text:
### 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("""

<button>$(text)</button>
$(reset_text)

""")

# ╔═╡ 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"
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[[Adapt]]
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[[ArgTools]]
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[[Artifacts]]
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[[Base64]]
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[[Bzip2_jll]]
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[[Cairo_jll]]
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[[ChainRulesCore]]
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[[ChangesOfVariables]]
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[[ColorSchemes]]
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[[ColorTypes]]
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[[Colors]]
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[[Compat]]
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[[CompilerSupportLibraries_jll]]
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[[Contour]]
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[[DataAPI]]
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[[DataStructures]]
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[[DataValueInterfaces]]
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[[Dates]]
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[[DelimitedFiles]]
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[[Distributed]]
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[[DocStringExtensions]]
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[[Downloads]]
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[[EarCut_jll]]
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[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
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[[FFMPEG]]
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[[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"
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[[FixedPointNumbers]]
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[[Fontconfig_jll]]
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git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
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[[Formatting]]
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[[FreeType2_jll]]
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git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
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[[FriBidi_jll]]
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[[GLFW_jll]]
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git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
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[[GR]]
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[[GR_jll]]
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git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
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[[GeometryBasics]]
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[[Gettext_jll]]
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git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
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[[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"
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[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
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[[Grisu]]
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[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
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[[HarfBuzz_jll]]
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git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
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[[Hyperscript]]
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[[HypertextLiteral]]
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[[IOCapture]]
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[[IniFile]]
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[[InteractiveUtils]]
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[[InverseFunctions]]
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[[IrrationalConstants]]
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[[IterTools]]
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[[IteratorInterfaceExtensions]]
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uuid = "82899510-4779-5014-852e-03e436cf321d"
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[[JLLWrappers]]
deps = ["Preferences"]
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uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
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[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
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uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
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[[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"
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[[LaTeXStrings]]
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[[Latexify]]
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git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
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version = "0.15.9"

[[LibCURL]]
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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]]
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[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
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[[Logging]]
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[[MacroTools]]
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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]]
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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
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# ╟─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
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# ╟─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

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text:
#!/usr/bin/julia

function base10ToAny(in_dig,base)
    if base >= 21
        println("Warning: There're not special characters for digits in base 21 or more")
    end
    digits_b10=[]
    q=in_dig
    while true
        if q % base <= 9
            push!(digits_b10,q % base)
        elseif q % base == 10
            push!(digits_b10,'A')
        elseif q % base == 11
            push!(digits_b10,'B')
        elseif q % base == 12
            push!(digits_b10,'C')
        elseif q % base == 13
            push!(digits_b10,'D')
        elseif q % base == 14
            push!(digits_b10,'E')
        elseif q % base == 15
            push!(digits_b10,'F')
        elseif q % base == 16
            push!(digits_b10,'G')
        elseif q % base == 17
            push!(digits_b10,'H')
        elseif q % base == 18
            push!(digits_b10,'I')
        elseif q % base == 19
            push!(digits_b10,'J')
        else
            r=(q % base)
            push!(digits_b10,"($r)")
        end
        q=div(q,base)
        if q == 0
            break
        end
    end
    l=length(digits_b10)
    for idx in 1:l
        print(pop!(digits_b10))
    end
end

function anyBaseTo10(iterDig,base)
    if base >= 21
        println("Error: Only works for a base 20 or less")
        return
    end
    if !isa(iterDig,AbstractString)
        println("Error: Input n should be a string")
        return
    end
    summation=0
    l=sizeof(iterDig)
    for idx in 1:l
        digit = iterDig[ l - (idx-1)]
        if digit == 'A'
            digit = 10
        elseif digit == 'B'
            digit = 11
        elseif digit == 'C'
            digit = 12
        elseif digit == 'D'
            digit = 13
        elseif digit == 'E'
            digit = 14
        elseif digit == 'F'
            digit = 15
        elseif digit == 'G'
            digit = 16
        elseif digit == 'H'
            digit = 17
        elseif digit == 'I'
            digit = 18
        elseif digit == 'J'
            digit = 19
        else
            digit = parse(Int64, digit)
        end
        summation = digit*(base^(idx-1)) + summation
    end
    println(summation)
end

function binAddition(in_bin_1,in_bin_2)
    ib1=string(in_bin_1)
    ib2=string(in_bin_2)
    l1=sizeof(ib1)
    l2=sizeof(ib2)
    if l1 > l2
        AddZeros = l1 - l2
        ib2=("0" ^ AddZeros) * ib2
        larger=l1
    elseif l2 > l1
        AddZeros = l2 - l1
        ib1=("0" ^ AddZeros) * ib1
        larger=l2
    else
        larger=l1
    end
    c=0
    all_s=[]
    for idx in 1:larger
        dig1= parse(Int64, ib1[ larger - (idx-1) ])
        dig2= parse(Int64, ib2[ larger - (idx-1) ])
        d=div( dig1 + dig2 + c, 2)
        s=dig1 + dig2 + c - 2d
        c=d
        push!(all_s,s)
    end
    push!(all_s,c)
    justZero = true
    #println("all_s is:", all_s)
    for idx in 1:length(all_s)
        if length(all_s) == 2 && join(all_s) == "00"
            print(all_s[ length(all_s) - (idx -1 ) ])
            break
        end
        if justZero && all_s[ length(all_s) - (idx -1 ) ] == 0
            continue
        end
        if all_s[ length(all_s) - (idx -1 ) ]  == 1
            justZero = false
        end
        print(all_s[ length(all_s) - (idx -1 ) ])
    end
end

function binMultiplication(a,b)
end

#21 * 21
#441
#110111001

a=10101
b=10101
a=string(a)
b=string(b)
la=sizeof(a)
lb=sizeof(b)
if la > lb
    AddZeros = la - lb
    b=("0" ^ AddZeros) * b
    larger=la
elseif lb > la
    AddZeros = lb - la
    a=("0" ^ AddZeros) * a
    larger=lb
else
    larger=la
end
c_partials=[]
for idx in 1:larger
    #println("b[larger - (idx -1)] is\t", b[larger - (idx -1)])
    if b[larger - (idx -1)] == '1'
        c = a * ("0" ^ (idx - 1))
        #println("This is a: \t",a)
        push!(c_partials,c)
    else
        c = "0"
        push!(c_partials,c)
    end
end
p = 0
#println("This is c_partials: \t",c_partials)
for partial in c_partials
    println("Partial is $partial")
    partial = parse(Int64, partial)

    println("Value of function is: ", binAddition(p,partial) )
    p = binAddition(p,partial)
end

ext: jl

max_stars_repo_name: elbecerrasoto/tutti-frutti

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text:
#
# Water - TMAO
#

using MDDF
using PDBTools
using Plots

# Here we use the PDBTools package to read the pdb file (from http://github.com/m3g/PDBTools)
using PDBTools
atoms = PDBTools.readPDB("./structure.pdb")

# The solute is water, with 3 atoms
solute_indexes = PDBTools.select(atoms,"water")
solute = MDDF.Selection( solute_indexes, natomspermol=3 )

# The solvent is TMAO, which has 14 atoms. Use the natomspermol to indicate how many
# atoms each molecule has, such that there is no ambiguity on how to split the coordinates
# of the selection into individual molecules.
solvent_indexes = PDBTools.select(atoms,"resname TMAO")
solvent = MDDF.Selection( solvent_indexes, natomspermol=14 )

# Input options for the calcualtion
options = MDDF.Options(binstep=0.2,n_random_samples=1000)

nlabel="lc"
rlabel="lcP"

# Run MDDF calculation, and get the resutls in the R structure
println("$nlabel:")
trajectory = MDDF.Trajectory("./trajectory.dcd",solute,solvent)
@time N = MDDF.mddf_linkedcells(trajectory,options)

# Run MDDF calculation, and get the resutls in the R structure
println("$rlabel:")
trajectory = MDDF.Trajectory("./trajectory.dcd",solute,solvent)
@time R = MDDF.mddf_linkedcells_parallel(trajectory,options)

