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
"""

# ╔═╡ f8779824-9d59-4458-926f-10beb3cd3866
abstract type TransitionRule end

# ╔═╡ 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);
		

		#Todo, wrap physical model as a struct with the parameters
		bm = BasicModel(
		    loss_param
		    ,loss_weights
		    ,0.01
		    ,0.001
		    ,5.0
		    ,0.05
		)
	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
begin
	#debris evolution 
	struct BasicDebrisEvolution <: TransitionRule
		physical_model::BasicModel
	end
	function (self::BasicDebrisEvolution)(
			stocks::Array{Float32}
			,debris::Array{Float32}
			,launches::Array{Float32}
		)
	    #get changes in debris from natural dynamics
	    natural_debris_dynamics = (1-self.physical_model.decay_rate + self.physical_model.autocatalysis_rate) * debris 
	    
	    #get changes in debris from satellite loss
	    satellite_loss_debris = self.physical_model.satellite_collision_debris_ratio * (1 .- survival(stocks,debris,self.physical_model))'*stocks 
	    
	    #get changes in debris from launches
	    launch_debris = self.physical_model.launch_debris_ratio*sum(launches)
	    
	    #return total debris level
	    return natural_debris_dynamics .+ satellite_loss_debris .+ launch_debris
	end
end

# ╔═╡ 25ac9438-2b1d-4f6b-9ff1-1695e1d52b51
begin
	#stock update rules
	struct BasicStockEvolution <: TransitionRule
		physical_model::BasicModel
	end
	function (self::BasicStockEvolution)(
			stocks::Array{Float32}
			,debris::Array{Float32}
			,launches::Array{Float32}
			
	)
	    return LinearAlgebra.diagm(survival(stocks,debris,self.physical_model) .- self.physical_model.decay_rate)*stocks + launches
	end
end

# ╔═╡ 6bf01e30-d054-4a98-9e0d-58d7da4e5524
begin
	H = BasicDebrisEvolution(bm)
	G = BasicStockEvolution(bm)
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

# ╔═╡ ae6681e0-c796-4145-a313-75f74b4993ad
#add branch generator

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

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

# ╔═╡ 206ac4cc-5102-4381-ad8a-777b02dc4d5a
begin #basic linear model
	struct EconModel1 <: EconomicModel
		β::Float32
		payoff_array::Array{Float32}
		policy_costs::Array{Float32}
	end
	function (em::EconModel1)(
		s::Vector{Float32}
		,d::Vector{Float32}
		,a::Vector{Float32}
		)
		return em.payoff_array*s - em.policy_costs*a
	end
end

# ╔═╡ eebb8706-a431-4fd1-b7a5-40f07a63d5cb
begin #basic CES model
	struct CESParams <: EconomicModel
		β::Float32
		r::Float32 #elasticity of subsititution
		payoff_array::Array{Float32}
		policy_costs::Array{Float32}
		debris_costs::Array{Float32}
	end
	function (em::CESParams)(
		s::Vector{Float32}
		,d::Vector{Float32}
		,a::Vector{Float32}
		)
		return (em.payoff_array*(s.^em.r) - em.debris_costs*(d.^em.r)).^(1/em.r) - em.policy_costs*a
	end
end

# ╔═╡ 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
"""

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

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

	#get updated stocks and debris
	s′ = stocks_transition(s,d,a)
	d′ = debris_transition(s,d,a)

	
	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

# ╔═╡ 89258b2e-cee5-4cbd-a42e-21301b7a2549
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}
		; #set default policy to the one held by the ConstellationOperator
		policy::Flux.Chain = operator.collected_policies
	)
		

		#get actions
		a = policy((s,d))
	
		#get updated stocks and debris
		s′ = stocks_transition(s ,d ,a)
		d′ = 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,co.econ_params) - co.econ_params.β*co.value((s′,d′))
	
		return sum(bellman_residuals.^2, maximization_condition)
	end


	
	#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...
		=#
		operators::Array{ConstellationOperatorLoss}
		planner_policy::Flux.Chain
		planner_params::Flux.Params
	end
	function (pl::PlannerLoss)(
		s::Vector{Float32}
		,d::Vector{Float32}
	) 
		l = 0.0
		for co in pl.operators
			l += co(s ,d ,pl.planner_policy)
		end
		return l
	end

	#TODO: Training Functions as routines
end

# ╔═╡ cd55e232-493d-4849-8bd7-b0ba85e21bab
md"""
# Set up Operators and Planner
"""

# ╔═╡ 08ef7fbf-005b-40b5-acde-f42750c04cd3
begin #setup operators
	
	const tops = [ 
		ConstellationOperator(,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())
	]
	#TODO: setup operator losses
	
	#sanity Check time
	@assert length(tops) == N_constellations "Mismatch in predetermined number of constellations and the number of operators initialized"
end

# ╔═╡ fb6aacff-c42d-4ec1-88cb-5ce1b2e8874f
#build out planner loss
planner_policy = planner_policy_function_generator();

# ╔═╡ 5abebc1a-370c-4f5f-8826-dc0b143d5166
md"""
# Training loop
"""

# ╔═╡ 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]

	#create a data constructor
	dc = DataConstructor(200)

	#get a bit of test data
	data1 = dc()
end

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

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


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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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