### A Pluto.jl notebook ###
# v0.17.1

using Markdown
using InteractiveUtils

# ╔═╡ b194c2fc-340b-480e-b1ec-53db2fe4e7ec
module PhysicsModule
	
	#Add exports here
	
	
	using Flux, LinearAlgebra
	using Zygote #included for saving and loading models
	
	#==#
	struct State
		stocks::Array{Float32}
		debris::Array{Float32}
	end
	
	
	### Physics
	
	
	abstract type PhysicalModel end
		
	struct BasicModel <: PhysicalModel
		#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
	function state_transition(
		physics::BasicModel 
		,state::State 
		,launches::Vector{Float32}
		)
		#=
		Physical Transitions
		=#
		survival_rate = survival(state,physics)
	
		# Debris
	
		# get changes in debris from natural dynamics
		natural_debris_dynamics = (1 - physics.decay_rate + physics.autocatalysis_rate) * state.debris 
		
		# get changes in debris from satellite loss
		satellite_loss_debris = physics.satellite_collision_debris_ratio * (1 .- survival_rate)'*state.stocks 
		
		# get changes in debris from launches
		launch_debris = physics.launch_debris_ratio * sum(launches)
		
		# total debris level
		debris′ = natural_debris_dynamics .+ satellite_loss_debris .+ launch_debris
	
	
		#stocks
		stocks′ = (LinearAlgebra.diagm(survival_rate) .- physics.decay_rate)*state.stocks + launches
	
	
		return State(stocks′,debris′)
	end 
	
	
	function survival(
			state::State
			,physical_model::BasicModel
		)	
	    return exp.(
			-(physical_model.satellite_collision_rates .+ physical_model.decay_rate) * state.stocks 
			.- (physical_model.debris_collision_rate * state.debris)
		)
	end
end #end physccs

# ╔═╡ 4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
using LinearAlgebra, BSON

# ╔═╡ 85897da8-bc22-40bd-8ec7-853f86ac4941
module NNTools
#= TupleDuplicator
This is used to create a tuple of size n with deepcopies of any object x
=#

using Flux,Zygote,BSON

struct TupleDuplicator
	n::Int
end
(f::TupleDuplicator)(x) = tuple([deepcopy(x) for i=1:f.n]...)

#=
This generates a policy function full of branches with the properly scaled sides
=#
struct BranchGenerator
	n::UInt8 
	#limit to 2^8 operators
end
function (b::BranchGenerator)(branch::Flux.Chain,join_fn::Function) 
	# used to deepcopy the branches and duplicate the inputs in the returned chain
	f = TupleDuplicator(b.n)
	
	return Flux.Chain(f,Flux.Parallel(join_fn,f(branch)))
end

## Couple of helpful policy generators, just for help.

function operator_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.tanh)
		        )
		        ,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.tanh)
			,Flux.Dense(number_params,number_params,Flux.tanh)
			,Flux.Dense(number_params,1,x -> Flux.relu.(sinh.(x)))
		)

end

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

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

end

# ╔═╡ 3be917ed-7107-46a3-bd8e-969e0e8e0fea
md"""
# testing

Define the basic dimensions of the model
 - 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)
"""

# ╔═╡ f4d11666-dd44-4340-8fe7-b5cf735dea67
md"""
## Physics
"""

# ╔═╡ 30622c11-32f3-4b68-b391-e526c3b09570
begin #Setup for State tests
	st = PhysicsModule.State([1,2,3,4],[3])
	launches = zeros(Float32,4)

	loss_param = 2e-3;
	loss_weights = loss_param*(ones(N_constellations,N_constellations) - LinearAlgebra.I);
	

	#Todo, wrap physical model as a struct with the parameters
	bm = PhysicsModule.BasicModel(
		loss_param
		,loss_weights
		,0.01
		,0.001
		,5.0
		,0.05
	)
end

