text:
Random.seed!(0)
@testset "fixed points" begin

#=
    Global objects.
=#

# Function converter for out of place --> in place.
function make_inplace(f::Function)
    function inplace_f(out, x)
        out .= f(x)
    end
    return inplace_f
end

# "Naive" simple iteration methods for comparison.
    # In place.
    function iterate!(f!, x0; residualnorm = (x -> norm(x,Inf)), tol = 1E-10, maxiter=100)
        residual = Inf
        iter = 1
        xold = x0
        xnew = copy(x0)
        while residual > tol && iter < maxiter
            f!(xnew, xold)
            residual = residualnorm(xold - xnew);
            xold = copy(xnew)
            iter += 1
        end
        return (xold,iter)
    end
    # Out of place.
    function iterate(f, x0; residualnorm = (x -> norm(x,Inf)), tol = 1E-10, maxiter=100)
        residual = Inf
        iter = 1
        xold = x0
        xnew = copy(x0)
        while residual > tol && iter < maxiter
            xnew = f(xold)
            residual = residualnorm(xold - xnew);
            xold = copy(xnew)
            iter += 1
        end
        return (xold,iter)
    end
    # Tests of these.
    A_1 = [0.7 0.0; 0.0 0.3];
    b_1 = [1.5; 3.2];
    f_1 = x -> A_1 * x + b_1;
    f_1! = make_inplace(f_1)
    init_x = [3.4, 4.3]
    @test iterate!(f_1!, init_x)[1] == iterate(f_1, init_x)[1] ≈ [5.0, 4.571428571428571]

#=
    Anderson tests.
=#

# Tests against the above example.
    @test fixedpoint(f_1!, [3.4, 4.3]).zero == fixedpoint(f_1, [3.4, 4.3]; inplace = false).zero ≈ [5.0, 4.571428571428571]
    @test fixedpoint(f_1!, [3.4, 4.3]; m = 2).zero == fixedpoint(f_1, [3.4, 4.3]; inplace = false, m = 2).zero ≈ [5.0, 4.571428571428571]

# Tests for some common functions.
    # x -> sin.(x)
    f_2 = x -> 0.5 * x
    f_2! = make_inplace(f_2)
    srand = 123 # For determinism in the random tests.
    init_x2 = rand(Float64, 4)
    @test fixedpoint(f_2!, init_x2; iterations = 10000, ftol = 1e-15).zero == fixedpoint(f_2, init_x2; inplace = false, iterations = 10000, ftol = 1e-15).zero
    @test isapprox(fixedpoint(f_2!, init_x2; iterations = 10000, ftol = 1e-15).zero, zeros(Float64, 4), atol = 1e-10)
    # x -> exp(-x)
    f_3 = x -> exp.(-x)
    f_3! = make_inplace(f_3)
    init_x3 = [rand(Float64)*100]
    @test fixedpoint(f_3!, init_x3).zero == fixedpoint(f_3, init_x3; inplace = false).zero ≈ [0.5671432953088511]
    @test fixedpoint(f_3!, init_x3; m = 4).zero == fixedpoint(f_3, init_x3; inplace = false, m = 4).zero ≈ [0.5671432953088511]

# Tests for...

#=
    Gradient method tests.
=#
    # Autodifferentiation tests.
    @test fixedpoint(f_3!, init_x3; autodiff = :forward).zero == fixedpoint(f_3, init_x3; inplace = false, autodiff = :forward).zero ≈ [0.5671432953088511]
    @test fixedpoint(f_3!, init_x3; autodiff = :central).zero == fixedpoint(f_3, init_x3; inplace = false, autodiff = :central).zero ≈ [0.5671432953088511]

    # Newton tests.
    @test fixedpoint(f_3!, init_x3; autodiff = :forward, method = :newton).zero == fixedpoint(f_3, init_x3; inplace = false, autodiff = :forward, method = :newton).zero ≈ [0.5671432953088511]
    @test fixedpoint(f_3!, init_x3; autodiff = :central, method = :newton).zero == fixedpoint(f_3, init_x3; inplace = false, autodiff = :central, method = :newton).zero ≈ [0.5671432953088511]

