### A Pluto.jl notebook ###
# v0.20.4

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)
    #! format: off
    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
    #! format: on
end

# ╔═╡ 2e940612-c20e-11ee-32c7-f9bc3c387af9
begin
	using Parameters # @with_kw
	using Tullio     # efficent einsum tensors via Tullio.jl
	using StatsBase  # min, max, L2dist
	using CairoMakie # plotting
	using PlutoUI 	# 
	using PlutoTeachingTools
end

# ╔═╡ 2de5529e-b585-4d7a-91c7-78f82aa43611
html"""
<style>
	main {
		margin: 0 auto;
		max-width: 2000px;
    	padding-left: max(160px, 10%);
    	padding-right: max(160px, 10%);
		font-size: x-large
	}
</style>
"""

# ╔═╡ 6b7eae7b-a5d3-4e90-849b-2496e4284cf6
# TableOfContents()

# ╔═╡ 99ac0194-716f-4820-a854-cb36ec1d1a12
md"""
# The Shimer and Smith (ECTA 2000) Model

## Environment

1. Fixed measure of workers indexed by $x \in \mathbb{X}$
1. Fixed measure of firms indexed by $y \in \mathbb{Y}$
1. production function $f(x,y)$
1. Common ranking $f_x > 0, f_y > 0$
1. Agents can make transfers if matched: the wage $w$.
1. Unemployed get $b(x)$. Vacancies cost $c(y)$
1. Workers and firms are both forward looking, i.e. they care about the expected present value (EPV)

## Allocations

1. The mass of unemployed workers is $u(x)$ , $v(y)$ the mass of vacancies
2. The mass of matches is $h(x,y)$ .
3. The wage is $w(x,y)$ and $M(x,y)$ is the matching decision (yes/no)

## Matching Process

* Unemployed find offers at rate $\lambda$
* vacancies find workers are rate $\mu$
* both can be endogenized with a matching function:
  * the number of matches is $N=m(U,V)$
  * then $\lambda = \frac{N}{U}, \mu=\frac{N}{V}$
  * a classic matching function is $m(u,v)=\alpha u^{0.5} v^{0.5}$
* matching is random: workers draw from $v(y)$, firms draw from $u(x)$

## Matching Process: Timing

1. Production: matches produce output and pay wages
2. meeting: U and V meet
3. matching: newly matched pairs decide whether to start a partnership
4. separating: existing matches destroyed at rate $\delta$

## match Surplus - Present Values

* EPV of employed and unemployed are $W_1(x,y,w)$ and $W_0(x)$
* EPV of job and vacancy are $\Pi_1(x,y,w)$ and $\Pi_0(y)$

Surplus is defined as:

$$S(x,y) := W_1(x,y,w) + \Pi_1(x,y,w) - W_0(x) - \Pi_0(y)$$

* Worker EPV: $rW_1(x,y,w) = w + \delta(W_0(x) -W_1(x,y,w))$
* Job EPV:    $r\Pi_1(x,y,w) = f(x,y) -w  + \delta(\Pi_0(y) -\Pi_1(x,y,w))$


## Value of Surplus

Some simple algebra gives us that:

$$(r+\delta) S(x,y) = f(x,y) - rW_0(x) - r\Pi_0(y)$$

* Note that we don't need to know the wage to compute this!
* Under TU, the matching decision is $M(x,y) = \mathbf{1}[S(x,y)\geq0]$
* Surplus can be non-monotonic because of option value!
* Surplus inherits complementarity directly from $f$.

"""

# ╔═╡ 413968b0-bce7-47da-850d-2e494716eef1
md"""

## Wages and Division of Surplus

* There an infinite number of ways to split the surplus
* S-S assume: nash bargaining with $\alpha$ the worker's bargaining power.
* then the optimal wage $w(x,y)$ solves


$$(1-\alpha)\left(W_1(x,y,w) - W_0(y) \right) = \alpha\left(\Pi_1(x,y,w) - \Pi_0(y)\right)$$

* Therefore, upon meeting
  * worker gets $W_0(x) + \alpha(S(x,y)$
  * firm gets $\Pi_0(x) + (1-\alpha)(S(x,y)$


## EPV of unemployed and vacancy

* EPV of the unemployed:
$$rW_0(x) = (1+r)b(x) + \lambda \int \alpha M(x,y) S(x,y) \frac{v(y)}{V}dy$$

