### A Pluto.jl notebook ###
# v0.18.0
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 $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ f9054310-4df5-11eb-3c52-97e77fdd3f68
using PlutoUI
# ╔═╡ 6e62acf0-4dfc-11eb-2712-1b627ae36d00
using Luxor
# ╔═╡ 0af95440-9a37-4176-a3ef-6fd085f73069
using Plots
# ╔═╡ acca2570-3719-4cd5-9961-b011598cc583
using LatexStrings
# ╔═╡ 81c44f7c-e505-4641-a8d5-e5e8a6b3b3b8
using SpecialFunctions
# ╔═╡ ab73e450-4e3e-11eb-30f2-0d5ba96a7726
md"""
## TODO
* Create a function to format the tick lables - Perhap unicode exponenets. Different formatting for value above and below 50%
* Consider making other sanity functions like labeling arrows.
* Implement text wrap boxes for the four boxes to prevent clipping
"""
# ╔═╡ d93685a0-4e3e-11eb-23ba-2919fb86c9ff
md"## Definitions"
# ╔═╡ 20416f70-4e33-11eb-229d-915f70a913ea
° = π/180
# ╔═╡ 61e242de-4e3a-11eb-1c0b-cfd0430f7189
exponent10(x) = sign(log10(x)) * ceil(abs(log10(x)))
# ╔═╡ 6aac5280-4e3a-11eb-1fad-7bef5ecf5669
mantissa(x) = x == 0 ? 0.0 : x * 10^(-exponent10(x))
# ╔═╡ 750cc81e-4e0f-11eb-2180-f58c05881cf0
scale_fwd(x, k=5) = 1 / (1 + ((1/x) - 1)^(1/k))
# ╔═╡ 782ea190-4e0f-11eb-2249-85cdb2437a5c
scale_rev(x, k=5) = 1 / (1 + ((1/x) - 1)^(k))
# ╔═╡ 637e36f3-b314-4d89-9e4d-720bf80b5a26
begin
probit(x) = sqrt(2)*erfinv(2x-1)
logit(x) = log(x/(1-x))
default(lw=2, color=:dodgerblue1,)
plot(probit, xx, label="probit",)
plot!(logit, xx, label="logit", color=:firebrick4)
plot!(ylim=(-4.1,4.1),
legend=:topleft,
framestyle=:zerolines,
size=(600,600)
)
annotate!(0.5, -2, L"sqrt(2)")
end
# ╔═╡ a13df330-4e3f-11eb-0f86-87202c9daa4f
function format_tick(x)
if x == 0.5
return "50%"
elseif x < 0.5
if x >= .01
return "$(convert(Int,(round(100*x))))%"
end
n = convert(Int,abs(exponent10(x)))
return "$(round(100*x, sigdigits=n))%"
else
a = 1 - x
n = convert(Int,abs(exponent10(a)))
if x <= .99
return "$(convert(Int,(round(100*x))))%"
end
return "$(round(100*x, sigdigits=n))%"
end
end
# ╔═╡ ec330e80-4e3e-11eb-3177-ef46e3e5df0f
md"## Calculating all Parameters"
# ╔═╡ 94dd15f0-4df7-11eb-29b6-b554cba6af12
md"""
`Simulated Patients = ` $(@bind N Slider(1000:1000:100_000))
`Prevalence = ` $(@bind Π_s Slider(0.001:0.001:0.999))
`Sensitivity = ` $(@bind TPR_s Slider(0.001:0.001:0.999))
`Specificity = ` $(@bind TNR_s Slider(0.001:0.001:0.999))
"""
# ╔═╡ 7a25fc30-4df8-11eb-0358-5fce59400ff5
begin
# N = 10_000
Π = scale_rev(Π_s,2)
TPR = scale_rev(TPR_s,2)
TNR = scale_rev(TNR_s,2)
pos = Π*N
neg = N - pos
FPR = 1 - TNR
FNR = 1 - TPR
tru_pos = round(pos * TPR)
fal_pos = round(neg * FPR)
fal_neg = round(pos * FNR)
tru_neg = round(neg * TNR)
PPV = tru_pos / pos
FDR = fal_pos / pos
FOR = fal_neg / neg
NPV = tru_neg / neg
LR_pos = TPR / FPR
LR_neg = FNR / TNR
DOR = LR_pos / LR_neg
F1 = (PPV * TPR) / (PPV + TPR)
TP = convert(Int,round(TPR * N))
FP = convert(Int,round(FPR * N))
FN = convert(Int,round(FNR * N))
TN = convert(Int,round(TNR * N))
Π_str = "$(round(100*Π, sigdigits=4)) %"
TPR_str = "$(round(100*TPR, sigdigits=4)) %"
FPR_str = "$(round(100*FPR, sigdigits=4)) %"
FNR_str = "$(round(100*FNR, sigdigits=4)) %"
TNR_str = "$(round(100*TNR, sigdigits=4)) %"
PPV_str = "$(round(100*PPV, sigdigits=4)) %"
FDR_str = "$(round(100*FDR, sigdigits=4)) %"
FOR_str = "$(round(100*FOR, sigdigits=4)) %"
NPV_str = "$(round(100*NPV, sigdigits=4)) %"
end
# ╔═╡ 897bb240-4dfa-11eb-0151-fb2d460fcf14
md"""
Prevalence = $(100*Π) %
Sensitivity = $(100*TPR) %
Specificity = $(100*TNR) %
"""
# ╔═╡ 990af440-4e0f-11eb-2014-f354b3c33558
md"""
`Image Size = ` $(@bind img_size Slider(200:10:700))
`Frame Size = ` $(@bind frm_size Slider(10:10:800))
`Scaling = ` $(@bind scale Slider(1:0.1:5))
"""
# ╔═╡ a26f9721-bc1d-4ed8-9dcf-c46b3075be0a
scale
# ╔═╡ 14f9ae40-4e36-11eb-26c0-415995909e1f
(img_size, frm_size, scale)
# ╔═╡ 137af6f0-4e09-11eb-09e3-05c039305bfb
begin
Drawing(img_size, img_size, "dx_test.png")
background("white")
o = Point( img_size÷2, img_size÷2)
# Corner Locations
offset = Point(frm_size÷2, frm_size÷2)
a1 = o - offset
d2 = o + offset
# Diagram Division Locations
Πx = frm_size * scale_fwd(Π, scale) + a1.x
b1 = Point(Πx, a1.y)
c2 = Point(Πx, d2.y)
tpr_y = scale_fwd(TPR, scale) * frm_size + a1.y
