juliaset.jl

### A Pluto.jl notebook ###
# v0.15.1

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 el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 750ded6c-f15d-11eb-02ef-5156d6bf3200
using BenchmarkTools, CUDA, Images, PlutoUI

# ╔═╡ 8548f5a7-de5b-44a1-a0f2-55314a6152b3
md"""
# Parallelizing the Julia Set

##### This notebook combines the Mandelbrot set example from the Julia Computing parallel programming class with the [Julia set example by Simon Danisch](https://nextjournal.com/sdanisch/julia-gpu-programming). 
##### Also see [this Discourse thread](https://discourse.julialang.org/t/julia-sets-in-julia-using-interact-jl-id-like-to-get-it-faster/35533) on the Julia set.
##### Interesting values for the parameter `c` were chosen from the [Julia set wikipedia page](https://en.wikipedia.org/wiki/Julia_set).
"""

# ╔═╡ 062c93ab-df7e-485e-a4bc-f7e39c013c3f
md"#### A macro to view stdout"

# ╔═╡ 6d12faf1-d8bc-400a-b934-e2c36a0fcc5c
macro terminal(stuff)
	quote
		with_terminal() do
			$(esc(stuff))
		end
	end
end

# ╔═╡ 9da77179-daff-4eb7-b95b-1c5b9da5e524
md"#### The escape/iteration function"

# ╔═╡ 81fa04e2-147d-496d-bea4-cfe14a67868a
function escape(z0, c, maxiter)
    z = z0
    for i ∈ 1:maxiter
        abs2(z) > 4 && return (i-1) % UInt8
         z = z*z + c
    end
    return maxiter % UInt8
end

# ╔═╡ 62c83a9e-d5ba-4479-b3b4-4584bbf2b70f
@terminal @code_warntype escape(1.0+1im, 0+0.5im, 5)

# ╔═╡ c05f8497-0ab5-4dae-8dac-3df2bfd36355
md"#### Loop through each pixel of the image and count the number of escape iterations."

# ╔═╡ 1001c583-b7ee-47e0-87ac-2d4be6e8b23b
function juliaset(;width=800, height=600, maxiter=255, c = ComplexF64(-0.512511498387847167, 0.521295573094847167))
	real = range(-1.5, 1.5, length=width)
	imag = range(-1.0, 1.0, length=height)*im
    result =  zeros(Int, height, width)
	for x = 1:width
		for y = 1:height
			z₀ = real[x] + imag[y]
			result[y, x] = escape(z₀, c, maxiter)
		end
	end
    return result
end

# ╔═╡ 55bfc407-6b22-413e-aff5-d17bfd343f87
@terminal @code_warntype juliaset()

# ╔═╡ 58eda8b1-5205-4527-8e0c-69f6a3cb7607
md"#### Plot a nice Julia set image"

# ╔═╡ 4aa12ee7-dce5-4e30-a1b8-569296760cb9
js = juliaset();

# ╔═╡ 6cd3120e-8164-4177-98cf-6b96953f9567
Gray.((js)/maximum(js))

# ╔═╡ 0ee22f75-e720-4fd2-b081-80eed5e57928
md"""
### Choose your own `c` value
##### Use arrows to shift by 0.05, or type a value in the field
"""

# ╔═╡ 7db79200-d9ba-4199-a2ea-4d0862b36015
md"""`real(c)` = $(@bind cr NumberField(-2:0.05:2, default=-0.4))
`imag(c)` = $(@bind ci NumberField(-2:0.05:2, default=0.6))
"""

# ╔═╡ a0cdf4a6-06ce-4379-b683-5c4d67192b21
md"#### Run the single-threaded benchmark on the default image"

# ╔═╡ 49f344df-bc93-4cee-9179-a75214f0f905
jss = @benchmark juliaset()

# ╔═╡ 6a9382e4-7e8f-44e8-9ca2-a50d19eb35c1
md"#### Parallelize with threads and benchmark"

# ╔═╡ add716ef-d45b-4aab-8e00-666adaf38c77
function juliaset_threads(;width=800, height=600, maxiter=256, c = ComplexF64(-0.512511498387847167, 0.521295573094847167))
	real = range(-1.5, 1.5, length=width)
	imag = range(-1, 1, length=height)*im
    result =  zeros(Int, height, width)
	Threads.@threads for x = 1:width
		for y = 1:height
			z₀ = real[x] + imag[y]
			result[y, x] = escape(z₀, c, maxiter)
		end
	end
    return result
end

