### 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

# ╔═╡ 53cbed91-a234-4e33-95c0-9b4a750c39ba
begin
	#try
		using Random
		using PlutoUI
		using Plots
		using Markdown
		using LaTeXStrings
		using InteractiveUtils
		using Statistics
		using StatsBase
		using Printf
		md""" 
		### - Packages
		
		All needed Packages available :) """
	#=
	catch
		using Pkg;
		Pkg.activate(mktempdir())
		Pkg.add("Random")
		Pkg.add("PlutoUI")
		Pkg.add("Plots")
		Pkg.add("LaTeXStrings")
		Pkg.add("Markdown")
		Pkg.add("InteractiveUtils")
		Pkg.add("Statistics")
		Pkg.add("StatsBase")
		Pkg.add("Printf")
		#Pkg.add("LinearAlgebra")
		#Pkg.add("SparseArrays")
		#Pkg.add("SpecialFunctions")
		#Pkg.add("StatsBase")
		#Pkg.add("Distributions")
		using Random
		using PlutoUI
		using Plots
		using Markdown
		using LaTeXStrings
		using InteractiveUtils
		using Statistics
		using StatsBase
		using Printf
		md""" 
		### - Packages
		
		Some Package sources not added, this will take approx. 3 minutes"""
	end
	=#
	
end

# ╔═╡ 36ebbc95-ca82-4e64-978c-7b51d0cd61ee
TableOfContents(aside = true)

# ╔═╡ b2ef74b7-fa8f-4647-a48c-8177395f55b2
md"# Nested Sampling 🎯

The goal of nested sampling is the evaluaiton of high-dimensional integrals of the form

$I = \int dV_{\vec x} f(\vec x)  p(\vec x)\;,$

where $p(\vec x)$ is the prior pdf.

As a simple example to illustrate the algorithm we use a 1D problem with uniform prior and 

$f(x) = \exp\bigg(-\frac{(x -x_1)^2}{2 \sigma_1^2}\bigg) + 1.5\; \exp\bigg(-\frac{(x -x_2)^2}{2 \sigma_2^2}\bigg)$

The exact result is $I = \sqrt{2 \pi \sigma_1^2} + 1.5\; \sqrt{2 \pi \sigma_2^2}$
## - Follow the algorithm step by step 🕵🏻‍♀️"

# ╔═╡ 93315217-1dd9-4a50-abeb-ef5ad5cf44ef
md"## - Check the integral"

# ╔═╡ 4659617d-b2ae-4e08-94e6-3ef71bcbf48e
md"# Auxiliary stuff"

# ╔═╡ fc692905-354b-4519-8956-f340b83ad661
md"""
## About the creators

This notebook was created by **Prof. Wolfgang von der Linden** and **Gerhard Dorn** in the context of the course **Bayesian probability theory**.

The course is a free massive open online course (MOOC) available on the platform [`IMOOX`](https://imoox.at/mooc/local/landingpage/course.php?shortname=bayes&lang=en)

$(Resource("https://raw.githubusercontent.com/Captain-Bayes/images/main/adventure_map.gif"))
"""

# ╔═╡ 54e74311-1892-4120-b58f-e2cf0dc28016

ClickCounterWithReset(text="Click", reset_text="Reset") = HTML("""
<div>
<button>$(text)</button>&nbsp;&nbsp;&nbsp;&nbsp;
<a id="reset" href="#">$(reset_text)</a>
</div>
<script id="blabla">
// Select elements relative to `currentScript`
const div = currentScript.previousElementSibling
const button = div.querySelector("button")
const reset = div.querySelector("#reset")
// we wrapped the button in a `div` to hide its default behaviour from Pluto
let count = 0
button.addEventListener("click", (e) => {
	count += 1
	
	div.value = count
	div.dispatchEvent(new CustomEvent("input"))
	e.stopPropagation()
})
	reset.addEventListener("click", (e) => {
	count = 0
	
	div.value = count
	div.dispatchEvent(new CustomEvent("input"))
	e.stopPropagation()
	e.preventDefault()
})
// Set the initial value
div.value = count
</script>
""")
	


