text:
### A Pluto.jl notebook ###
# v0.17.5

using Markdown

# ╔═╡ 51dfc4a3-d921-4bfb-90fe-4c46f71262b6
using Plots, StatsPlots, DataFrames, CSV, Query, ColorSchemes, Random, Dates, StatsBase

# ╔═╡ 5e70c04a-7aea-11ec-1954-c1abedfba9b1
html"""<style>
pluto-output {    font-size: 1.2em;   }
pluto-input .cm-content { font-size: 0.9em !important; }
"""

# ╔═╡ 1dd2142c-64dd-4a7d-8767-371d3bbc460d
md"""
# QALY i DALY — ekonomiczna ocena usług zdrowotnych. Częsć 03
"""

# ╔═╡ a1638102-90f3-4459-a6d1-2ecf7fbfb0cf

md"""
Jak połączyć wskaźniki PYLL (potencjalne lata utracone przez chorobę) i YLD (lata przeżyte z chorobą)?

Ponieważ oba wskaźniki mają ten sam wymiar można je po prostu dodać. Ten wskaźnik jest nazywany DALY (disability-adjusted life years). Czyli utracone lata skorygowane niepełnosprawnością.
"""

# ╔═╡ 4a987dd3-b5ba-42c8-92f5-4875b32ba25a
begin
	zad5_skrocenie_zycia = 20
	zad5_obnizenie_jakosci = 0.5
	zad5_okres_chorowania = 16
	nothing
end

# ╔═╡ 39509739-a137-4b49-8596-eaf167d3b26c
md"""
**Zadanie 5.** Ile lat DALY zabiera choroba, która skraca życie o $(zad5_skrocenie_zycia) oraz powoduje obniżenie jakości życia o $(zad5_obnizenie_jakosci*100) % przez $(zad5_okres_chorowania) lat?
"""

# ╔═╡ 566c835a-ee2a-4692-9161-dee4bde4aa29
md"""
Narysujmy najpierw wykres:
"""

# ╔═╡ 5a29ad55-d0ab-4136-84c9-db1ee0efcbdb
begin
	rectangle(x, y, w, h) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])

	function plotDALY(;
		skrocenie_zycia,
		czas_choroby,
		obnizenie_jakosci,
		plot_choroba=true,
		plot_pyll=false,
		plot_yld=false,
		legend=:topright,
		srednia_dlugosc_zycia = 78.58,
		labels = true,
	)
		wiek_smierci = srednia_dlugosc_zycia - skrocenie_zycia
		wiek_zachorowania = wiek_smierci - czas_choroby
		jakoscZyciaZdrowego = DataFrame(
			:Year    => [0,   srednia_dlugosc_zycia, srednia_dlugosc_zycia*1.1 ],
			:Quality => [1.0, 0.0,   0.0 ],
		)
		jakoscZyciaChorego = DataFrame(
			:Year    => [0, wiek_zachorowania,       wiek_smierci],
			:Quality => [1.0, 1.0-obnizenie_jakosci, 0.0  ],
		)

		p = plot(
			jakoscZyciaZdrowego.Year, jakoscZyciaZdrowego.Quality,
			label= labels ? "Życie zdrowego człowieka" : "",
			xlabel= labels ?  "Lata życia" : "", ylabel= labels ?  "Jakość życia [%]" : "",
			seriestype=:steppost, linewidth = 3, linecolor = :green,
			fill = (0, 0.5, :green), legend=legend,
		)
		if plot_choroba
			plot!(p,
				jakoscZyciaChorego.Year, jakoscZyciaChorego.Quality,
				label="Życie chorego człowieka",
				seriestype=:steppost, linewidth = 3, linecolor = :red,
				fill = (0, 0.99, :darkred),
			)

			plot!(p,
				[25,jakoscZyciaChorego.Year[2]], [0.9,jakoscZyciaChorego.Quality[2]], arrow=(:closed, 2.0), color = :white, label=nothing,
				ann=[(25,0.9, text("Zachorowanie", 8, :white))]
			)
			plot!(p,
				[62,wiek_smierci], [0.2,0.0], arrow=(:closed, 2.0), color = :white, label=nothing,
				ann=[(62,0.2, text("Śmierć", 8, :white))]
			)
		end

		if plot_pyll
			plot!(p,
				rectangle(wiek_smierci, 0, skrocenie_zycia, 1.0),
				color = :black, opacity = 0.9, label="PYLL",
				ann= labels ? [(wiek_smierci + skrocenie_zycia/2,0.5, text("PYLL", 8, :white))] : []
			)
		end

		if plot_yld
			plot!(p,
				rectangle(wiek_zachorowania, 1.0-obnizenie_jakosci, czas_choroby, obnizenie_jakosci),
				color = :black, opacity = 0.8, label="YLD",
				ann= labels ? [(wiek_zachorowania + czas_choroby/2,1.0-obnizenie_jakosci/2, text("YLD", 8, :white))] : []
			)
		end

		p
	end

	plot_daly_choroba = plotDALY(
		skrocenie_zycia = zad5_skrocenie_zycia,
		obnizenie_jakosci = zad5_obnizenie_jakosci,
		czas_choroby = zad5_okres_chorowania,
	)
end

# ╔═╡ df848c66-05dc-422e-8d75-1b8baa3b3131
plot_daly_choroba_pyll = plotDALY(
		skrocenie_zycia = zad5_skrocenie_zycia,
		obnizenie_jakosci = zad5_obnizenie_jakosci,
		czas_choroby = zad5_okres_chorowania,
		plot_pyll = true
)

# ╔═╡ d7f05e14-5416-4c07-bd93-1b40cd76004d
plot_daly_choroba_pyll_yld = plotDALY(
		skrocenie_zycia = zad5_skrocenie_zycia,
		obnizenie_jakosci = zad5_obnizenie_jakosci,
		czas_choroby = zad5_okres_chorowania,
		plot_pyll = true,
		plot_yld = true
)

# ╔═╡ 95bbecce-7aa6-4111-9ed3-3b86334da8ba
plot_daly_pyll_yld = plotDALY(
		skrocenie_zycia = zad5_skrocenie_zycia,
		obnizenie_jakosci = zad5_obnizenie_jakosci,
		czas_choroby = zad5_okres_chorowania,
		plot_pyll = true,
		plot_yld = true,
		plot_choroba = false
)

# ╔═╡ cb4e1442-3ecc-47a9-8e7e-e2e3fc3d6b66
begin
	plots = [
		plot_daly_choroba,
		plot_daly_choroba,
		plot_daly_choroba,
		plot_daly_choroba_pyll,
		plot_daly_choroba_pyll_yld,
		plot_daly_pyll_yld
	]
	anim = @animate for i ∈ plots
    	plot(i)
	end
	gif(anim, fps = 1)
end

# ╔═╡ ef0bf3a9-f322-4364-aab9-5ebeaa682af2
begin
	struct Choroba
    	skrocenie_zycia::Int
		czas_trwania::Float64
		obnizenie_jakosci::Float64
    end

	format_procent(f::Float64) = string(Int(floor(f*100))) * "%"
	opisz(ch::Choroba) = "skraca życie o $(ch.skrocenie_zycia) lat, obniża jakość o $(format_procent(ch.obnizenie_jakosci)) przez $(ch.czas_trwania) lat"

	zad6_chorobaA = Choroba(15, 30, 0.06)
	zad6_chorobaB = Choroba(5, 2, 0.50)
	nothing
end

# ╔═╡ ea7157f0-dbc1-4f8e-a20a-15bc379d7703
md"""
**Zadanie 6.** Która choroba jest bardziej obciążająca?

- Choroba A: $(opisz(zad6_chorobaA)) (a więc o typie nadciśnienia / choroby wieńcowej)
- Choroba B: $(opisz(zad6_chorobaB)) (a więc o typie nowotworu złośliwego)
"""

# ╔═╡ ff8ce60b-d73c-407c-823a-1ba1af58b1f2
begin
	yld(ch::Choroba) = ch.czas_trwania * ch.obnizenie_jakosci
	daly(ch::Choroba) = yld(ch) + ch.skrocenie_zycia
end

# ╔═╡ 0a45afb4-877b-4d17-b494-434359a88964
md"""
Rozwiązanie: obliczmy DALY
1. Obliczamy YLD czyli ilość lat przeżytych z niepełną sprawnością:

     Choroba A: $(zad6_chorobaA.czas_trwania) lat ⨉ $(format_procent(zad6_chorobaA.obnizenie_jakosci)) = $(round(yld(zad6_chorobaA),digits=1)) lat

     Choroba B: $(zad6_chorobaB.czas_trwania) lat ⨉ $(format_procent(zad6_chorobaB.obnizenie_jakosci)) = $(round(yld(zad6_chorobaB),digits=1)) lat

2. Obliczamy PYLL czyli ilość potencjalnych lat życia utraconych z powodu choroby. W tym przypadku PYLL jest po prostu równy skróceniu życia przez chorobę

    Choroba A: $(zad6_chorobaA.skrocenie_zycia) lat

    Choroba B: $(zad6_chorobaB.skrocenie_zycia) lat

3. Sumujemy wartości:

    Choroba A: DALYa= $(zad6_chorobaA.skrocenie_zycia) lat + $(round(yld(zad6_chorobaA),digits=1)) lat = $(round(daly(zad6_chorobaA),digits=1)) lat