# ╔═╡ 2ee833fe-31e2-4784-be9a-1a4331ee10f5
jst = @benchmark juliaset_threads()

# ╔═╡ 6ffd8442-f7fc-44bc-b3e4-a7d6ddb0fb1f
md"#### Parallelize with tasks"

# ╔═╡ b39c8c16-9162-46e7-9fbf-4400eb69dd17
function juliaset_spawn(;width=800, height=600, maxiter=256, c = ComplexF64(-0.512511498387847167, 0.521295573094847167))
	real = range(-1.5, 1.5, length=width)
	imag = range(-1, 1, length=height)*im
    result =  zeros(Int, height, width)
	@sync for x = 1:width
		Threads.@spawn for y = 1:height
			z₀ = real[x] + imag[y]
			result[y, x] = escape(z₀,c, maxiter)
		end
	end
    return result
end

# ╔═╡ c1f94c04-6796-4945-9adf-b97a4ef06d56
js_image = juliaset_spawn(c=cr+ci*im);

# ╔═╡ 0d5b251f-e0bb-46fd-a3ad-6ea3618eed5b
Gray.(js_image/maximum(js_image))

# ╔═╡ d7ffd22f-d634-46d2-92ed-2d8bbacb0ad5
jsp = @benchmark juliaset_spawn()

# ╔═╡ f1620901-49ca-4bb5-90b7-c258c25a3e7a
has_cuda() ||	md"#### WARNING: CUDA not available!"

# ╔═╡ 6ddaf0d0-ee62-4f36-94c6-05f3bfb18e49
function run!(in, out, c; maxiter=16)
    out .= escape.(in, c, maxiter)
end

# ╔═╡ 6341b004-4426-4e30-9015-b1ee1a75e0da
function juliaset_gpu(;width=800, height=600, maxiter=256, c = ComplexF64(-0.512511498387847167, 0.521295573094847167))
    q =  CuArray([ComplexF64(real, imag) for imag in range(-2.0, 0.5, length=width), real in range(-1.0, 1.0, length=height)])
    result = CuArray(zeros(UInt8, size(q)))
    run!(q, result, maxiter=maxiter)
    return result
end

# ╔═╡ 509fa4b9-c9a6-45da-a7a5-574f5a57b8cf
if has_cuda()
	jsg = @benchmark juliaset_gpu(width=width, height=height)
	jsgt = round(jsg.times[1]/1e6, digits=2)
else
	jsgt = 1.1 # milliseconds, approx time on a K80 (via JuliaHub)
end

# ╔═╡ 3185c612-de1e-4acb-a232-dd5dfd3949d2
md"
##### 1-thread: $(round(jss.times[1]/1e6, digits=2)) ms
##### $(Threads.nthreads())-threads: $(round(jst.times[1]/1e6, digits=2)) ms
##### $(800*600)-tasks: $(round(jsp.times[1]/1e6, digits=2)) ms
##### GPU version: $jsgt ms
"

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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git-tree-sha1 = "1198f85fa2481a3bb94bf937495ba1916f12b533"
uuid = "2996bd0c-7a13-11e9-2da2-2f5ce47296a9"
version = "0.2.2"

[[ImageShow]]
deps = ["Base64", "FileIO", "ImageCore", "OffsetArrays", "Requires", "StackViews"]
git-tree-sha1 = "832abfd709fa436a562db47fd8e81377f72b01f9"
uuid = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
version = "0.3.1"

[[ImageTransformations]]
deps = ["AxisAlgorithms", "ColorVectorSpace", "CoordinateTransformations", "IdentityRanges", "ImageCore", "Interpolations", "OffsetArrays", "Rotations", "StaticArrays"]
git-tree-sha1 = "d966631de06f36c8cd4bec4bb2e8fa731db16ed9"
uuid = "02fcd773-0e25-5acc-982a-7f6622650795"
version = "0.8.12"

[[Images]]
deps = ["AxisArrays", "Base64", "ColorVectorSpace", "FileIO", "Graphics", "ImageAxes", "ImageContrastAdjustment", "ImageCore", "ImageDistances", "ImageFiltering", "ImageIO", "ImageMagick", "ImageMetadata", "ImageMorphology", "ImageQualityIndexes", "ImageShow", "ImageTransformations", "IndirectArrays", "OffsetArrays", "Random", "Reexport", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "TiledIteration"]
git-tree-sha1 = "8b714d5e11c91a0d945717430ec20f9251af4bd2"
uuid = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
version = "0.24.1"

[[IndirectArrays]]
git-tree-sha1 = "c2a145a145dc03a7620af1444e0264ef907bd44f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "0.5.1"

[[Inflate]]
git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
version = "0.1.2"

[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2018.0.3+2"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "1470c80592cf1f0a35566ee5e93c5f8221ebc33a"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.3"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.3"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.1"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LLVM]]
deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
git-tree-sha1 = "733abcbdc67337bb6aaf873c6bebbe1e6440a5df"
uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
version = "4.1.1"