#=
    `inplace` flag tests.
=#
    # default behavior
    foo = x -> 0.5 * x
    @test norm(fixedpoint(foo, init_x2, xtol = 1e-10, ftol = 0.0).zero) ≈ 0.0 atol = 1e-10
    bar = make_inplace(foo)
    @test norm(fixedpoint(bar, init_x2, xtol = 1e-10, ftol = 0.0).zero) ≈ 0.0 atol = 1e-10
    # error handling
    @test_throws MethodError fixedpoint(foo, init_x2, xtol = 1e-10, ftol = 0.0, inplace = true).zero
    @test_throws MethodError fixedpoint(bar, init_x2, xtol = 1e-10, ftol = 0.0, inplace = false).zero
    # concurrency tests
    baz(x) = 0.5*x
    function baz(out, x)
        out .= 0.5*x
    end
    @test fixedpoint(baz, init_x2).zero == fixedpoint(foo, init_x2).zero # use the one-argument (out of place) method if it exists
    # edge case
    zak(x) = map!(n -> 1/2 * n, x, x) # one-argument in-place function
    @test (fixedpoint(zak, init_x2).zero == fixedpoint(baz, init_x2).zero) == false # should fail
end


text:
# this file in only included

# Model
function device_F(V1::Float64, V2::Float64, atol)
    if CUDAnative.abs(V1) < atol
        return 0.
    else
        return V2 * V2 / V1 + 0.5 * 9.81 * V1 * V1
    end
end

# Scheme
function kernel_LaxFriedrich!(V, Vold, lambdas, Cx, atol)
    nx = length(lambdas)

    # index and stride of the cell that this gpu core will update
    gid = (blockIdx().x - 1) * blockDim().x + threadIdx().x
    lid = threadIdx().x

    sdata = CUDAnative.@cuDynamicSharedMem(Float64, 3 * (blockDim().x + 2))
    sVold = view(sdata, 1:2*(blockDim().x+2))
    sLmb = view(sdata, 2*(blockDim().x+2)+1:3*(blockDim().x+2))

    if gid <= nx
        sVold[2 * lid + 1] = Vold[2 * gid - 1]
        sVold[2 * lid + 2] = Vold[2 * gid]
        sLmb[lid + 1] = lambdas[gid]
        if lid == 1 && blockIdx().x > 1
            sVold[1] = Vold[2 * gid - 3]
            sVold[2] = Vold[2 * gid - 2]
            sLmb[1] = lambdas[gid - 1]
        end

        if lid == blockDim().x && blockIdx().x < gridDim().x
            sVold[2 * lid + 3] = Vold[2 * gid + 1]
            sVold[2 * lid + 4] = Vold[2 * gid + 2]
            sLmb[lid + 2] = lambdas[gid + 1]
        end
    end

    CUDAnative.sync_threads()

    if gid > 1 && gid < nx
        # mid-cell
        f_hu_m = device_F(sVold[2*lid-1], sVold[2*lid], atol)
        f_hu_p = device_F(sVold[2*lid+3], sVold[2*lid+4], atol)

        mlm = CUDAnative.max(sLmb[lid], sLmb[lid+1])
        mlp = CUDAnative.max(sLmb[lid+1], sLmb[lid+2])

        V[2*gid-1] += 0.5 * Cx * ((sVold[2*lid] - sVold[2*lid+4]) - mlm * (sVold[2*lid+1] - sVold[2*lid-1]) + mlp * (sVold[2*lid+3] - sVold[2*lid+1]))
        V[2*gid] += 0.5 * Cx * ((f_hu_m - f_hu_p) - mlm * (sVold[2*lid+2] - sVold[2*lid]) + mlp * (sVold[2*lid+4] - sVold[2*lid+2]))
    elseif gid==1
        # first cell
        f_hu_m = device_F(sVold[3], sVold[4], atol)
        f_hu_p = device_F(sVold[5], sVold[6], atol)
        ml = CUDAnative.max(sLmb[2], sLmb[3])