    Choroba B: DALYb= $(zad6_chorobaB.skrocenie_zycia) lat + $(round(yld(zad6_chorobaB),digits=1)) lat = $(round(daly(zad6_chorobaB),digits=1)) lat

Jasno widać, że choroba A jest znacznie większym obciążeniem.
"""

# ╔═╡ 00ff8ef6-411a-43ea-aed6-9f85f4fedeb3
begin
	zad6_plot_choroba(ch::Choroba) = plotDALY(
		skrocenie_zycia = ch.skrocenie_zycia,
		obnizenie_jakosci = ch.obnizenie_jakosci,
		czas_choroby = ch.czas_trwania,
		plot_pyll = true,
		plot_yld = true,
		plot_choroba = false,
		legend=:bottomleft
	)
	zad6_plot_chorobaA = zad6_plot_choroba(zad6_chorobaA)
	zad6_plot_chorobaB = zad6_plot_choroba(zad6_chorobaB)
	plot(zad6_plot_chorobaA, zad6_plot_chorobaB, layout = (1, 2), size=(900,300))
end

# ╔═╡ 30c07113-fe95-4d31-828a-3d01e090cb35
begin
	zad6_anim = @animate for i ∈ [zad6_plot_chorobaA,zad6_plot_chorobaB]
    	plot(i)
	end
	gif(zad6_anim, fps = 1)
end

# ╔═╡ 6f3fbc75-5581-4f09-a79f-f3476365839b
begin
	zad7_p_lagodny = Choroba(0, 2, 0.3)
	zad7_p_smiertelny = Choroba(15, 1, 0.9)
	zad7_p_powiklany = Choroba(4, 7, 0.15)
	zad7_przebiegi = DataFrame(
		:Przebieg => [zad7_p_lagodny, zad7_p_smiertelny, zad7_p_powiklany],
		:Czestosc => [0.72, 0.08,0.2]
	)
	nothing
end

# ╔═╡ 2e19b761-dcde-49dc-8a97-9eb369006943
md"""
No dobrze, ale zajmijmy się bardziej życiowym przykładem — fikcyjną chorobą COVID23!

Założmy, że podobnie jak w COVID19, COVID23 w większości przypadków ma łagodny przebieg. Możemy wyróżnić trzy scenariusze:

- przebieg łagodny: $(opisz(zad7_p_lagodny))
- przebieg śmiertelny: $(opisz(zad7_p_smiertelny))
- przebieg powikłany: $(opisz(zad7_p_powiklany)) - np. mgła COVID23

Wiemy jak policzyć obciążenie chorobą DALY dla każdego z wariantów oddzielnie. Ale jak policzyć dla całej choroby? Należy poznać częstość tych przebiegów. Założmy, że:

- przebieg łagodny występuje z częstością $(format_procent(zad7_przebiegi[1,2]))
- przebieg śmiertelny występuje z częstością $(format_procent(zad7_przebiegi[2,2]))
- przebieg powikłany występuje z częstością $(format_procent(zad7_przebiegi[3,2]))

**Zadanie 7.** Jakie będzie DALY COVID23?

*Uwaga: na poniższych wykresach średnia długość życia jest skrócona, żeby lepiej zobrazować przebiegi*
"""

# ╔═╡ f2cc6dca-95f6-4d6f-9d94-046e7c5c670f
begin
	function zad7_plotDALY_z_prawdopodobienstwem(przebiegi)
		ch = StatsBase.sample(przebiegi.Przebieg, ProbabilityWeights(przebiegi.Czestosc))
		plotDALY(
			skrocenie_zycia = ch.skrocenie_zycia,
			obnizenie_jakosci = ch.obnizenie_jakosci,
			czas_choroby = ch.czas_trwania,
			srednia_dlugosc_zycia = 30,
			plot_pyll = true,
			plot_yld = true,
			plot_choroba = false,
			legend=nothing,
			labels = false
		)
	end
	zad7_plots = [
		zad7_plotDALY_z_prawdopodobienstwem(zad7_przebiegi) for i in 1:54
	]
	plot(zad7_plots..., layout=(9,6), size=(900,900), xticks = nothing, yticks=nothing)
end

# ╔═╡ 26b096b4-eb9b-4e3c-8fea-9c7870a98485
begin
	zad7_pyll_sredni = sum([p.Przebieg.skrocenie_zycia * p.Czestosc for p in eachrow(zad7_przebiegi)])
	zad7_yld_sredni = sum([yld(p.Przebieg) * p.Czestosc for p in eachrow(zad7_przebiegi)])
	zad7_daly_sredni = zad7_pyll_sredni + zad7_yld_sredni
	nothing
end

# ╔═╡ 155423f0-8ecd-43de-aa45-f9c142877178
md"""
Rozwiązanie: możemy to zadanie rozwiązać na dwa sposoby, populacyjnie lub z prawdopodobieństwa.

1. Możemy obliczyć średni PYLL i średnie YLD:

   PYLL łagodny * częstość łagodna + PYLL śmiertelny * częstość śmiertelna + PYLL powikłany * częstość powikłana = średnio $(zad7_pyll_sredni) lat

2. Analogicznie obliczamy YLD:

   YLD łagodny * częstość łagodna + YLD śmiertelny * częstość śmiertelna + YLD powikłany * częstość powikłana = średnio $(zad7_yld_sredni) lat

3. Czyli średnie DALY wyniesie: YLD + PYLL = $(zad7_daly_sredni) lat

"""

# ╔═╡ e0c3d63b-f6c5-45b0-9a39-e203e6032cc2
begin
	zad7_daly_na_przebieg = [
		daly(p.Przebieg) for p in eachrow(zad7_przebiegi)
	]

	zad7_daly_wazone = [
		daly(p.Przebieg) * p.Czestosc for p in eachrow(zad7_przebiegi)
	]

	zad7_daly_suma = sum(zad7_daly_wazone)
end

# ╔═╡ 39e02898-d1cf-4a2c-9f3c-e83bef185b4e
md"""
Analogicznie możemy najpierw policzyć DALY każdej z postaci i przemnożyć razy częstość:

- Łagodnej: $(zad7_daly_na_przebieg[1]) lat * $(zad7_przebiegi.Czestosc[1]) = $(round(zad7_daly_wazone[1],digits=1))
- Śmiertelnej: $(zad7_daly_na_przebieg[2]) lat * $(zad7_przebiegi.Czestosc[2]) = $(round(zad7_daly_wazone[2],digits=1))
- Powikłanej: $(zad7_daly_na_przebieg[3]) lat * $(zad7_przebiegi.Czestosc[3]) = $(round(zad7_daly_wazone[3],digits=1))

Suma wyniesie: $(round(zad7_daly_suma,digits=1)) lat
"""

# ╔═╡ 08e05b49-e4c6-45b3-83e7-289292b96636
begin
	jakoscZyciaZdrowego = DataFrame(
		:Year    => [0,   78.58, 85 ],
		:Quality => [1.0, 0.0,   0.0 ],
	)
	jakoscZyciaNieleczonego = DataFrame(
		:Year    => [0,   30,   35,                    55,   77,   78.58],
		:Quality => [1.0, 1.0,  0.8,                   0.55, 0.0,  0.0  ],
	)
	jakoscZyciaLeczonego = DataFrame(
		:Year    => [0,   30,   35,  39,   45,   60,   70,  77,   78.58],
		:Quality => [1.0, 1.0,  0.8, 0.85, 0.8,  0.75, 0.4, 0.0,  0.0  ],
	)

	plotJakosc = plot(
		jakoscZyciaZdrowego.Year, jakoscZyciaZdrowego.Quality,
		label="Życie zdrowego człowieka",
		xlabel="Lata życia", ylabel="Jakość życia [%]",
		seriestype=:steppost, linewidth = 3, linecolor = :green,
		fill = (0, 0.5, :green),
	)
	plot!(plotJakosc,
		jakoscZyciaLeczonego.Year, jakoscZyciaLeczonego.Quality,
		label="Życie leczonego człowieka",
		seriestype=:line, linewidth = 3, linecolor = :orange,
		fill = (0, 0.99, :darkorange),
	)
	plot!(plotJakosc,
		jakoscZyciaNieleczonego.Year, jakoscZyciaNieleczonego.Quality,
		label="Życie nieleczonego człowieka",
		seriestype=:line, linewidth = 3, linecolor = :red,
		fill = (0, 0.99, :darkred),
	)
	plot!(plotJakosc,
		[25,30], [0.9,1.0], arrow=(:closed, 2.0), color = :white, label=nothing,
		ann=[(25,0.9, text("Zachorowanie", 8, :white))]
	)
	plot!(plotJakosc,
		[34,39], [0.7,0.85], arrow=(:closed, 2.0), color = :white, label=nothing,
		ann=[(34,0.7, text("Poprawa\npo leczeniu", 8, :white))]
	)
	plot!(plotJakosc,
		[62,77], [0.2,0.0], arrow=(:closed, 2.0), color = :white, label=nothing,
		ann=[(62,0.2, text("Niecznacznie\nprzedwczesna\nśmierć", 8, :white))]
	)
end

