bench-roots.jl

### A Pluto.jl notebook ###
# v0.19.17

using Markdown
using InteractiveUtils

# ╔═╡ f4620c0b-92bc-4087-9a0e-df8f11879b95
using Random: default_rng, AbstractRNG, shuffle!

# ╔═╡ 8271c26e-8f1f-43b1-b002-62eaaef423a9
using PlutoTest

# ╔═╡ e248d08f-fccd-42f2-80b3-e4e37fe77b86
using CairoMakie

# ╔═╡ fd20a949-7e32-4fce-a470-2f73f676ead5
using BenchmarkTools

# ╔═╡ 8f77ee82-2f8a-44b5-8d9e-245bd9831867
using ForwardDiff

# ╔═╡ 620687a2-a48e-4622-8b2c-d33a91db7606
using IntervalArithmetic

# ╔═╡ 4459251a-f5c4-4c93-8c79-9c83744d273b
using Roots

# ╔═╡ 6707f0c1-261d-45db-88c7-5b01170ef2be
import IntervalRootFinding

# ╔═╡ f3e5a7b0-b6ab-4f44-8b61-99c15d6cbec0
struct Brute end

# ╔═╡ c0773a01-91d1-4720-80fc-39d9f79e86b2
function findroot(f, (lb, ub)::Tuple{T, T}, xtol::T, method::Brute) where T <: Real
	bx, bf = lb, Inf  # init best so far input and function value
	for x in range(lb, ub; step=xtol)  # search interval in steps of xtol
		fx = f(x)  # evaluate function at candidate position
		if abs(fx) < abs(bf) # if candiate closer to zero
			bx, bf = x, fx  # update best so far
		end
	end
	bx  # return best so far
end

# ╔═╡ 7f3f0fb5-9499-4f32-931f-a9b2993f361f
struct Bisection end

# ╔═╡ 6ffe1466-2576-41be-bbbb-93ea51499792
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, method::Bisection
) where T <: Real
	a, b = lb, ub
	fa, fb = f(a), f(b)
	sign(fa) == zero(T) && return a
	sign(fb) == zero(T) && return b
	while abs(b - a) >= 2xtol
		# c = (a*fb - b*fa) / (fb - fa)
		c = (a + b) / 2
		fc = f(c)
		if sign(fc) == sign(fa)
			a, fa = c, fc
		elseif sign(fc) == sign(fb)
			b, fb = c, fc
		elseif sign(fc) == zero(T)
			return c
		end
	end
	(a + b) / 2
end

# ╔═╡ 34f3c0a7-eb71-4610-9d7d-46decaca881e
struct ITP{T<:Real}
	n0::Int
	k1::T
end

# ╔═╡ 327ab5c9-3451-4312-8aad-bf7b65989f05
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, (;n0, k1)::ITP{T}
) where T <: Real
	a = lb
	fa = f(a)
	sa = sign(fa)
	sign(a) == zero(T) && return a

	b = ub
	fb = f(b)
	sign(b) == zero(T) && return b

	if sign(fa) == one(T)
		a, b = b, a
		fa, fb = fb, fa
	end

	r0 = xtol * 2^(n0 + ceil(Int, log2(abs(ub - lb) / xtol)) - 1)
	while abs(b - a) > 2xtol
		xm = (a + b) / 2
		xf = (a * fb - b * fa) / (fb - fa)

		sigma = xm - xf
		delta = k1 * abs2(b - a)
		xt = delta <= abs(sigma) ? xf + copysign(delta, sigma) : xm

		r = r0 - abs(b - a) / 2
		xitp = abs(xt - xm) <= r ? xt : xm - copysign(r, sigma)
		fitp = f(xitp)
		sitp = sign(fitp)
		if sitp == one(T)
            b = xitp
            fb = fitp
		elseif sitp == -one(T)
            a = xitp
            fa = fitp
        else
            a = xitp
            b = xitp
		end
		r0 *= T(0.5)
	end