#println("naive:")
#trajectory = MDDF.NamdDCD("./trajectory.dcd",solute,solvent)
#@time naive = MDDF.mddf_naive(trajectory,options)

plot(layout=(8,1))

sp=1
plot!(ylabel="MDDF",subplot=sp)
plot!(N.d,N.mddf,subplot=sp,label="$nlabel - mddf")
plot!(N.d,N.rdf,subplot=sp,label="$nlabel - rdf")
scatter!(R.d,R.mddf,subplot=sp,label="$rlabel - mddf")
scatter!(R.d,R.rdf,subplot=sp,label="$rlabel - rdf")
plot!(legend=:topright,subplot=sp)

sp=2
plot!(ylabel="KB",subplot=sp)
plot!(N.d,N.kb,subplot=sp,label="$nlabel - mddf")
plot!(N.d,N.kb_rdf,subplot=sp,label="$nlabel - rdf")
scatter!(R.d,R.kb,subplot=sp,label="$rlabel - mddf")
scatter!(R.d,R.kb_rdf,subplot=sp,label="$rlabel - rdf")
plot!(legend=:topright,subplot=sp)

sp=3
plot!(ylabel="Count",subplot=sp)
plot!(N.d,N.md_count,subplot=sp,label="$nlabel",linewidth=3,alpha=0.5)
scatter!(R.d,R.md_count,subplot=sp,label="$rlabel")
plot!(N.d,N.md_count_random,subplot=sp,label="$nlabel - rand",linewidth=3,alpha=0.5)
scatter!(R.d,R.md_count_random,subplot=sp,label="$rlabel -rand")

sp=4
plot!(ylabel="Shell vol", subplot=sp)
plot!(N.d,N.volume.shell,subplot=sp,label="$nlabel")
scatter!(R.d,R.volume.shell,subplot=sp,label="$rlabel")

sp=5
plot!(ylabel="Sum MD", subplot=sp)
plot!(N.d,N.sum_md_count,subplot=sp,label="$nlabel - md")
scatter!(R.d,R.sum_md_count,subplot=sp,label="$rlabel - md")

sp=6
plot!(ylabel="Sum RAND", subplot=sp)
plot!(N.d,N.sum_md_count_random,subplot=sp,label="$nlabel - rand")
plot!(N.d,N.sum_rdf_count,subplot=sp,label="$nlabel - rdf")
scatter!(R.d,R.sum_md_count_random,subplot=sp,label="$rlabel - rand")
scatter!(R.d,R.sum_rdf_count,subplot=sp,label="$rlabel - rdf")
plot!(legend=:topleft,subplot=sp)

sp=7
plot!(ylabel="Atom contributions", subplot=sp)
plot!(N.d,N.solute_atom,subplot=sp,label="$nlabel")
scatter!(R.d,R.solute_atom,subplot=sp,label="$rlabel")

sp=8
plot!(ylabel="Count RDF",subplot=sp)
plot!(N.d,N.rdf_count,subplot=sp,label="$nlabel",linewidth=3,alpha=0.5)
scatter!(R.d,R.rdf_count,subplot=sp,label="$rlabel")
plot!(N.d,N.rdf_count_random,subplot=sp,label="$nlabel - rand",linewidth=3,alpha=0.5)
scatter!(R.d,R.rdf_count_random,subplot=sp,label="$rlabel -rand")

plot!(size=(800,1500))
savefig("./example2.pdf")
savefig("./plots.pdf")


text:
@testset "Effect size" begin
    @testset "One Normal Sample" begin
        mu = 0
        sd = 2.5
        n = 100
        stats = NormalStatistics(meanx=mu, sdx=sd, n=n)
        @test effectsize(stats) == mu / sd

        mu0 = 0.3
        @test effectsize(stats, μ0=mu0) == (mu-mu0)/sd
    end

    @testset "Two samples" begin
        # Example taken from "lsr" cohensD function
        gradesA = [55, 65, 65, 68, 70]
        gradesB = [56, 60, 62, 66]
        stats = TwoNormalStatistics(NormalStatistics(gradesA), NormalStatistics(gradesB))
        @test isapprox(effectsize(stats), 0.699892)
    end
end

@testset "Normal Statistics batch update" begin
    Random.seed!(12)
    data1 = rand(Normal(0.01, 1), 100_000)
    data2 = rand(Normal(0.03, 2), 100_000);
    s1 = NormalStatistics(data1)
    s2 = NormalStatistics(data2)
    stats1 = update!(s1, s2)
    stats2 = NormalStatistics([data1;data2])

    @test stats1.n == stats2.n
    @test isapprox(stats1.meanx, stats2.meanx, atol=0.0001)
    @test isapprox(stats1.sdx, stats2.sdx, atol=0.0001)
end

@testset "Merge two sample statistics" begin
    @testset "Two samples with equal sizes and variances" begin
        stats1= NormalStatistics(meanx=0.8, sdx=1.32, n=100)
        stats2= NormalStatistics(meanx=0.85, sdx=1.32, n=100)
        twostats = TwoNormalStatistics(stats1, stats2)
        stats = merge(twostats)
        @test stats.n == effsamplesize(stats1.n, stats2.n)
        @test stats.meanx == stats1.meanx - stats2.meanx
        @test stats.sdx == pooledsd(stats1.sdx, stats2.sdx, stats1.n, stats2.n)
    end
end


text:
using CSV,DataFrames,SurveyDataWeighting

hhs=CSV.File( "house_info.tab" )|>DataFrame
people = CSV.File( "person_info.tab")|>DataFrame
targets = CSV.File( "pop_targets.csv")|>DataFrame
nhh = size(hhs)[1]
out = DataFrame(
    # hhid = zeros(Int,nhh),

    female_00_04=zeros(Int, nhh),
    male_00_04=zeros(Int, nhh),

    female_05_09=zeros(Int, nhh),
    male_05_09=zeros(Int, nhh),

    female_10_14=zeros(Int, nhh),
    male_10_14=zeros(Int, nhh),

    female_15_19=zeros(Int, nhh),
    male_15_19=zeros(Int, nhh),

    female_20_24=zeros(Int, nhh),
    male_20_24=zeros(Int, nhh),

    female_25_29=zeros(Int, nhh),
    male_25_29=zeros(Int, nhh),

    female_30_34=zeros(Int, nhh),
    male_30_34=zeros(Int, nhh),

    female_35_39=zeros(Int, nhh),
    male_35_39=zeros(Int, nhh),

    female_40_44=zeros(Int, nhh),
    male_40_44=zeros(Int, nhh),

    female_45_49=zeros(Int, nhh),
    male_45_49=zeros(Int, nhh),

    female_50_54=zeros(Int, nhh),
    male_50_54=zeros(Int, nhh),

    female_55_59=zeros(Int, nhh),
    male_55_59=zeros(Int, nhh),

    female_60_64=zeros(Int, nhh),
    male_60_64=zeros(Int, nhh),

    female_65_69=zeros(Int, nhh),
    male_65_69=zeros(Int, nhh),

    female_70_74=zeros(Int, nhh),
    male_70_74=zeros(Int, nhh),

    female_75_79=zeros(Int, nhh),
    male_75_79=zeros(Int, nhh),

    female_80_plus=zeros(Int, nhh),
    male_80_plus=zeros(Int, nhh)
)

ages = [
    "00_04","05_09",
    "10_14","15_19",
    "20_24","25_29",
    "30_34","35_39",
    "40_44","45_49",
    "50_54","55_59",
    "60_64","65_69",
    "70_74","75_79",
    "80_plus" ]

for i in 1:nhh
    hh = hhs[i,:]
    println( "on hh $i hh.UQNo=$(hh.UQNo)")
    hpers = people[(people.UQNo .== hh.UQNo),:]
    for hp in eachrow(hpers)
        a = hp.AgeGrp
        if (hp.Gender <= 2) && (a < 19)
            sexstr = hp.Gender == 1 ? "male" : "female"
            if a in 1:17
                agestr = ages[a]
            elseif a == 18
                agestr = ages[a-1]
            end
            s = Symbol("$(sexstr)_$agestr")
            out[i,s] += 1
        end
    end
end
nc=size(targets)[2]
p=0
ps=[]
for r in eachrow(out)
    global p,ps
    p += 1
    s = sum(r[2:nc-1])
    if s == 0
       push!(ps,p)
       println("zero")
    end
end
delete!(out,ps)
CSV.write( "popnfile.csv", out )