# ╔═╡ 1ef53516-d25c-467e-af04-a15580aa3f4b
begin
	function leczenieSkracaPlot()
		jakoscZyciaZdrowego = DataFrame(
			:Year    => [0,   78.58, 85 ],
			:Quality => [1.0, 0.0,   0.0 ],
		)
		jakoscZyciaNieleczonego = DataFrame(
			:Year    => [0,   30,   35,                    55,   77,   78.58],
			:Quality => [1.0, 1.0,  0.8,                   0.55, 0.0,  0.0  ],
		)
		jakoscZyciaLeczonego = DataFrame(
			:Year    => [0,   30,   35,  39,   45,   60,   70,  77,   78.58],
			:Quality => [1.0, 1.0,  0.8, 0.85, 0.8,  0.75, 0.0, 0.0,  0.0  ],
		)

		plotJakosc = plot(
			jakoscZyciaZdrowego.Year, jakoscZyciaZdrowego.Quality,
			label="Życie zdrowego człowieka",
			xlabel="Lata życia", ylabel="Jakość życia [%]",
			seriestype=:steppost, linewidth = 3, linecolor = :green,
			fill = (0, 0.5, :green),
		)
		plot!(plotJakosc,
			jakoscZyciaLeczonego.Year, jakoscZyciaLeczonego.Quality,
			label="Życie leczonego człowieka",
			seriestype=:line, linewidth = 3, linecolor = :orange,
			fill = (0, 0.99, :darkorange),
		)
		plot!(plotJakosc,
			jakoscZyciaNieleczonego.Year, jakoscZyciaNieleczonego.Quality,
			label="Życie nieleczonego człowieka",
			seriestype=:line, linewidth = 3, linecolor = :red,
			fill = (0, 0.5, :darkred),
		)
		plot!(plotJakosc,
			[25,30], [0.9,1.0], arrow=(:closed, 2.0), color = :white, label=nothing,
			ann=[(25,0.9, text("Zachorowanie", 8, :white))]
		)
		plot!(plotJakosc,
			[34,39], [0.7,0.85], arrow=(:closed, 2.0), color = :white, label=nothing,
			ann=[(34,0.7, text("Poprawa\npo leczeniu", 8, :white))]
		)
	end
	leczenieSkracaPlot()
end

# ╔═╡ 9d35de41-34a3-436d-96d6-039ca025bbae
begin
	function plotQALYDesc()
		jakoscZyciaZdrowego = DataFrame(
			:Year    => [0,   78.58, 85 ],
			:Quality => [1.0, 0.0,   0.0 ],
		)
		jakoscZyciaNieleczonego = DataFrame(
			:Year    => [0,   30,   35,                    55,   77,   78.58],
			:Quality => [1.0, 1.0,  0.8,                   0.55, 0.0,  0.0  ],
		)
		jakoscZyciaLeczonego = DataFrame(
			:Year    => [0,   30,   35,  39,   45,   60,   70,  77,   78.58],
			:Quality => [1.0, 1.0,  0.8, 0.85, 0.8,  0.75, 0.4, 0.0,  0.0  ],
		)

		plotJakosc = plot(
			jakoscZyciaZdrowego.Year, jakoscZyciaZdrowego.Quality,
			label="Życie zdrowego człowieka",
			xlabel="Lata życia", ylabel="Jakość życia [%]",
			seriestype=:steppost, linewidth = 3, linecolor = :green,
			fill = (0, 0.5, :green),
		)
		plot!(plotJakosc,
			jakoscZyciaLeczonego.Year, jakoscZyciaLeczonego.Quality,
			label="Życie leczonego człowieka",
			seriestype=:line, linewidth = 3, linecolor = :orange,
			fill = (0, 0.99, :darkorange),
		)
		plot!(plotJakosc,
			jakoscZyciaNieleczonego.Year, jakoscZyciaNieleczonego.Quality,
			label="Życie nieleczonego człowieka",
			seriestype=:line, linewidth = 3, linecolor = :red,
			fill = (0, 0.99, :darkred),
		)
		plot!(plotJakosc,
			ann=[(53,0.69, text("uratowane\nQALY", 10, :white))]
		)
	end
	plotQALYDesc()
end

# ╔═╡ d6192862-9577-4c10-b6dc-98c1441ca284
begin
	pv(fv::Float64, r::Float64, n::Float64) = fv / ((1+r)^n)

	x = [i for i in 0:20]
	fv = 15.0

	plot(x,[pv(fv, 0.035, Float64(n)) for n in x], label = "Spadek wartości zdrowia w tempie 3.5%/rok")
	plot!(x,[pv(fv, 0.05, Float64(n)) for n in x], label = "Spadek wartości pieniądza w tempie 5%/rok")
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
ColorSchemes = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Query = "1a8c2f83-1ff3-5112-b086-8aa67b057ba1"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

[compat]
CSV = "~0.10.2"
ColorSchemes = "~3.16.0"
DataFrames = "~1.3.1"
Plots = "~1.25.5"
PlutoUI = "~0.7.30"
Query = "~1.0.0"
StatsBase = "~0.33.14"
StatsPlots = "~0.14.30"
"""

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

julia_version = "1.7.1"
manifest_format = "2.0"

[[deps.AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.1.0"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"

[[deps.Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.3"

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

[[deps.Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
git-tree-sha1 = "2ff92b71ba1747c5fdd541f8fc87736d82f40ec9"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.4.0"

[[deps.Arpack_jll]]
deps = ["Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.0+3"

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

[[deps.AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.1"

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

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

[[deps.CSV]]
deps = ["CodecZlib", "Dates", "FilePathsBase", "InlineStrings", "Mmap", "Parsers", "PooledArrays", "SentinelArrays", "Tables", "Unicode", "WeakRefStrings"]
git-tree-sha1 = "9519274b50500b8029973d241d32cfbf0b127d97"
uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
version = "0.10.2"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"

[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "54fc4400de6e5c3e27be6047da2ef6ba355511f8"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.11.6"

[[deps.ChangesOfVariables]]
deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.2"

[[deps.Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "75479b7df4167267d75294d14b58244695beb2ac"
uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
version = "0.14.2"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.0"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "6b6f04f93710c71550ec7e16b650c1b9a612d0b6"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.16.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[deps.Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.41.0"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[deps.Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[deps.Crayons]]
git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.1.1"

[[deps.DataAPI]]
git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"

[[deps.DataFrames]]
deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
git-tree-sha1 = "cfdfef912b7f93e4b848e80b9befdf9e331bc05a"
uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
version = "1.3.1"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.11"

[[deps.DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[deps.DataValues]]
deps = ["DataValueInterfaces", "Dates"]
git-tree-sha1 = "d88a19299eba280a6d062e135a43f00323ae70bf"
uuid = "e7dc6d0d-1eca-5fa6-8ad6-5aecde8b7ea5"
version = "0.4.13"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[deps.DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[deps.DensityInterface]]
deps = ["InverseFunctions", "Test"]
git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
version = "0.4.0"

[[deps.Distances]]
deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.7"

[[deps.Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[deps.Distributions]]
deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
git-tree-sha1 = "08f8555cb66936b871dcfdad09a4f89e754181db"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.40"

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

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

[[deps.EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
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version = "2.2.3+0"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
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[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
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[[deps.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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[[deps.FFTW]]
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git-tree-sha1 = "463cb335fa22c4ebacfd1faba5fde14edb80d96c"
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[[deps.FFTW_jll]]
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git-tree-sha1 = "c6033cc3892d0ef5bb9cd29b7f2f0331ea5184ea"
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[[deps.FilePathsBase]]
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[[deps.FillArrays]]
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[[deps.FixedPointNumbers]]
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[[deps.Fontconfig_jll]]
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git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
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[[deps.Formatting]]
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[[deps.FreeType2_jll]]
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[[deps.FriBidi_jll]]
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[[deps.Future]]
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[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
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[[deps.GR]]
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[[deps.GR_jll]]
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[[deps.GeometryBasics]]
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[[deps.Gettext_jll]]
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[[deps.Glib_jll]]
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[[deps.Graphite2_jll]]
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[[deps.Grisu]]
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[[deps.HTTP]]
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git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
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[[deps.HarfBuzz_jll]]
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git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
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[[deps.Hyperscript]]
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[[deps.HypertextLiteral]]
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[[deps.IOCapture]]
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[[deps.IniFile]]
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[[deps.InlineStrings]]
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git-tree-sha1 = "8d70835a3759cdd75881426fced1508bb7b7e1b6"
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uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
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[[deps.SentinelArrays]]
deps = ["Dates", "Random"]
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[[deps.Serialization]]
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[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
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[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
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[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
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[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
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[[deps.StaticArrays]]
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git-tree-sha1 = "2884859916598f974858ff01df7dfc6c708dd895"
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[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.StatsAPI]]
git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
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[[deps.StatsBase]]
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uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
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[[deps.StatsFuns]]
deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.14"

[[deps.StatsPlots]]
deps = ["Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "e1e5ed9669d5521d4bbdd4fab9f0945a0ffceba2"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
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[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "d21f2c564b21a202f4677c0fba5b5ee431058544"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
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[[deps.SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

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

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

[[deps.TableShowUtils]]
deps = ["DataValues", "Dates", "JSON", "Markdown", "Test"]
git-tree-sha1 = "14c54e1e96431fb87f0d2f5983f090f1b9d06457"
uuid = "5e66a065-1f0a-5976-b372-e0b8c017ca10"
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[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

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

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

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

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

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

[[deps.URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

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

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

[[deps.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[deps.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"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[deps.WeakRefStrings]]
deps = ["DataAPI", "InlineStrings", "Parsers"]
git-tree-sha1 = "c69f9da3ff2f4f02e811c3323c22e5dfcb584cfa"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
version = "1.4.1"