        V[1] -= 0.5 * Cx * ((sVold[6] + sVold[4]) - ml * (sVold[5] - sVold[3]))
        V[2] += Cx * (f_hu_m - sLmb[2] * sVold[4]) - 0.5 * Cx * ((f_hu_p + f_hu_m) - ml * (sVold[6] - sVold[4]))
    elseif gid==nx
        # last cell
        f_hu_m = device_F(sVold[2*lid-1], sVold[2*lid], atol)
        f_hu_p = device_F(sVold[2*lid+1], sVold[2*lid+2], atol)

        ml = CUDAnative.max(sLmb[lid], sLmb[lid+1])

        V[2*nx-1] += 0.5 * Cx * ((sVold[2*lid+2] + sVold[2*lid]) - ml * (sVold[2*lid+1] - sVold[2*lid-1]))
        V[2*nx] += 0.5 * Cx * ((f_hu_p + f_hu_m) - ml * (sVold[2*lid+2] - sVold[2*lid])) - Cx * (f_hu_p + sLmb[lid+1] * sVold[2*lid+2])
    end

    return nothing
end

# Update the eigenvalues
function kernel_UpdateEigenvalues!(lambdas, V, atol)
    nx = length(lambdas)

    # index and stride of the cell that this gpu core will update
    index = (blockIdx().x - 1) * blockDim().x + threadIdx().x

    if index <= nx
        if CUDAnative.abs(V[2*index-1]) < atol
            lambdas[index] = 0.
        else
            lambdas[index] = CUDAnative.abs(V[2*index] / V[2*index-1]) + CUDAnative.sqrt(9.81 * V[2*index-1])
        end
    end

    return nothing
end

# compute max of x for each block and put the values in mx
function reduce_max(x, mx, smem)
    nx = length(x)
    sdata = CUDAnative.@cuDynamicSharedMem(Float64, smem)

    tid = threadIdx().x
    i = (blockIdx().x - 1) * blockDim().x * 2 + threadIdx().x

    if i <= nx
        sdata[tid] = x[i]
        if i + blockDim().x < nx
            sdata[tid] = CUDAnative.max(sdata[tid], x[i + blockDim().x])
        end
    else
        sdata[tid] = -1.0
    end
    CUDAnative.sync_threads()

    if blockDim().x >= 512 && tid <= 256
        sdata[tid] = CUDAnative.max(sdata[tid], sdata[tid + 256])
    end
    CUDAnative.sync_threads()

    if blockDim().x >= 256 && tid <= 128
        sdata[tid] = CUDAnative.max(sdata[tid], sdata[tid + 128])
    end
    CUDAnative.sync_threads()

    if blockDim().x >= 128 && tid <= 64
        sdata[tid] = CUDAnative.max(sdata[tid], sdata[tid + 64])
    end
    CUDAnative.sync_threads()

    if tid <= 32
        if blockDim().x >= 64
            sdata[tid] = CUDAnative.max(sdata[tid], sdata[tid + 32])
        end

        offset = 16
        while offset >= 1
            sdata[tid] = CUDAnative.max(sdata[tid], CUDAnative.shfl_down(sdata[tid], offset))
            offset = CUDAnative.div(offset, 2)
        end
    end

    if tid == 1
        mx[blockIdx().x] = sdata[tid]
    end

    return nothing
end

ext: jl

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text:
#!/usr/bin/env julia

#= julia script to run 1 simulation
argument: integer that will be mapped to a combination of parameters
assumptions:
- directory "simresults/" created prior to running the script
- packages Distributions and StatsFuns already "added"

This is to be used with slurm, which defines a shell variable SLURM_ARRAY_TASK_ID.
This variable will serve the integer argument to the script,
to determine the combination of parameters that each slurm task will run.