# ╔═╡ 98567be3-d02e-4b32-b760-e25bd185c8d5
begin
	md"""$(@bind counter ClickCounterWithReset("NEXT STEP", "RESET"))"""
	#md"""Increase the steps 👉$(@bind counter NumberField(0:40; default=0))"""
	
end

# ╔═╡ 2f3bb4ef-2239-4617-b9fd-f6cffd0653e4
begin

	hint(txt1,text)   = Markdown.MD(Markdown.Admonition("hint",txt1, [text]))		
	danger(txt1,text) = Markdown.MD(Markdown.Admonition("danger", txt1, [text]))
	note(txt1,text) = Markdown.MD(Markdown.Admonition("note", txt1, [text]))
	tip(txt1,text) = Markdown.MD(Markdown.Admonition("tip", txt1, [text]))
	hintx(txt1)   = Markdown.MD(Markdown.Admonition("hint",txt1, []))	
	dangerx(txt1) = Markdown.MD(Markdown.Admonition("danger", txt1, []))	
	notex(txt1) = Markdown.MD(Markdown.Admonition("note", txt1, []))	
	tipx(txt1) = Markdown.MD(Markdown.Admonition("tip", txt1, []))
	
	wrong = Markdown.MD(Markdown.Admonition("danger", "😞 sorry, not correct", []))	
	select = Markdown.MD(Markdown.Admonition("note","🤔 please select", []))	
	correct = Markdown.MD(Markdown.Admonition("beware", "👍 great  🏆", []))	
	md"### - admonitions"
end

# ╔═╡ de042b85-4f4d-447f-8ec3-8406ca031718
begin
	x0 = 0.0
	𝜎_1  = 0.2
	𝜎_2  = 0.1
	f_𝜎_1 = 1/(2*𝜎_1^2)
	f_𝜎_2 = 1/(2*𝜎_2^2)	

	
	x_max = 2
	Nclim = 30 # number of single steps

	Ω = x_max 	
	
	
	

	md"### - initial values"
end

# ╔═╡ 627e437a-c271-4098-920e-12becf65b79c
begin
	flag_integral_checkbox = @bind flag_integral CheckBox()
	flag_prior_mass_checkbox = @bind flag_prior_mass CheckBox()
	seed_2_slider = @bind seed2 Slider(1:200, show_value=true,default=123)
	N_wi_slider = @bind N_wi Slider(1:200, show_value=true,default=100)
	md"### - Checkboxes and Sliders"
end

# ╔═╡ 7007f520-b514-456a-a2b3-70d8611b2f48
if counter > Nclim
	md"""
	Start testing the constraint prior mass distribution! 👉 $(flag_prior_mass_checkbox)
	"""
end

# ╔═╡ a7bb1c76-97e2-4c79-8928-99b173ce0f6d
if counter > Nclim && flag_prior_mass 
  md"   
	here you see the histogram of the distribution of the prior masses of the n-th step for n=1,...,6 in the a NESA run
	To this end, the initial n-steps of NESA are performed and f_n computed.
	From f_n the prior mass X_n is computed analytically (which is possible in this simple example)
	
$X_n = \int dx \;p(x) \;\theta(f(x) > f_n)$
	
	The NESA runs are performed repeatedly and histograms of X_n are ploted
	"
end

# ╔═╡ 0816fdd9-c529-48e1-8c31-40e4a700240e
if counter > Nclim && flag_prior_mass 
  md"   
The numerically obtained histogram is compared with the exact pdf, obtained from 
	order statistics

$p(X) = \frac{{\cal N}^n}{\Gamma(n)} \ln(X)^{n-1} X^{{\cal N}-1}$
	
number of walkers: ${\cal N}$
	"
end

# ╔═╡ b9c105d5-d296-4a57-8bc0-5294081dbba7
if counter > Nclim && flag_prior_mass
	md"the red vertical line depicts the mean of $<X_n> = (\frac{N}{N+1})^n$ that enters the computation of the Riemann sum
	"
end

# ╔═╡ 246d932a-5d4d-4628-bf5a-a2ac848779ec
if counter > Nclim && flag_prior_mass
	tipx("We find very good agreement 👍👏🏆 and can be convinced that NESA works	")
end

# ╔═╡ 585cb5a1-7276-4c82-8609-e6637166d048
if counter > Nclim && flag_prior_mass
	hintx("Next we want to see whether it also gives the right answer for the integral")
end