	(a + b) / 2
end

# ╔═╡ c38797d4-90c5-40d2-8142-604e9fcee8db
struct CounterNewton{N} end

# ╔═╡ e9ed7870-b279-4dad-8b5b-4bc012c47a25
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, method::CounterNewton{N}
) where {N, T <: Real}
	D(x) = ForwardDiff.derivative(f, x)
	L = ub - lb
	a, b = lb, ub
	fa, fb = f(a), f(b)
	fa == zero(T) && return a  # return early if 0 found
	fb == zero(T) && return b
	for _ in 1:N  # do bisection a few times first
		c = (a + b) / 2
		fc = f(c)
		if sign(fc) == sign(fa)
			a, fa = c, fc
		elseif sign(fc) == sign(fb)
			b, fb = c, fc
		else
			@assert sign(fc) == zero(T)
			return c
		end
	end
	if abs(fb) < abs(fa)  # switch if b closer than a
		a, b = b, a
		fa, fb = fb, fa
	end
	@assert sign(fa * fb) == -one(T)
	Da = D(a)
	while abs(b - a) > 2xtol
		cn = a - fa / Da
		lo, hi = minmax(a, b)  # if newton candidate in interval, use it
		c = lo < cn < hi ? cn : (a + b) / 2  # else, use bisection
		fc = f(c)
		Da = D(c)
		if sign(fc) == sign(fa)  # replace a
			a = c
			fa = fc
		elseif sign(fc) == sign(fb)  # replace b and switch
			a, b = c, a
			fa, fb = fc, fa
		else
			@assert fc == zero(T)
			return c
		end
	end
	(a + b) / 2
end

# ╔═╡ 3f217ed8-c39d-4b70-88c9-1d3546d8a4ae
struct IntervalNewton end

# ╔═╡ 8841f6d9-6a09-4fd7-b2ab-107267d20815
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, method::IntervalNewton
) where T <: Real
	X = interval(lb, ub)
	D(x) = ForwardDiff.derivative(f, x)
	while diam(X) > xtol
		m = interval(mid(X))
		fm = f(m)
    	Y = m - (fm / D(X))
        NX = Y ∩ X
        if NX == X
			s = sign(f(X.lo) * fm.hi) 
			if s == -one(T)
				X = interval(minmax(X.lo, m.hi)...)
			elseif s == one(T)
				X = interval(minmax(m.hi, X.hi)...)
			elseif fm.hi == zero(T)
				return m
			else
				return X.lo
			end
		else
			X = NX
		end
    end

    return mid(X)
end

# ╔═╡ f8d9a832-7ab5-4a05-9a5c-b37f1c1ed58e
struct CalumSecant end

# ╔═╡ 31782043-158c-4de6-8cdc-7491b6427de1
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, method::CalumSecant
) where T <: Real
	seed = (lb + ub)/2
	seed1 = seed + 0.0000001
	for i in 1:1000
		fr = f(seed)
		fr1 = f(seed1)
		d = (seed1 * fr - seed * fr1) / (fr - fr1)
		dif = f(seed)/d
		seed1 = seed
		seed = seed - dif
		if seed < lb || seed > ub
			seed = (lb + ub)/2
		end
		if sign(f(seed)) == sign(f(lb))
			lb = seed
		elseif sign(f(seed)) == sign(f(ub))
			ub = seed
		end
		if isnan(seed)
			seed = (lb + ub) / 2
		end
	end
	return seed
end

# ╔═╡ cd6274c1-6534-4055-afb0-f67181160ab5
struct DamianTwoThirdSecant end

# ╔═╡ e6100249-1c50-4c1b-a3a9-3206c7be2404
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, method::DamianTwoThirdSecant
) where T <: Real
	x = find_zero(f, (lb, ub), Order1())
	return x > ub || x < lb ? find_zero(f, (lb, ub)) : x
end

# ╔═╡ 18782c85-eee8-4397-88d1-367102dc884e
struct ChrisBisection end

# ╔═╡ 18209d69-c592-4654-8677-4db0c57a165f
function findroot(
	f, (lb, ub)::Tuple{T, T}, xtol::T, method::ChrisBisection
) where T <: Real
	sign(f(lb)) == sign(f(ub)) && throw(
		ArgumentError("function has the same sign at both ends of interval."))

	md = (lb + ub) / 2
	while abs((ub-lb)/2) > xtol
		sign(f(md)) == sign(f(lb)) ? lb = md : ub = md
		md = (lb + ub) / 2
	end
	return md
end