* EPV of a vacancy:
$$r\Pi_0(x) = -(1+r)c(y) + \mu \int (1-\alpha) M(x,y) S(x,y) \frac{u(x)}{U}dx$$

* Matching Distribution
$$\delta h(c,y) = \frac{\lambda}{V}M(x,y)u(x)v(y)$$

## Equlibrium

Given the primitives $f(x,y),c(y),b(x),r,\delta,\alpha, \lambda,\mu$, a stationary search equilibrium is defined by

* EPVs: $S(x,y),W_0,W_1,\Pi_1,\Pi_0$
* Allocations: $h(x,y),u(x),v(y)$
* wage $w(x,y)$ and matching functions $M(x,y)$


such that

* the EPVs solve the Bellman Equations
* the wage is the Nash barginaing solution
* the distributions satisfy stationarity and adding up propoerties.

"""

# ╔═╡ 0a3d5332-10cb-4d71-8b41-5055aef45a91
md"""

# Numerical Implementation

The equilibrium of Shimer and Smith can be solved by iterating on the Bellman equations of an unemployed worker $W_0$, of an unfilled vacancy $\Pi_0$ and the surplus function $S$. They all depend on each other and are given by:

$(r+s)S(x,y) = f(x,y) -r W_0(x) - r \Pi_0(y)$

$r W_0(x) = b + \kappa  \alpha \int \max \{ S(x,y') , 0\} v(y') dy'$

$r \Pi_0(y) = -c + \kappa (1-\alpha)  \int \max \{ S(x',y) , 0\} u(x') dx'$

The equilibrium condition is that the in and out flows from and to the match distribution $h(x,y)$ equalize, i.e. that $h$ is stable, or, _in equilibrium_. $h(x,y)$ is given by

$h(x,y) = (1-s)  h(x,y)  1[S(x,y)\geq 0] + \kappa 1[S(x,y)\geq 0] u(x) v(y)$

Notice here that $S(x,y) \geq 0$ selects only viable matches (i.e. ones with non-negative surplus), and that $s$ is the exogenous separation rate. So, the next version of $h$ (on the LHS) will be the mass of matches $h(x,y)$ which are viable, and survived the separation shock ($(1-s)  h(x,y)  1[S(x,y)\geq 0]$) plus all newly formed matches. 

The $\kappa$ in the worker value function is a reformulation of the full problem, which is 

$r W_0(x) = b + \lambda  \alpha \int \max \{ S(x,y') , 0\} \frac{v(y')}{V} dy'$

where $V=\int v(x)dx$ is the mass of all vacancies. With the matching function $N=m(x,y)$ and defining $\lambda = \frac{N}{U}$ we get the above formulation by realizing that $\kappa = \frac{N}{UV}$.

"""

# ╔═╡ cdf7ff76-c77c-4650-af19-89f9965fa4c3
TODO(md"""
1. Define solution algorithm class
2. Rewrite equations in iteration form
3. Think about how to efficiently perform the integrations on the RHS or $W_0$ and $\Pi_0$.
4. Create a parameter struct to carry useful information
5. Solve.
""", heading="Computational Strategy")

# ╔═╡ 042f81b5-c587-48c3-8b56-58b5bcb10f8e
md"""
1. Will solve by the 4 equation by value function iteration. Given current guesses for $W_0$ and $\Pi_0$, get a new $S$. Given a new $S$ get a new $W_0$ etc. Do this until changes from one version to the next become very small. Also check that $h$ converges. Let's update each equation slowly, i.e. let's take a convex combination of new and old values.
2. That easy:

$S(x,y) = \frac{f(x,y) -r W_0(x) - r \Pi_0(y)}{(r+s)}$

$W_0(x) = \frac{b + \kappa  \alpha \int \max \{ S(x,y') , 0\} v(y') dy'}{r}$

$\Pi_0(y) = \frac{-c + \kappa (1-\alpha)  \int \max \{ S(x',y) , 0\} u(x') dx'}{r}s$

3. We will discretiz the model, such that integrations like $\int \max \{ S(x,y') , 0\} v(y') dy'$ can be approximated with a sum $\sum_{i=1}^{N_y} \max \{ S(x,i) , 0\} v(i)$, where $N_y$ is the number of grid points in the $y$ space, and where $v(y)$ is the mass of firms of type $y$. Notice that the location of gridpoints $i$ could play a role here, particularly if we want to save on points; We will choose a reasonably large number so that a uniform grid of points will not do too bad. The simplest approach is probably to write a loop:

```julia
integral = zeros(nx)
S = randn(nx,ny)  # to make the point
for ix in 1:nx
	for iy in 1:ny
		integral[ix] += max(S[x,iy],0) * v[iy]
	end
end
```

and while this works perfectly fine, it is a lot of code floating around. Couldn't we let `julia` write those loops for us? 🤔

