Orbits/julia_code/BellmanResidual_Operators.jl

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

using Markdown
using InteractiveUtils

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

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


"""

# ╔═╡ 9fa41b7c-1923-4c1e-bfc6-20ce4a1a2ede
md"""
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)
"""

# ╔═╡ 0d209540-29ad-4b2f-9e91-fac2bbee47ff
md"""
## Describe the physics of the world

Three key functions
 - Survival function, describing how colisions occur
 - Debris Evolution
 - Constellation Satellite Stocks Evolution
"""

# ╔═╡ 9b1c2f62-ec19-4667-8f93-f8b52750e317
	md"""
	### Parameterize the physical world
	"""

# ╔═╡ 90446134-4e45-471c-857d-4e165e51937a
begin
	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
	

end

# ╔═╡ 5b45b29e-f0f4-41e9-91e7-d444687feb4e
#implement survival function
function survival(
		stocks::Array{Float32}
		,debris::Array{Float32}
		,physical_model::BasicModel
	)	
    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{Float32}
		,debris::Array{Float32}
		,launches::Array{Float32}
		, physical_model::BasicModel
	)
    #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{Float32}
		,debris::Array{Float32}
		,launches::Array{Float32}
		, physical_model::BasicModel
)
    return LinearAlgebra.diagm(survival(stocks,debris,physical_model) .- physical_model.decay_rate)*stocks + launches
end

# ╔═╡ 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
#I don't think that these are going to be needed
begin
	#= CUSTOM LAYERS

	=#
	#Custom passthrough layer
	passthrough(x::Array{Float32}) = x


	# custom split layer
	struct Split{T}
	  paths::T
	end
	Split(paths...) = Split(paths)
	Flux.@functor Split
	(self::Split)(x::AbstractArray{Float32}) = tuple(map(f -> f(x), self.paths))

	
	### TESTING ###


	#multiple branches
	Flux.Parallel(vcat,
		passthrough, passthrough, passthrough
	)(([1f0],[2f0,3],[4f0]))


end

# ╔═╡ bbca5143-f314-40ea-a20e-8a043272e362
md"""
# Defining economic parameters and payoff functions
"""

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

# ╔═╡ 206ac4cc-5102-4381-ad8a-777b02dc4d5a
begin #basic linear model
	struct EconModel1 <: EconomicParameters
		β::Float32
		payoff_array::Array{Float32}
		policy_costs::Array{Float32}
	end

	function payoff1(
	s::Vector{Float32}
	,d::Vector{Float32}
	,a::Vector{Float32}
	,em::EconModel1
)
	return em.payoff_array*s - em.policy_costs*a
end

end

# ╔═╡ eebb8706-a431-4fd1-b7a5-40f07a63d5cb
begin #basic CES model
		struct CESParams <: EconomicParameters
			β::Float32
			r::Float32 #elasticity of subsititution
			payoff_array::Array{Float32}
			policy_costs::Array{Float32}
			debris_costs::Array{Float32}
		end
	function CES_with_debris(
		s::Vector{Float32}
		,d::Vector{Float32}
		,a::Vector{Float32}
		,em::CESParams
	)
		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
	#policy_params::Flux.Params #cutting this for now
end
#TODO: create a function that takes this struct and checks backprop

# ╔═╡ b433a7ec-8264-48d6-8b95-53d2ec4bad05
md"""
### 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
=#

# ╔═╡ 4452ab2c-813b-4b7b-8cb3-388ec507a24c
md"""
## Setup Operators Policy Functions
"""

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

# ╔═╡ 41271ab4-1ec7-431f-9efb-0f7c3da2d8b4
#Constellation operator loss function
function Ξ(
	s::Vector{Float32}
	,d::Vector{Float32}
	,physical_model::PhysicalParameters
	,co::ConstellationOperator
	,policy::Flux.Chain
)
	#get actions
	a = policy((s,d))

	#get updated stocks and debris
	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

# ╔═╡ 9d4a668a-23e3-4f36-86f4-60e242caee3b
begin #testing data
	s1 = ones(Float32,N_constellations)
	d1 = ones(Float32,N_debris)
end

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

# ╔═╡ 08ef7fbf-005b-40b5-acde-f42750c04cd3
begin
	const tops = [ 
		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())
	]

