### A Pluto.jl notebook ###
# v0.19.25

using Markdown
using InteractiveUtils

# ╔═╡ 0829eb90-1d74-46b6-80ec-482a2b71c6fe
using PlutoUI, Flux,LinearAlgebra,PlutoUI

# ╔═╡ d2d1ca64-d220-450f-a7af-1e77da98efbe


# ╔═╡ 66f0e667-d722-4e1e-807b-84a39cbc41b1
md"""
# Bellman Residual Minimization


"""

# ╔═╡ 9fa41b7c-1923-4c1e-bfc6-20ce4a1a2ede
md"""
Number of Constellations: $(const N_constellations = 4)

Number of Debris Trackers: $(const N_debris = 1)

Number of Overall States: $(const N_states = N_constellations + N_debris)
"""

# ╔═╡ 90446134-4e45-471c-857d-4e165e51937a
begin
	abstract type PhysicalParameters end
	
	#setup physical model
	struct BasicModel <: PhysicalParameters
	    #rate at which debris hits satellites
	    debris_collision_rate::Real
	    #rate at which satellites of different constellations collide
	    satellite_collision_rates::Matrix{Float64}
	    #rate at which debris exits orbits
	    decay_rate::Real
	    #rate at which satellites
	    autocatalysis_rate::Real
	    #ratio at which a collision between satellites produced debris
	    satellite_collision_debris_ratio::Real
	    #Ratio at which launches produce debris
	    launch_debris_ratio::Real
	end

		#Getting loss parameters together.
	loss_param = 2e-3;
	loss_weights = loss_param*(ones(N_constellations,N_constellations) - LinearAlgebra.I);
	
	#orbital decay rate
	decay_param = 0.01;
	
	#debris generation parameters
	autocatalysis_param = 0.001;
	satellite_loss_debris_rate = 5.0;
	launch_debris_rate = 0.05;
	
	#Todo, wrap physical model as a struct with the parameters
	bm = BasicModel(
	    loss_param
	    ,loss_weights
	    ,decay_param
	    ,autocatalysis_param
	    ,satellite_loss_debris_rate
	    ,launch_debris_rate
	)
end

# ╔═╡ 5b45b29e-f0f4-41e9-91e7-d444687feb4e
#implement survival function
function survival(
		stocks::Array{T}
		,debris::Array{T}
		,physical_model::BasicModel
	)	where T <: Number
    return exp.(
		-(physical_model.satellite_collision_rates .- physical_model.decay_rate) * stocks 
		.- (physical_model.debris_collision_rate*debris)
	)
end

# ╔═╡ 152f3a3c-a565-41bb-8e59-6ab0d2315ffb
#debris evolution 
function H(
		stocks::Array{T}
		,debris::Array{T}
		,launches::Array{T}
		, physical_model::BasicModel
) where T <: Number
    #get changes in debris from natural dynamics
    natural_debris_dynamics = (1-physical_model.decay_rate+physical_model.autocatalysis_rate) * debris 
    
    #get changes in debris from satellite loss
    satellite_loss_debris = physical_model.satellite_collision_debris_ratio * (1 .- survival(stocks,debris,physical_model))'*stocks 
    
    #get changes in debris from launches
    launch_debris = physical_model.launch_debris_ratio*sum(launches)
    
    #return total debris level
    return natural_debris_dynamics .+ satellite_loss_debris .+ launch_debris
end

# ╔═╡ 25ac9438-2b1d-4f6b-9ff1-1695e1d52b51
#stock update rules
function G(
		stocks::Array{T}
		,debris::Array{T}
		,launches::Array{T}
		, physical_model::BasicModel
) where T <: Number
    return LinearAlgebra.diagm(survival(stocks,debris,physical_model) .- physical_model.decay_rate)*stocks + launches
end

