### A Pluto.jl notebook ###
# v0.19.12

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

# ╔═╡ b573185c-25aa-11eb-14ee-4f35f39e4f60
using DelimitedFiles, Plots, PlutoUI, FFTW; gr(size = (640, 360)); PlutoUI.TableOfContents(depth=4)

# ╔═╡ 00c34a30-2834-11eb-331c-95de2567ce32
using Interpolations

# ╔═╡ 9c0deb3c-25a8-11eb-239d-b739f0934042
md"""
# Numerical Methods of Medical Imaging - Exercise 3

[Institute for Biomedical Imaging](https://www.tuhh.de/ibi/home.html), Hamburg University of Technology

* 👨‍🏫 Prof. Dr. Tobias Knopp
* 👨‍🏫 Dr. Martin Möddel
"""

# ╔═╡ ed576dc2-25a8-11eb-12c3-35fcb09a7d44
md"""
# Computed Tomography - Part II

* 📅 Due date: 22.11.2022, 12 a.m.
* You can earn 1 point for each task (7 points in total).
* 💣 Part II contains also a small coding challenge for those interested (1 bonus point).

The inverse problem in computed tomography is to determine the attenuation given some Radon data. Here, two different inversion strategies are discussed.
"""

# ╔═╡ 499a2a82-25ad-11eb-1cc4-91e69d30a6e6
md"""
## Shepp Logan Phantom

To start off we are going to load and visualize the Shepp Logan phantom Radon data.
"""

# ╔═╡ 9cfc0e64-25aa-11eb-19c4-d78e0f6b03e8
begin
	p = readdlm("sheppLogan.dat")
	M,N = size(p)
	ξs=range(-1/sqrt(2)*(1-1/M),step=2/sqrt(2)/M,length=M)
	γs = range(0.0,step=π/N,length=N)
end

# ╔═╡ d64e93ec-25aa-11eb-129c-bd82a7f07ffa
heatmap(γs,ξs,p,
	c = :viridis,
	xlabel = "γ",
	ylabel = "ξ"
)

# ╔═╡ 12d9ae66-25ad-11eb-102b-7ddeebec9526
md"""
## 4. Filtered Backprojection

In practice Radon data $p(\xi,\gamma)$ is inverted using the filtered backprojection, which consists of three steps:

* The first step consists of a 1D Fourier transformation along the $\xi$-dimension

$P(q,\gamma) = \int_{\mathbb R} p(\xi,\gamma)e^{-2\pi i \xi q} d\xi.$

* Next, a ramp filter is applied and the result is transformed back into Radon space

$h(\xi,\gamma) = \int_{\mathbb R} P(q,\gamma)\vert q \vert e^{2\pi i\xi q}dq.$

* Last, the attanuation coefficient is obtained by integrating $h(\xi,\gamma)$ along the path $\xi(\gamma) = x\cos \gamma +y\sin\gamma$

$\mu(x,y) = \int_0^\pi h(\xi(\gamma),\gamma)d\gamma.$
"""

# ╔═╡ 92d01a86-25bc-11eb-3736-7f409c153fd7
md"""
#### 🎓 Task

Calculate `P` from the discrete Shepp Logan phantom Radon data `p` by 1D Fourier transformation along the $\xi$-dimension. Exploit the fact that `p` is a real array and use the `rfft` instead of the `fft`.
"""

# ╔═╡ 32c477c8-25b3-11eb-20f8-fb55bc0566b5
P = p;

# ╔═╡ ead8c092-25b3-11eb-28ec-7514cf5ffb06
heatmap(abs.(P),
	c = :viridis,
	xlabel = "γ",
	ylabel = "ξ"
)

# ╔═╡ 08158066-25bc-11eb-0820-c361b2249fc8
md"""
#### 🎓 Task
Calculate `h` by filtering and back transformation of `P`. Use the `irfft` function for efficient inverse Fourier transformation.
"""