out_m=Matrix{Float64}(out)
nr=size(out_m)[1]
tv = Vector{Float64}(targets[30,2:nc])
nc = size(tv)[1] # no year col
iw = 530.0 # mean weight from data
initial_weights = ones(nr)*iw
# mean weight from 2019 household count
sa_hhlds = 17_100_000 # statistica
iw = sa_hhlds/nr
# @assert sum(initial_weights) ≈ sa_hhlds
initial_weighted_popn = (initial_weights' * out_m)'
println( "initial-weighted_popn vs targets" )
for c in 1:nc
        diffpc = 100*(initial_weighted_popn[c]-tv[c])/tv[c]
        println( "$c $(tv[c]) $(initial_weighted_popn[c]) $diffpc%")
end
# .. or mean weight from person counts
tp=0
for r in eachrow(out)
   global tp
   tp += sum(r)
end
ip = sum(tv)
iw = ip/tp
initial_weights = ones(nr)*iw
# ...
wchi = do_chi_square_reweighting( out_m, initial_weights, tv )
weighted_popn_chi = (wchi' * out_m)'
@assert weighted_popn_chi ≈ tv
lower_multiple = 0.25 # any smaller min and d_and_s_constrained fails on this dataset
upper_multiple = 4
for m in [constrained_chi_square] #instances( DistanceFunctionType ) all other methods fail!
      println( "on method $m")
      rw = do_reweighting(
            data               = out_m,
            initial_weights    = initial_weights,
            target_populations = tv,
            functiontype       = m,
            lower_multiple     = lower_multiple,
            upper_multiple     = upper_multiple,
            tolx               = 0.000001,
            tolf               = 0.000001 )
      println( "results for method $m = $(rw.rc)" )
      weights = rw.weights
      weighted_popn = (weights' * out_m)'
      println( "weighted_popn = $weighted_popn" )
      @assert weighted_popn ≈ tv
      if m != chi_square
         for w in weights # check: what's the 1-liner for this?
            @assert w > 0.0
         end
      else
         @assert weights ≈ wchi # chisq the direct way should match chisq the iterative way
      end
      if m in [constrained_chi_square, d_and_s_constrained ]
         # check the constrainted methods keep things inside ll and ul
         for r in 1:nr
            @assert weights[r] <= initial_weights[r]*upper_multiple
            @assert weights[r] >= initial_weights[r]*lower_multiple
         end
      end
end

max_stars_repo_name: grahamstark/ScottishTaxBenefitModel

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text:
using Plots

f(x) = cos(x)

x = 0.0:0.2:2pi

y = f.(x)

plot(x, y)


text:
module DiffEqEnvironments

using ControlSystems: ss, lqr, state_space_validation, Continuous
using DiffEqBase: AbstractODEAlgorithm
using DifferentialEquations
using LinearAlgebra
using OrdinaryDiffEq: isadaptive
using Random
using ReinforcementLearningBase

include("rewards.jl")
include("observations.jl")
include("ic_samplers.jl")
include("environment.jl")
include("constructors.jl")
include("policies.jl")

# Export reward functions
export SASReward, SAReward, ASReward, QuadraticReward, DecrementingReward

# Export observation functions
export CustomObservation, LinearObservation
export CustomStateObservation, LinearStateObservation, FullStateObservation

# Export IC samplers
export UniformSampler

# Export Policies
export FeedbackPolicy, LinearFeedbackPolicy, LQRPolicy

# Export environment
export DiffEqEnv
export LTIQuadraticEnv

end # module


text:
using Quon
circ = tait_swap()
contract!(circ, tait_swap())
# plot(circ)

Quon.simplify!(circ, Quon.Rule(:swap_genus))
match(Quon.Rule(:x_fusion), circ)
Quon.simplify!(circ, Quon.Rule(:x_fusion))
match(Quon.Rule(:yang_baxter_triangle), circ)

plot(circ; backend = :compose)

using ZXCalculus
zxg = ZXGraph(ZXDiagram(circ))
zxg |> full_reduction |> ancilla_extraction |> plot


text:
function Base.:~(w::Wire)
  #if any of them are undefined we have a problem.
  assigned(w) || throw(UnassignedError())
  Wire(~w.values)
end

macro sidescheck()
  esc(quote
    assigned(lhs) || throw(UnassignedError())
    assigned(rhs) || throw(UnassignedError())
    length(lhs) == length(rhs) || throw(SizeMismatchError())
  end)
end

function Base.:&(lhs::Wire, rhs::Wire)
  @sidescheck
  Wire(lhs.values & rhs.values)
end

function Base.:|{N}(lhs::Wire{N}, rhs::Wire{N})
  @sidescheck
  Wire(lhs.values | rhs.values)
end

function Base.:^{N}(lhs::Wire{N}, rhs::Wire{N})
  @sidescheck
  Wire(lhs.values $ rhs.values)
end

#unary operators
function Base.:&{N}(tgt::Wire{N})
  assigned(tgt) || throw(UnassignedError())
  Wire((&)(tgt.values...))
end

function Base.:|{N}(tgt::Wire{N})
  assigned(tgt) || throw(UnassignedError())
  Wire((|)(tgt.values...))
end

function Base.:^{N}(tgt::Wire{N})
  assigned(tgt) || throw(UnassignedError())
  Wire(($)(tgt.values...))
end

#negated operators
and(x) = (&)(x)
or(x) = (|)(x)
xor(x) = (^)(x)
nand(x) = ~((&)(x))
nor(x)  = ~((|)(x))
xnor(x) = ~((^)(x))
nand(x,y) = ~((&)(x,y))
nor(x,y)  = ~((|)(x,y))
xnor(x,y) = ~((^)(x,y))
Base.:~(::typeof(&)) = nand
Base.:~(::typeof(|)) = nor
Base.:~(::typeof(^)) = xnor

function xorxnor(w::Wire)
  assigned(w) || throw(UnassignedError())
  Wire([(^)(w), (~^)(w)])
end

export xorxnor, and, or, nand, nor, xnor


text:
__precompile__()

module DiffEqDiffTools

using LinearAlgebra, SparseArrays, StaticArrays, ArrayInterface, Requires

import Base: resize!

include("iteration_utils.jl")
include("function_wrappers.jl")
include("finitediff.jl")
include("derivatives.jl")
include("gradients.jl")
include("jacobians.jl")
include("hessians.jl")

end # module


text:
# hack until we figure out how to detect automatically
if Sys.iswindows()
	const libniscope = "C:/Program Files/IVI Foundation/IVI/Bin/niScope_64"
	const libnidmm   = "C:/Program Files/IVI Foundation/IVI/Bin/nidmm_64"
	const libnifgen  = "C:/Program Files/IVI Foundation/IVI/Bin/niFgen_64"
	const libnihsdio = "C:/Program Files/IVI Foundation/IVI/Bin/niHSDIO_64"
	const libvisa    = "C:/Windows/System32/visa64"
elseif Sys.islinux()
	@error "Please add the lib paths manually and rebuild the package!"
	const libniscope = ""
	const libnidmm = ""
	const libnifgen = ""
	const libnihsdio = ""
	const libvisa = ""
elseif Sys.isapple()
	@error "Please add the lib paths manually and rebuild the package!"
	const libniscope = ""
	const libnidmm = ""
	const libnifgen = ""
	const libnihsdio = ""
	const libvisa = ""
elseif Sys.isunix()
	@error "Please add the lib paths manually and rebuild the package!"
	const libniscope = ""
	const libnidmm = ""
	const libnifgen = ""
	const libnihsdio = ""
	const libvisa = ""
end


text:
module Badge

using Genie, Stipple, StippleUI, StippleUI.API
import Genie.Renderer.Html: HTMLString, normal_element

export badge

Genie.Renderer.Html.register_normal_element("q__badge", context = @__MODULE__)

"""
floating::Bool = false
transparent::Bool = false
multiline::Bool = true
label::String = "Label"
align::String = "top" # middle, bottom
outline::Bool = true
color::String = "blue"
textcolor::String = "teal-10"
"""
function badge( fieldname::Union{Symbol,Nothing} = nothing,
                args...;
                wrap::Function = StippleUI.DEFAULT_WRAPPER,
                kwargs...) where {T<:Stipple.ReactiveModel}
  wrap() do
    q__badge(args...;
            attributes(
              [:fieldname => fieldname, kwargs...],
              StippleUI.API.ATTRIBUTES_MAPPINGS
            )...)
  end
end

end


text:
export richardson_lucy_iterative

"""
    richardson_lucy_iterative(measured, psf; <keyword arguments>)

Classical iterative Richardson-Lucy iteration scheme for deconvolution.
`measured` is the measured array and `psf` the point spread function.
Converges slower than the optimization approach of `deconvolution`

# Keyword Arguments
- `regularizer=GR()`: A regularizer function. Can be exchanged
- `λ=0.05`: A float indicating the total weighting of the regularizer with
    respect to the global loss function
- `iterations=100`: Specifies number of iterations.