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

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.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"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[deps.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"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

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

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

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

[[deps.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:
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# ╠═5a29ad55-d0ab-4136-84c9-db1ee0efcbdb
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# ╠═ef0bf3a9-f322-4364-aab9-5ebeaa682af2
# ╟─ea7157f0-dbc1-4f8e-a20a-15bc379d7703
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max_stars_repo_name: Jblew/towards-julia-notebook

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max_forks_repo_name: Jblew/towards-julia-notebook


text:
struct DeivVecTag end

# J(f(x))*v
function auto_jacvec!(du, f, x, v,
                      cache1 = ForwardDiff.Dual{DeivVecTag}.(x, v),
                      cache2 = ForwardDiff.Dual{DeivVecTag}.(x, v))
    cache1 .= Dual{DeivVecTag}.(x, v)
    f(cache2,cache1)
    du .= partials.(cache2, 1)
end
function auto_jacvec(f, x, v)
    partials.(f(Dual{DeivVecTag}.(x, v)), 1)
end

function num_jacvec!(du,f,x,v,cache1 = similar(v),
                     cache2 = similar(v);
                     compute_f0 = true)
    compute_f0 && (f(cache1,x))
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    @. x += ϵ*v
    f(cache2,x)
    @. x -= ϵ*v
    @. du = (cache2 - cache1)/ϵ
end

function num_jacvec(f,x,v,f0=nothing)
    f0 === nothing ? _f0 = f(x) : _f0 = f0
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(minimum(x)))
    (f(x.+ϵ.*v) .- f(x))./ϵ
end

function num_hesvec!(du,f,x,v,
                     cache1 = similar(v),
                     cache2 = similar(v),
                     cache3 = similar(v))
    cache = DiffEqDiffTools.GradientCache(v[1],cache1,Val{:central})
    g = let f=f,cache=cache
        (dx,x) -> DiffEqDiffTools.finite_difference_gradient!(dx,f,x,cache)
    end
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    @. x += ϵ*v
    g(cache2,x)
    @. x -= 2ϵ*v
    g(cache3,x)
    @. du = (cache2 - cache3)/(2ϵ)
end

function num_hesvec(f,x,v)
    g = (x) -> DiffEqDiffTools.finite_difference_gradient(f,x)
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    x += ϵ*v
    gxp = g(x)
    x -= 2ϵ*v
    gxm = g(x)
    (gxp - gxm)/(2ϵ)
end

function numauto_hesvec!(du,f,x,v,
                     cache = ForwardDiff.GradientConfig(f,v),
                     cache1 = similar(v),
                     cache2 = similar(v))
    g = let f=f,x=x,cache=cache
        g = (dx,x) -> ForwardDiff.gradient!(dx,f,x,cache)
    end
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    @. x += ϵ*v
    g(cache1,x)
    @. x -= 2ϵ*v
    g(cache2,x)
    @. du = (cache1 - cache2)/(2ϵ)
end

function numauto_hesvec(f,x,v)
    g = (x) -> ForwardDiff.gradient(f,x)
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    x += ϵ*v
    gxp = g(x)
    x -= 2ϵ*v
    gxm = g(x)
    (gxp - gxm)/(2ϵ)
end

function autonum_hesvec!(du,f,x,v,
                     cache1 = similar(v),
                     cache2 = ForwardDiff.Dual{DeivVecTag}.(x, v),
                     cache3 = ForwardDiff.Dual{DeivVecTag}.(x, v))
    cache = DiffEqDiffTools.GradientCache(v[1],cache1,Val{:central})
    g = (dx,x) -> DiffEqDiffTools.finite_difference_gradient!(dx,f,x,cache)
    cache2 .= Dual{DeivVecTag}.(x, v)
    g(cache3,cache2)
    du .= partials.(cache3, 1)
end

function autonum_hesvec(f,x,v)
    g = (x) -> DiffEqDiffTools.finite_difference_gradient(f,x)
    partials.(g(Dual{DeivVecTag}.(x, v)), 1)
end

function num_hesvecgrad!(du,g,x,v,
                     cache2 = similar(v),
                     cache3 = similar(v))
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    @. x += ϵ*v
    g(cache2,x)
    @. x -= 2ϵ*v
    g(cache3,x)
    @. du = (cache2 - cache3)/(2ϵ)
end

function num_hesvecgrad(g,x,v)
    T = eltype(x)
    # Should it be min? max? mean?
    ϵ = sqrt(eps(real(T))) * max(one(real(T)), abs(norm(x)))
    x += ϵ*v
    gxp = g(x)
    x -= 2ϵ*v
    gxm = g(x)
    (gxp - gxm)/(2ϵ)
end

function auto_hesvecgrad!(du,g,x,v,
                     cache2 = ForwardDiff.Dual{DeivVecTag}.(x, v),
                     cache3 = ForwardDiff.Dual{DeivVecTag}.(x, v))
    cache2 .= Dual{DeivVecTag}.(x, v)
    g(cache3,cache2)
    du .= partials.(cache3, 1)
end

function auto_hesvecgrad(g,x,v)
    partials.(g(Dual{DeivVecTag}.(x, v)), 1)
end

### Operator Forms

struct JacVec{F,T1,T2,uType}
    f::F
    cache1::T1
    cache2::T2
    u::uType
    autodiff::Bool
end

function JacVec(f,u::AbstractArray;autodiff=true)
    if autodiff
        cache1 = ForwardDiff.Dual{DeivVecTag}.(u, u)
        cache2 = ForwardDiff.Dual{DeivVecTag}.(u, u)
    else
        cache1 = similar(u)
        cache2 = similar(u)
    end
    JacVec(f,cache1,cache2,u,autodiff)
end

Base.size(L::JacVec) = (length(L.cache1),length(L.cache1))
Base.size(L::JacVec,i::Int) = length(L.cache1)
Base.:*(L::JacVec,x::AbstractVector) = L.autodiff ? auto_jacvec(_u->L.f(_u),L.u,x) : num_jacvec(_u->L.f(_u),L.u,x)

function LinearAlgebra.mul!(du::AbstractVector,L::JacVec,v::AbstractVector)
    if L.autodiff
        auto_jacvec!(du,(_du,_u)->L.f(_du,_u),L.u,v,L.cache1,L.cache2)
    else
        num_jacvec!(du,(_du,_u)->L.f(_du,_u),L.u,v,L.cache1,L.cache2)
    end
end

struct HesVec{F,T1,T2,uType}
    f::F
    cache1::T1
    cache2::T2
    cache3::T2
    u::uType
    autodiff::Bool
end

function HesVec(f,u::AbstractArray;autodiff=true)
    if autodiff
        cache1 = ForwardDiff.GradientConfig(f,u)
        cache2 = similar(u)
        cache3 = similar(u)
    else
        cache1 = similar(u)
        cache2 = similar(u)
        cache3 = similar(u)
    end
    HesVec(f,cache1,cache2,cache3,u,autodiff)
end

Base.size(L::HesVec) = (length(L.cache2),length(L.cache2))
Base.size(L::HesVec,i::Int) = length(L.cache2)
Base.:*(L::HesVec,x::AbstractVector) = L.autodiff ? numauto_hesvec(L.f,L.u,x) : num_hesvec(L.f,L.u,x)

function LinearAlgebra.mul!(du::AbstractVector,L::HesVec,v::AbstractVector)
    if L.autodiff
        numauto_hesvec!(du,L.f,L.u,v,L.cache1,L.cache2,L.cache3)
    else
        num_hesvec!(du,L.f,L.u,v,L.cache1,L.cache2,L.cache3)
    end
end

struct HesVecGrad{G,T1,T2,uType}
    g::G
    cache1::T1
    cache2::T2
    u::uType
    autodiff::Bool
end

function HesVecGrad(g,u::AbstractArray;autodiff=false)
    if autodiff
        cache1 = ForwardDiff.Dual{DeivVecTag}.(u, u)
        cache2 = ForwardDiff.Dual{DeivVecTag}.(u, u)
    else
        cache1 = similar(u)
        cache2 = similar(u)
    end
    HesVecGrad(g,cache1,cache2,u,autodiff)
end

Base.size(L::HesVecGrad) = (length(L.cache2),length(L.cache2))
Base.size(L::HesVecGrad,i::Int) = length(L.cache2)
Base.:*(L::HesVecGrad,x::AbstractVector) = L.autodiff ? auto_hesvecgrad(L.g,L.u,x) : num_hesvecgrad(L.g,L.u,x)

function LinearAlgebra.mul!(du::AbstractVector,L::HesVecGrad,v::AbstractVector)
    if L.autodiff
        auto_hesvecgrad!(du,L.g,L.u,v,L.cache1,L.cache2)
    else
        num_hesvecgrad!(du,L.g,L.u,v,L.cache1,L.cache2)
    end
end

ext: jl


text:
module TestStatsModels
using DataFrames
using Base.Test
using Compat

# Tests for statsmodel.jl

# A dummy RegressionModel type
immutable DummyMod <: RegressionModel
    beta::Vector{Float64}
    x::Matrix
    y::Vector
end

