purchase = Distributions.params(fitted_u_given_purchase)
	
	utility_normal_plot = plot(Normal(distr_new_u_given_purchase[1], distr_new_u_given_purchase[2]), label = "U | α ~ LogNormal", fill = true, alpha = 0.5)
	plot!(Normal(distr_u_given_purchase[1], distr_u_given_purchase[2]), label = "U | α = 1", fill = true, alpha = 0.5)
end

# ╔═╡ 04ac0744-57cf-46c7-81b4-b205d9fdd593
md"""
The estimated choice probabilities are the same as the aggregate market shares

Let's take a look:
"""

# ╔═╡ e4a3299c-9c2e-40fc-a116-a62e6856ff40
begin
	market_share_ln_vs_1= plot(summary.j, summary.market_share2, label = "α ~ LogNormal", legend = :topleft)
	plot!(summary.j, summary.market_share1, label = "α = 1")
	ylabel!("Market Share")
	xlabel!("j")
end

# ╔═╡ c01df32a-b39a-4989-bc16-91724ffa1cc9
begin
	utility_vs_α = plot(summary.α_mean, summary.new_u_given_purchase_mean, seriestype = :scatter, ylims = (0, maximum(summary.new_u_given_purchase_mean) + 2), label = "utility | purchase")

	xlabel!("α")
	ylabel!("Utility | Purchase")
end

# ╔═╡ 625a3680-2ef1-4f63-b151-a949b5c00b74
md"""
***
Now let's look at question 3:
"""

# ╔═╡ 2ec78271-81b1-439d-abb8-b586c83a806f
# Question 3
q3_df = DataFrame(
    i = repeat(1:I, 1), 
    j = repeat([9], I),
	ϵ = rand(GeneralizedExtremeValue(0,1,0), 10000),
	chosen = repeat([false], 10000),
	α = unique(q2_df, α).α,
	x = repeat([3.0], 10000),
	ξ = repeat([8.0], 10000),
	p = repeat([10.0], 10000),
	new_u = repeat([0.0], 10000)
)

# ╔═╡ 807778f6-49c1-43ac-982a-06e1d67fc433
# Calculate utility
begin
	q3_df.new_u = β .* q3_df.x .- q3_df.α .* q3_df.p .+ q3_df.ξ .+ q3_df.ϵ
	q3_df
end

# ╔═╡ 40ce5598-c400-4815-a521-dfb10c45acc8
names(q3_df)

# ╔═╡ bbf5635e-f283-4f73-b72d-fe11f452a9ec
names(q2_df)

# ╔═╡ 5d40fc26-aa5f-4aeb-b681-2c13f0cb2a0d
q4_df = append!(
	q3_df,
	select(
		rename(q2_df, :chosen2 => :chosen), 
		Not([:new_u_maximum, :new_u_given_purchase])
	)
)

# ╔═╡ 32f1cb93-f10f-4926-8406-6f9aa28a569f
describe(q4_df)

# ╔═╡ 16187462-3f7f-4d08-b9fa-4643e8c1074c
# Group by individual, calculate maximumⱼ(uᵢⱼ)
transform!(groupby(q4_df, :i), :new_u => maximum => :new_u_maximum)

# ╔═╡ 41c5a94b-5f4c-4fb4-ad2a-fc2ed0d7580a
# rename!(q2_df, :chosen => :chosen2)
q4_df.chosen = q4_df.new_u .== q4_df.new_u_maximum .≥ 0

# ╔═╡ 623b1ac9-28fe-4121-a5f1-23dc303454e5
transform!(q4_df, [:chosen, :new_u] => ((x,y) -> x .* y) => :new_u_given_purchase)

# ╔═╡ aea29755-d83a-41f9-9cc7-c463d4bf011f
q4_df_purchased = filter(row -> row.chosen ==1.0, q4_df)

# ╔═╡ fce2c865-3a3b-419c-a4bc-cdcb1e76299d
freqtable(q4_df, :chosen, :j)

# ╔═╡ d43d88ba-c16f-4be6-aca5-babd92917480
q4_df_summary = combine(groupby(q4_df_purchased, :j), :chosen => sum, :α => mean, :new_u_given_purchase => mean)

# ╔═╡ c9173715-88c2-4ed3-ab0e-f4c7091d58cd
begin
	transform!(q4_df_summary, :chosen_sum => (x -> 100x / sum(x)) => :market_share)
	q4_df_summary.cum_chosen = cumsum(q4_df_summary.chosen_sum)
	q4_df_summary.market_share = round.(q4_df_summary.market_share, digits = 2)
end

# ╔═╡ ee0ccd8e-bf3c-4993-8d97-6c5b0ed10422
md"Now have to do the same steps to combine the new data with the original df"