# ╔═╡ ed044362-b36f-488f-bb4f-eeff47d624fa


# ╔═╡ 29ff1777-d276-4e8f-8582-4ca191f2e2ff
md"""
## Setup Neural Networks
"""

# ╔═╡ f7aabe43-9a2c-4fe0-8099-c29cdf66566c
function value_function_generator(number_params=32)
	return Flux.Chain(
	    Flux.Parallel(vcat
		        #parallel joins together stocks and debris, after a little bit of preprocessing
		        ,Flux.Chain(
					Flux.Dense(N_constellations, number_params*2,Flux.relu)
		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
		        )
		        ,Flux.Chain(
					Flux.Dense(N_debris, number_params,Flux.relu)
		            ,Flux.Dense(number_params, number_params,Flux.σ)
				)
			)
		    #Apply some transformations to the preprocessed data.
			,Flux.Dense(number_params*3,number_params,Flux.σ)
			,Flux.Dense(number_params,number_params,Flux.σ)
			,Flux.Dense(number_params,1)
		)

end

# ╔═╡ d816b252-bdca-44ba-ac5c-cb21163a1e9a
function planner_policy_function_generator(number_params=32)
	return Flux.Chain(
	    Flux.Parallel(vcat
		        #parallel joins together stocks and debris
		        ,Flux.Chain(
					Flux.Dense(N_constellations, number_params*2,Flux.relu)
		            ,Flux.Dense(number_params*2, number_params*2,Flux.σ)
		        )
		        ,Flux.Chain(
					Flux.Dense(N_debris, number_params,Flux.relu)
		            ,Flux.Dense(number_params, number_params)
				)
			)
		    #Apply some transformations
			,Flux.Dense(number_params*3,number_params,Flux.σ)
			,Flux.Dense(number_params,number_params,Flux.σ)
			,Flux.Dense(number_params,N_constellations,Flux.relu)
		)

end

# ╔═╡ 95bfc9d8-8427-41d6-9f0f-f155296eef91
#not needed yet
begin
	#= CUSTOM LAYERS

	=#
	#Custom passthrough layer
	passthrough(x::Array) = x


	# custom split layer
	struct Split{T}
	  paths::T
	end
	Split(paths...) = Split(paths)
	Flux.@functor Split
	(m::Split)(x::AbstractArray) = tuple(map(f -> f(x), m.paths))

	struct Duplicate
	  n::Int
	end
	Flux.@functor Duplicate
	(m::Duplicate)(x::Tuple) = [x for i=1:m.n]
	
	### TESTING ###


	#multiple branches
	Flux.Parallel(vcat,
		passthrough, passthrough, passthrough
	)(([1],[2,3],[4]))


end

# ╔═╡ 6a3b5f7a-a535-450f-8c5f-19bdcc280146
function operators_policy_function_generator(number_params=32)
	function f()
		return Flux.Chain(
	    Flux.Parallel(vcat
		        #parallel joins together stocks and debris
		        ,Flux.Chain(
					Flux.Dense(N_constellations, number_params,Flux.relu)
		            ,Flux.Dense(number_params, number_params,Flux.σ)
		        )
		        ,Flux.Chain(
					Flux.Dense(N_debris, number_params,Flux.relu)
		            ,Flux.Dense(number_params, number_params)
				)
			)
		    #Apply some transformations
			,Flux.Dense(number_params*3,number_params,Flux.σ)
			,Flux.Dense(number_params,number_params,Flux.σ)
			,Flux.Dense(number_params,1,Flux.relu)
		)
	end

	a = [f() for i=1:N_constellations]

	Flux.Chain(
		Duplicate(N_constellations)
		
	)

end

# ╔═╡ 0ba48a75-36db-4003-95c0-2329d4fb29c5
# ╠═╡ disabled = true
# ╠═╡ skip_as_script = true
#=╠═╡
Duplicate(2)(([1.0f0 2],[3f0]))
  ╠═╡ =#