fpr_y = scale_fwd(FPR, scale) * frm_size + a1.y
a2 = Point(Πx, tpr_y)
b2 = Point(d2.x, fpr_y)
c1 = Point(a1.x, tpr_y)
d1 = Point(Πx, fpr_y)
ac = midpoint(a1, a2)
bc = midpoint(b1, b2)
cc = midpoint(c1, c2)
dc = midpoint(d1, d2)
setopacity(0.5)
sethue("lightgreen");
box(a1, a2, :fill)
box(d1, d2, :fill)
sethue("pink");
box(c1, c2, :fill)
box(b1, b2, :fill)
sethue("grey");
setopacity(1.0)
box(a1, a2, :stroke)
box(d1, d2, :stroke)
box(c1, c2, :stroke)
box(b1, b2, :stroke)
sethue("black");
setline(2.5)
setopacity(1.0)
box(a1, d2, :stroke)
fontsize(15)
shift_E = Point(20, 0)
shift_N = Point(0, 20)
text("Numer of Patients (N): $(N)", Point(d2.x, a1.y) - shift_N,
halign=:right, valign=:bottom)
# Arrows ----------------------------------------------
# Prevalence Arrow
sethue("red");
Π_arr_beg = a1 - shift_N/2
Π_arr_end = b1 - shift_N/2
Π_arr_cen = midpoint(Π_arr_beg, Π_arr_beg)
arrow(Π_arr_beg, Π_arr_end, linewidth=3)
text("Prevalence (Π): $(Π_str)", Π_arr_cen - shift_N,
halign=:left, valign=:top)
# TPR Arrow (Sensitivity)
TPR_arr_beg = a1 - shift_E/2
TPR_arr_end = c1 - shift_E/2
TPR_arr_cen = midpoint(TPR_arr_beg, TPR_arr_end)
arrow(TPR_arr_beg, TPR_arr_end, linewidth=3)
text("Sensitivity (TPR): $(TPR_str)", TPR_arr_beg - shift_E,
halign=:left, valign=:bottom, angle=90°)
# TNR Arrow (Specificity)
TNR_arr_beg = d2 + shift_E/2
TNR_arr_end = b2 + shift_E/2
TNR_arr_cen = midpoint(TNR_arr_beg, TNR_arr_end)
arrow(TNR_arr_beg, TNR_arr_end, linewidth=3)
text("Specificity (TNR): $(TNR_str)", TNR_arr_beg + shift_E,
halign=:left, valign=:bottom, angle=-90°)
# Ticks ------------------------------------------------
setline(1.5)
setdash("dot")
sethue("gray")
setopacity(0.3)
tick_locs = scale_rev.(0.1:0.1:0.5, scale)
mm = round.(mantissa.(tick_locs))
ee = exponent10.(tick_locs)
ticks = mm .* 10 .^ ee
ticks = sort(unique([ticks; ones(length(ticks)) .- ticks]))
for t in ticks
t1 = Point(a1.x + frm_size * scale_fwd(t, scale), a1.y)
t2 = Point(a1.x + frm_size * scale_fwd(t, scale), d2.y)
line(t1, t2, :stroke)
m = convert(Int,round(mantissa(t)))
e = convert(Int,round(exponent10(t)))
setopacity(1.0)
text(format_tick(t), t2+0.25*shift_N, halign=:left, valign=:middle, angle=90°)
setopacity(0.3)
end
for t in ticks
t1 = Point(a1.x, a1.y + frm_size * scale_fwd(t, scale)) - 2*shift_E
t2 = Point(d2.x, a1.y + frm_size * scale_fwd(t, scale))
line(t1, t2, :stroke)
m = convert(Int,round(mantissa(t)))
e = convert(Int,round(exponent10(t)))
setopacity(1.0)
text(format_tick(t), t1, halign=:right, valign=:middle)
setopacity(0.3)
end
sethue("black")
setopacity(1.0)
# fontface("Georgia-Bold")
setfont("Georgia Bold", 18)
settext("TP\n$(TPR_str)\n$(TP)",
ac, halign = "center", valign = "center", markup = true)
settext("FP\n$(FPR_str)\n$(FP)",
bc, halign = "center", valign = "center", markup = true)
settext("FN\n$(FNR_str)\n$(FN)",
cc, halign = "center", valign = "center", markup = true)
settext("TN\n$(TNR_str)\n$(TN)",
dc, halign = "center", valign = "center", markup = true)
# settext("TP\n$(TPR_str)\n$(TP)",
# ac, halign = "center", valign = "center", markup = true)
# settext("FP\n$(FPR_str)\n$(FP)",
# bc, halign = "center", valign = "center", markup = true)
# settext("FN\n$(FNR_str)\n$(FN)",
# cc, halign = "center", valign = "center", markup = true)
# settext("TN\n$(TNR_str)\n$(TN)",
# dc, halign = "center", valign = "center", markup = true)
finish()
preview()
end
# ╔═╡ 1e6a98f0-4df9-11eb-0d93-bb58b573c572
md"""
Simulated Patients: $(N)
True Positive: $(tru_pos)
False Positive: $(fal_pos)
False Negative: $(fal_neg)
True Negative: $(tru_neg)
Positive predictive value: $(PPV_str)
False discovery rate: $(FDR_str)
False omission rate: $(FOR_str)
Negative predictive value: $(NPV_str))
Positive likelihood ratio (LR+): $(round(100*LR_pos, sigdigits=4)) %
Negative likelihood ratio (LR-): $(round(100*LR_neg, sigdigits=4)) %
Diagnostic odds ratio (DOR): $(round(100*DOR, sigdigits=4)) %
F1 score: $(round(100*F1, sigdigits=4)) %
"""
# ╔═╡ 0c44ac00-4ee0-11eb-05fe-bfa63cfa3175
pos, neg, pos/N
# ╔═╡ 51e70eb2-4ee0-11eb-0230-eb6efa74a7a2
FPR/TPR, TNR/FNR
# ╔═╡ d664d55e-4df9-11eb-3912-592ef5e13db5
md"""
$ F_1 = $(round(100*F1, sigdigits=4)) \% $
"""