## dumb fit method: just copy the x and y input over
StatsBase.fit(::Type{DummyMod}, x::Matrix, y::Vector) =
    DummyMod(collect(1:size(x, 2)), x, y)
StatsBase.model_response(mod::DummyMod) = mod.y
## dumb coeftable: just prints the "beta" values
StatsBase.coeftable(mod::DummyMod) =
    CoefTable(reshape(mod.beta, (size(mod.beta,1), 1)),
              ["'beta' value"],
              ["" for n in 1:size(mod.x,2)],
              0)

## Test fitting
d = DataFrame()
d[:y] = [1:4;]
d[:x1] = [5:8;]
d[:x2] = [9:12;]
d[:x3] = [13:16;]
d[:x4] = [17:20;]

f = @formula(y ~ x1 * x2)
m = fit(DummyMod, f, d)
@test model_response(m) == d[:y]

## test prediction method
## vanilla
StatsBase.predict(mod::DummyMod) = mod.x * mod.beta
@test predict(m) == [ ones(size(d,1)) d[:x1] d[:x2] d[:x1].*d[:x2] ] * collect(1:4)

## new data from matrix
StatsBase.predict(mod::DummyMod, newX::Matrix) = newX * mod.beta
mm = ModelMatrix(ModelFrame(f, d))
@test predict(m, mm.m) == mm.m * collect(1:4)

## new data from DataFrame (via ModelMatrix)
@test predict(m, d) == predict(m, mm.m)

d2 = deepcopy(d)
d2[3, :x1] = NA
@test length(predict(m, d2)) == 4

## test copying of names from Terms to CoefTable
ct = coeftable(m)
@test ct.rownms == ["(Intercept)", "x1", "x2", "x1 & x2"]

## show with coeftable defined
io = IOBuffer()
show(io, m)

## with categorical variables
d[:x1p] = PooledDataArray(d[:x1])
f2 = @formula(y ~ x1p)
m2 = fit(DummyMod, f2, d)

@test coeftable(m2).rownms == ["(Intercept)", "x1p: 6", "x1p: 7", "x1p: 8"]

## predict w/ new data missing levels
@test predict(m2, d[2:4, :]) == predict(m2)[2:4]

## predict w/ new data with _extra_ levels (throws an error)
d3 = deepcopy(d)
d3[1, :x1] = 0
d3[:x1p] = PooledDataArray(d3[:x1])
@test_throws ArgumentError predict(m2, d3)

## fit with contrasts specified
d[:x2p] = PooledDataArray(d[:x2])
f3 = @formula(y ~ x1p + x2p)
m3 = fit(DummyMod, f3, d)
fit(DummyMod, f3, d, contrasts = Dict(:x1p => EffectsCoding()))
fit(DummyMod, f3, d, contrasts = Dict(:x1p => EffectsCoding(),
                                      :x2p => DummyCoding()))
@test_throws Exception fit(DummyMod, f3, d, contrasts = Dict(:x1p => EffectsCoding(),
                                                             :x2p => 1))

## Another dummy model type to test fall-through show method
immutable DummyModTwo <: RegressionModel
    msg::Compat.UTF8String
end

StatsBase.fit(::Type{DummyModTwo}, ::Matrix, ::Vector) = DummyModTwo("hello!")
Base.show(io::IO, m::DummyModTwo) = println(io, m.msg)

m2 = fit(DummyModTwo, f, d)
show(io, m2)

end


text:
include("conway_test.jl")
using ConwayTest
turbine_test()
blinker_test()


text:
"""
    VStaticGraph{T,N,D}

`LightGraphs.AbstractGraph` with fixed-number of vertices and varying number of edges.
The adjacency list is stored using an `SVector`.

`T` is the integer type, `N` the number of vertices, `D` is the directedness.

## Examples

```julia
julia> g = VStaticGraph{Int,6,false}()
julia> g2 = VStaticGraph{Int}(Val{6}())
```
"""
mutable struct VStaticGraph{T,N,D,BT <: Union{SVector{N, Vector{T}},Nothing}} <: LG.AbstractSimpleGraph{T}
    ne::Int
    fadjlist::SVector{N, Vector{T}} # [src]: (dst, dst, dst)
    badjlist::BT                    # [dst]: (src, src, src)
    function VStaticGraph{T,N,true}(ne, fadjlist) where {T,N}
        badjlist = SVector{N,Vector{T}}([Vector{T}() for _ = 1:N])
        return new{T,N,true,SVector{N, Vector{T}}}(ne, fadjlist, badjlist)
    end
    function VStaticGraph{T,N,false}(ne, fadjlist) where {T,N}
        return new{T,N,false,Nothing}(ne, fadjlist, nothing)
    end
end

badj(g::VStaticGraph{T,N,true}) where {T,N} = g.badjlist
badj(g::VStaticGraph{T,N,false}) where {T,N} = g.fadjlist

fadj(g::VStaticGraph) = g.fadjlist

function VStaticGraph{T,N,D}() where {T,N,D}
    fadjlist = SVector{N,Vector{T}}([Vector{T}() for _ = 1:N])
    return VStaticGraph{T,N,D}(0, fadjlist)
end

function VStaticGraph{T}(::Val{N}) where {T,N}
    return VStaticGraph{T,N,false}()
end

function VStaticGraph(::Val{N}) where {N}
    return VStaticGraph{Int,N,false}()
end

function VStaticGraph{T}(::Val{N}, ::Val{D}) where {T,N,D}
    return VStaticGraph{T,N,D}()
end

function VStaticGraph(::Val{N}, ::Val{D}) where {N,D}
    return VStaticGraph{Int,N,D}()
end


text:
module TestShow
using Compat
using Compat.Test
using Compat.Dates
using CategoricalArrays

# The type is prefixed after Dates moved to the stdlib
if VERSION >= v"0.7.0-DEV.2575"
    const DateStr = "Dates.Date"
else
    const DateStr = "Date"
end

@testset "show() for CategoricalPool{String} and its values" begin
    pool = CategoricalPool(["c", "b", "a"])

    opool = CategoricalPool(["c", "b", "a"], ["a", "b", "c"], true)

    nv1 = CategoricalArrays.catvalue(1, pool)
    nv2 = CategoricalArrays.catvalue(2, pool)
    nv3 = CategoricalArrays.catvalue(3, pool)

    ov1 = CategoricalArrays.catvalue(1, opool)
    ov2 = CategoricalArrays.catvalue(2, opool)
    ov3 = CategoricalArrays.catvalue(3, opool)

    @test sprint(show, pool) == "$CategoricalPool{String,UInt32}([\"c\",\"b\",\"a\"])"
    @test sprint(show, opool) == "$CategoricalPool{String,UInt32}([\"a\",\"b\",\"c\"]) with ordered levels"

    @test sprint(show, nv1) == "$CategoricalString{UInt32} \"c\""
    @test sprint(show, nv2) == "$CategoricalString{UInt32} \"b\""
    @test sprint(show, nv3) == "$CategoricalString{UInt32} \"a\""

    @test sprint(show, ov1) == "$CategoricalString{UInt32} \"c\" (3/3)"
    @test sprint(show, ov2) == "$CategoricalString{UInt32} \"b\" (2/3)"
    @test sprint(show, ov3) == "$CategoricalString{UInt32} \"a\" (1/3)"

    if VERSION >= v"0.7.0-DEV.4524"
        @test sprint(show, nv1, context=:typeinfo=>typeof(nv1)) == "\"c\""
        @test sprint(show, nv2, context=:typeinfo=>typeof(nv2)) == "\"b\""
        @test sprint(show, nv3, context=:typeinfo=>typeof(nv3)) == "\"a\""

        @test sprint(show, ov1, context=:typeinfo=>typeof(ov1)) == "\"c\""
        @test sprint(show, ov2, context=:typeinfo=>typeof(ov2)) == "\"b\""
        @test sprint(show, ov3, context=:typeinfo=>typeof(ov3)) == "\"a\""
    else
        @test sprint(showcompact, nv1) == sprint(showcompact, ov1) == "\"c\""
        @test sprint(showcompact, nv2) == sprint(showcompact, ov2) == "\"b\""
        @test sprint(showcompact, nv3) == sprint(showcompact, ov3) == "\"a\""
    end

    @test sprint(print, nv1) == sprint(print, ov1) == "c"
    @test sprint(print, nv2) == sprint(print, ov2) == "b"
    @test sprint(print, nv3) == sprint(print, ov3) == "a"

    @test string(nv1) == string(ov1) == "c"
    @test string(nv2) == string(ov2) == "b"
    @test string(nv3) == string(ov3) == "a"

    @test repr(nv1) == repr(ov1) == "\"c\""
    @test repr(nv2) == repr(ov2) == "\"b\""
    @test repr(nv3) == repr(ov3) == "\"a\""
end

@testset "show() for CategoricalPool{Date} and its values" begin
    pool = CategoricalPool([Date(1999, 12), Date(1991, 8), Date(1993, 10)])

    opool = CategoricalPool([Date(1999, 12), Date(1991, 8), Date(1993, 10)],
                            [Date(1991, 8), Date(1993, 10), Date(1999, 12)], true)

    nv1 = CategoricalArrays.catvalue(1, pool)
    nv2 = CategoricalArrays.catvalue(2, pool)
    nv3 = CategoricalArrays.catvalue(3, pool)

    ov1 = CategoricalArrays.catvalue(1, opool)
    ov2 = CategoricalArrays.catvalue(2, opool)
    ov3 = CategoricalArrays.catvalue(3, opool)