# ╔═╡ 799493e6-6190-49d6-83a2-975d5b042d63
# add α column to original df
df[:,"α"] = repeat([1.0], 90000)

# ╔═╡ 2d5fec2b-f4b8-4dbf-9ac5-de4416678170
names(df)

# ╔═╡ f1baa106-9524-426d-9afe-e31375493bb9
q5_df = append!(
	(DataFrame(
    i = repeat(1:I, 1), 
    j = repeat([9], I),
	ϵ = rand(GeneralizedExtremeValue(0,1,0), 10000),
	chosen = repeat([0.0], 10000),
	α = repeat([1.0], 10000),
	x = repeat([3.0], 10000),
	ξ = repeat([8.0], 10000),
	p = repeat([10.0], 10000),
	u = repeat([0.0], 10000)
)),
	select(
		rename(df, :chosen1 => :chosen), 
		Not([:u_given_purchase, :u_maximum])
	)
)

# ╔═╡ 6667d7ca-aebe-4a76-96c9-be4ded0872e5
q5_df.u = β .* q5_df.x .- q5_df.α .* q5_df.p .+ q5_df.ξ .+ q5_df.ϵ

# ╔═╡ cdbdfdd6-8d37-4621-82d8-5f2389722045
# Group by individual, calculate maximumⱼ(uᵢⱼ)
transform!(groupby(q5_df, :i), :u => maximum => :u_maximum)

# ╔═╡ 7957c107-d1a9-479e-ae2a-5e1c208ab14c
# rename!(q5_df, :chosen => :chosen2)
q5_df.chosen = q5_df.u .≥ q5_df.u_maximum .≥ 0

# ╔═╡ 89a5c551-b5de-4784-a7fe-e534b9372073
transform!(q5_df, [:chosen, :u] => ((x,y) -> x .* y) => :u_given_purchase)

# ╔═╡ 2c491612-bc63-4ca8-bfbe-a628e0a78b8f
begin
	q5_df_summary = combine(groupby(filter(row -> row.chosen ==1.0, q5_df), :j), :chosen => sum, :α => mean, :u_given_purchase => mean, :p => mean)
	q5_df_summary.cum_chosen = cumsum(q5_df_summary.chosen_sum)
end

# ╔═╡ 847226a5-c264-4a1c-a767-78d007b94934
transform!(q5_df_summary, :chosen_sum => (x -> 100x / sum(x)) => :market_share)

# ╔═╡ f4efcbe1-180e-4fa6-813e-6b0fdf0acf0a
md"""
It looks like CS gain is slightly higher under the first model with α = 1, but only because total welfare is higher in that scenario. 

The percentage change is actually higher on scenario two; however, the change is negligible:
"""

# ╔═╡ 9ae79f5b-7c09-49a4-b480-9738c044eb96
wellfare_gain_cons_percent = (sum(q5_df_summary.chosen_sum .* q5_df_summary.u_given_purchase_mean ./ q5_df_summary.α_mean) - sum(df_summary.chosen1_sum .* df_summary.u_given_purchase_mean))./sum(df_summary.chosen1_sum .* df_summary.u_given_purchase_mean).*100

# ╔═╡ 0c18d990-5406-4099-96ed-42da12d29680
wellfare_gain_uncertainty_percent = (sum(q4_df_summary.chosen_sum .* q4_df_summary.new_u_given_purchase_mean ./ q4_df_summary.α_mean) - sum(q2_df_summary.chosen2_sum .* q2_df_summary.new_u_given_purchase_mean ./ q2_df_summary.α_mean)) ./ sum(q2_df_summary.chosen2_sum .* q2_df_summary.new_u_given_purchase_mean ./ q2_df_summary.α_mean) .* 100

# ╔═╡ 4bc4f6a8-c72e-4b18-b97d-355ee2b082f6
md"Time to look at some graphs"

# ╔═╡ 847917f8-2684-4315-8575-9736d43c39e3
begin
	market_share_plot = plot(legend = :top)
	plot!(q5_df_summary.j, q5_df_summary.market_share,label = "J = 9, α = 1", lw = 3, la = 0.7)
	plot!(df_summary.j, summary.market_share1, lw = 3, ls = :dash, la = 0.8, label = "J = 8, α = 1")
	plot!(q4_df_summary.j, q4_df_summary.market_share, lw = 3, la = 0.6, label = "J=9, α~LNorm")
	plot!(summary.j, summary.market_share2, lw = 3, ls = :dash, la = 0.8, label = "J=8, α~LNorm")
	xlabel!("J")
	ylabel!("Market Share (%)")
end