# ╔═╡ 5497cf84-0fc1-4d47-8a1d-58f862000828
PhysicsModule.state_transition(bm,st,launches)

# ╔═╡ 7ad063fa-70e1-4ffd-ad1a-8c65306bb2cc
md"""
## Neural Networks
"""

# ╔═╡ 2879d65a-4a2e-4486-ac26-a0490a80f23e
NNTools.value_function_generator()

# ╔═╡ f7febfdd-81f0-4f67-8986-fb52e6e7d9fe
md"""
## Operator Models
"""

# ╔═╡ 99aabead-81d0-4f66-994a-bc5485c08af5
### Economics
module BenefitFunctions
	abstract type EconomicModel end
	
	#basic linear model
	struct LinearModel <: EconomicModel
		β::Float32
		payoff_array::Array{Float32}
		policy_costs::Array{Float32}
	end
	function (em::LinearModel)(
		s::Vector{Float32}
		,d::Vector{Float32}
		,a::Vector{Float32}
		)
		return em.payoff_array*s - em.policy_costs*a
	end
	
	#basic CES model
	struct CES <: EconomicModel
		β::Float32
		r::Float32 #elasticity of subsititution
		payoff_array::Array{Float32}
		policy_costs::Array{Float32}
		debris_costs::Array{Float32}
	end
	function (em::CES)(
		s::Vector{Float32}
		,d::Vector{Float32}
		,a::Vector{Float32}
		)
	
		#issue here with multiplication
		r1 = em.payoff_array .* (s.^em.r) 
		r2 = - em.debris_costs .* (d.^em.r) 
		r3 = - em.policy_costs .* (a.^em.r)
		return (r1 + r2 + r3) .^ (1/em.r)
	
	end
	
	#basic CRRA
	struct CRRA <: EconomicModel
		β::Float32
		σ::Float32 #elasticity of subsititution
		payoff_array::Array{Float32}
		policy_costs::Array{Float32}
		debris_costs::Array{Float32}
	end
	function (em::CRRA)(
		s::Vector{Float32}
		,d::Vector{Float32}
		,a::Vector{Float32}
		)
		#issue here with multiplication
		core = (em.payoff_array*s - em.debris_costs*d - em.policy_costs).^(1 - em.σ)
	
		return (core-1)/(1-em.σ)
	end
	
end #end module

# ╔═╡ 473c1c21-c3b8-4ca8-8e76-cc42b3ea0da4
begin
	#=
	This struct organizes information about a given constellation operator
	Used to provide an interable loss function for training

	=#
	struct ConstellationOperatorLoss
		#econ model describing operator
		econ_model::EconomicModel
		#Operator's value and policy functions, as well as which parameters the operator can train.
		operator_value_fn::Flux.Chain
		collected_policies::Flux.Chain #this is held by all operators
		operator_policy_params::Flux.Params
		#Transition functions
		debris_transition::BasicDebrisEvolution
		stocks_transition::BasicStockEvolution
	end
	# overriding function to calculate operator loss
	function (operator::ConstellationOperatorLoss)(
		s::Vector{Float32}
		,d::Vector{Float32}
	)
		

		#get actions
		a = operator.collected_policies((s,d))
	
		#get updated stocks and debris
		s′ = operator.stocks_transition(s ,d ,a)
		d′ = operator.debris_transition(s ,d ,a)
	
		
		bellman_residuals = operator.operator_value_fn((s,d)) - operator.econ_model(s,d,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
		
		maximization_condition = - operator.econ_model(s ,d ,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
	
		return Flux.mae(bellman_residuals.^2 ,maximization_condition)
	end
	
	function (operator::ConstellationOperatorLoss)(
		s::Vector{Float32}
		,d::Vector{Float32}
		,policy::Flux.Chain #allow for another policy to be subsituted
	)
		

		#get actions
		a = policy((s,d))
	
		#get updated stocks and debris
		s′ = operator.stocks_transition(s ,d ,a)
		d′ = operator.debris_transition(s ,d ,a)
	
		
		bellman_residuals = operator.operator_value_fn((s,d)) - operator.econ_model(s,d,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
		
		maximization_condition = - operator.econ_model(s ,d ,a) - operator.econ_model.β * operator.operator_value_fn((s′,d′))
	
		return Flux.mae(bellman_residuals.^2 ,maximization_condition)
	end
end

# ╔═╡ c5d4b5af-ec04-4941-b84f-c70e9665810b
begin
	
	#do the same thing with the planner's problem
	struct PlannerLoss
		#=
		Ideally, with just a well formed PlannerLoss and the training functions below, we should be able to train the approximation.