# ╔═╡ a1f6cf26-9ae1-4b30-811b-f39e9a705067
testmethod = DamianTwoThirdSecant()

# ╔═╡ 1f3db068-872b-45c8-8e62-d3e1e13b55cd
test_tol = 1e-11

# ╔═╡ 7e6cc62d-778a-49a8-98e9-f970a584359f
findroot(x -> (x - 4) * (x - 1), (-3.0, 3.0), test_tol, testmethod)

# ╔═╡ 96562840-e187-4efa-8bb9-a4f4ef92edc2
findroot(identity, (-1.0, 3.0), test_tol, testmethod)

# ╔═╡ 952cf622-14ed-48f8-b72a-b07e0db09289
@test abs(findroot(identity, (-1.0, 3.0), test_tol, testmethod)) < test_tol

# ╔═╡ dec53edb-f7b0-405d-bd88-1b4d53825581
let f(x) = (exp(x)-1) / (exp(x)+1), x0 = 0.0, I=(-50.0, 10.0)
	@test abs(findroot(f, I, test_tol, testmethod) - x0) < test_tol
end

# ╔═╡ 61506dd8-f7ba-45ab-b0a1-a41b9e6a33c8
let f(x) = sinpi(x), x0 = 0.0, I=(-0.25, 0.3)
	r = findroot(f, I, test_tol, testmethod)
	@test abs(r - x0) < test_tol
end

# ╔═╡ 2f5dba56-08bb-4e94-a89a-d85e8baf4dcd
begin
	struct BenchFunction{T<:Real}
		a::T
		r::T
		f::T
		p::T
	end

	function ((; a, r, f, p)::BenchFunction)(x::T) where T<:Real
		y1 = a * (x - r)
		y2 = one(T)+T(2//3)*sinpi(f*(x+p))
		return y1 * y2
	end
end

# ╔═╡ aadd6284-7d3f-4701-94ce-9355aaf90475
begin
	import Random: rand
	using Random: SamplerType

	function rand(rng::AbstractRNG, ::SamplerType{BenchFunction{T}}) where T<:Real
		r = 2*rand(rng, T)-1
		f = T(1//3) + rand(rng, T) * T(1.25)
		p = 2*rand(rng, T)-1
		a = randn(rng, T)
		while a == zero(T)
			a = randn(rng, T)
		end
		BenchFunction{T}(a, r, f, p)
	end
end

# ╔═╡ e8bd48d0-9f59-4277-94ee-8433c02173b4
testbf = rand(BenchFunction{Float64})

# ╔═╡ 4dbf84b1-f751-445b-9606-a20f5495e743
testr = findroot(testbf, (-1.0, 1.0), test_tol, testmethod)

# ╔═╡ 62172ddb-6a37-42d1-96ab-b30483fabb3c
@test abs(testr - testbf.r) < test_tol

# ╔═╡ 44c74ecf-0b05-4e81-b9ae-0e2446a243f0
@benchmark testbf($0.1)

# ╔═╡ ac28a6f4-bb90-4ec7-a683-9cdf12d6c991
testbfs = rand(BenchFunction{Float64}, 10_000)

# ╔═╡ b9b29f42-4bdf-4f9a-9bfb-ec3125e29336
benchbfs = rand(BenchFunction{Float64}, 1_000)

# ╔═╡ 3781cf2a-087d-4558-8b22-11d6e9f5245e
benchmark(method::M, bfs, tol) where M = maximum(bfs) do bf
	abs(findroot(x -> bf(x), (-1.0, 1.0), tol, method) - bf.r)
end

# ╔═╡ 79271e78-1076-4872-8d96-7fd928963e9a
benchmark(testmethod, testbfs, test_tol)

# ╔═╡ a499d91b-5bf1-400a-a08d-fe78b018f75c
begin
	benchmethods = Dict(
		"Bisection" => Bisection(),
		"ITP" => ITP(4, 0.1),
		"CounterNewton" => CounterNewton{2}(),
		"IntervalNewton" => IntervalNewton(),
		"DamianTwoThirdSecant" => DamianTwoThirdSecant(),
		"ChrisBisection" => ChrisBisection()
	)
	suite = BenchmarkGroup()
	for (k, v) in pairs(benchmethods)
		suite[k] = @benchmarkable benchmark($v, $benchbfs, 1e-15) setup=(shuffle!(benchbfs))
	end
	suite
end