    @test sprint(show, pool) == "$CategoricalPool{$DateStr,UInt32}([1999-12-01,1991-08-01,1993-10-01])"
    @test sprint(show, opool) == "$CategoricalPool{$DateStr,UInt32}([1991-08-01,1993-10-01,1999-12-01]) with ordered levels"

    @test sprint(show, nv1) == "$CategoricalValue{$DateStr,UInt32} 1999-12-01"
    @test sprint(show, nv2) == "$CategoricalValue{$DateStr,UInt32} 1991-08-01"
    @test sprint(show, nv3) == "$CategoricalValue{$DateStr,UInt32} 1993-10-01"

    @test sprint(show, ov1) == "$CategoricalValue{$DateStr,UInt32} 1999-12-01 (3/3)"
    @test sprint(show, ov2) == "$CategoricalValue{$DateStr,UInt32} 1991-08-01 (1/3)"
    @test sprint(show, ov3) == "$CategoricalValue{$DateStr,UInt32} 1993-10-01 (2/3)"

    if VERSION >= v"0.7.0-DEV.4524"
        @test sprint(show, nv1, context=:typeinfo=>typeof(nv1)) == "1999-12-01"
        @test sprint(show, nv2, context=:typeinfo=>typeof(nv2)) == "1991-08-01"
        @test sprint(show, nv3, context=:typeinfo=>typeof(nv3)) == "1993-10-01"

        @test sprint(show, ov1, context=:typeinfo=>typeof(ov1)) == "1999-12-01"
        @test sprint(show, ov2, context=:typeinfo=>typeof(ov2)) == "1991-08-01"
        @test sprint(show, ov3, context=:typeinfo=>typeof(ov3)) == "1993-10-01"
    else
        @test sprint(showcompact, nv1) == sprint(showcompact, ov1) == "1999-12-01"
        @test sprint(showcompact, nv2) == sprint(showcompact, ov2) == "1991-08-01"
        @test sprint(showcompact, nv3) == sprint(showcompact, ov3) == "1993-10-01"
    end

    @test sprint(print, nv1) == sprint(print, ov1) == "1999-12-01"
    @test sprint(print, nv2) == sprint(print, ov2) == "1991-08-01"
    @test sprint(print, nv3) == sprint(print, ov3) == "1993-10-01"

    @test string(nv1) == string(ov1) == "1999-12-01"
    @test string(nv2) == string(ov2) == "1991-08-01"
    @test string(nv3) == string(ov3) == "1993-10-01"

    @test repr(nv1) == repr(ov1) == "1999-12-01"
    @test repr(nv2) == repr(ov2) == "1991-08-01"
    @test repr(nv3) == repr(ov3) == "1993-10-01"
end

using JSON
@testset "JSON.lower" for pool in (CategoricalPool(["a"]),
                                   CategoricalPool([1]),
                                   CategoricalPool([1.0]))
    v = CategoricalArrays.catvalue(1, pool)
    @test JSON.lower(v) == JSON.lower(get(v))
    @test typeof(JSON.lower(v)) == typeof(JSON.lower(get(v)))
end

end


text:
mutable struct GroupedList{T}
    ng::Int                 # number of groups
    elems::Vector{T}        # concatenated element list
    offs::Vector{Int}       # offsets
end

"""Construct a grouped list from counts."""
function grlist_from_counts{T}(elems::Vector{T}, cnts::AbstractVector{Int})
    ng = length(cnts)
    offs = Vector{Int}(ng + 1)
    offs[1] = 0
    for k = 1:ng
        offs[k+1] = offs[k] + cnts[k]
    end
    offs[ng+1] == length(elems) ||
        throw(ArgumentError("Mismatch between sum(cnts) and length(elems)."))
    GroupedList{T}(ng, elems, offs)
end

"""Construct a grouped list by a group-index mapping function."""
function grlist_by{T}(es::AbstractVector{T}, ng::Int, f::Function)
    len = length(es)

    elems = Vector{T}(len)
    offs = Vector{Int}(ng + 1)
    cnts = zeros(Int, ng)
    for e in es
        k = f(e)::Int
        0 < k <= ng || throw(BoundsError("Group index out of bound."))
        cnts[k] += 1
    end

    offs[1] = 0
    for i = 1:ng
        offs[i+1] = offs[i] + cnts[i]
    end
    @assert offs[ng + 1] == len

    fill!(cnts, 0)
    for e in es
        k = f(e)::Int
        elems[1 + offs[k] + cnts[k]] = e
        cnts[k] += 1
    end
    GroupedList{T}(ng, elems, offs)
end

eltype{T}(gl::GroupedList{T}) = T
length(gl::GroupedList) = length(gl.elems)
ngroups(gl::GroupedList) = gl.ng

eachindex(gl::GroupedList) = eachindex(gl.elems)
getindex(gl::GroupedList, i) = gl.elems[i]

start(gl::GroupedList) = start(gl.elems)
next(gl::GroupedList, state) = next(gl.elems, state)
done(gl::GroupedList, state) = done(gl.elems, state)

group_length(gl::GroupedList, k::Int) = gl.offs[k+1] - gl.offs[k]
group(gl::GroupedList, k::Int) = view(gl.elems, gl.offs[k]+1:gl.offs[k+1])

"""
A list whose elements can be accessed by both index or name.
"""
mutable struct NamedList{T}
    elems::Vector{T}
    imap::Dict{String,Int}
end

"""Construct a named list from a list of named elements."""
function namedlist{T}(es::AbstractVector{T}, namefun::Function)
    elems = Vector{T}()
    imap = Dict{String,Int}()
    len = length(es)
    sizehint!(elems, len)
    sizehint!(imap, len)

    for e in es
        k = namefun(e)::String
        !haskey(imap, k) || throw(KeyError("Duplicated name: '$(k)'."))
        push!(elems, e)
        imap[k] = length(elems)
    end
    NamedList{T}(elems, imap)
end

"""Construct a named list from name-element pairs."""
function namedlist_from_pairs{T}(ps::AbstractVector{Tuple{String, T}})
    elems = Vector{T}()
    imap = Dict{String,Int}()
    len = length(ps)
    sizehint!(elems, len)
    sizehint!(imap, len)

    for (k, e) in ps
        !haskey(imap, k) || throw(KeyError("Duplicated name: '$(k)'."))
        push!(elems, e)
        imap[k] = length(elems)
    end
    NamedList{T}(elems, imap)
end

eltype{T}(nl::NamedList{T}) = T
ndims(nl::NamedList) = 1
length(nl::NamedList) = length(nl.elems)
size(nl::NamedList) = (length(nl),)

eachindex(nl::NamedList) = eachindex(nl.elems)
getindex(nl::NamedList, i::Int) = nl.elems[i]
getindex(nl::NamedList, id::String) = nl.elems[nl.imap[id]]

start(nl::NamedList) = start(nl.elems)
next(nl::NamedList, state) = next(nl.elems, state)
done(nl::NamedList, state) = done(nl.elems, state)

indexof(id::String, nl::NamedList) = nl.imap[id]
indexof(ids, nl::NamedList) = Int[indexof(id, nl) for id in ids]

function show{T}(io::IO, nl::NamedList{T})
    println(io, "NamedList{$T} with $(length(nl)) elements:")
    for e in nl.elems
        println(io, e)
    end
end


text:
#
#	apply TM
#
function applyTM_OP(MPS_ket::AbstractArray{<:Number}, MPS_bra::AbstractArray{<:Number}, Op::localOp{DT,D},
		    x::AbstractArray{<:Number}; left::Bool = true) where {DT<:Number, D}

	res = zeros(eltype(x), size(MPS_bra)[[1,3][left+1]], size(MPS_ket)[[1,3][left+1]])
	tmp = zeros(eltype(x), size(x)[2], size(MPS_bra)[[1,3][left+1]])

	if left == true
		@inbounds for op in eachoperation(Op)

			c = ComplexF64(op[1])
			mket = @view MPS_ket[:, op[2], :] #α_ket, β_ket
			mbra = @view MPS_bra[:, op[3], :] #α_bra, β_bra

			LinearAlgebra.BLAS.gemm!('T','N', c, x, conj.(mbra), ComplexF64(0.0), tmp)  #α_ket, β_bra
			LinearAlgebra.BLAS.gemm!('T', 'N', ComplexF64(1.0), tmp, mket, ComplexF64(1.0), res)
		end

	else

		@inbounds for op in eachoperation(Op)

			c = ComplexF64(op[1])
			mket = @view MPS_ket[:, op[2], :] #α_ket, β_ket
			mbra = @view MPS_bra[:, op[3], :] #α_bra, β_bra

			LinearAlgebra.BLAS.gemm!('T','T', c, x, conj.(mbra), ComplexF64(0.0), tmp)  #β_ket, α_bra
			LinearAlgebra.BLAS.gemm!('T', 'T', ComplexF64(1.0), tmp, mket, ComplexF64(1.0), res)
		end

	end

	return res
end

function applyTM_OP(MPSket::Vector{<:Any}, MPSbra::Vector{<:Any}, Op_string::NTuple{N,Int}, vecMPO::Vector{<:MPOsparseT},
 		  x::AbstractArray{<:Number}; left::Bool = true) where {N}