# ╔═╡ 61dbb53c-25b9-11eb-387c-fdc757db0931
h = p;

# ╔═╡ 9d07c95c-25b9-11eb-1945-b72a11da9806
heatmap(γs,ξs,h,
	c = :viridis,
	xlabel = "γ",
	ylabel = "ξ"
)

# ╔═╡ c1db14a0-25b9-11eb-109f-41ec55c0146c
md"""
#### 🎓 Task

Write a function `μ(h,x,y)` to approximate

$\mu(x,y) = \int_0^\pi h(\xi(\gamma),\gamma)d\gamma$

from `h`. Approximate this integral by taking the discretization of your data into account. Make use of every angle available along the $\gamma$-direction of the discrete data `h` for approximation using a simple Riemann sum.

Along the $\xi$-direction $\xi(\gamma)$ will likely not fall onto the discretization grid, in which case the exact value $h(\xi(\gamma),\gamma)$ is unknown. To this end, search for the nearest data point in `h` (nearest-neighbor interpolation) along the $\xi$-direction and use it as an estimate for $h(\xi(\gamma),\gamma)$.
"""

# ╔═╡ c07167ce-25c1-11eb-2290-cd8871136b7a
function μ(h,x,y)
	M,N = size(h)
	ξs = range(-1/sqrt(2)*(1-1/M),step=2/sqrt(2)/M,length=M)
	γs = range(0.0,step=π/N,length=N)
	out = zero(eltype(h))
	
	# do stuff
	
	return out
end

# ╔═╡ d2a7da5d-2290-4d78-9567-6b0a24ca0156
md"Adapt the grid size:"

# ╔═╡ 7edc23ac-2815-11eb-24db-27b9485ebf22
@bind L Slider(1:150, default=25, show_value=true)

# ╔═╡ 63135366-2815-11eb-3c25-cdfc9853385e
locations = range(-1/2*(1-1/L),step=1/L,length=L)

# ╔═╡ 693919f0-281b-11eb-1f01-87295724208e
md"""
## 5. Fourier Based Reconstruction in Computed Tomography

* 💣 This is no regular exercise but a small coding challenge for those interested.

![](https://imgs.xkcd.com/comics/frequency/car_germany.gif)

"Frequency" taken from [xkcd](https://xkcd.com/1331/) is licensed under [CC](https://en.wikipedia.org/wiki/en:Creative_Commons) [BY-NC 2.5](https://creativecommons.org/licenses/by-nc/2.5/) license. Check out the link for more!

The Radon transformation is given by

$p(\xi,\gamma) = \int_{-\infty}^\infty \mu(\xi \cos\gamma - \eta \sin\gamma, \xi\sin \gamma +\eta \cos\gamma)\text{d}\eta,$

the 1D-Fourier transform of $p(\xi,\gamma)$ along the first dimension by

$P(q,\gamma) = \int_{-\infty}^\infty p(\xi,\gamma) e^{-2\pi i q\xi} \text{d}\xi$

the 2D-Fourier transform of the attenuation coefficients $\mu(x,y)$ by

$M(u,v) = \int_{\mathbb R^2} \mu(x,y) e^{-2\pi i (xu+yv)} \text{d}x\text{d}y.$

The **Fourier-Slice-Theorem** states that

$P(q,\gamma) = M(q\cos\gamma,q\sin\gamma)$

which can be used for a reconstruction of our Radon data

$\mu(x,y) = \int_{\mathbb R^2} M(u,v) e^{2\pi i (xu+yv)} \text{d}u\text{d}v.$

The steps neccessary are:
* First, a 1D discrete Fourier transform of $p$ along the $\xi$-direction.
* Second, an interpolation from polar to Cartesian grid. I.e. a direct application of the theorem.
* Last, an inverse 2D Fourier transform of $M$.