# ╔═╡ 340da189-f443-4376-a82d-7699a21ab7a2
abstract type EconomicParameters end

# ╔═╡ 206ac4cc-5102-4381-ad8a-777b02dc4d5a
begin #basic linear model
	struct EconModel1{T} <: EconomicParameters where T <: Number
		β::T
		payoff_array::Array{T}
		policy_costs::Array{T}
	end

	function payoff1(
	s::Vector{T}
	,d::Vector{T}
	,a::Vector{T}
	,em::EconModel1
)where T <: Number
	return em.payoff_array*s - em.policy_costs*a
end

end

# ╔═╡ eebb8706-a431-4fd1-b7a5-40f07a63d5cb
begin #basic CES model 
		struct CESParams{T} <: EconomicParameters 
			β::T
			r::T #elasticity of subsititution
			payoff_array::Array{T}
			policy_costs::Array{T}
			debris_costs::Array{T}
		end
	function CES_with_debris(
		s::Vector{T}
		,d::Vector{T}
		,a::Vector{T}
		,em::CESParams
	) where T <: Number
		return (em.payoff_array*(s.^em.r) - em.debris_costs*(d.^em.r)).^(1/em.r) - em.policy_costs*a
	end
end

# ╔═╡ f8d582cb-10cf-4c72-8127-787f662e0567
#=
This struct organizes information about a given constellation operator
=#
struct ConstellationOperator
	payoff_fn::Function
	econ_params::EconomicParameters
	value::Flux.Chain
end
#TODO: create a function that takes this struct and checks backprop

# ╔═╡ 5946daa3-4608-43f3-8933-dd3eb3f4541c
md"""
# Loss function specification
"""

# ╔═╡ cba3b6ec-e0c3-4ee4-b0b5-8ad247fd28cf


# ╔═╡ b433a7ec-8264-48d6-8b95-53d2ec4bad05
md"""
# Setup examples of parameter models
"""

# ╔═╡ 65e0b1fa-d5e1-4ff6-8736-c9d6b5f40150
begin
	em1_a = EconModel1(0.95, [1.0 0 0 0], [5 0 0 0])
	em1_b = EconModel1(0.95, [0 1.0 0 0], [0 5 0 0])
	em1_c = EconModel1(0.95, [0 0 1.0 0], [0 0 5 0])
	em1_d = EconModel1(0.95, [0 0 0 1.0], [0 0 0 5])
	#=
	This is the most basic profit model
	
	You earn 1 per operating satellite and it costs 5 per launch.
	Only interaction is through debris.
	=#
end

# ╔═╡ 19ccfc3a-6dbb-4c64-bf03-e2e219ef0efe
begin
	em2_a = EconModel1(0.95, [1 -0.02 -0.02 0], [5.0 0 0 0])
	em2_b = EconModel1(0.95, [-0.02 1 -0.02 0], [0.0 5 0 0])
	em2_c = EconModel1(0.95, [0 -0.02 1 -0.02], [0.0 0 5 0])
	em2_d = EconModel1(0.95, [0 -0.02 -0.02 1], [0.0 0 0 5])
	#=
	This is a simple addition to the basic model, where you lose some benefit based 
	the size of your competitor's satellites.
	Constellations interact throuch debris and imposing costs on one another.
	=#
end

# ╔═╡ dc614254-c211-4552-b985-03020bfc5ab3
em3 = CESParams(0.95,0.6,[1 0 0 0], [5 0 0 0], Vector([0.002]))
#=
This is a variation on a CES model.

The model is CES the relationship between payoffs and debris.
In this particular specification, the only interaction is in debris
=#

# ╔═╡ cd55e232-493d-4849-8bd7-b0ba85e21bab
md"""
# Start setting things up
"""

# ╔═╡ fb6aacff-c42d-4ec1-88cb-5ce1b2e8874f
policy = planner_policy_function_generator();

# ╔═╡ 41271ab4-1ec7-431f-9efb-0f7c3da2d8b4
#Constellation level loss function
function Ξ(
	s::Vector{T}
	,d::Vector{T}
	, physical_model::PhysicalParameters
	,co::ConstellationOperator
) where T <: Number
	a = policy((s,d))
	s′ = G(s,d,a,physical_model)
	d′ = H(s,d,a,physical_model)