"""

# ╔═╡ 0f5b0956-b7e0-44ba-b20a-6e02e57acf5c
tip(md"we can. checkout [https://github.com/mcabbott/Tullio.jl](https://github.com/mcabbott/Tullio.jl)")

# ╔═╡ e19785cd-708f-4cf4-938d-c9095ca11e5d
md"""
In an ideal world, we just want to stare at our iteration equation:

$W_0(x) = \frac{b + \kappa  \alpha \sum_{i=1}^{N_y} \max \{ S(x,i) , 0\} v(i)}{r}$

... and write the corresponding code below it like:

```julia
@tullio W[x] := (p.b + κ * p.α * max(S[x,y],0) * V[y] ) / p.r
```

👀

the `@tullio` macro here creates a new array `W` by summing over indices `y` on the RHS of the expression. This works for almost all expressions you could imagine, including `max` and boolean indicators. It basically just writes the loop for us![^footnote1]



"""

# ╔═╡ 52448e6a-f978-49c8-9690-dacff71ba709
md"""
[^footnote1]: Well, it does plenty more actually. It can compute the gradient of your tensor via autodiff, it can run on multiple threads and it uses AVX instructions by default.
"""

# ╔═╡ 44dde1f8-7c9a-48e1-91c4-baf9d73a749c
md"""
## Solve the Model

Ok, let's create a param struct `p` with some default values. 
"""

# ╔═╡ 0472732b-f1d8-4cb6-86ab-6e2a44dd54aa
p = @with_kw (
	ay    = 0.2,
	nx    = 50,     # number of worker types
	ny    = 49,     # number of firm types
	sep   = 0.02,  # separation rate
	r     = 0.05,  # interest rate
	ρ     = -2,    # prod func assortative strength 2,
	b     = 0,     # unemp
	c     = 0,     # vacancy cost
	α     = 0.5, # bargaining power
	fsize = 50,  # firm size
	m     = 0.4,   # matching function parameter
	M     = 1.5 ,     # mass of firms / mass of workers
	noise = 0.5 , # wage disturbance
	rs    = 0.5 , # relaxation parameter for S convergence
	rh    = 0.8 , # relaxation parameter for H convergence
	rw    = 0.5 , # relaxation parameter for W convergence
	tol   = 1e-7  # convergence tolerance
)

# ╔═╡ e3cb6fcb-9073-48ee-8d77-1b4e26fc6e1d
md"""
Also, I want to have the tensors to be as efficient as possible, so I will define functions that modify preallocated arrays in-place, like this:

```julia
# create the tullio tensors which modify in-place
doS2!(S,F,W,P,p) = @tullio S[x,y] = (F[x,y] - p.r * W[x] - p.r * P[y]) / (p.r + p.sep)
doW2!(W,S,V,p,κ) = @tullio W[x] = (p.b + κ * p.α * max(S[x,y],0) * V[y] ) / p.r
doP2!(P,S,U,p,κ) = @tullio P[y] = (-p.c + κ * (1-p.α) * max(S[x,y],0) * U[x] ) / p.r
doH2!(H2,H,S,U,V,p,κ) = @tullio H2[x,y] = (1 - p.sep) * H[x,y] * (S[x,y] >= 0) + κ * (S[x,y] >= 0) * U[x] * V[y]
```

Here is the production function we'll use:
"""

# ╔═╡ ff0a9a8a-12a9-44d1-93c6-1ddb51f6e3d7
"production function after Hagedorn, Law and Manovskii 2013"
pf(x,y,p::NamedTuple) = ( x^p.ρ + y^p.ρ )^(1/p.ρ) + p.ay