#### 🎓💣 Task
Implement a function returning $\mu$ given the radon data `p` and final grid size `K` using the Fourier based reconstruction method just described.

Hints:
* Consider a vector `v`. Use the functions [`fftshift`, `ifftshift`](https://juliamath.github.io/AbstractFFTs.jl/stable/api/#AbstractFFTs.fftshift) for a circular shift of the periodic signal so that it becomes centered at index 1. Its discrete Fourier transform `fftshift(fft(ifftshift(v)))` then has frequencies 
```julia
M = length(fftshift(fft(ifftshift(v))))
if iseven(M)
    frequencies = -div(M,2):div(M,2)-1
else
    frequencies = -div(M-1,2):div(M-1,2)
end
```

* In this particular case you only have angles $0\le\gamma<\pi$ available. Hence, you will need to make use of $(q\cos(\gamma),q\sin(\gamma)) = -(q\cos(\gamma-\pi),q\sin(\gamma-\pi))$ for polar-to-Cartesian transformation.
* For interpolation (and extrapolation if you need it) you can use the `Interpolations` package. Of special interest will be [this](https://juliamath.github.io/Interpolations.jl/latest/control/#Gridded-interpolation-1) segment in the documentation.
"""

# ╔═╡ 6d65d24c-2821-11eb-304e-4f59c903950e
function μ(p, K=100)
	
	# do some cool stuff
	
	return zeros(eltype(p),K,K)
end

# ╔═╡ d575d7c2-2814-11eb-32ae-1991037b7658
phantom = [μ(h,x,y) for x in locations, y in locations];

# ╔═╡ 16c687b2-2815-11eb-1535-d95a9253aeb7
heatmap(locations,locations,phantom,
	c = :viridis,
	xlims = (-0.5,0.5),
	ylims = (-0.5,0.5),
	aspect_ratio = 1,
	xlabel = "x",
	ylabel = "y"
)

# ╔═╡ cf191765-4d82-4f3e-b4f6-788bdd4f7d8c
md"Adapt the grid size `K`:"

# ╔═╡ 231e5ff4-283c-11eb-091b-ff43ad805431
@bind K Slider(1:1:150, default=41, show_value=true)

# ╔═╡ d90abf40-2834-11eb-3861-eda6ee7a1000
heatmap(abs.(μ(p,K)),
	c = :viridis,
	aspect_ratio = 1,
	xlabel = "x",
	ylabel = "y"
)

# ╔═╡ b7469c30-0b02-425f-b064-149ef2f86d4b
begin
	hint(text) = Markdown.MD(Markdown.Admonition("hint", "Hint", [text]))
	not_defined(variable_name) = Markdown.MD(Markdown.Admonition("danger", "Oh, oh! 😱", [md"Variable **$(Markdown.Code(string(variable_name)))** is not defined. You should probably do something about this."]))
	failed_test(text=md"Some tests failed. Keep working on it!") = Markdown.MD(Markdown.Admonition("danger", "Oh, oh! 😱", [text]))
	still_missing(text=md"Replace `missing` with your solution.") = Markdown.MD(Markdown.Admonition("warning", "Let's go!", [text]))
	keep_working(text=md"The answer is not quite right.") = Markdown.MD(Markdown.Admonition("danger", "Keep working on it!", [text]));
	yays = [md"Great! 🥳", md"Correct! 👏", md"Tada! 🎉"]
	correct(text=md"$(rand(yays)) Let's move on to the next task.") = Markdown.MD(Markdown.Admonition("correct", "Got it!", [text]))
end;

# ╔═╡ d649e96f-f54d-450e-9fb8-b1d306f3de4a
if size(P) != (184,180)
	keep_working(md"The size of `P` is not quite right.")
elseif !(isapprox(8044.0 + 0.0im,P[1,1],atol=1e-5)) || !(isapprox(-3.1296370420222672 - 13.524313951361393im,P[100,100],atol=1e-5))
	keep_working(md"`P` is not quite right.")
else
	correct()
end