# ╔═╡ 2122d407-f992-44cc-83dc-7535c0197764
xx = 0:0.1:1.0
# ╔═╡ 7b40febb-d2ae-434e-83cc-3150c5effde2
begin
xx = 0:0.000001:1.0
default(lw=2, color=:dodgerblue1,)
plot( scale_fwd, xx, label="k=5")
plot!(scale_rev, xx, label="k=1/5", ls=:dash,)
plot!(xx, xx, lw=2, ls=:dot, color=:gray, label="x=y")
plot!(aspect_ratio=:equal,
xlim=(-0.1,1.1),
ylim=(-0.1,1.1),
legend=:topleft,
framestyle=:zerolines,
size=(600,600)
)
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Luxor = "ae8d54c2-7ccd-5906-9d76-62fc9837b5bc"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
[compat]
Luxor = "~3.0.0"
Plots = "~1.25.11"
PlutoUI = "~0.7.35"
SpecialFunctions = "~2.1.3"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
julia_version = "1.7.0"
manifest_format = "2.0"
[[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.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[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.Cairo]]
deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b"
uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
version = "1.0.5"
[[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 = "c9a6160317d1abe9c44b3beb367fd448117679ca"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.13.0"
[[deps.ChangesOfVariables]]
deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.2"
[[deps.ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "12fc73e5e0af68ad3137b886e3f7c1eacfca2640"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.17.1"
[[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.DataAPI]]
git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"
[[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.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
[[deps.DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
[[deps.Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
[[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"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.2.3+0"
[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ae13fcbc7ab8f16b0856729b050ef0c446aa3492"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.4.4+0"
[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"
[[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"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.0+0"
[[deps.FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "80ced645013a5dbdc52cf70329399c35ce007fae"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.13.0"
[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"
[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"
[[deps.Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"
[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"
[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"
[[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 = "51d2dfe8e590fbd74e7a842cf6d13d8a2f45dc01"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.6+0"
[[deps.GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "RelocatableFolders", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "9f836fb62492f4b0f0d3b06f55983f2704ed0883"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.64.0"
[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "a6c850d77ad5118ad3be4bd188919ce97fffac47"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.64.0+0"
[[deps.GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"
[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"
[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "a32d672ac2c967f3deb8a81d828afc739c838a06"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+2"
[[deps.Graphics]]
deps = ["Colors", "LinearAlgebra", "NaNMath"]
git-tree-sha1 = "1c5a84319923bea76fa145d49e93aa4394c73fc2"
uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
version = "1.1.1"
[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"
[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"
[[deps.HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.17"
[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"
[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"
[[deps.HypertextLiteral]]
git-tree-sha1 = "2b078b5a615c6c0396c77810d92ee8c6f470d238"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.3"