# ╔═╡ 1166b1ba-f08c-43cf-9ef1-19e664c3233f
if counter > Nclim && flag_prior_mass
	md"""
See, how the NESA integration performs?  👉 $(flag_integral_checkbox)
	"""
end

# ╔═╡ cf0f3b29-f601-4776-acd8-0f4a809819e4
if counter > Nclim && flag_integral
md"We use the formula $int = \sum_{n=1}^{\infty} f_n (X_{n-1}-X_{n})$

where we use that once $f_n$ does not change anymore the remainings sum can be summed by the geometric series.
"
end

# ╔═╡ 75fbf125-14e1-483a-8c8d-996166703057
if counter > Nclim && flag_integral
md"seed of the random number generator   $(seed_2_slider)
 _with a new seed you get a new sample_"
end

# ╔═╡ 026c059e-eaf9-479b-a8a4-ca44c3b60b1e
if counter > Nclim && flag_integral
md"number of walkers N   $(N_wi_slider)"
end

# ╔═╡ d1dbd77c-caaf-4e1c-b691-5f1ba201e21d
begin
	function likelihood(x,f_𝜎_1,f_𝜎_2)
		y1 = exp.(-f_𝜎_1 .* (x .- 1.0).^2) 
		y2 = exp.(-f_𝜎_2 .* (x .- 1.5).^2) 	
		return y1 .+ 1.5 .* y2
	end
	md"### - likelihood function"
end

# ╔═╡ dc7a78e0-3b84-4ee0-9db4-c5670183857a

#=
begin
N_steps = 100
N_w = 10

function one_run(N_steps,N_w,f_𝜎_1,f_𝜎_2)

	del = 0.05
	L_f_min = zeros(N_steps)
	L_x_min = zeros(N_steps)	

	L_x_pos = rand(rng,N_w) .* 2
	L_f_pos = likelihood(L_x_pos,f_𝜎_1,f_𝜎_2)
	ind     = argmin(L_f_pos)

	
	L_f_min = zeros(N_steps)
	L_x_min = zeros(N_steps)	
	L_f_new = zeros(N_steps)
	L_x_new = zeros(N_steps)		
	
	
	for i = 1: N_steps
		M_x_pos[i,:] = L_x_pos
		M_f_pos[i,:] = L_f_pos	

		
		f_thresh  = L_f_pos[1]  
		L_f_min[i] = f_thresh
		L_x_min[i] = L_x_pos[1]
		it = rand(rng,2:N_w)
		xt0 = L_x_pos[it]
		xt  = xt0 + del*randn(rng)
		ft  = likelihood(xt,f_𝜎_1,f_𝜎_2)
		while ft < f_thresh
			xt  = xt0 + del*randn(rng)
			ft  = likelihood(xt,f_𝜎_1,f_𝜎_2)
		end
		L_f_pos[1] = ft
		L_x_pos[1] = xt
		ind     = sortperm(L_f_pos)
		L_x_pos = L_x_pos[ind]
		L_f_pos = L_f_pos[ind]
		L_x_new[i] = xt
		L_f_new[i] = ft		
	end

end
end
=#

# ╔═╡ c0ce8108-4a56-4157-b180-d52c61e20964
begin
	function one_run(N_steps,N_w,f_𝜎_1,f_𝜎_2,x_max,rng)

		N_step_max = 1000	# for constraint prior sampling

		L_f_min = zeros(N_steps)
		L_x_pos = rand(rng,N_w) .* x_max
		L_f_pos = likelihood(L_x_pos,f_𝜎_1,f_𝜎_2)

		L_f_min = zeros(N_steps)
		let

		for i = 1: N_steps
			del        = std(L_x_pos)*10
			ind_min    = argmin(L_f_pos)
			f_thresh   = L_f_pos[ind_min]
			L_f_min[i] = f_thresh
			it 		   = rand(rng,1:N_w)
			while it == ind_min
				it = rand(rng,1:N_w)
			end
			xt0 = L_x_pos[it]

			for j = 1: N_step_max
				global xt  = xt0 + del*randn(rng)
				global ft  = likelihood(xt,f_𝜎_1,f_𝜎_2)
				if ft > f_thresh
					break
				end
			end	
			L_f_pos[ind_min] = ft
			L_x_pos[ind_min] = xt
		end
		end	
		return L_f_min
	end
	
	function trial_step(N_iter_max,xt0,f_thresh,del, rng)
		xt = 0.
		ft = 0.
		for j = 1: N_iter_max
			xt  = xt0 + del*randn(rng)
			ft  = likelihood(xt,f_𝜎_1,f_𝜎_2)
			if ft > f_thresh
				break
			end
		end	
		return xt, ft
	end
	md"### - some subroutines"
end