# ╔═╡ 47db0f4a-dd92-400a-86f5-99c8a27778f4
let x = zeros(5,5); x[3,3] = 1.0; μtest(r) = norm(r,2)<=0.5 ? 1.0 : 0.0
	if size(h) != (367,180)
		keep_working(md"The size of `h` is not quite right.")
	elseif !(isapprox(-13.520243,h[1,1],atol=1e-5)) || !(isapprox(55.643539,h[100,100],atol=1e-5))
		keep_working(md"`h` is not quite right.")
	else
		correct()
	end
end

# ╔═╡ af59d647-cfe7-4da5-ae93-8876eb11dee3
let x = [-0.134134  -22.1585  -13.1535  -14.7317   -18.8289   -22.5123  -21.4767   -26.1091
  -8.60523   -16.9745  -23.3918   62.7502    50.3356   -16.8203   -6.31704   -2.70192
 -23.227      56.7793   61.2494   67.9982    -8.25005   70.4288   52.8148   -29.4127
 335.286      65.2589  -13.2265   -4.30947  -19.1694    89.4779   59.0391   346.347
 333.685      49.3326   55.06    -14.7453    63.2481   101.868    61.9505   328.903
 -13.1561     67.9968   69.4684   67.1149    65.531     49.8706   65.5727   -20.2306
 -20.0441    -32.0541   55.7314   66.39      61.8352    74.1205   -9.05851   -9.72341
 -14.7304    -13.8669  -16.8306  -10.9165   -22.3654   -23.9891  -33.9383   -24.2068]
	locations = range(-1/2*(1-1/8),step=1/8,length=8)
	M = [μ(h,xx,yy) for xx in locations, yy in locations]
	if !(isapprox(x,M,atol=1e-3))
		keep_working(md"Your version of `μ` is not quite right.")
	else
		correct()
	end
end

# ╔═╡ 2fee5db2-4b63-4c57-8e5c-778fdc4d7153
let locations = range(-1/2*(1-1/8),step=1/8,length=8)
	M = abs.(μ(p,20))
	if !(isapprox(M[1,1],19.67317,atol=1e-3)) || !(isapprox(M[10,10],6.75829,atol=1e-3))
		keep_working(md"Your version of `μ` is not quite right.")
	else
		correct()
	end
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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[compat]
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[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"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[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"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "d972031d28c8c8d9d7b41a536ad7bb0c2579caca"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.8+0"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "cf7bf90e483228f6c988e474b420064e5351b892"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.69.4"

[[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 = "bc9f7725571ddb4ab2c4bc74fa397c1c5ad08943"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.69.1+0"

[[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"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "fb83fbe02fe57f2c068013aa94bcdf6760d3a7a7"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.74.0+1"

[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[HTTP]]
deps = ["Base64", "CodecZlib", "Dates", "IniFile", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "4abede886fcba15cd5fd041fef776b230d004cee"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.4.0"

[[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"

[[Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"

[[HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "c47c5fa4c5308f27ccaac35504858d8914e102f9"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.4"

[[IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"

[[IniFile]]
git-tree-sha1 = "f550e6e32074c939295eb5ea6de31849ac2c9625"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.1"

[[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 = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "842dd89a6cb75e02e85fdd75c760cdc43f5d6863"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.14.6"

[[InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "49510dfcb407e572524ba94aeae2fced1f3feb0f"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.8"

[[IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"

[[JLFzf]]
deps = ["Pipe", "REPL", "Random", "fzf_jll"]
git-tree-sha1 = "f377670cda23b6b7c1c0b3893e37451c5c1a2185"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.5"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.4.1"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.3"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b53380851c6e6664204efb2e62cd24fa5c47e4ba"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.2+0"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "3.0.0+1"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
git-tree-sha1 = "ab9aa169d2160129beb241cb2750ca499b4e90e9"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.17"