[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"
[[deps.IniFile]]
git-tree-sha1 = "f550e6e32074c939295eb5ea6de31849ac2c9625"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.1"
[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
[[deps.InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.2"
[[deps.IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"
[[deps.IterTools]]
git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.4.0"
[[deps.IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"
[[deps.JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.4.1"
[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.3"
[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b53380851c6e6664204efb2e62cd24fa5c47e4ba"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.2+0"
[[deps.Juno]]
deps = ["Base64", "Logging", "Media", "Profile"]
git-tree-sha1 = "07cb43290a840908a771552911a6274bc6c072c7"
uuid = "e5e0dc1b-0480-54bc-9374-aad01c23163d"
version = "0.8.4"
[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"
[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"
[[deps.LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"
[[deps.Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a6552bfeab40de157a297d84e03ade4b8177677f"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.12"
[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
[[deps.LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"
[[deps.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"
[[deps.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"
[[deps.Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"
[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"
[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"
[[deps.Librsvg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pango_jll", "Pkg", "gdk_pixbuf_jll"]
git-tree-sha1 = "25d5e6b4eb3558613ace1c67d6a871420bfca527"
uuid = "925c91fb-5dd6-59dd-8e8c-345e74382d89"
version = "2.52.4+0"
[[deps.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"
[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"
[[deps.LinearAlgebra]]
deps = ["Libdl", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
[[deps.LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.6"
[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
[[deps.Luxor]]
deps = ["Base64", "Cairo", "Colors", "Dates", "FFMPEG", "FileIO", "Juno", "LaTeXStrings", "Random", "Requires", "Rsvg"]
git-tree-sha1 = "81a4fd2c618ba952feec85e4236f36c7a5660393"
uuid = "ae8d54c2-7ccd-5906-9d76-62fc9837b5bc"
version = "3.0.0"
[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.9"
[[deps.Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"
[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
[[deps.Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"
[[deps.Media]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "75a54abd10709c01f1b86b84ec225d26e840ed58"
uuid = "e89f7d12-3494-54d1-8411-f7d8b9ae1f27"
version = "0.5.0"
[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"
[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
[[deps.NaNMath]]
git-tree-sha1 = "b086b7ea07f8e38cf122f5016af580881ac914fe"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.7"
[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"
[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.13+0"
[[deps.OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"
[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"
[[deps.OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"
[[deps.PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"
[[deps.Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a121dfbba67c94a5bec9dde613c3d0cbcf3a12b"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.50.3+0"
[[deps.Parsers]]
deps = ["Dates"]
git-tree-sha1 = "13468f237353112a01b2d6b32f3d0f80219944aa"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.2.2"
[[deps.Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"
[[deps.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"
[[deps.PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"
[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "6f1b25e8ea06279b5689263cc538f51331d7ca17"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.1.3"