# ╔═╡ 7822f358-dbc7-461d-948b-8c5b60d4a59f
begin
	seed = 135
	rng   = MersenneTwister(seed) 
	let
		L_x = [0.0:.01:2.0;]
		L_y = likelihood(L_x,f_𝜎_1,f_𝜎_2)
	
		N_iter_max = 100
		
		N_steps = 100
		global N_w     = 10


		 L_f_min = zeros(N_steps)
		 L_x_min = zeros(N_steps)	

		 L_x_pos = rand(rng,N_w) .* x_max
		 L_f_pos = likelihood(L_x_pos,f_𝜎_1,f_𝜎_2)

		 M_x_pos = zeros(N_steps,N_w)
		 M_f_pos = zeros(N_steps,N_w)	

		 L_f_min = zeros(N_steps)
		 L_x_min = zeros(N_steps)	
		 L_f_new = zeros(N_steps)
		 L_x_new = zeros(N_steps)	
		
		for i = 1: N_steps
			ind_min    = argmin(L_f_pos)
			M_x_pos[i,:] = L_x_pos
			M_f_pos[i,:] = L_f_pos	

			del        = std(L_x_pos)*10

			f_thresh   = L_f_pos[ind_min]
			L_f_min[i] = f_thresh
			L_x_min[i] = L_x_pos[ind_min]			
			it 		   = rand(rng,1:N_w)
			while it == ind_min
				it = rand(rng,1:N_w)
			end
			xt0 = L_x_pos[it]
		
			xt, ft = trial_step(N_iter_max,xt0,f_thresh,del, rng)



			L_x_pos[ind_min] = xt			
			L_f_pos[ind_min] = ft
			L_x_new[i] = xt
			L_f_new[i] = ft							
		end
		
		# Plot 1
		
		
		
		global plot1
		if 0 < counter
				plot1 = plot(L_x,L_y, label = false)

				plot1 = plot!(title = @sprintf("n = %3.0d, N_walker = %3.0d",counter,N_w))		
				plot1 = plot!(M_x_pos[counter,:],M_f_pos[counter,:],
					seriestype = :scatter,markercolor = :green, marker = :dot, label = false)
				x_rej = L_x_min[counter]
				f_rej = L_f_min[counter]

				plot1 = plot!([x_rej],[f_rej],
					seriestype = :scatter,markercolor = :red, marker = :x,
					markersize = 8, label = false)
				x_new = L_x_new[counter]
				f_new = L_f_new[counter]		
				plot1 = plot!([x_new],[f_new],
					seriestype = :scatter,markercolor = :red, marker = :dot,
					markersize = 8, label = false)	

				plot1 = plot!([x_new,x_new],[f_new+.2,f_new+.05], 
					arrow=(:closed, 4.0),label =  false)
				plot1 = annotate!(x_new,f_new+.3,"added")

				plot1 = plot!([x_rej+.2,x_rej+0.05],[f_rej,f_rej], 
					arrow=(:closed, 4.0),label =  false)	
				plot1 = annotate!(x_rej+0.3,f_rej,"discarded",
				xlim = (0.,2.6),
				ylim = (-.2,2.9))
				plot1 = plot!([0,2.0],[0,0],color=:black,label=false)		

				plot1 = annotate!(2.08,3.1 ,text(latexstring("n \\ \\qquad   f_n \\qquad \\qquad X_n"),:left,8))

				plot1 = annotate!(2.05,2.95, text(@sprintf("%2.0d)   %8.4f   %8.4f",0,0.0,1.0),:left,7))


				for m = 1:counter
					plot1 = annotate!(2.05, 2.95 - m * 0.1 ,text(@sprintf("%2.0d)   %8.4f   %8.4f",m,L_f_min[m],(N_w/(N_w+1))^m),:left,7))
				end 

		end
	end


	md"### - prepare data for single step mode"
	
end

# ╔═╡ a3528065-dfa6-4cad-8080-c188583f638a

begin

	if counter == 0
		tipx("you can now perform individually the first $(Nclim) NESA steps
		by repeatedly pressing the NEXT STEP button")
		