	# TODO check that MPSket is the same length as MPSbra and that phys dim match
	mps_chainLength = length(MPSket)
	mps_chainLength == length(MPSbra) || throw(ArgumentError("length of ket and bra MPS do not match."))
	mps_chainLength == N || throw(ArgumentError("MPO and MPS length do not match."))

	if left == true
		A = MPSket[1]
        	B = MPSbra[1]
		local_op = vecMPO[1][Op_string[1]]
	else
		A = MPSket[end]
		B = MPSbra[end]
		local_op = vecMPO[end][Op_string[end]]
	end

	res = left == true ? applyTM_OP(A, B, local_op, x; left = true) : applyTM_OP(A, B, local_op, x; left = false)

	# go thorugh unit cell
	if mps_chainLength > 1
		if left == true
			res = applyTM_OP(MPSket[2:end], MPSbra[2:end], Op_string[2:end], vecMPO[2:end], res; left = true)
		else
			res = applyTM_OP(MPSket[1:end-1], MPSbra[1:end-1], Op_string[1:end-1], vecMPO[1:end-1], res; left = false)
		end
	end

	return res # (α_bra , α_ket)
end

function applyTM_MPO(MPSket::Vector{<:Any}, MPSbra::Vector{<:Any}, MPOvec::Vector{<:MPOsparseT}, x::Vector{<:Any}; left::Bool = true) where {DT<:Number, D}
	mps_chainLength = length(MPSket)
	mps_chainLength == length(MPSbra) || throw(ArgumentError("length of ket and bra MPS do not match."))
	mps_chainLength == length(MPOvec) || throw(ArgumentError("MPO and MPS length do not match."))

	#check if same length then MPOvec

	A = left == true ? MPSket[1] : MPSket[end]
	B = left == true ? MPSbra[1] : MPSbra[end]
	local_MPO = left == true ? MPOvec[1] : MPOvec[end]
	b_dim = length(local_MPO.bDim) == 1 ? (local_MPO.bDim, local_MPO.bDim) : local_MPO.bDim
	Op_idx = local_MPO.Op_index
	d_phys = size(MPSket[1])[2]

	if left == true
		YLa = Vector{Any}(undef,b_dim[2])

		for diag_idx = b_dim[2]:-1:1 #go through outgoing bond dim

                	a = diag_idx
			YLa[a] = zeros(ComplexF64,size(B)[3],size(A)[3])

			for b = 1:b_dim[1]

				Op = local_MPO[b, a]

				if Op != nothing

					tmp = x[b]
					tmp = applyTM_OP(A, B, Op, tmp; left = true)
					YLa[a] = YLa[a] + tmp #(α_bra ,α_ket)
				else

					YLa[a] = YLa[a] #(α_bra ,α_ket)
				end

                	end
                end
	else
		YRa = Vector{Any}(undef,b_dim[1])
		for diag_idx = 1:b_dim[1]
			a = diag_idx
			YRa[a] = zeros(ComplexF64,size(B)[1],size(A)[1])

			for b = b_dim[2]:-1:1

				Op = local_MPO[a, b]

				if Op != nothing

					tmp = x[b]
					tmp = applyTM_OP(A, B, Op, tmp; left = false)
					YRa[a] = YRa[a] + tmp #(α_bra ,α_ket)
				else

					YRa[a] = YRa[a] #(α_bra ,α_ket)
				end

			end
		end

	end

	if mps_chainLength > 1
		if left == true
			YLa = applyTM_MPO(MPSket[2:end], MPSbra[2:end], MPOvec[2:end], YLa; left = true)
		else
			YRa = applyTM_MPO(MPSket[1:end-1], MPSbra[1:end-1], MPOvec[1:end-1], YRa; left = false)
		end

	end

	return res = left == true ? YLa : YRa
end

applyTM_MPO(MPS::Vector{<:Any}, MPOvec::Vector{<:MPOsparseT}, x::Vector{<:Any}; left::Bool = true) where {DT<:Number, D} = applyTM_MPO(MPS, MPS, MPOvec, x; left = left)

max_stars_repo_name: Gawatz/finiteMPS

max_issues_repo_name: Gawatz/finiteMPS

max_forks_repo_name: Gawatz/finiteMPS


text:
include(joinpath(dirname(@__FILE__),"..", "src/KABSCH", "kabsch.jl"))
include(joinpath(dirname(@__FILE__),"..", "src/PDB", "pdb.jl"))
using Kabsch
using PDB
# julia uses MATLAB-style syntax for matrices
P = [0.1 0.2 0.3; 0.5 -0.5 -0.3; 0.2 -0.3 8.3]
centroid = calc_centroid(P)
@test_approx_eq_eps centroid[1] 0.266667 1e-4
@test_approx_eq_eps centroid[2] -0.199999 1e-4
@test_approx_eq_eps centroid[3] 2.766666666666667 1e-4

P = [51.65 -1.90 50.07;
    50.40 -1.23 50.65;
    50.68 -0.04 51.54;
    50.22 -0.02 52.85]

Q = [51.30 -2.99 46.54;
     51.09 -1.88 47.58;
     52.36 -1.20 48.03;
     52.71 -1.18 49.38]

T1, T2, centroid_p1, centroid_p2 = translate_points(P, Q)

# (bad) lazy test if translated matrices are OK ("collisions" obviously can exist)
@test_approx_eq_eps sum(T1) -2.2828578949e-05 1e-4
@test_approx_eq_eps sum(T2) 1.09672546387e-05 1e-4

c_1 = [ 50.73750305  -0.79750001  51.27750397]
c_2 = [ 51.86499786  -1.81249988  47.88249969]

@test_approx_eq_eps centroid_p1[1] c_1[1] 1e-4
@test_approx_eq_eps centroid_p1[2] c_1[2] 1e-4
@test_approx_eq_eps centroid_p1[3] c_1[3] 1e-4

@test_approx_eq_eps rmsd(P,Q) 3.87845580529 1e-4

#@test_approx_eq_eps kabsch_rmsd(P,Q) 72.14091715529968 1e-5

structure = get_structure("2HHB.pdb")
chains = get_chains(structure)

alpha_1 = chains[1]
alpha_2 = chains[3]

beta_1 = chains[2]
beta_2 = chains[4]

#@test_approx_eq_eps kabsch_rmsd(alpha_1,alpha_2) 17.789580172997187 1e-6

#@test_approx_eq_eps kabsch_rmsd(beta_1,beta_2) 19.320217378889485 1e-6

P = [-1. 0. 0.; 0. 2. 0.; 0. 1. 0.; 0. 1. 1]
Q = [0. -1. -1.; 0. -1. 0; 0. 0. 0.; -1. 0. 0.]

@test_approx_eq_eps kabsch_rmsd(P, Q) 0.6947710216026161 1e-6


text:
# This file was generated, do not modify it. # hide
hitters = dataset("ISLR", "Hitters")
@show size(hitters)
names(hitters) |> pprint


text:
function KlobucharIonoCoefficientsLoader()
    return KlobucharIonoCoefficientsLoader(())
end

function KlobucharIonoCoefficientsLoader(arg0::JString)
    return KlobucharIonoCoefficientsLoader((JString,), arg0)
end

function KlobucharIonoCoefficientsLoader(arg0::JString, arg1::DataProvidersManager)
    return KlobucharIonoCoefficientsLoader((JString, DataProvidersManager), arg0, arg1)
end

function get_alpha(obj::KlobucharIonoCoefficientsLoader)
    return jcall(obj, "getAlpha", Vector{jdouble}, ())
end

function get_beta(obj::KlobucharIonoCoefficientsLoader)
    return jcall(obj, "getBeta", Vector{jdouble}, ())
end

function get_supported_names(obj::KlobucharIonoCoefficientsLoader)
    return jcall(obj, "getSupportedNames", JString, ())
end

function load_data(obj::KlobucharIonoCoefficientsLoader, arg0::InputStream, arg1::JString)
    return jcall(obj, "loadData", void, (InputStream, JString), arg0, arg1)
end

function load_klobuchar_ionospheric_coefficients(obj::KlobucharIonoCoefficientsLoader)
    return jcall(obj, "loadKlobucharIonosphericCoefficients", void, ())
end

function load_klobuchar_ionospheric_coefficients(obj::KlobucharIonoCoefficientsLoader, arg0::DateComponents)
    return jcall(obj, "loadKlobucharIonosphericCoefficients", void, (DateComponents,), arg0)
end

function still_accepts_data(obj::KlobucharIonoCoefficientsLoader)
    return jcall(obj, "stillAcceptsData", jboolean, ())
end


text:
using BinDeps
using Compat

@BinDeps.setup
libnames = ["libCLFFT", "clFFT", "libclFFT"]
libCLFFT = library_dependency("libCLFFT", aliases = libnames)
version = "2.12.2"
baseurl = "https://github.com/clMathLibraries/clFFT/releases/download/v$(version)/clFFT-$(version)-"