# ╔═╡ 7d4fa13f-f240-413f-bb0b-2240ae0cb77a
function solve(p::NamedTuple)
	# setup some data containers
	
	X = range(0,(p.nx-1)/p.nx, length = p.nx)
	Y = range(0,(p.ny-1)/p.ny, length = p.ny)
	F = [pf(ix,iy,p) for ix in X, iy in Y]  # production function values
	W = zeros(p.nx)  # initial guess of unemployed worker value function
	P = zeros(p.ny)  # initial guess of unfilled vacancy value function
	H = zeros(p.nx,p.ny)  # worker-firm match distribution
	U = fill(1/p.nx, p.nx)  # unemployment distribution
	V = p.M .* fill(1/p.ny, p.ny)  # vacancy distribution
	S = F ./ p.r  # match surplus

	# create interation versions of arrays
	S2 = similar(S)  # iteration version of S
	W2 = similar(W)  # iteration version of W
	P2 = similar(P)  # iteration version of P
	H2 = similar(H)  # iteration version of H

	# create the tullio tensors which modify in-place
	doS2!(S,F,W,P,p) = @tullio S[x,y] = (F[x,y] - p.r * W[x] - p.r * P[y]) / (p.r + p.sep)
	doW2!(W,S,V,p,κ) = @tullio W[x] = (p.b + κ * p.α * max(S[x,y],0) * V[y] ) / p.r
	doP2!(P,S,U,p,κ) = @tullio P[y] = (-p.c + κ * (1-p.α) * max(S[x,y],0) * U[x] ) / p.r
	doH2!(H2,H,S,U,V,p,κ) = @tullio H2[x,y] = (1 - p.sep) * H[x,y] * (S[x,y] >= 0) + κ * (S[x,y] >= 0) * U[x] * V[y]


	# value function iteration difference tracker
	diff = 100.0

    # initial guesses for U and V
	U0 = fill(1/p.nx, p.nx)
	V0 = fill(p.M/p.ny, p.ny)

    # VFI loop
	κ = 0.0  # initialize out of the while scope to preserve it's value
    itercount = 0
	while diff > p.tol
        itercount += 1

		κ = min(min(sum(U), p.m * sum(U)^(0.5) * sum(V)^(0.5)), sum(V) ) / (sum(U) * sum(V))

		doS2!(S2,F,W,P,p)
		ΔS = L2dist(S,S2)
		# update S slowly
		S = p.rs .* S .+ (1 - p.rs) .* S2
		@assert !(any(isnan.(S2))) "NaN in S2"

		# compute new version of W and P and update
		doW2!(W2,S,V,p,κ)
		W = p.rw .* W .+ (1 - p.rw) .* W2
        @assert !(any(isnan.(W2))) "NaN in W2"

        doP2!(P2,S,U,p,κ)
        P = p.rw .* P .+ (1 - p.rw) .* P2
        @assert !(any(isnan.(P2))) "NaN in P2"

        # new firm distribution
		doH2!(H2,H,S,U,V,p,κ)
		ΔH = L2dist(H,H2)

		# update H slowly
		H = p.rh .* H .+ (1 - p.rh) .* H2

		# update U and V
		U = U0 - sum(H,dims = 2)[:]
		V = V0 - sum(H,dims = 1)[:]

		# update diff measure
		diff = max(ΔS,ΔH)
                
        if itercount % 500 == 0
            @info "iter: $itercount, diff: $diff"
        end
	end
    @info "VFI done."
    w = p.α * (p.sep + p.r) .* S .+ p.r .* repeat(W,1,p.ny)
    @tullio c_rate := κ * (S[x,y] >= 0) * V[y]


    return Dict(:S => S,:W => W,:P => P,:H => H,:U => U,:V => V, :wage => w, :contact_rate => c_rate,:X => X, :Y => Y, :F => F)
end

# ╔═╡ 9be4da7b-257c-4d3a-af6a-da6aff1cb96a
md"""
Parameter  | value | Parameter  | value    
---------  | ------| ---------  | ------
``\rho``     | $(@bind ρ PlutoUI.Slider(-10:0.01:-2.0, show_value = true,default = -2))  | ``\alpha`` | $(@bind α PlutoUI.Slider(0.01:0.01:0.5, show_value = true,default = 0.5))
``b``     | $(@bind b PlutoUI.Slider(0:0.001:0.1, show_value = true,default = 0))  | ``c`` | $(@bind c PlutoUI.Slider(0.0:0.001:0.1, show_value = true,default = 0))

"""