example use, with default of 2 replicates per parameter combination, combination 14:
julia onesimulation.jl 14
or simply:
./onesimulation.jl 14
then look at result file in the result directory

example use with 2000 replicates per parameter combination:
julia onesimulation.jl 14 2000
=#

resultdirectory = "simresults"

"""
    onesimulation(N, n_rare_cat, mu, seed)

Simulate data from a multinomial distribution with 3 categories
and `N` units total.
- `n_rare_cat` = 1 or 2 rare categories, with very small probabilities
- `mu`: expected (or mean) number of observations in each rare category.
  The probability that each observation is in a given rare category is p=mu/N.

With 2 rare categories, the probabilities are [p,p,1-2p].
With 1 rare category, the probabilities are [p,(1-p)/2,(1-p)/2].

The data (counts in each category) are analyzed for a goodness-of-fit test:
1. using the Pearson test statistics: sum of (oi - ei)^2 / ei
   where ei = expected count in category i, oi = observed count
2. using the G statistics, or - 2 loglikelihood ratio: 2 × sum of oi × log(oi/ei)
Both test statistics are compared to a chi-square distribution
with 2 degrees of freedom to obtain p-values.

output: (pearson_stat, G_stat, pearson_pvalue, G_pvalue)

examples:

```julia
onesimulation( 50, 1, 0.1, 123)
onesimulation(500, 2, 2.0, 123)
```
"""
function onesimulation(N, nrarecat, mu, seed)
  Random.seed!(seed)
  p = mu/N
  @assert p>=0.0 && p<=0.5 "the rare category/ies cannot have a negative or >.5 probability"
  probs = ( nrarecat==1 ? [p,(1-p)/2,(1-p)/2] : [p, p, (1-2p)] )
  observed = rand(Multinomial(N,probs), 1) # 3x1 array
  phat = observed./N # estimated probabilities of the 3 categories
  pearson = N * sum((phat - probs).^2 ./probs)
  gstat  = 2N * sum(xlogy.(phat, phat ./ probs))
  # ccdf = complementary cumulative distribution function: P(random value >  x)
  p_pearson = ccdf(Chisq(2), pearson) # df=2 because 3 categories
  p_gstat   = ccdf(Chisq(2), gstat)
  return pearson,gstat, p_pearson,p_gstat
end

"""
    arrayID_to_parameters(arrayID, total_n_reps)

Convert a single integer into 4 parameters to be used for the simulation:
`replicate_number, sample_size, n_rare_categories, mu`.
The integer is meant to be used as the "array ID" when submitting all these
simulations with slurm and with a slurm array.

Assumption: parameters vary in
- sample_size: 30, 1000
- n_rare_categories: 1, 2
- mu: 0.1, 1.0, 2.0
- replicate_number: from 1 to total_n_reps (input: to start small when developing the script)
"""
function arrayID_to_parameters(arrayID::Int, Nrep::Int)
  # start with Nrep = 2 to develop the julia + slurm script
  samplesizes = [30, 1000]
  nrarecats = [1, 2]
  mus = [0.1, 1., 2.]

  Nssize    = length(samplesizes)
  Nnrarecat = length(nrarecats)
  Nmu       = length(mus)

  ntotal = Nrep * Nssize * Nnrarecat * Nmu
  @assert arrayID <= ntotal "ID must be between 1 and $ntotal"
  indices = CartesianIndices( (Nrep,Nssize,Nnrarecat,Nmu) )
  I = indices[arrayID].I # coordinates corresponding to the linear index arrayID
  rep = I[1]
  samplesize = samplesizes[I[2]]
  nrarecat = nrarecats[I[3]]
  mu = mus[I[4]]
  return rep, samplesize, nrarecat, mu
end

#-----------------------------------------------------#
#  finally: read script argument and run 1 simulation #
#-----------------------------------------------------#