# download a pre-compiled binary (built by GLFW)
if is_windows()
    if Sys.ARCH == :x86_64
        uri = URI(baseurl * "Windows-x64.zip")
        basedir = joinpath(@__DIR__, "clFFT-$(version)-Windows-x64")
        provides(
            Binaries, uri,
            libCLFFT, unpacked_dir = basedir,
            installed_libpath = joinpath(basedir, "bin"), os = :Windows
        )
    else
        error("Only 64 bits windows supported with automatic build")
    end
end

if is_linux()
    provides(AptGet, "libclfft-dev", libCLFFT)
    if Sys.ARCH == :x86_64
        uri = URI(baseurl * "Linux-x64.tar.gz")
        basedir = joinpath(@__DIR__, "clFFT-$(version)-Linux-x64")
        provides(
            Binaries, uri,
            libCLFFT, unpacked_dir = basedir,
            installed_libpath = joinpath(basedir, "lib64"), os = :Linux
        )
    end
end

if is_apple()
    using Homebrew
    provides(Homebrew.HB, "homebrew/core/clfft", libCLFFT, os = :Darwin)
end

@BinDeps.install Dict("libCLFFT" => "libCLFFT")


text:
export LDMatrix,
    save,
    posWindow,
    cMWindow,
    markers,
    markersDF,
    ldscore

using Distributions
using LinearAlgebra
using SparseArrays

cMWindow(cM) = (m1, m2) -> abs(m1.cm - m2.cm) <= cM
posWindow(dist) = (m1, m2) -> abs(m1.pos - m2.pos) <= dist

struct LDMatrix
    markers::Vector{Marker}
    markerIndex::Dict{String, Int64}
    r::Symmetric{Float64, SparseMatrixCSC{Float64, Int64}}
end

"""
    LDMatrix(p::PlinkReader, mIdx0, mIdx1; alpha = 0.9, window = posWindow(1_000_000))

Compute LDMatrix from genotypes in Plink file.
"""
function LDMatrix(p::PlinkReader, mIdx0, mIdx1; alpha = 0.9, window = posWindow(1_000_000))
    LDMatrix(markers(p)[mIdx0:mIdx1],
             Dict([m.id => idx for (idx, m) in enumerate(markers(p))]),
             Symmetric(ld(p, mIdx0, mIdx1; alpha = alpha, window = window), :L))
end

"""
    LDMatrix(path::AbstractString)

Load LDMatrix from .bim and .lds files at `path`.
"""
function LDMatrix(path::AbstractString)
    markers = load_bim(path)
    r = loadSparseCSC(path * ".lds")
    LDMatrix(markers,
             Dict([m.id => idx for (idx, m) in enumerate(markers)]),
             Symmetric(r, :L))
end

"""
    markers(ld::LDMatrix)

Get array of `Marker` structs for all markers in LDMatrix `ld`.
"""
markers(ld::LDMatrix) = ld.markers
marker_index(ld::LDMatrix, marker) = ld.markerIndex[marker]
Base.size(ld::LDMatrix) = size(ld.r)

"""
    markersDF(ld::LDMatrix)

Get data frame with marker info.

Returns data frame with columns

- Chrom
- Name
- cM
- Pos
- A1
- A2
- Idx
"""
function markersDF(ld::LDMatrix)
    m = DataFrame(Chrom = String[], Name = String[], cM = Float64[],
                  Pos = Int64[], A1 = String[], A2 = String[],
                  Idx = Int64[])

    for (idx, mrk) in enumerate(markers(ld))
        push!(m, (mrk.chrom, mrk.id, mrk.cm, mrk.pos, mrk.a1, mrk.a2, idx))
    end
    m
end

"""
    corr_thresh(n, alpha = 0.05)

Compute significance threshold for Pearson correlation.

r (estimated from n data pairs) significant at alpha
if r >= t/sqrt(n-2+t*t)
where t is quantile(TDist(n-2), 1-alpha/2)

see e.g. Wikipedia article for Pearson correlation
"""
function corr_thresh(n, alpha = 0.05)
    n > 2 || return Inf
    t = quantile(TDist(n - 2), 1.0 - alpha/2.0)
    t / sqrt(n - 2 + t*t)
end

# 20201222 set diagonal element to 0.0 if variance = 0.0

"""
    ld(p::PlinkReader, mIdx0, mIdx1; alpha = 0.9, window = posWindow(1_000_000))

Compute LD block for markers mIdx0..mIdx1 (usually one chromosome),
restricting to window and r significant at alpha.

output is sparse LD matrix with indices 1 .. (mIdx1 - mIdx0 + 1)
"""
function ld(p::PlinkReader, mIdx0, mIdx1; alpha = 0.9, window = posWindow(1_000_000))

    # a2counts[gt + 1] = counts of allele2 for gt
    # Plink convention is
    # 0b00 Hom1, 0b01 Het, 0b10 missing, 0b11 Hom2
    a2counts = [0, 1, -1, 2]

    thresh = corr_thresh.(1:nsamples(p), alpha)

    colInd = Int64[1]    # colInd[j] index into rowInd, where column j starts
    rowInd = Int64[]
    nzvalue = Float64[]  # make this Float64 so we can use LinAlg routines from SparseSuite

    for m0 = mIdx0:mIdx1
        # compute variance of marker m0
        xSum0 = 0
        xxSum0 = 0
        nGood = 0
        for s = 1:nsamples(p)
            x = a2counts[p[s, m0] + 1]
            x < 0 && continue
            nGood += 1
            xSum0 += x
            xxSum0 += x*x
        end # s
        #println("m0 = $m0, xSum0 = $xSum0, xxSum0 = $xxSum0, nGood = $nGood, var=$(xxSum0 - xSum0*xSum0/nGood)")
        # set diagonal to 1f0
        # ONLY DO THIS IF VARIANCE > 0!
        push!(rowInd, m0 - mIdx0 + 1)
        if (xxSum0 - xSum0*xSum0/nGood > 0.0)
            push!(nzvalue, 1f0)

            for m =(m0+1):mIdx1
                nGood = 0  # number of valid x and y genotypes
                xSum = xSum0
                xxSum = xxSum0
                ySum = 0
                yySum = 0
                xySum = 0

                # check we are within window, or break
                window(markers(p)[m], markers(p)[m0])||break

                for s = 1:nsamples(p)
                    x = a2counts[p[s, m0] + 1]
                    x == -1 && continue

                    y = a2counts[p[s, m] + 1]
                    if y == -1
                        # here y genotype missing but x genotype present
                        # need to correct xSum and xxSum for missing pair
                        xSum -= x
                        xxSum -= x*x
                        continue
                    end

                    nGood += 1
                    ySum += y
                    yySum += y*y
                    xySum += x*y

                end # s

                nGood == 0 && continue

                cov_xy = xySum - xSum*ySum/nGood
                var_x = xxSum - xSum*xSum/nGood
                var_y = yySum - ySum*ySum/nGood

                r = cov_xy / sqrt(var_x * var_y)

                if abs(r) >= thresh[nGood]
                    push!(rowInd, m - mIdx0 + 1)
                    push!(nzvalue, r)
                end

            end # m

        else
            push!(nzvalue, 0f0)
        end #Var(m0) > 0
        push!(colInd, length(rowInd) + 1)
    end # m0

    # create sparse matrix from colInd, rowInd, value
    SparseMatrixCSC(mIdx1 - mIdx0 + 1,
                    mIdx1 - mIdx0 + 1,
                    colInd,
                    rowInd,
                    nzvalue)

end

function writeSparseCSC( s::SparseMatrixCSC, path::AbstractString)

    fh = open(path, "w")

    nb = 0

    m = s.m
    n = s.n
    nnz = length(s.nzval)

    nb += write(fh, Int64(m), Int64(n), Int64(nnz))

    for i = 1:(n+1)
        nb += write(fh, Int64(s.colptr[i]))
    end

    for i = 1:nnz
        nb += write(fh, Int64(s.rowval[i]))
    end

    for i = 1:nnz
        nb += write(fh, Float64(s.nzval[i]))
    end

    close(fh)

end

function loadSparseCSC(path::AbstractString)

    fh = open(path, "r")

    m = read(fh, Int64)
    n = read(fh, Int64)
    nnz = read(fh, Int64)

    offset = position(fh)
    colptr = Mmap.mmap(fh, Vector{Int64}, n + 1, offset; shared = false)

    offset += (n + 1) * 8
    rowval = Mmap.mmap(fh, Vector{Int64}, nnz, offset; shared = false)

    offset += nnz * 8
    nzval = Mmap.mmap(fh, Vector{Float64}, nnz, offset; shared = false)

    SparseMatrixCSC(m, n, colptr, rowval, nzval)

end

"""
    save(ld::LDMatrix, path::AbstractString)

Save `LDMatrix` to `path`.
"""
function save(ld::LDMatrix, path::AbstractString)
    save_bim(ld.markers, path * ".bim")
    writeSparseCSC(ld.r.data, path * ".lds")
end

function save_bim(markers, path)
    fh = open(path, "w")
    for m in markers
        println(fh, "$(m.chrom)\t$(m.id)\t$(m.cm)\t$(m.pos)\t$(m.a1)\t$(m.a2)")
    end
    close(fh)
end

"""
    ldscore(ld::LDMatrix)

Compute LD scores for markers in LDMatrix `ld`.
"""
function ldscore(ld::LDMatrix)
    # get underlying SparseMatrixCSC
    s = ld.r.data
    ldsc = diag(s)   #ones(Float64, s.n)  # diagonal elts can be 0.0

    for col = 1:(s.n-1)
        for idx = s.colptr[col]:(s.colptr[col+1]-1)
            row = s.rowval[idx]
            x = s.nzval[idx]
            # x is now r[row, col]
            row != col || continue
            r2 = x*x
            ldsc[col] += r2
            ldsc[row] += r2
        end

    end
    ldsc
end