# ╔═╡ 7e23cbdb-6e37-4fdd-85ee-aed92dfa2c68
p0 = p(ρ = ρ, α = α, tol = 0.001, b = b, c = c)

# ╔═╡ c01afcbf-cf66-4074-adf3-3e0a2cd90099
m = solve(p0);

# ╔═╡ f04318dd-8f5f-424a-acae-16daf01c9b72
let
	fig = Figure()
	g = fig[1,1] = GridLayout() 
	
	ax1 = Axis(g[1,1], aspect = 1, title = "contours S")
	ax2 = Axis3(g[1, 2], aspect = (1, 1, 1), azimuth = 1.2 * pi, title = "S")
	ax3 = Axis3(g[2, 1], aspect = (1, 1, 1), azimuth = 1.2 * pi, title = "F")
	ax4 = Axis(g[2, 2], title = "wage")
	ax5 = Axis(g[3, 1], title = "unemployment")

	ax = [ax1,ax2,ax3]
	contourf!(ax[1], m[:X],m[:Y],(m[:S] .>= 0) .* m[:S])
	wireframe!(ax[2],m[:X],m[:Y],(m[:S] .>= 0) .* m[:S], aspect = :data)
	surface!(ax[3],m[:X],m[:Y],m[:F], aspect = (1, 1, 1))
	lines!(ax4,m[:X],m[:W] )
	lines!(ax5,m[:X],m[:U] )


	# tweak
	hidedecorations!(ax1, grid = false)
	hidedecorations!(ax2, grid = false)
	hidedecorations!(ax3, grid = false)
	# Label(fig[1,1:2,Top()], "test")
	colgap!(g, 0)
	rowgap!(g, 0)
	fig
end

# ╔═╡ 669ee78c-db02-477e-a466-ef5ddfc84653
FootnotesInlineStyleSuperscript()

# ╔═╡ 9f54d5d7-b3b5-473f-aa30-6516bbf8ff25
FootnotesNumbered()

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
PlutoTeachingTools = "661c6b06-c737-4d37-b85c-46df65de6f69"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
Tullio = "bc48ee85-29a4-5162-ae0b-a64e1601d4bc"

[compat]
CairoMakie = "~0.11.6"
Parameters = "~0.12.3"
PlutoTeachingTools = "~0.2.14"
PlutoUI = "~0.7.55"
StatsBase = "~0.34.2"
Tullio = "~0.3.7"
"""

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uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "1.0.0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "6a451c6f33a176150f315726eba8b92fbfdb9ae7"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.13.4+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "a54ee957f4c86b526460a720dbc882fa5edcbefc"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.41+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "15e637a697345f6743674f1322beefbc5dcd5cfc"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.6.3+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.6+0"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.11+0"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "bcd466676fef0878338c61e655629fa7bbc69d8e"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "555d1076590a6cc2fdee2ef1469451f872d8b41b"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.6+1"

[[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"]
git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.9.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.2+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.3+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.44+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "7dfa0fd9c783d3d0cc43ea1af53d69ba45c447df"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+1"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.libwebp_jll]]
deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"]
git-tree-sha1 = "ccbb625a89ec6195856a50aa2b668a5c08712c94"
uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2"
version = "1.4.0+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "35976a1216d6c066ea32cba2150c4fa682b276fc"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.0+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "dcc541bb19ed5b0ede95581fb2e41ecf179527d2"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.6.0+0"
"""

# ╔═╡ Cell order:
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# ╟─2e940612-c20e-11ee-32c7-f9bc3c387af9
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# ╟─042f81b5-c587-48c3-8b56-58b5bcb10f8e
# ╟─0f5b0956-b7e0-44ba-b20a-6e02e57acf5c
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# ╟─52448e6a-f978-49c8-9690-dacff71ba709
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# ╠═0472732b-f1d8-4cb6-86ab-6e2a44dd54aa
# ╟─e3cb6fcb-9073-48ee-8d77-1b4e26fc6e1d
# ╠═ff0a9a8a-12a9-44d1-93c6-1ddb51f6e3d7
# ╠═7d4fa13f-f240-413f-bb0b-2240ae0cb77a
# ╠═7e23cbdb-6e37-4fdd-85ee-aed92dfa2c68
# ╟─9be4da7b-257c-4d3a-af6a-da6aff1cb96a
# ╠═f04318dd-8f5f-424a-acae-16daf01c9b72
# ╠═c01afcbf-cf66-4074-adf3-3e0a2cd90099
# ╟─669ee78c-db02-477e-a466-ef5ddfc84653
# ╟─9f54d5d7-b3b5-473f-aa30-6516bbf8ff25
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002