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

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.3"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "7.84.0+0"

[[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"
version = "1.10.2+0"

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

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.4.0+0"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

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

[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "94d9c52ca447e23eac0c0f074effbcd38830deb5"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.18"

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

[[LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "5d4d2d9904227b8bd66386c1138cf4d5ffa826bf"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "0.4.9"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "41d162ae9c868218b1f3fe78cba878aa348c2d26"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2022.1.0+0"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.10"

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

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "Random", "Sockets"]
git-tree-sha1 = "6872f9594ff273da6d13c7c1a1545d5a8c7d0c1c"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.6"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.0+0"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

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

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2022.2.1"

[[NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "a7c3d1da1189a1c2fe843a3bfa04d18d20eb3211"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.1"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "1ea784113a6aa054c5ebd95945fa5e52c2f378e7"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.12.7"

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"

[[OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.20+0"

[[OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+0"

[[OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "ebe81469e9d7b471d7ddb611d9e147ea16de0add"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.2.1"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e60321e3f2616584ff98f0a4f18d98ae6f89bbb3"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.17+0"

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

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

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

[[PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.40.0+0"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "595c0b811cf2bab8b0849a70d9bd6379cc1cfb52"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.4.1"

[[Pipe]]
git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
version = "1.3.0"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.8.0"

[[PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "8162b2f8547bc23876edd0c5181b27702ae58dce"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.0.0"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "SnoopPrecompile", "Statistics"]
git-tree-sha1 = "21303256d239f6b484977314674aef4bb1fe4420"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.3.1"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SnoopPrecompile", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
git-tree-sha1 = "524d9ff1b2f4473fef59678c06f9f77160a204b1"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.35.3"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "2777a5c2c91b3145f5aa75b61bb4c2eb38797136"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.43"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.3.0"

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

[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "c6c0f690d0cc7caddb74cef7aa847b824a16b256"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+1"

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

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

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "dc84268fe0e3335a62e315a3a7cf2afa7178a734"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.3"

[[RecipesBase]]
deps = ["SnoopPrecompile"]
git-tree-sha1 = "612a4d76ad98e9722c8ba387614539155a59e30c"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.0"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase", "SnoopPrecompile"]
git-tree-sha1 = "9b1c0c8e9188950e66fc28f40bfe0f8aac311fe0"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.7"

[[Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "90bc7a7c96410424509e4263e277e43250c05691"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.0"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "f94f779c94e58bf9ea243e77a37e16d9de9126bd"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.1"

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

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

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[SimpleBufferStream]]
git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.1.0"

[[SnoopPrecompile]]
git-tree-sha1 = "f604441450a3c0569830946e5b33b78c928e1a85"
uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c"
version = "1.0.1"

[[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", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "d75bda01f8c31ebb72df80a46c88b25d1c79c56d"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.7"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
git-tree-sha1 = "f86b3a049e5d05227b10e15dbb315c5b90f14988"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.5.9"

[[StaticArraysCore]]
git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.0"

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

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

[[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"

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

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

[[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"

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "8a75929dcd3c38611db2f8d08546decb514fcadf"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.9"

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

[[URIs]]
git-tree-sha1 = "e59ecc5a41b000fa94423a578d29290c7266fc10"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.0"

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

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

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

[[Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

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

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "58443b63fb7e465a8a7210828c91c08b92132dff"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.14+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

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

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

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

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

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

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

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

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

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

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

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

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

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

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

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

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

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

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
# ╟─9c0deb3c-25a8-11eb-239d-b739f0934042
# ╠═b573185c-25aa-11eb-14ee-4f35f39e4f60
# ╟─ed576dc2-25a8-11eb-12c3-35fcb09a7d44
# ╟─499a2a82-25ad-11eb-1cc4-91e69d30a6e6
# ╟─9cfc0e64-25aa-11eb-19c4-d78e0f6b03e8
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