	bellman_residuals = co.value((s,d)) - co.payoff_fn(s,d,a,co.econ_params) - co.econ_params.β*co.value((s′,d′))
	maximization_condition = - co.payoff_fn(s,d,a,co.econ_params) - co.econ_params.β*co.value((s′,d′))

	return sum([bellman_residuals.^2 maximization_condition])
end

# ╔═╡ f30904a7-5caa-449a-a5bd-f2aa78777a9a
begin
	#setup the operators
	operators = [ ConstellationOperator(payoff1,em2_a,value_function_generator())
			,ConstellationOperator(payoff1,em2_b,value_function_generator())
			,ConstellationOperator(payoff1,em2_c,value_function_generator())
			,ConstellationOperator(payoff1,em2_d,value_function_generator())
	]

	#check whether or not we've matched the setup correctly.
	@assert length(operators) == N_constellations "Mismatch in predetermined number of constellations and the number of operators initialized"
end

# ╔═╡ 43b99708-0052-4b78-886c-92ac2b532f29
begin #testing
	s1 = ones(Float64,N_constellations)
	d1 = ones(Float64,N_debris)
	Ξ(s1,d1,bm,operators[1])
end

# ╔═╡ dff642d9-ec5a-4fed-a059-6c07760a3a58
#planner's loss function
function planners_loss(
	s::Vector{Float32}
	,d::Vector{Float32}
) 
	l = 0.0
	for co in operators
		l += Ξ(s,d,bm,co)
	end
	return l
end
		

# ╔═╡ 5abebc1a-370c-4f5f-8826-dc0b143d5166
md"""
## Constructing data and training
"""

# ╔═╡ a20959be-65e4-4b69-9521-503bc59f0854
begin
	N=200 #increase later
	data = [(rand(1:500f0, N_constellations),rand(1:500f0, N_debris)) for n=1:N]
end

# ╔═╡ 6bf8d29a-7990-4e91-86e6-d9894ed3db27
#optimizer
ADAM = Flux.Optimise.ADAM(0.1)

# ╔═╡ e7ee1a0f-ab9b-439e-a7be-4a6d3b8f160d
begin
	local accum1 = 0.0
	for d in data
		accum1 += planners_loss(d...)
	end
	accum1/N
end

# ╔═╡ 74f5fde3-0593-46fc-a688-f1db7ab28c64
# Social planners problem
for epoch in 1:20
	data1 = [(rand(1:500f0, N_constellations),rand(1:500f0, N_debris)) for n=1:N]
	
	#train the social planner's policy funciton
	Flux.Optimise.train!(planners_loss, params(policy), data1, ADAM)
	
	#Sweep through training the value functions
	for co in operators
		Flux.Optimise.train!(planners_loss, params(co.value), data1, ADAM)
	end
end

# ╔═╡ 02f3fe78-e7a7-453f-9ddf-acddf08d8676
begin
	local accum = 0.0
	for d in data
		accum += planners_loss(d...)
		
	end
	accum/N
end

# ╔═╡ c50b1d39-fe87-441b-935c-c5fe971d09ef
policy(data[3])

# ╔═╡ 14e61097-f28f-4029-b6b4-5fb119620fc3
begin
	n=15
	
	[operators[1].value(data[n])
	,operators[2].value(data[n])
	,operators[3].value(data[n])
	,operators[4].value(data[n])]
end

# ╔═╡ bf0c6061-daf4-45ac-82bc-b26e093ac6a7
with_terminal() do
	for d in data
		println(d)
		println("\t",policy(d))
	end
end

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

[[deps.ProgressLogging]]
deps = ["Logging", "SHA", "UUIDs"]
git-tree-sha1 = "80d919dee55b9c50e8d9e2da5eeafff3fe58b539"
uuid = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
version = "0.1.4"