# parse the integer argument
@assert length(ARGS)>0 "need 1 parameters: arrayID"
arrayID = parse(Int, ARGS[1])
# Nreps = 2nd argument. 2 reps by default, if no second argument
Nreps = (length(ARGS)==1 ? 2 : parse(Int, ARGS[2]))
rep, samplesize, nrarecat, mu = arrayID_to_parameters(arrayID, Nreps)
@info ""  arrayID replicate=rep samplesize number_rare_categories=nrarecat mu

# load the packages that the simulation function needs
using Distributions # for Multinomial, Chisq, ccdf
using StatsFuns     # for xlogy
using Random        # no install: standard library
using Printf        # standard library

# run simulation. use arrayID as seed: will be different for each replicate
pearson, gstat, p_pearson, p_gstat = onesimulation(samplesize, nrarecat, mu, arrayID)

# save the result in tiny csv-formatted file
# (later, all these files will be concatenated with "cat")
outputfile = joinpath(resultdirectory, "simulation_" * @sprintf("%04d", arrayID) * ".csv")
open(outputfile, "w") do g
  write(g, "$arrayID,$rep,$samplesize,$nrarecat,$mu,") # input
  write(g, "$pearson,$gstat,$p_pearson,$p_gstat\n")    # output
end
@info "ID $arrayID is done"

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text:
"""
`MaternKernel([ρ=1.0,[ν=1.0]])`
The matern kernel is an isotropic Mercer kernel given by the formula:
```
    κ(x,y) = 2^{1-ν}/Γ(ν)*(√(2ν)‖x-y‖)^ν K_ν(√(2ν)‖x-y‖)
```
For `ν=n+1/2, n=0,1,2,...` it can be simplified and you should instead use [`ExponentialKernel`](@ref) for `n=0`, [`Matern32Kernel`](@ref), for `n=1`, [`Matern52Kernel`](@ref) for `n=2` and [`SqExponentialKernel`](@ref) for `n=∞`.
"""
struct MaternKernel{Tν<:Real} <: BaseKernel
    ν::Vector{Tν}
    function MaternKernel(;nu::T=1.5, ν::T=nu) where {T<:Real}
        @check_args(MaternKernel, ν, ν > zero(T), "ν > 0")
        return new{T}([ν])
    end
end

@inline function kappa(κ::MaternKernel, d::Real)
    ν = first(κ.ν)
    iszero(d) ? one(d) :
    exp(
        (one(d) - ν) * logtwo - logabsgamma(ν)[1] +
        ν * log(sqrt(2ν) * d) +
        log(besselk(ν, sqrt(2ν) * d))
    )
end

metric(::MaternKernel) = Euclidean()

"""
`Matern32Kernel([ρ=1.0])`
The matern 3/2 kernel is an isotropic Mercer kernel given by the formula:
```
    κ(x,y) = (1+√(3)ρ‖x-y‖)exp(-√(3)ρ‖x-y‖)
```
"""
struct Matern32Kernel <: BaseKernel end

kappa(κ::Matern32Kernel, d::Real) = (1 + sqrt(3) * d) * exp(-sqrt(3) * d)

metric(::Matern32Kernel) = Euclidean()

"""
`Matern52Kernel([ρ=1.0])`
The matern 5/2 kernel is an isotropic Mercer kernel given by the formula:
```
    κ(x,y) = (1+√(5)ρ‖x-y‖ + 5ρ²‖x-y‖^2/3)exp(-√(5)ρ‖x-y‖)
```
"""
struct Matern52Kernel <: BaseKernel end

kappa(κ::Matern52Kernel, d::Real) = (1 + sqrt(5) * d + 5 * d^2 / 3) * exp(-sqrt(5) * d)

metric(::Matern52Kernel) = Euclidean()


text:
export CacheForever,
    CacheNever,
    CacheTTL,
    CacheLRU,
    CacheFilter

# TODO: Strategy composition, e.g. TTL eviction with filtered insertion.

"""
A method of handling cache insertion and eviction.
"""
abstract type CacheStrategy end