# Example
```julia-repl
julia> using DeconvOptim, TestImages, Colors, Noise;

julia> img = Float32.(testimage("resolution_test_512"));

julia> psf = Float32.(generate_psf(size(img), 30));

julia> img_b = conv(img, psf);

julia> img_n = poisson(img_b, 300);

julia> @time res = richardson_lucy_iterative(img_n, psf);
```
"""
function richardson_lucy_iterative(measured, psf;
                                   regularizer=GR(),
                                   λ=0.05,
                                   iterations=100,
                                   conv_dims=1:ndims(psf))

    otf, conv_temp = plan_conv(measured, psf, conv_dims)
    otf_conj = conj.(otf)
    # initializer
    rec = abs.(conv_temp(measured, otf))#ones(eltype(measured), size(measured))

    # buffer for gradient

    buffer_grad =  let
        if !isnothing(regularizer)
            gradient(regularizer, rec)[1]
        else
            nothing
        end
    end

    ∇reg(x) = buffer_grad .= gradient(regularizer, x)[1]

    buffer = copy(measured)

    iter_without_reg(rec) = begin
        buffer .= measured ./ (conv_temp(rec, otf))
        conv_temp(buffer, otf_conj)
    end
    iter_with_reg(rec) = buffer .= (iter_without_reg(rec) .- λ .* Base.invokelatest(∇reg, rec))

    iter = isnothing(regularizer) ? iter_without_reg : iter_with_reg

    for i in 1:iterations
        rec .*= iter(rec)
    end

    return rec
end


text:
@testset "Term and Polynomial tests" begin
    @testset "Term" begin
        @polyvar x
#       @test coefficienttype(1x) == Int
#       @test coefficienttype(1.0x^2) == Float64
#       @test coefficienttype(Term{true, Int}) == Int
        @test zeroterm(Term{false, Int}).α == 0
        @test one(Term{true, Int}).α == 1
        @polyvar x
        @test typeof(Term(1x)) == Term{true, Int}
        @test Term(1x) == 1x
        @test typeof(convert(Any, 1x)) == Term{true, Int}
        @test typeof(one(1x)) == Term{true, Int}
        @test typeof(zeroterm(1x)) == Term{true, Int}
        @test typeof(zero(1x)) == Polynomial{true, Int}
        @test typeof(one(1.0x)) == Term{true, Float64}
        @test typeof(zeroterm(1.0x)) == Term{true, Float64}
        @test typeof(zero(1.0x)) == Polynomial{true, Float64}

        @test typeof(constantterm(1, x)) == Term{true, Int}
        @inferred constantterm(1, x)
        @test typeof(polynomial(1:2, monomials([x], 1:2))) == Polynomial{true, Int}
    end

    @testset "Polynomial" begin
        #@test eltype(Polynomial{true, Int}) == Int
        @polyvar x
        @test_throws ArgumentError Polynomial{true, Int}([1, 2], [x])
        @test_throws ArgumentError Polynomial{true, Int}([1, 2], MonomialVector([x]))
        @test_throws InexactError Polynomial{true, Int}([1.5], [x])
        @test Polynomial(1 + x) == 1 + x
        @test typeof(one(1 + x)) == Polynomial{true, Int}
        @test typeof(zeroterm(1 + x)) == Term{true, Int}
        @test typeof(zero(1 + x)) == Polynomial{true, Int}
        @test typeof(one(1.0 + x)) == Polynomial{true, Float64}
        @test typeof(zeroterm(1.0 + x)) == Term{true, Float64}
        @test typeof(zero(1.0 + x)) == Polynomial{true, Float64}

        p = Polynomial([4, 9], [x, x*x])
        p.a == [9, 4]
        p.x[1] == x^2
        p.x[2] == x

        @inferred Polynomial(i -> float(i), [x, x*x])
        @inferred Polynomial(i -> 3 - float(i), MonomialVector([x*x, x]))
        for p in (Polynomial(i -> float(i), [x, x*x]),
                  Polynomial(i -> 3 - float(i), MonomialVector([x*x, x])))
            @test typeof(p) == Polynomial{true, Float64}
            @test p.a == [2.0, 1.0]
            @test p.x == MonomialVector([x^2, x])
        end

        @ncpolyvar ncpolyvar u v
        @inferred Polynomial(i -> i, [u, u*u, 1])
        p = Polynomial(i -> i, [u, u*u, 1])
        @test typeof(p) == Polynomial{false, Int}
        @test p.a == [2, 1, 3]
        @test p.x == MonomialVector([u^2, u, 1])

        @test u + v*u + 1 != v*u + u
        @test removemonomials(u + v*u + 1, [1, u*v]) == v*u + u
        @test removemonomials(u + u*v + 1, [u*v]) == 1 + u

        @inferred polynomial(2u)
        @inferred polynomial(2.0u, Int)
    end

    @testset "Evaluation" begin
        @polyvar x y
        @test (x^2+y^3)(2, 3) == 31
        @test (x^2+y^3)((2, 3)) == 31
        @test (x^2+y^3)([2, 3]) == 31
        @test (2x^2*y)(3,2) == 36
        @test (2x^2*y)((3,2)) == 36
        @test (2x^2*y)([3,2]) == 36
        @test (2x^2)(3) == 18
        err = ArgumentError("Variable `y` was not assigned a value. Use `subs` to substitute only a subset of the variables.")
        t = 2x^2 * y
        @test_throws err t(x => 1)
        p = 2x^2 + y
        @test_throws err p(x => 1)
        err = ArgumentError("Variable `x` was not assigned a value. Use `subs` to substitute only a subset of the variables.")
        @test_throws err t(y => 1)
        @test_throws err p(y => 1)
    end
end


text:
#Rieman problem solvers

#HLLE solver
function hlle(hyd::data1d)
    fluxdiff = zeros(hyd.n, 3)

    #compute eigenvalues
    evl = zeros(hyd.n, 3)
    evr = zeros(hyd.n, 3)
    smin = zeros(hyd.n)
    smax = zeros(hyd.n)
    csp = sqrt(eos_cs2(hyd.rhop, hyd.epsp, gamma))
    csm = sqrt(eos_cs2(hyd.rhom, hyd.epsm, gamma))

    for i = 2:(hyd.n-1)
        evl[i,1] = hyd.velp[i]
        evr[i,1] = hyd.velm[i+1]
        evl[i,2] = hyd.velp[i] - csp[i]
        evr[i,2] = hyd.velm[i+1] - csm[i+1]
        evl[i,3] = hyd.velp[i] + csp[i]
        evr[i,3] = hyd.velm[i+1] +csm[i+1]

        #min and max eigenvalues
        smin[i] = min(evl[i,1], evl[i,2], evl[i,3],
                      evr[i,1], evr[i,2], evr[i,3], 0.0)
        smax[i] = max(evl[i,1], evl[i,2], evl[i,3],
                      evr[i,1], evr[i,2], evr[i,3], 0.0)
    end

    #set up flux left L and right R of the interface
    #at i+1/2
    fluxl = zeros(hyd.n, 3)
    fluxr = zeros(hyd.n, 3)

    for i = 2:(hyd.n-1)
        fluxl[i,1] = hyd.qp[i,1] * hyd.velp[i]
        fluxl[i,2] = hyd.qp[i,2] * hyd.velp[i] + hyd.pressp[i]
        fluxl[i,3] = (hyd.qp[i,3] + hyd.pressp[i]) * hyd.velp[i]

        fluxr[i,1] = hyd.qm[i+1,1] * hyd.velm[i+1]
        fluxr[i,2] = hyd.qm[i+1,2] * hyd.velm[i+1] + hyd.pressm[i+1]
        fluxr[i,3] = (hyd.qm[i+1,3] + hyd.pressm[i+1]) * hyd.velm[i+1]
    end

    #solve the Riemann problem for the i+1/2 interface
    ds = smax .- smin
    flux = zeros(hyd.n, 3)

    for j = 1:3
        for i = hyd.g:(hyd.n-hyd.g+1)
            flux[i,j] = (smax[i]*fluxl[i,j] - smin[i]*fluxr[i,j] + smax[i]*smin[i]*(hyd.qm[i+1,j] - hyd.qp[i,j])) / ds[i]
        end
    end

    #flux difference
    for j = 1:3
        for i = (hyd.g+1):(hyd.n-hyd.g+1)
            rm = hyd.xi[i]
            rp = hyd.xi[i+1]
            dxi = 1.0/(rp - rm)
            fluxdiff[i, j] = dxi * (flux[i, j]  - flux[i-1, j])
        end
    end

    return fluxdiff
end

#HLLC solver
function hllc(hyd::data1d)