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

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

[[deps.Random123]]
deps = ["Random", "RandomNumbers"]
git-tree-sha1 = "552f30e847641591ba3f39fd1bed559b9deb0ef3"
uuid = "74087812-796a-5b5d-8853-05524746bad3"
version = "1.6.1"

[[deps.RandomNumbers]]
deps = ["Random", "Requires"]
git-tree-sha1 = "043da614cc7e95c703498a491e2c21f58a2b8111"
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
version = "1.5.3"

[[deps.RealDot]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
version = "0.1.0"

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

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

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

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "30449ee12237627992a99d5e30ae63e4d78cd24a"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.0"

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

[[deps.Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "1.1.1"

[[deps.ShowCases]]
git-tree-sha1 = "7f534ad62ab2bd48591bdeac81994ea8c445e4a5"
uuid = "605ecd9f-84a6-4c9e-81e2-4798472b76a3"
version = "0.1.0"

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

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

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "c60ec5c62180f27efea3ba2908480f8055e17cee"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.1.1"

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

[[deps.SpecialFunctions]]
deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "ef28127915f4229c971eb43f3fc075dd3fe91880"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.2.0"
weakdeps = ["ChainRulesCore"]

    [deps.SpecialFunctions.extensions]
    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"

[[deps.SplittablesBase]]
deps = ["Setfield", "Test"]
git-tree-sha1 = "e08a62abc517eb79667d0a29dc08a3b589516bb5"
uuid = "171d559e-b47b-412a-8079-5efa626c420e"
version = "0.1.15"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
git-tree-sha1 = "832afbae2a45b4ae7e831f86965469a24d1d8a83"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.5.26"

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

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.9.0"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "45a7769a04a3cf80da1c1c7c60caf932e6f4c9f7"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.6.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "75ebe04c5bed70b91614d684259b661c9e6274a4"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.0"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "GPUArraysCore", "StaticArraysCore", "Tables"]
git-tree-sha1 = "521a0e828e98bb69042fec1809c1b5a680eb7389"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.15"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "5.10.1+6"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[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 = "1544b926975372da01227b382066ab70e574a3ec"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.10.1"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

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

[[deps.TimerOutputs]]
deps = ["ExprTools", "Printf"]
git-tree-sha1 = "f548a9e9c490030e545f72074a41edfd0e5bcdd7"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.23"

[[deps.Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
git-tree-sha1 = "25358a5f2384c490e98abd565ed321ffae2cbb37"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.76"

[[deps.Tricks]]
git-tree-sha1 = "aadb748be58b492045b4f56166b5188aa63ce549"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.7"

[[deps.URIs]]
git-tree-sha1 = "074f993b0ca030848b897beff716d93aca60f06a"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.2"

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

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

[[deps.UnsafeAtomics]]
git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278"
uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
version = "0.2.1"

[[deps.UnsafeAtomicsLLVM]]
deps = ["LLVM", "UnsafeAtomics"]
git-tree-sha1 = "ea37e6066bf194ab78f4e747f5245261f17a7175"
uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
version = "0.1.2"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+0"

[[deps.Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "GPUArrays", "GPUArraysCore", "IRTools", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "PrecompileTools", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "5be3ddb88fc992a7d8ea96c3f10a49a7e98ebc7b"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.62"

    [deps.Zygote.extensions]
    ZygoteColorsExt = "Colors"
    ZygoteDistancesExt = "Distances"
    ZygoteTrackerExt = "Tracker"

    [deps.Zygote.weakdeps]
    Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
    Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.ZygoteRules]]
deps = ["ChainRulesCore", "MacroTools"]
git-tree-sha1 = "977aed5d006b840e2e40c0b48984f7463109046d"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.3"

[[deps.cuDNN]]
deps = ["CEnum", "CUDA", "CUDNN_jll"]
git-tree-sha1 = "f65490d187861d6222cb38bcbbff3fd949a7ec3e"
uuid = "02a925ec-e4fe-4b08-9a7e-0d78e3d38ccd"
version = "1.0.4"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+0"

[[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"
"""

# ╔═╡ Cell order:
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