	elseif counter ≤ Nclim 
		
		plot(plot1,size=(600,400))

	else
		hintx("Now that you know how NESA works, let's check whether the constraint prior mass has the assumed properties")
	end
	
	
end

# ╔═╡ 311a6427-767b-49f3-af28-0903116ecc98
begin
	# details for constraint prior mass test
	let
	L_x_X = [0.0:.00001:x_max;]
	N_x_X = length(L_x_X)
	L_y_X = likelihood(L_x_X,f_𝜎_1,f_𝜎_2)
	

	n_hist = 6
	N_rep  = 1000
	N_wh    = 40
	L_hist = zeros(N_rep,n_hist)
	
	for i = 1: N_rep
		L_fh = one_run(n_hist,N_wh,f_𝜎_1,f_𝜎_2,x_max,rng)
		L_Xh = [sum(L_y_X .> L_fh[j])/N_x_X for j = 1: n_hist]
		L_hist[i,:] = L_Xh
	end

	L_plot = Vector{Any}(undef,n_hist)
	L_mean = zeros(n_hist)

	for n = 1: n_hist
		h = fit(Histogram, L_hist[:,n], nbins=40)
		r = h.edges[1]
		local x = first(r)+step(r)/2:step(r):last(r)
		hh = h.weights./sum(h.weights)
		plotx = plot(x, hh, seriestype = :scatter,
		marker=:dot,
		markersize = 2,
		label = false
		)

		p = ((log.(x)).^(n-1)) .* x.^(N_wh-1)
		p = p/sum(p)
		plotx = plot!(x,p,
			legendfont = 6,
			label = false,
			xaxis = ("X", (0,1.1),0:0.5:1,font(6, "Verdana")),
			yaxis = ("p(X)", (0,.16),0:0.1:0.2,font(6, "Verdana")),
			)

		plotx = annotate!(.2,0.14,text("n=$(n)", :left, 8))
		avg = (N_wh/(N_wh+1))^n
		plotx = plot!([avg,avg],[0,2],color=:red,linewidth = 2)
		L_plot[n] = plotx
		
       L_mean[n] = sum(x.*p)
	end


	global plot2 = plot(L_plot...)
	end
	md"## - Check the constraint prior mass distribution"
end

# ╔═╡ 9ecef464-1a0d-4830-8d27-7de069e11380
if counter > Nclim && flag_prior_mass 
	plot(plot2,size = (600,600))
end

# ╔═╡ 5a5a20be-cc27-4f06-a2ee-ffff9a4a59a2
begin
	if counter > Nclim && flag_integral
	rng2   = MersenneTwister(seed2) 
	N_stepsi = 1000
	N_repi   = 100
	L_ni = [0:N_stepsi-1;]
	L_dX_mean = (1/(N_wi+1)) .* (N_wi/(N_wi+1)) .^ L_ni
	L_int = zeros(N_repi)

	for i = 1: N_repi
		L_fa = one_run(N_stepsi,N_wi,f_𝜎_1,f_𝜎_2,x_max,rng2)
		L_sumand = L_fa .* L_dX_mean
		int_nesa_1 = Ω *sum(L_sumand)
		L_int[i]  = int_nesa_1 + Ω * L_fa[end] * (N_w/(N_w+1)) ^ N_stepsi
	end

	int_ex = sqrt(2*π*𝜎_1^2) + 1.5 * sqrt(2*π*𝜎_2^2)
	L_int  = L_int ./ int_ex

	L_avg = zeros(N_repi)
	L_ste = zeros(N_repi)
	for i = 1: N_repi
		L_aux    = L_int[1:i]
		L_avg[i] = mean(L_aux)
		L_ste[i] = 2*std(L_aux) / sqrt(i)
	end
	L_ste[1] = 0.1