# ╔═╡ c2e66fe8-0b0c-4617-9a98-9908c9fcfe42
begin
	cumsum_purchases_plot = plot(legend = :left, legendfontsize = 9)
	plot!(q5_df_summary.j, cumsum(q5_df_summary.chosen_sum), label = "J=9, α=1", lw = 4, la = 0.5)
	plot!(df_summary.j, cumsum(summary.chosen1_sum), ls = :dash, lw = 4, label = "J=8, α=1")
	plot!(q4_df_summary.j, cumsum(q4_df_summary.chosen_sum), lw = 4, la = 0.5, label = "J=9, α~LNorm")
	plot!(summary.j, cumsum(summary.chosen2_sum), ls = :dash, lw = 4, label = "J=8, α ~ LNorm")
	xlabel!("J")
	ylabel!("Cumulative Sum of Number of Purchases")
end

# ╔═╡ 611ee000-36fa-4c65-b7a1-ba1dcb8e0a10
q1_df = transform(df, [:u, :ϵ] => ((x,y) -> x .- y) => :δ)

# ╔═╡ 850285f0-db39-4077-8cc5-d2a934251093
q1_df.exp_δ = exp.(q1_df.δ)

# ╔═╡ de6f9175-314a-4ca2-b03b-441b7be7d429
# Calculate the sum of exp(δⱼ) ∀ j. Add to q1_df
transform!(groupby(q1_df, :i), :δ => (x -> sum(exp.(x))) => :sum_exp_δⱼ)

# ╔═╡ ea67d5de-15a5-430d-81e3-2907dbea1823
# Calculate choice probabilities by logit instead of by market share

transform!(groupby(q1_df, :j), [:exp_δ, :sum_exp_δⱼ] => ((x,y) -> round.(100 .* x ./ (1 .+ y), digits = 2)) => :prob)

# ╔═╡ ec25c08c-df0d-4e57-8ff1-3673f64797dd
q1_summary = combine(groupby(q1_df, :j), :prob => mean)

# ╔═╡ 83281bef-80a8-40ef-80d4-84015afdbab4
pretty_table(q1_summary)

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[[KernelDensity]]
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[[LAME_jll]]
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[[LZO_jll]]
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[[LaTeXStrings]]
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[[Latexify]]
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[[LazyArtifacts]]
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[[LibCURL]]
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[[LibCURL_jll]]
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[[LibGit2]]
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[[LibSSH2_jll]]
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libmount_jll]]
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[[MKL_jll]]
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[[Markdown]]
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[[MbedTLS]]
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[[MbedTLS_jll]]
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[[Measures]]
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[[MozillaCACerts_jll]]
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[[Ogg_jll]]
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[[OpenSSL_jll]]
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[[OpenSpecFun_jll]]
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[[Opus_jll]]
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[[PCRE_jll]]
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[[PlotThemes]]
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[[SHA]]
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[[Scratch]]
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git-tree-sha1 = "eb007bb78d8a46ab98cd14188e3cec139a4476cf"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.14.28"

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

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

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

[[TableIOInterface]]
git-tree-sha1 = "9a0d3ab8afd14f33a35af7391491ff3104401a35"
uuid = "d1efa939-5518-4425-949f-ab857e148477"
version = "0.1.6"

[[TableOperations]]
deps = ["SentinelArrays", "Tables", "Test"]
git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.2.0"

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

[[TableTraitsUtils]]
deps = ["DataValues", "IteratorInterfaceExtensions", "Missings", "TableTraits"]
git-tree-sha1 = "78fecfe140d7abb480b53a44f3f85b6aa373c293"
uuid = "382cd787-c1b6-5bf2-a167-d5b971a19bda"
version = "1.0.2"

[[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"

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

[[URIParser]]
deps = ["Unicode"]
git-tree-sha1 = "53a9f49546b8d2dd2e688d216421d050c9a31d0d"
uuid = "30578b45-9adc-5946-b283-645ec420af67"
version = "0.4.1"

[[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"

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

[[Vega]]
deps = ["DataStructures", "DataValues", "Dates", "FileIO", "FilePaths", "IteratorInterfaceExtensions", "JSON", "JSONSchema", "MacroTools", "NodeJS", "Pkg", "REPL", "Random", "Setfield", "TableTraits", "TableTraitsUtils", "URIParser"]
git-tree-sha1 = "43f83d3119a868874d18da6bca0f4b5b6aae53f7"
uuid = "239c3e63-733f-47ad-beb7-a12fde22c578"
version = "2.3.0"

[[VegaLite]]
deps = ["Base64", "DataStructures", "DataValues", "Dates", "FileIO", "FilePaths", "IteratorInterfaceExtensions", "JSON", "MacroTools", "NodeJS", "Pkg", "REPL", "Random", "TableTraits", "TableTraitsUtils", "URIParser", "Vega"]
git-tree-sha1 = "3e23f28af36da21bfb4acef08b144f92ad205660"
uuid = "112f6efa-9a02-5b7d-90c0-432ed331239a"
version = "2.6.0"

[[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"

[[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"

[[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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