[[deps.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", "Unzip"]
git-tree-sha1 = "5c907bdee5966a9adb8a106807b7c387e51e4d6c"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.25.11"
[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "85bf3e4bd279e405f91489ce518dedb1e32119cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.35"
[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "de893592a221142f3db370f48290e3a2ef39998f"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.4"
[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
[[deps.Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
[[deps.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"
[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
[[deps.Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
[[deps.RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"
[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "995a812c6f7edea7527bb570f0ac39d0fb15663c"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.5.1"
[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"
[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "cdbd3b1338c72ce29d9584fdbe9e9b70eeb5adca"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "0.1.3"
[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"
[[deps.Rsvg]]
deps = ["Cairo", "Glib_jll", "Librsvg_jll"]
git-tree-sha1 = "3d3dc66eb46568fb3a5259034bfc752a0eb0c686"
uuid = "c4c386cf-5103-5370-be45-f3a111cca3b8"
version = "1.0.0"
[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"
[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"
[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"
[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "85e5b185ed647b8ee89aa25a7788a2b43aa8a74f"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.3"
[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "6354dfaf95d398a1a70e0b28238321d5d17b2530"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.4.0"
[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c3d8ba7f3fa0625b062b82853a7d5229cb728b6b"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.2.1"
[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.16"
[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "57617b34fa34f91d536eb265df67c2d4519b8b98"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.5"
[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"
[[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.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 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"
[[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 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"
[[deps.gdk_pixbuf_jll]]
deps = ["Artifacts", "Glib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Xorg_libX11_jll", "libpng_jll"]
git-tree-sha1 = "c23323cd30d60941f8c68419a70905d9bdd92808"
uuid = "da03df04-f53b-5353-a52f-6a8b0620ced0"
version = "2.42.6+1"
[[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:
# ╟─ab73e450-4e3e-11eb-30f2-0d5ba96a7726
# ╠═f9054310-4df5-11eb-3c52-97e77fdd3f68
# ╠═6e62acf0-4dfc-11eb-2712-1b627ae36d00
# ╠═0af95440-9a37-4176-a3ef-6fd085f73069
# ╠═acca2570-3719-4cd5-9961-b011598cc583
# ╟─81c44f7c-e505-4641-a8d5-e5e8a6b3b3b8
# ╟─d93685a0-4e3e-11eb-23ba-2919fb86c9ff
# ╠═20416f70-4e33-11eb-229d-915f70a913ea
# ╠═6aac5280-4e3a-11eb-1fad-7bef5ecf5669
# ╠═61e242de-4e3a-11eb-1c0b-cfd0430f7189
# ╠═750cc81e-4e0f-11eb-2180-f58c05881cf0
# ╠═2122d407-f992-44cc-83dc-7535c0197764
# ╠═7b40febb-d2ae-434e-83cc-3150c5effde2
# ╠═637e36f3-b314-4d89-9e4d-720bf80b5a26
# ╠═782ea190-4e0f-11eb-2249-85cdb2437a5c
# ╠═a13df330-4e3f-11eb-0f86-87202c9daa4f
# ╟─ec330e80-4e3e-11eb-3177-ef46e3e5df0f
# ╠═7a25fc30-4df8-11eb-0358-5fce59400ff5
# ╟─897bb240-4dfa-11eb-0151-fb2d460fcf14
# ╟─94dd15f0-4df7-11eb-29b6-b554cba6af12
# ╠═990af440-4e0f-11eb-2014-f354b3c33558
# ╠═a26f9721-bc1d-4ed8-9dcf-c46b3075be0a
# ╟─14f9ae40-4e36-11eb-26c0-415995909e1f
# ╠═137af6f0-4e09-11eb-09e3-05c039305bfb
# ╟─1e6a98f0-4df9-11eb-0d93-bb58b573c572
# ╠═0c44ac00-4ee0-11eb-05fe-bfa63cfa3175
# ╠═51e70eb2-4ee0-11eb-0230-eb6efa74a7a2
# ╠═d664d55e-4df9-11eb-3912-592ef5e13db5
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002