	#sanity Check time
	@assert length(tops) == N_constellations "Mismatch in predetermined number of constellations and the number of operators initialized"
end

# ╔═╡ 43b99708-0052-4b78-886c-92ac2b532f29
begin #testing
	Ξ(s1,d1,bm,tops[1],collected_policies)
end

# ╔═╡ 89258b2e-cee5-4cbd-a42e-21301b7a2549
begin
	#=
	Used to provide an interable loss function for training
	=#
	struct OperatorLoss
		physical_model::PhysicalParameters
		co::ConstellationOperator
		collected_policies::Flux.Chain
		policy_params::Flux.Params
	end
	function (self::OperatorLoss)(
		s::Vector{Float32}
		,d::Vector{Float32}
	)
		Ξ(s ,d ,self.physical_model ,self.co ,self.collected_policies )
	end

	#do the same thing with the planner's problem
	struct PlannerLoss
	end
	function planners_loss(
		s::Vector{Float32}
		,d::Vector{Float32}
	) 
		l = 0.0
		for (i,co) in enumerate(tops)
			l += Ξ(s,d,bm,tops,i)
		end
		return l
	end
end

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

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

# ╔═╡ a20959be-65e4-4b69-9521-503bc59f0854
begin
	struct DataConstructor
		N::UInt64
	end
	(dc::DataConstructor)(bottom=1f0,top=500f0) = [(rand(bottom:top, N_constellations),rand(bottom:top, N_debris)) for n=1:dc.N]

	data = DataConstructor(200)

	data1 = data()
end

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

# ╔═╡ 30417194-6cd1-4e10-9e25-1fa1c0761b9a


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

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

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

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

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

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git-tree-sha1 = "8756f9935b7ccc9064c6eef0bff0ad643df733a3"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.12.7"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Flux]]
deps = ["AbstractTrees", "Adapt", "ArrayInterface", "CUDA", "CodecZlib", "Colors", "DelimitedFiles", "Functors", "Juno", "LinearAlgebra", "MacroTools", "NNlib", "NNlibCUDA", "Pkg", "Printf", "Random", "Reexport", "SHA", "SparseArrays", "Statistics", "StatsBase", "Test", "ZipFile", "Zygote"]
git-tree-sha1 = "e8b37bb43c01eed0418821d1f9d20eca5ba6ab21"
uuid = "587475ba-b771-5e3f-ad9e-33799f191a9c"
version = "0.12.8"

[[ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "ef3fec65f9db26fa2cf8f4133c697c5b7ce63c1d"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.22"

[[Functors]]
git-tree-sha1 = "e4768c3b7f597d5a352afa09874d16e3c3f6ead2"
uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
version = "0.2.7"

[[GPUArrays]]
deps = ["Adapt", "LinearAlgebra", "Printf", "Random", "Serialization", "Statistics"]
git-tree-sha1 = "7772508f17f1d482fe0df72cabc5b55bec06bbe0"
uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
version = "8.1.2"

[[GPUCompiler]]
deps = ["ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "TimerOutputs", "UUIDs"]
git-tree-sha1 = "77d915a0af27d474f0aaf12fcd46c400a552e84c"
uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
version = "0.13.7"

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

[[HypertextLiteral]]
git-tree-sha1 = "5efcf53d798efede8fee5b2c8b09284be359bf24"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.2"

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

[[IRTools]]
deps = ["InteractiveUtils", "MacroTools", "Test"]
git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
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 = "f0c6489b12d28fb4c2103073ec7452f3423bd308"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.1"

[[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"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[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 = "6a2af408fe809c4f1a54d2b3f188fdd3698549d6"
uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
version = "0.0.11+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", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "6193c3815f13ba1b78a51ce391db8be016ae9214"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.4"

[[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 = "5203a4532ad28c44f82c76634ad621d7c90abcbd"
uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
version = "0.7.29"

[[NNlibCUDA]]
deps = ["CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
git-tree-sha1 = "04490d5e7570c038b1cb0f5c3627597181cc15a9"
uuid = "a00861dc-f156-4864-bf3c-e6376f28a68d"
version = "0.1.9"

[[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"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.1.2"

[[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"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "57312c7ecad39566319ccf5aa717a20788eb8c1f"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.18"

[[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 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.12"

[[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 = "0fc9959bcabc4668c403810b4e851f6b8962eac9"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.29"

[[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:
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