    #compute eigenvalues
    smin = zeros(hyd.n)
    smax = zeros(hyd.n)
    smid = zeros(hyd.n)
    csp = sqrt(eos_cs2(hyd.rhop, hyd.epsp, gamma))
    csm = sqrt(eos_cs2(hyd.rhom, hyd.epsm, gamma))

    for i = 2:(hyd.n-1)
        #min and max eigenvalues

        #minus = right
        #plus = left
        #min = left
        #max = right

        smin[i] = min(hyd.velxp[i],
                      hyd.velxp[i] - csp[i],
                      hyd.velxp[i] + csp[i],
                      hyd.velxm[i+1],
                      hyd.velxm[i+1] - csm[i+1],
                      hyd.velxm[i+1] + csm[i+1],
                      hyd.velyp[i], #trans
                      hyd.velyp[i] - csp[i],
                      hyd.velyp[i] + csp[i],
                      hyd.velym[i+1],
                      hyd.velym[i+1] - csm[i+1],
                      hyd.velym[i+1] + csm[i+1])

        smax[i] = max(hyd.velxp[i],
                      hyd.velxp[i] - csp[i],
                      hyd.velxp[i] + csp[i],
                      hyd.velxm[i+1],
                      hyd.velxm[i+1] - csm[i+1],
                      hyd.velxm[i+1] + csm[i+1],
                      hyd.velyp[i], #trans
                      hyd.velyp[i] - csp[i],
                      hyd.velyp[i] + csp[i],
                      hyd.velym[i+1],
                      hyd.velym[i+1] - csm[i+1],
                      hyd.velym[i+1] + csm[i+1])

        smid[i] = (hyd.pressm[i+1] - hyd.pressp[i] + hyd.rhop[i]*hyd.velxp[i]*(smin[i] - hyd.velxp[i]) - hyd.rhom[i+1]*hyd.velxm[i+1]*(smax[i] - hyd.velxm[i+1]))/(hyd.rhop[i]*(smin[i]-hyd.velxp[i]) - hyd.rhom[i+1]*(smax[i]-hyd.velxm[i+1]))
    end

    #set up flux left L and right R of the interface
    #at i+1/2
    fluxl = zeros(hyd.n, 4)
    fluxr = zeros(hyd.n, 4)

    for i = 2:(hyd.n-1)
        fluxl[i,1] = hyd.qp[i,1] * hyd.velxp[i]
        fluxl[i,2] = hyd.qp[i,2] * hyd.velxp[i] + hyd.pressp[i]
        fluxl[i,3] = hyd.qp[i,3] * hyd.velyp[i]
        fluxl[i,4] = (hyd.qp[i,4] + hyd.pressp[i]) * hyd.velxp[i]

        fluxr[i, 1] = hyd.qm[i+1, 1] * hyd.velxm[i+1]
        fluxr[i, 2] = hyd.qm[i+1, 2] * hyd.velxm[i+1] + hyd.pressm[i+1]
        fluxr[i, 3] = hyd.qm[i+1, 3] * hyd.velym[i+1]
        fluxr[i, 4] = (hyd.qm[i+1, 4] + hyd.pressm[i+1]) * hyd.velxm[i+1]
    end

    #solve the Riemann problem for the i+1/2 interface
    ds = smax .- smin
    flux = zeros(hyd.n, 4)

    for i = (hyd.g-1):(hyd.n-hyd.g+1)
    #for i = 1:hyd.n
        if smin[i] >= 0.0
            flux[i,1] = fluxl[i,1]
            flux[i,2] = fluxl[i,2]
            flux[i,3] = fluxl[i,3]
            flux[i,4] = fluxl[i,4]
        elseif smin[i] <= 0.0 && smid[i] >= 0.0
            #f_*,left

            #original hllc (p_*,l = p_*,r) (not working)
            #qsl0 = hyd.rhop[i]*((smin[i]-hyd.velp[i])/(smin[i]-smid[i]))
            #qsl3 = hyd.epsp[i]/hyd.rhop[i]+(smid[i]-hyd.velp[i])*(smid[i]+hyd.pressp[i]/(hyd.rhop[i]*(smin[i]-hyd.velp[i])))
            #flux[i,1] = fluxl[i,1] + smin[i]*(qsl0 - hyd.qp[i, 1])
            #flux[i,2] = fluxl[i,2] + smin[i]*(qsl0*smid[i] - hyd.qp[i, 2])
            #flux[i,3] = fluxl[i,3] + smin[i]*(qsl0*qsl3 - hyd.qp[i, 3])

            #hllc v1.1
            #flux[i,1] = smid[i]*(smin[i]*hyd.qp[i,1]-fluxl[i,1])/(smin[i]-smid[i])
            #flux[i,2] = (smid[i]*(smin[i]*hyd.qp[i,2]-fluxl[i,2])+smin[i]*(hyd.pressp[i]+hyd.rhop[i]*(smin[i]-hyd.velp[i])*(smid[i]-hyd.velp[i])))/(smin[i]-smid[i])
            #flux[i,3] = (smid[i]*(smin[i]*hyd.qp[i,3]-fluxl[i,3])+smid[i]*smin[i]*(hyd.pressp[i]+hyd.rhop[i]*(smin[i]-hyd.velp[i])*(smid[i]-hyd.velp[i])))/(smin[i]-smid[i])

            #hllc v1.2 (arithmetic mean of star-area pressures)
            plr = 0.5*(hyd.pressp[i]+hyd.pressm[i+1]+hyd.rhop[i]*(smin[i]-hyd.velxp[i])*(smid[i]-hyd.velxp[i])+hyd.rhom[i+1]*(smax[i]-hyd.velxm[i+1])*(smid[i]-hyd.velxm[i+1]))
            flux[i,1] = smid[i]*(smin[i]*hyd.qp[i,1]-fluxl[i,1])/(smin[i]-smid[i])
            flux[i,2] = (smid[i]*(smin[i]*hyd.qp[i,2]-fluxl[i,2]) + smin[i]*plr)/(smin[i]-smid[i])
            flux[i,3] = (smid[i]*(smin[i]*hyd.qp[i,3]-fluxl[i,3]))/(smin[i]-smid[i])
            flux[i,4] = (smid[i]*(smin[i]*hyd.qp[i,4]-fluxl[i,4]) + smid[i]*smin[i]*plr)/(smin[i]-smid[i])

        elseif smid[i] <= 0.0 && smax[i] > 0.0
            #f_*,right

            #original hllc (p_*,l = p_*,r) (not working)
            #qsl0 = hyd.rhom[i+1]*((smax[i]-hyd.velm[i+1])/(smax[i]-smid[i]))
            #qsl3 = (hyd.epsm[i+1]/hyd.rhom[i+1])+(smid[i]-hyd.velm[i+1])*(smid[i]+hyd.pressm[i+1]/(hyd.rhom[i+1]*(smax[i]-hyd.velm[i+1])))
            #flux[i,1] = fluxr[i,1] + smax[i]*(qsl0 - hyd.qm[i+1, 1])
            #flux[i,2] = fluxr[i,2] + smax[i]*(qsl0*smid[i] - hyd.qm[i+1, 2])
            #flux[i,3] = fluxr[i,3] + smax[i]*(qsl0*qsl3 - hyd.qm[i+1, 3])

            #hllc v1.1
            #flux[i,1] = smid[i]*(smax[i]*hyd.qm[i+1,1]-fluxr[i,1])/(smax[i]-smid[i])
            #flux[i,2] = (smid[i]*(smax[i]*hyd.qm[i+1,2]-fluxr[i,2])+smax[i]*(hyd.pressm[i+1]+hyd.rhom[i+1]*(smax[i]-hyd.velm[i+1])*(smid[i]-hyd.velm[i+1])))/(smax[i]-smid[i])
            #flux[i,3] = (smid[i]*(smax[i]*hyd.qm[i+1,3]-fluxr[i,3])+smid[i]*smax[i]*(hyd.pressm[i+1]+hyd.rhom[i+1]*(smax[i]-hyd.velm[i+1])*(smid[i]-hyd.velm[i+1])))/(smax[i]-smid[i])