[[LLVMExtra_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b36c0677a0549c7d1dc8719899a4133abbfacf7d"
uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
version = "0.0.6+0"

[[LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[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"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["DocStringExtensions", "LinearAlgebra"]
git-tree-sha1 = "7bd5f6565d80b6bf753738d2bc40a5dfea072070"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.2.5"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "c253236b0ed414624b083e6b72bfe891fbd2c7af"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+1"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.6"

[[MappedArrays]]
git-tree-sha1 = "18d3584eebc861e311a552cbb67723af8edff5de"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.0"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.0"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.3"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[Netpbm]]
deps = ["ColorVectorSpace", "FileIO", "ImageCore"]
git-tree-sha1 = "09589171688f0039f13ebe0fdcc7288f50228b52"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.0.1"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "4f825c6da64aebaa22cc058ecfceed1ab9af1c7e"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.3"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "520e28d4026d16dcf7b8c8140a3041f0e20a9ca8"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
version = "0.3.7"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "0fa5e78929aebc3f6b56e1a88cf505bb00a354c4"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.8"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "2276ac65f1e236e0a6ea70baff3f62ad4c625345"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.2"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "94bf17e83a0e4b20c8d77f6af8ffe8cc3b386c0a"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "1.1.1"

[[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"

[[PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
version = "0.1.1"

[[PlutoUI]]
deps = ["Base64", "Dates", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "Suppressor"]
git-tree-sha1 = "44e225d5837e2a2345e69a1d1e01ac2443ff9fcb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.9"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.1"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[Random123]]
deps = ["Libdl", "Random", "RandomNumbers"]
git-tree-sha1 = "0e8b146557ad1c6deb1367655e052276690e71a3"
uuid = "74087812-796a-5b5d-8853-05524746bad3"
version = "1.4.2"

[[RandomNumbers]]
deps = ["Random", "Requires"]
git-tree-sha1 = "56ead4aaafc41d83694e17b0dd89d3e929d01a14"
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
version = "1.5.0"

[[RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[Ratios]]
git-tree-sha1 = "37d210f612d70f3f7d57d488cb3b6eff56ad4e41"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.0"

[[Reexport]]
git-tree-sha1 = "5f6c21241f0f655da3952fd60aa18477cf96c220"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.1.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[Rotations]]
deps = ["LinearAlgebra", "StaticArrays", "Statistics"]
git-tree-sha1 = "2ed8d8a16d703f900168822d83699b8c3c1a5cd8"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.2"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
git-tree-sha1 = "508822dca004bf62e210609148511ad03ce8f1d8"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.6.0"

[[StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
version = "0.1.1"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "62701892d172a2fa41a1f829f66d2b0db94a9a63"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.3.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "885838778bb6f0136f8317757d7803e0d81201e4"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.9"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "fed1ec1e65749c4d96fc20dd13bea72b55457e62"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.9"

[[Suppressor]]
git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787"
uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
version = "0.2.0"

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

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

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

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

[[TiffImages]]
deps = ["ColorTypes", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "OrderedCollections", "PkgVersion", "ProgressMeter"]
git-tree-sha1 = "03fb246ac6e6b7cb7abac3b3302447d55b43270e"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.4.1"

[[TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "52c5f816857bfb3291c7d25420b1f4aca0a74d18"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
version = "0.3.0"

[[TimerOutputs]]
deps = ["ExprTools", "Printf"]
git-tree-sha1 = "209a8326c4f955e2442c07b56029e88bb48299c7"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.12"

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

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

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

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

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

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

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

# ╔═╡ Cell order:
# ╟─8548f5a7-de5b-44a1-a0f2-55314a6152b3
# ╠═750ded6c-f15d-11eb-02ef-5156d6bf3200
# ╟─062c93ab-df7e-485e-a4bc-f7e39c013c3f
# ╠═6d12faf1-d8bc-400a-b934-e2c36a0fcc5c
# ╟─9da77179-daff-4eb7-b95b-1c5b9da5e524
# ╠═81fa04e2-147d-496d-bea4-cfe14a67868a
# ╠═62c83a9e-d5ba-4479-b3b4-4584bbf2b70f
# ╟─c05f8497-0ab5-4dae-8dac-3df2bfd36355
# ╠═1001c583-b7ee-47e0-87ac-2d4be6e8b23b
# ╠═55bfc407-6b22-413e-aff5-d17bfd343f87
# ╟─58eda8b1-5205-4527-8e0c-69f6a3cb7607
# ╠═4aa12ee7-dce5-4e30-a1b8-569296760cb9
# ╠═6cd3120e-8164-4177-98cf-6b96953f9567
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