# ╔═╡ d3a5554e-c064-4e8a-9c83-93a66ff5e669
benchresults = run(suite)

# ╔═╡ 472fb499-f71f-4c66-95d0-afeab06bf54b
minbenchresults = minimum(benchresults)

# ╔═╡ a1bd52b6-6199-486f-b07b-02071b22ada0
rand(BenchFunction{Float64})

# ╔═╡ b8f33e5c-413e-492f-95a1-cdb229e027a1
let fig = Figure()
	ax = Axis(fig[1, 1])
	ylims!(ax, (-2.0, 2.0))

	xs = range(-1.0, 1.0, length=1_000)
	for _ in 1:5
		bf = rand(BenchFunction{Float64})
		lines!(ax, xs, bf.(xs))
	end

	hlines!(ax, [0.0], color=:black)

	fig
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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version = "2.0.8"

[[deps.RoundingEmulator]]
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[[deps.SHA]]
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version = "0.7.0"

[[deps.SIMD]]
git-tree-sha1 = "bc12e315740f3a36a6db85fa2c0212a848bd239e"
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[[deps.ScanByte]]
deps = ["Libdl", "SIMD"]
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[[deps.Scratch]]
deps = ["Dates"]
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[[deps.Serialization]]
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[[deps.SetRounding]]
git-tree-sha1 = "d7a25e439d07a17b7cdf97eecee504c50fedf5f6"
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[[deps.Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
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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.SignedDistanceFields]]
deps = ["Random", "Statistics", "Test"]
git-tree-sha1 = "d263a08ec505853a5ff1c1ebde2070419e3f28e9"
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[[deps.SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
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[[deps.Sixel]]
deps = ["Dates", "FileIO", "ImageCore", "IndirectArrays", "OffsetArrays", "REPL", "libsixel_jll"]
git-tree-sha1 = "8fb59825be681d451c246a795117f317ecbcaa28"
uuid = "45858cf5-a6b0-47a3-bbea-62219f50df47"
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[[deps.SnoopPrecompile]]
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[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "a4ada03f999bd01b3a25dcaa30b2d929fe537e00"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
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[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "d75bda01f8c31ebb72df80a46c88b25d1c79c56d"
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[[deps.StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
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[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
git-tree-sha1 = "ffc098086f35909741f71ce21d03dadf0d2bfa76"
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version = "1.5.11"

[[deps.StaticArraysCore]]
git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
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[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f9af7f195fb13589dd2e2d57fdb401717d2eb1f6"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.5.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "d1bf48bfcc554a3761a133fe3a9bb01488e06916"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.21"

[[deps.StatsFuns]]
deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "ab6083f09b3e617e34a956b43e9d51b824206932"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "1.1.1"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "GPUArraysCore", "StaticArraysCore", "Tables"]
git-tree-sha1 = "b03a3b745aa49b566f128977a7dd1be8711c5e71"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.14"

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

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

[[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", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "c79322d36826aa2f4fd8ecfa96ddb47b174ac78d"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.10.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.1"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

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

[[deps.TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "7e6b0e3e571be0b4dd4d2a9a3a83b65c04351ccc"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.6.3"

[[deps.TimeZones]]
deps = ["Dates", "Downloads", "InlineStrings", "LazyArtifacts", "Mocking", "Printf", "RecipesBase", "Scratch", "Unicode"]
git-tree-sha1 = "a92ec4466fc6e3dd704e2668b5e7f24add36d242"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
version = "1.9.1"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "e4bdc63f5c6d62e80eb1c0043fcc0360d5950ff7"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.10"

[[deps.Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"

[[deps.TriplotBase]]
git-tree-sha1 = "4d4ed7f294cda19382ff7de4c137d24d16adc89b"
uuid = "981d1d27-644d-49a2-9326-4793e63143c3"
version = "0.1.0"

[[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.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 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.10.3+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_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_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_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"
version = "1.2.12+3"

[[deps.isoband_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.3+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+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"
version = "5.1.1+0"

[[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.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+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"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[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"
"""

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