            #hllc v1.2 (arithmetic mean of star-area pressures)
            plr = 0.5*(hyd.pressp[i]+hyd.pressm[i+1]+hyd.rhop[i]*(smin[i]-hyd.velxp[i])*(smid[i]-hyd.velxp[i])+hyd.rhom[i+1]*(smax[i]-hyd.velxm[i+1])*(smid[i]-hyd.velxm[i+1]))
            flux[i,1] = smid[i]*(smax[i]*hyd.qm[i+1,1]-fluxr[i,1])/(smax[i]-smid[i])
            flux[i,2] = (smid[i]*(smax[i]*hyd.qm[i+1,2]-fluxr[i,2]) + smax[i]*plr)/(smax[i]-smid[i])
            flux[i,3] = (smid[i]*(smax[i]*hyd.qm[i+1,3]-fluxr[i,3]))/(smax[i]-smid[i])
            flux[i,4] = (smid[i]*(smax[i]*hyd.qm[i+1,4]-fluxr[i,4]) + smid[i]*smax[i]*plr)/(smax[i]-smid[i])

        elseif smax[i] <= 0.0
            flux[i,1] = fluxr[i,1]
            flux[i,2] = fluxr[i,2]
            flux[i,3] = fluxr[i,3]
            flux[i,4] = fluxr[i,4]
        end
    end

    return flux
end

#x-sweep
function xsweep(hyd::data2d)
    flux = zeros(hyd.ny, hyd.nx, 4)
    for j = (hyd.g-1):(hyd.ny-hyd.g+1)
        hyd1 = splice(hyd, j, 1)
        fluxi = hllc(hyd1)

        for i = (hyd.g-1):(hyd.nx-hyd.g+1)
            flux[j, i, 1] = fluxi[i, 1]
            flux[j, i, 2] = fluxi[i, 2]
            flux[j, i, 3] = fluxi[i, 3]
            flux[j, i, 4] = fluxi[i, 4]
        end
    end

    return flux
end

#y-sweep
function ysweep(hyd::data2d)
    flux = zeros(hyd.ny, hyd.nx, 4)
    for j = (hyd.g-1):(hyd.nx-hyd.g+1)
        hyd1 = splice(hyd, j, 2)
        fluxi = hllc(hyd1)

        for i = (hyd.g-1):(hyd.ny-hyd.g+1)
            flux[i, j, 1] = fluxi[i, 1]
            flux[i, j, 3] = fluxi[i, 2]
            flux[i, j, 2] = fluxi[i, 3]
            flux[i, j, 4] = fluxi[i, 4]
        end
    end

    return flux
end

#Split 2-dimensional flux
function ssflux(hyd::data2d, dt, iter)
    fluxdiff = mod(iter, 2) == 0 ? xsweep(hyd) : ysweep(hyd)
    return fluxdiff
end

function ssyflux(hyd::data2d, dt, iter)
    fluxdiff = ysweep(hyd)
    return fluxdiff
end

#Split 2-dimensional flux
function sflux(hyd::data2d, dt, iter)

    hyd2 = hyd

    qold = copy(hyd2.q)
    fluxdiff = mod(iter, 2) == 0 ? xsweep(hyd2) : ysweep(hyd2)
    hyd2.q = qold - dt*fluxdiff
    hyd2.rho, hyd2.eps, hyd2.press, hyd2.velx, hyd2.vely = con2prim(hyd2.q)
    hyd2 = apply_bcs(hyd2)
    hyd2 = reconstruct(hyd2)
    fluxdiff = mod(iter, 2) == 0 ? ysweep(hyd2) : xsweep(hyd2)

    return fluxdiff
end

function uflux(hyd::data2d, dt)

    #transverse fluxes
    fx = xsweep(hyd)
    fy = ysweep(hyd)

    # U_xl[i,j,:] = U_xl[i,j,:] - 0.5*dt/dy * (F_y[i-1,j+1,:] - F_y[i-1,j,:])
    # U_xr[i,j,:] = U_xr[i,j,:] - 0.5*dt/dy * (F_y[i,j+1,:] - F_y[i,j,:])

    # U_yl[i,j,:] = U_yl[i,j,:] - 0.5*dt/dx * (F_x[i+1,j-1,:] - F_x[i,j-1,:])
    # U_yr[i,j,:] = U_yr[i,j,:] - 0.5*dt/dx * (F_x[i+1,j,:] - F_x[i,j,:])

    #TODO: relax dx & dy calculations
    for j = (hyd.g-1):(hyd.ny-hyd.g+1), i = (hyd.g-1):(hyd.nx-hyd.g+1)
        for k = 1:4
            hyd.qp[j,i,k,1] -= 0.5dt*(fy[j+1, i-1, k] - fy[j, i-1, k])/(hyd.yi[j+1]-hyd.yi[j])
            hyd.qm[j,i,k,1] -= 0.5dt*(fy[j+1, i, k] - fy[j, i, k])/(hyd.yi[j+1]-hyd.yi[j])

            hyd.qp[j,i,k,2] -= 0.5dt*(fx[j-1, i+1, k] - fx[j-1, i, k])/(hyd.xi[i+1]-hyd.xi[i])
            hyd.qm[j,i,k,2] -= 0.5dt*(fx[j, i+1, k] - fx[j, i, k])/(hyd.xi[i+1]-hyd.xi[i])
        end
    end

    #update conserved variables
    hyd.rhom[:,:,1], hyd.epsm[:,:,1], hyd.pressm[:,:,1], hyd.velxm[:,:,1], hyd.velym[:,:,1] = con2prim(hyd.qm[:,:,:,1])
    hyd.rhop[:,:,1], hyd.epsp[:,:,1], hyd.pressp[:,:,1], hyd.velxp[:,:,1], hyd.velyp[:,:,1] = con2prim(hyd.qp[:,:,:,1])

    hyd.rhom[:,:,2], hyd.epsm[:,:,2], hyd.pressm[:,:,2], hyd.velxm[:,:,2], hyd.velym[:,:,2] = con2prim(hyd.qm[:,:,:,2])
    hyd.rhop[:,:,2], hyd.epsp[:,:,2], hyd.pressp[:,:,2], hyd.velxp[:,:,2], hyd.velyp[:,:,2] = con2prim(hyd.qp[:,:,:,2])

    #fluxes normal to the surface
    fx = xsweep(hyd)
    fy = ysweep(hyd)

    return fx, fy
end

max_stars_repo_name: natj/hydro

max_issues_repo_name: natj/hydro

max_forks_repo_name: natj/hydro


text:
@testset "Diffusion Simulation" begin

gx = complete_graph(5)

for g in testgraphs(gx)  # this makes graphs of different eltypes
    # Most basic
    @test @inferred(diffusion_rate(g, 1.0, 4)) == [1, 5, 5, 5]
end

for i in 1:5
  add_vertex!(gx)
end

for g in testgraphs(gx)  # this makes graphs of different eltypes

    ######
    # Check on fully connected, prob = 1
    ######

    # Add disconnected for more dynamics

    # Basic test. Watch connected vertices
    @test @inferred(diffusion_rate(g, 1.0, 4,
                                   watch=collect(1:5),
                                   initial_infections=[2]
                                   )) == [1, 5, 5, 5]

    # Watching unconnected vertices
    @test @inferred(diffusion_rate(g, 1.0, 4,
                                   watch=collect(6:10),
                                   initial_infections=[2]
                                   )) == [0, 0, 0, 0]

    # Watch subset
    @test @inferred(diffusion_rate(g, 1.0, 4,
                                   watch=collect(1:2),
                                   initial_infections=[2]
                                   )) == [1, 2, 2, 2]

    @test @inferred(diffusion_rate(g, 1.0, 4,
                                   watch=collect(1:5),
                                   initial_infections=[10]
                                   )) == [0, 0, 0, 0]

end

######
# Check along path graph
######

gx = path_graph(5)

for g in testgraphs(gx)  # this makes graphs of different eltypes

    @test @inferred(diffusion_rate(g, 1.0, 4,
                                   watch=collect(1:5),
                                   initial_infections=[1]
                                   )) == [1, 2, 3, 4]

    @test @inferred(diffusion_rate(g, 1.0, 4,
                                   watch=collect(1:5),
                                   initial_infections=[3]
                                   )) == [1, 3, 5, 5]
end

gx = path_graph(30)
for g in testgraphs(gx)
    # Check normalize
    @test @inferred(diffusion_rate(g,
                                  1.0,
                                  6,
                                  initial_infections=[15],
                                  normalize=false
                                  )) == [1, 3, 5, 7, 9, 11]

    @test @inferred(diffusion_rate(g, 2.0, 6,
                                   initial_infections=[15],
                                   normalize=true)
                                   ) == [1, 3, 5, 7, 9, 11]