		There is an issue with appropriately training the value functions.
		In this case, it is not happening...
		=#
		β::Float32
		
		operators::Array{ConstellationOperatorLoss}
		
		policy::Flux.Chain
		policy_params::Flux.Params
		value::Flux.Chain
		value_params::Flux.Params
		
		debris_transition::BasicDebrisEvolution
		stocks_transition::BasicStockEvolution
	end
	function (planner::PlannerLoss)(
		s::Vector{Float32}
		,d::Vector{Float32}
	) 
		a = planner.policy((s ,d))
		#get updated stocks and debris
		s′ = planner.stocks_transition(s ,d ,a)
		d′ = planner.debris_transition(s ,d ,a)
		
		
		
			#calculate the total benefit from each of the models
		benefit = sum([ co.econ_model(s ,d ,a) for co in planner.operators])
			#issue here with mutating. Maybe generators/list comprehensions?
		
		
		bellman_residuals = planner.value((s,d)) - benefit - planner.β .* planner.value((s′,d′))

		maximization_condition = - benefit - planner.β .* planner.value((s′,d′))
		
		return Flux.mae(bellman_residuals.^2 ,maximization_condition)
	end
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[compat]
BSON = "~0.3.4"
Flux = "~0.12.8"
Zygote = "~0.6.30"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
version = "0.4.3"

[[IfElse]]
git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
version = "0.1.1"

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

[[InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.2"

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

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

[[Juno]]
deps = ["Base64", "Logging", "Media", "Profile"]
git-tree-sha1 = "07cb43290a840908a771552911a6274bc6c072c7"
uuid = "e5e0dc1b-0480-54bc-9374-aad01c23163d"
version = "0.8.4"

[[LLVM]]
deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
git-tree-sha1 = "46092047ca4edc10720ecab437c42283cd7c44f3"
uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
version = "4.6.0"

[[LLVMExtra_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9436f02a0c9f726d914cc6539f87850701be18fc"
uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
version = "0.0.12+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"

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

[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.5"

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

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.9"

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

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

[[Media]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "75a54abd10709c01f1b86b84ec225d26e840ed58"
uuid = "e89f7d12-3494-54d1-8411-f7d8b9ae1f27"
version = "0.5.0"

[[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"

[[NNlib]]
deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
git-tree-sha1 = "2eb305b13eaed91d7da14269bf17ce6664bfee3d"
uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
version = "0.7.31"

[[NNlibCUDA]]
deps = ["CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
git-tree-sha1 = "38358632d9c277f7bf8d202c127f601e8467aa4d"
uuid = "a00861dc-f156-4864-bf3c-e6376f28a68d"
version = "0.1.10"

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

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

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

[[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"

[[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"

[[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"

[[Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"

[[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 = "043da614cc7e95c703498a491e2c21f58a2b8111"
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
version = "1.5.3"

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

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

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

[[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"

[[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 = "f0bccf98e16759818ffc5d97ac3ebf87eb950150"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.8.1"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.4.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.13"

[[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", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.13"

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

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

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

[[TimerOutputs]]
deps = ["ExprTools", "Printf"]
git-tree-sha1 = "7cb456f358e8f9d102a8b25e8dfedf58fa5689bc"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.13"

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

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

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

[[ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "3593e69e469d2111389a9bd06bac1f3d730ac6de"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.9.4"

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

[[Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "2c30f2df0ba43c17e88c8b55b5b22c401f7cde4e"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.30"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

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

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

# ╔═╡ Cell order:
# ╟─b194c2fc-340b-480e-b1ec-53db2fe4e7ec
# ╟─3be917ed-7107-46a3-bd8e-969e0e8e0fea
# ╠═f4d11666-dd44-4340-8fe7-b5cf735dea67
# ╠═4e66c6cc-ad36-47e3-b2c0-2e9ca594ad04
# ╠═30622c11-32f3-4b68-b391-e526c3b09570
# ╠═5497cf84-0fc1-4d47-8a1d-58f862000828
# ╠═7ad063fa-70e1-4ffd-ad1a-8c65306bb2cc
# ╟─85897da8-bc22-40bd-8ec7-853f86ac4941
# ╠═2879d65a-4a2e-4486-ac26-a0490a80f23e
# ╠═f7febfdd-81f0-4f67-8986-fb52e6e7d9fe
# ╟─99aabead-81d0-4f66-994a-bc5485c08af5
# ╠═473c1c21-c3b8-4ca8-8e76-cc42b3ea0da4
# ╠═c5d4b5af-ec04-4941-b84f-c70e9665810b
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002