	L_n   = [1:N_repi;]
	ploti = plot(L_n,L_int, 
	seriestype = :scatter,
	marker = :dot,
	ylim = (0.5,1.5),
	label = latexstring("\\mathrm{nesa \\ data}")
	)

	ploti = plot!(L_n,L_avg,
	ribbon = L_ste,
	linewidth = 2,
	label = latexstring("\\mathrm{mean\\ and \\ 2 \\sigma \\ uncertainty}")
	)
txtx = @sprintf("N walker = %3.0d",N_wi)
	ploti  = plot!([0,N_repi],[1,1],color = :black,
	label  = latexstring("\\mathrm{exact}"),
	xlabel = latexstring("\\mathrm{no. \\ of\\ repeated \\ nesa \\ runs}"),
	ylabel = latexstring("\\mathrm{integral}"),
	title = txtx,
	titlefont = 8
			)

end

end

# ╔═╡ 38257648-8beb-49c1-9c7c-11204cb6cd08
if counter > Nclim && flag_integral
	txt = @sprintf("int_nesa/int_exact = %8.3f ± %8.3f (2σ)" ,mean(L_int),std(L_int)/sqrt(N_repi))
	md"The numerical result yields:     $txt"
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"

[compat]
LaTeXStrings = "~1.3.0"
Plots = "~1.24.0"
PlutoUI = "~0.7.20"
StatsBase = "~0.33.13"
"""

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

[[AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "0bc60e3006ad95b4bb7497698dd7c6d649b9bc06"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.1"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[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 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.11.1"

[[ChangesOfVariables]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "9a1d594397670492219635b35a3d830b04730d62"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.1"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "a851fec56cb73cfdf43762999ec72eff5b86882a"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.15.0"

[[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 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.40.0"

[[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 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.10"

[[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"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.6"

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

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.2.3+0"

[[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", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.0+0"

[[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 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[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 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

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

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

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.62.1"

[[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 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.62.0+0"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"

[[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 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+0"

[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+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 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.17"

[[HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+0"

[[Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"

[[HypertextLiteral]]
git-tree-sha1 = "2b078b5a615c6c0396c77810d92ee8c6f470d238"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.3"

[[IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"

[[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"

[[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"

[[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"

[[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"

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

[[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 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

[[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 = "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"

[[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"

[[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 = "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"

[[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 = "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"

[[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"

[[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"

[[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:
# ╟─36ebbc95-ca82-4e64-978c-7b51d0cd61ee
# ╟─b2ef74b7-fa8f-4647-a48c-8177395f55b2
# ╟─98567be3-d02e-4b32-b760-e25bd185c8d5
# ╟─a3528065-dfa6-4cad-8080-c188583f638a
# ╟─7007f520-b514-456a-a2b3-70d8611b2f48
# ╟─311a6427-767b-49f3-af28-0903116ecc98
# ╟─a7bb1c76-97e2-4c79-8928-99b173ce0f6d
# ╟─0816fdd9-c529-48e1-8c31-40e4a700240e
# ╟─9ecef464-1a0d-4830-8d27-7de069e11380
# ╟─b9c105d5-d296-4a57-8bc0-5294081dbba7
# ╟─246d932a-5d4d-4628-bf5a-a2ac848779ec
# ╟─93315217-1dd9-4a50-abeb-ef5ad5cf44ef
# ╟─585cb5a1-7276-4c82-8609-e6637166d048
# ╟─1166b1ba-f08c-43cf-9ef1-19e664c3233f
# ╟─cf0f3b29-f601-4776-acd8-0f4a809819e4
# ╟─75fbf125-14e1-483a-8c8d-996166703057
# ╟─026c059e-eaf9-479b-a8a4-ca44c3b60b1e
# ╟─5a5a20be-cc27-4f06-a2ee-ffff9a4a59a2
# ╟─38257648-8beb-49c1-9c7c-11204cb6cd08
# ╟─4659617d-b2ae-4e08-94e6-3ef71bcbf48e
# ╟─fc692905-354b-4519-8956-f340b83ad661
# ╟─54e74311-1892-4120-b58f-e2cf0dc28016
# ╟─2f3bb4ef-2239-4617-b9fd-f6cffd0653e4
# ╟─53cbed91-a234-4e33-95c0-9b4a750c39ba
# ╟─de042b85-4f4d-447f-8ec3-8406ca031718
# ╟─627e437a-c271-4098-920e-12becf65b79c
# ╟─d1dbd77c-caaf-4e1c-b691-5f1ba201e21d
# ╟─7822f358-dbc7-461d-948b-8c5b60d4a59f
# ╟─dc7a78e0-3b84-4ee0-9db4-c5670183857a
# ╟─c0ce8108-4a56-4157-b180-d52c61e20964
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