    # Test probability accurate
    # In a Path network,
    # number of nodes infected (minus 1)
    # is equal to number of successes of a
    # Burnoulli process.
    # So if p = 0.2, in 5 steps (seed +
    # 4 trials) expected value is 0.8,
    # with standard deviation 0.8.

    means = Dict(0.2 => 0.8, 0.4 => 1.6)
    stds = Dict(0.2 => 0.8, 0.4 => 0.98)
    runs = 20
    for p in [0.2, 0.4]
        final_value = 0.0

        for i in 1:20
            result = @inferred(diffusion_rate(g, p, 5,
                                     initial_infections=[1]))
            final_value += result[5]
        end

        # Pretty loose bounds so don't get lots of failed tests.
        # Just want some safeguard.
        # Note 5 steps = 4 Bernoullis + initial infection.
        # False rate less than 1 in 1000
        # Subtract 1 for initial infection
        avg = final_value / runs - 1
        @test avg < means[p] + stds[p] / sqrt(runs) * 3.5
        @test avg > means[p] - stds[p] / sqrt(runs) * 3.5
    end
end

gx = path_digraph(10)

for g in testdigraphs(gx)

    ######
    # Check on digraphs
    ######

    @test @inferred(diffusion_rate(g, 1.0, 9,
                                  initial_infections=[1]
                                  )) == collect(1:9)

    @test @inferred(diffusion_rate(g, 1.0, 9,
                                  initial_infections=[10]
                                  )) == ones(Int, 9)

    # Check probabilities.
    # See note in analogous tests above for undirected tests.
    runs = 20
    means = Dict(0.2 => 2, 0.4 => 4)
    stds = Dict(0.2 => 1.2649110640673518,
                0.4 => 1.5491933384829668)

    for p in [0.2, 0.4]
        final_value = 0.0

        for i in 1:20
            result = @inferred(diffusion_rate(g, p, 11,
                                     initial_infections=[1]))
            final_value += result[11]

        end

        # Pretty loose bounds so don't get lots of failed tests.
        # Just want some safeguard.
        # False rate less than 1 in 1000
        # Subtract 1 for initial infection
        avg = final_value / runs - 1
        @test avg < means[p] + stds[p] / sqrt(runs) * 3.5
        @test avg > means[p] - stds[p] / sqrt(runs) * 3.5
    end
end
end


text:
# Note that this script can accept some limited command-line arguments, run
# `julia build_tarballs.jl --help` to see a usage message.
using BinaryBuilder, Pkg

name = "RadeonProRender"
version = v"2.2.7"

# Collection of sources required to complete build
sources = [
    GitSource("https://github.com/GPUOpen-LibrariesAndSDKs/RadeonProRenderSDK.git", "50200b1be97606e73b15baa17c568247e71d0116")
]

# TODO, also ship headers for Clang.jl generation!?
script = raw"""
echo ${target}
cd $WORKSPACE/srcdir/RadeonProRenderSDK/RadeonProRender
if [[ ${target} == x86_64-linux-gnu ]]; then
    cp binUbuntu18/* ${libdir}/
elif [[ ${target} == x86_64-apple-darwin* ]]; then
    cp binMacOS/* ${libdir}/
elif [[ ${target} == x86_64-w64-mingw32 ]]; then
    cp binWin64/* ${libdir}/
fi
"""

# TODO, can we add centos7?
platforms = [
    Platform("x86_64", "linux"),
    Platform("x86_64", "macos"),
    Platform("x86_64", "windows")
]

# Fix warning in BinaryBuilder:
platforms = expand_cxxstring_abis(platforms)

# TODO, Hybrid doesn't exist on OSX, so I guess we can't include it?!
products = [
    # LibraryProduct("Hybrid", :Hybrid),
    # LibraryProduct("HybridPro", :HybridPro),

    # I don't think we need the executables:
    # BinaryProduct("RprTextureCompiler64", :RprTextureCompiler64),
    # BinaryProduct("RprsRender64", :RprsRender64),
    LibraryProduct(["Northstar64", "libNorthstar64"], :libNorthstar64),
    LibraryProduct(["ProRenderGLTF", "libProRenderGLTF"], :libProRenderGLTF),
    LibraryProduct(["RadeonProRender64", "libRadeonProRender64"], :libRadeonProRender64),
    LibraryProduct(["RprLoadStore64", "libRprLoadStore64"], :libRprLoadStore64),
    LibraryProduct(["Tahoe64", "libTahoe64"], :libTahoe64),
]

# Dependencies that must be installed before this package can be built
dependencies = [

    # Not really needed for repacking, but if we ever want to
    # build from scratch we'll need at least these:

    # HostBuildDependency("GLEW_jll"),
    # HostBuildDependency("GLU_jll"),
    # HostBuildDependency("Lua_jll"),
    # BuildDependency("Vulkan_Headers_jll"),
    # BuildDependency("OpenCL_Headers_jll"),
    # BuildDependency("ROCmDeviceLibs_jll"),
    # BuildDependency("ROCmOpenCLRuntime_jll"),
    # BuildDependency("ROCmCompilerSupport_jll"),

    # fix warning from BinaryBuilder:
    Dependency(PackageSpec(name="CompilerSupportLibraries_jll", uuid="e66e0078-7015-5450-92f7-15fbd957f2ae"))
]

# Build the tarballs, and possibly a `build.jl` as well.
build_tarballs(ARGS, name, version, sources, script, platforms, products, dependencies)

max_stars_repo_name: plut/Yggdrasil

max_issues_repo_name: plut/Yggdrasil

max_forks_repo_name: plut/Yggdrasil


text:
isgpu(x) = false
function __init__()
    @require CuArrays="3a865a2d-5b23-5a0f-bc46-62713ec82fae" begin
        gpu_or_cpu(x::CuArrays.CuArray) = CuArrays.CuArray
        gpu_or_cpu(x::TrackedArray{<:Any,<:Any,<:CuArrays.CuArray}) = CuArrays.CuArray
        gpu_or_cpu(x::Transpose{<:Any,<:CuArrays.CuArray}) = CuArrays.CuArray
        gpu_or_cpu(x::Adjoint{<:Any,<:CuArrays.CuArray}) = CuArrays.CuArray
        gpu_or_cpu(x::Adjoint{<:Any,TrackedArray{<:Any,<:Any,<:CuArrays.CuArray}}) = CuArrays.CuArray
        gpu_or_cpu(x::Transpose{<:Any,TrackedArray{<:Any,<:Any,<:CuArrays.CuArray}}) = CuArrays.CuArray
        isgpu(::CuArrays.CuArray) = true
        isgpu(::TrackedArray{<:Any,<:Any,<:CuArrays.CuArray}) = true
        isgpu(::Transpose{<:Any,<:CuArrays.CuArray}) = true
        isgpu(::Adjoint{<:Any,<:CuArrays.CuArray}) = true
        isgpu(::Adjoint{<:Any,TrackedArray{<:Any,<:Any,<:CuArrays.CuArray}}) = true
        isgpu(::Transpose{<:Any,TrackedArray{<:Any,<:Any,<:CuArrays.CuArray}}) = true
    end
end


text:
function main(window)
    push!(window.assets, "widgets")

    # Button
    btn_inp = Signal(Escher.MouseButton, leftbutton)
    bt = hbox(
        button("Click") >>> btn_inp,
        hskip(1em), "Clicks: ", hskip(1em), foldp((x, _) -> x + 1, 0, btn_inp)
    ) |> packacross(center)

    # Checkbox
    cbox_inp = Signal(false)
    cbx = consume(cbox_inp) do x
        hbox(
            checkbox(x, "Label", disabled=false) >>> cbox_inp, hskip(1em),
            intent(!, checkbox(!x, "Label", disabled=false)) >>> cbox_inp,
        )
    end

    # Toggle button
    tb_inp = Signal(false)
    tb = consume(tb_inp) do x
        hbox(
            togglebutton(x, disabled=false) >>> tb_inp, hskip(1em),
            intent(!, togglebutton(!x, disabled=false)) >>> tb_inp,
        )
    end

    # Slider
    sl_inp = Signal(1)
    foo(x) = round(sqrt(x))
    sl = consume(sl_inp) do x
        hbox(
            slider(1:10, value=x) >>> sl_inp,
            intent(foo, slider(1:100, value=x^2)) >>> sl_inp,
        )
    end

    tx_input = Signal("")
    tx = consume(tx_input) do x
        vbox(
            textinput(x, pattern="[a-Z]+", minlength=2, charcounter=true, maxlength=20, error="Letters only!", label="Label") >>> tx_input,
            textinput(x, multiline=true, minlength=2, charcounter=true, maxlength=20, error="Letters only!", label="Label") >>> tx_input,
        )
    end

    rb_inp = Signal("x")
    rb = consume(rb_inp) do x
        vbox(
        radiogroup([
            radio("x", "X"),
            radio("y", "Y"),
        ], selected=x) >>> rb_inp,
        radiogroup([
            radio("x", "X"),
            radio("y", "Y"),
        ], selected=x) >>> rb_inp,
        )
    end

    page = vbox(
        title(2, "widget sampler"),
        vskip(1em),
        vskip(1em),
        bt,
        vskip(1em),
        sl,
        vskip(1em),
        cbx,
        vskip(1em),
        tb,
        tx,
        rb,
        consume(x -> Escher.spinner(x), cbox_inp),
        consume(x -> progress(x, secondaryprogress=x), sl_inp),
        vskip(2em),
        consume(x -> container(5em, 5em) |> paper(floor(x/2)), sl_inp),
    ) |> packacross(center) |> pad(2em)

end


text:
l_vertex = 2.
center = 5.
r_vertex = 7.

mf = TriangularMF(l_vertex, center, r_vertex)

# Evaluation tests
@assert Fuzzy.eval(mf, center) == 1
@assert Fuzzy.eval(mf, l_vertex) == Fuzzy.eval(mf, r_vertex) == 0.
@assert Fuzzy.eval(mf, (l_vertex + center) / 2.) == Fuzzy.eval(mf, (r_vertex + center) / 2.) == 0.5

# Mean finding tests
@assert Fuzzy.mean_at(mf, 1.) == center
@assert Fuzzy.mean_at(mf, 0.) == (l_vertex + r_vertex) / 2.


text:
using Test
using SmartShockFinder

@testset "Test_Meshes" begin
    @testset "1d_Meshes" begin
        # Todo: Number of meshes needs to be adaptive / idea : while not thrown exeption
        for i in 1:5
            @test_nowarn SmartShockFinder.get_mesh_1d(i)
            meshes = SmartShockFinder.get_mesh_1d(i)
            for mesh in meshes
                @test ndims(mesh) == 1
                @test SmartShockFinder.n_directions(mesh.tree) == 2
                @test SmartShockFinder.has_any_neighbor(mesh.tree, 1, 1) == true
            end
        end
    end

    @testset "Test_2d_Meshes" begin
        # Todo: Number of meshes needs to be adaptive
        for i in 1:6
            @test_nowarn SmartShockFinder.get_mesh_2d(i)
            meshes = SmartShockFinder.get_mesh_2d(i)
            for mesh in meshes
                @test ndims(mesh) == 2
                @test SmartShockFinder.n_directions(mesh.tree) == 4
                @test SmartShockFinder.has_any_neighbor(mesh.tree, 1, 1) == true
            end
        end
    end

end


text:
module PercolationModel

using Judycon
import Judycon: connect!

struct Percolation
    grid :: Matrix{Bool}
    li :: LinearIndices
    ny :: Int
    nx :: Int
    wuf1 :: QuickUnion
    wuf2 :: QuickUnion
    node1 :: Int
    node2 :: Int
end

function Percolation(ny, nx)
    grid = zeros(Bool, ny, nx)
    li = LinearIndices(grid)
    wuf1 = QuickUnion(nx*ny + 2)
    wuf2 = QuickUnion(nx*ny + 1)
    return Percolation(grid, li, ny, nx, wuf1, wuf2, nx*ny + 1, nx*ny + 2)
end

function connect!(p::Percolation, i, j)
    connect!(p.wuf1, i, j)
    connect!(p.wuf2, i, j)
end

function isopen(p::Percolation, i, j)
    return p.grid[i, j]
end

function number_of_open(p::Percolation)
    return sum(p.grid)
end

function isfull(p::Percolation, i, j)
    !isopen(p, i, j) && return false
    return isconnected(p.wuf2, p.node1, p.li[i, j])
end

function percolates(p::Percolation)
    return isconnected(p.wuf1, p.node1, p.node2)
end

function open!(p::Percolation, i, j)
    isopen(p, i, j) && return
    p.grid[i, j] = true

    i == 1       && connect!(p, p.node1, p.li[i, j])
    i == p.ny    && connect!(p.wuf1, p.node2, p.li[i, j])

    i > 1        && isopen(p, i-1, j) && connect!(p, p.li[i, j], p.li[i-1, j])
    i < p.ny - 1 && isopen(p, i+1, j) && connect!(p, p.li[i, j], p.li[i+1, j])
    j > 1        && isopen(p, i, j-1) && connect!(p, p.li[i, j], p.li[i, j-1])
    j < p.nx - 1 && isopen(p, i, j+1) && connect!(p, p.li[i, j], p.li[i, j+1])
end

using Statistics

struct Result{T}
    samples :: Vector{T}
    mean :: Float64
    stddev :: Float64
    confidence_lo :: Float64
    confidence_hi :: Float64
end

const CONFIDENCE_95 = 1.96

function Result(samples)
    n = length(samples)
    m = mean(samples)
    s = std(samples)
    cl = m - CONFIDENCE_95 * s / sqrt(n)
    ch = m + CONFIDENCE_95 * s / sqrt(n)
    return Result(samples, m, s, cl, ch)
end

using Printf

function Base.show(io::IO, r::Result)
    @printf("% 25s =  %d\n", "samples", length(r.samples))
    @printf("% 25s =  %0.3f\n", "mean", r.mean)
    @printf("% 25s =  %0.3f\n", "stddev", r.stddev)
    @printf("% 25s = [%0.3f, %0.3f]\n", "95% confidence interval", r.confidence_lo, r.confidence_hi)
end

function run_one(ny, nx)
    p = Percolation(ny, nx)
    while !percolates(p)
        open!(p, rand(1:ny), rand(1:nx))
    end
    return p
end

function run(n, trials)
    thresholds = zeros(trials)
    for i=1:trials
        p = run_one(n, n)
        thresholds[i] = number_of_open(p) / n^2
    end
    return Result(thresholds)
end

end


text:
module Exceptions
export @ModuleInternalError, @IncoherentCallError, @NotInitializedError, @IncoherentArgumentError, @KeywordArgumentError, @ArgumentEvaluationError, @ArgumentError, @InsecureRecognitionException
export ModuleInternalError, IncoherentCallError, NotInitializedError, IncoherentArgumentError, KeywordArgumentError, ArgumentEvaluationError, InsecureRecognitionException

macro ModuleInternalError(msg) esc(:(throw(ModuleInternalError($msg)))) end
macro IncoherentCallError(msg) esc(:(throw(IncoherentCallError($msg)))) end
macro NotInitializedError(msg) esc(:(throw(NotInitializedError($msg)))) end
macro IncoherentArgumentError(msg) esc(:(throw(IncoherentArgumentError($msg)))) end
macro KeywordArgumentError(msg) esc(:(throw(KeywordArgumentError($msg)))) end
macro ArgumentEvaluationError(msg) esc(:(throw(ArgumentEvaluationError($msg)))) end
macro ArgumentError(msg) esc(:(throw(ArgumentError($msg)))) end
macro InsecureRecognitionException(msg) esc(:(throw(InsecureRecognitionException($msg)))) end

struct ModuleInternalError <: Exception
    msg::String
end
Base.showerror(io::IO, e::ModuleInternalError) = print(io, "ModuleInternalError: ", e.msg)

struct IncoherentCallError <: Exception
    msg::String
end
Base.showerror(io::IO, e::IncoherentCallError) = print(io, "IncoherentCallError: ", e.msg)

struct NotInitializedError <: Exception
    msg::String
end
Base.showerror(io::IO, e::NotInitializedError) = print(io, "NotInitializedError: ", e.msg)

struct IncoherentArgumentError <: Exception
    msg::String
end
Base.showerror(io::IO, e::IncoherentArgumentError) = print(io, "IncoherentArgumentError: ", e.msg)

struct KeywordArgumentError <: Exception
    msg::String
end
Base.showerror(io::IO, e::KeywordArgumentError) = print(io, "KeywordArgumentError: ", e.msg)

struct ArgumentEvaluationError <: Exception
    msg::String
end
Base.showerror(io::IO, e::ArgumentEvaluationError) = print(io, "ArgumentEvaluationError: ", e.msg)

struct InsecureRecognitionException <: Exception
    msg::String
end
Base.showerror(io::IO, e::InsecureRecognitionException) = print(io, "InsecureRecognitionException: ", e.msg)

end # Module Exceptions