"""
    CacheForever() -> CacheForever

Store everything and never evict items from the cache.
"""
struct CacheForever <: CacheStrategy end

"""
    CacheNever() -> CacheNever

Don't store anything in the cache.
"""
struct CacheNever <: CacheStrategy end

"""
    CacheTTL(ttl::Period) -> CacheTTL

Evict items from the cache after `ttl` has elapsed.
"""
struct CacheTTL <: CacheStrategy
    ttl::Period
end

"""
    CacheLRU(size::Int) -> CacheLRU

Evict the least recently used item from the cache when there are more than `size` items.
"""
struct CacheLRU <: CacheStrategy
    size::Int
end

"""
    CacheFilter(f::Function) -> CacheFilter

Only store value `v` at key `k` if `f(v) === true` (`k` is always `v.id`).
"""
struct CacheFilter <: CacheStrategy
    f::Function
end

# A dict-like object with a caching strategy.
struct Store{D <: AbstractDict, S <: CacheStrategy}
    data::D
    strat::S

    Store(d::D, s::CacheStrategy) where D = new{D, typeof(s)}(d, s)
end

Store(::CacheForever, V::Type) = Store(Dict{Snowflake, V}(), CacheForever())
Store(::CacheNever, V::Type) = Store(Dict{Snowflake, V}(), CacheNever())
Store(s::CacheTTL, V::Type) = Store(TTL{Snowflake, V}(s.ttl), s)
Store(s::CacheLRU, V::Type) = Store(LRU{Snowflake, V}(s.size), s)
Store(s::CacheFilter, V::Type) = Store(Dict{Snowflake, V}(), s)

Base.eltype(s::Store) = eltype(s.data)
Base.get(s::Store, key, default) = get(s.data, key, default)
Base.getindex(s::Store, key) = s.data[key]
Base.haskey(s::Store, key) = haskey(s.data, key)
Base.isempty(s::Store) = isempty(s.data)
Base.keys(s::Store) = keys(s.data)
Base.values(s::Store) = values(s.data)
Base.length(s::Store) = length(s.data)
Base.iterate(s::Store) = iterate(s.data)
Base.iterate(s::Store, i) = iterate(s.data, i)
Base.touch(s::Store, k) = nothing
Base.delete!(s::Store, key) = (delete!(s.data, key); s)
Base.empty!(s::Store) = (empty!(s.data); s)
Base.filter!(f, s::Store) = (filter!(s.data); s)
Base.setindex!(s::Store, value, key) = (setindex!(s.data, value, key); s)

Base.touch(s::Store{<:AbstractDict, CacheTTL}, key) = touch(s.data, key)
Base.setindex!(s::Store{<:AbstractDict, CacheNever}, value, key) = s
function Base.setindex!(s::Store{<:AbstractDict, CacheFilter}, value, key)
    try
        s.strat.f(value) === true && setindex!(s.data, value, key)
    catch
        # TODO: Log this?
    end
    return s
end

# Container for all client state.
mutable struct State
    v::Int                                 # Discord API version.
    session_id::String                     # Gateway session ID.
    _trace::Vector{String}                 # Servers (not guilds) connected to.
    user::Nullable{User}                   # Bot user.
    guilds::Store                          # Guild ID -> guild.
    channels::Store                        # Channel ID -> channel.
    users::Store                           # User ID -> user.
    messages::Store                        # Message ID -> message.
    presences::Dict{Snowflake, Store}      # Guild ID -> user ID -> presence.
    members::Dict{Snowflake, Store}        # Guild ID -> member ID -> member.
    sem::Base.Semaphore                    # Internal mutex.
    strats::Dict{DataType, CacheStrategy}  # Caching strategies per type.
end

function State(strats::Dict{DataType, <:CacheStrategy})
    return State(
        0,        # v
        "",       # session_id
        [],       # _trace
        nothing,  # user
        Store(strats[Guild], AbstractGuild),            # guilds
        Store(strats[DiscordChannel], DiscordChannel),  # channels
        Store(strats[User], User),                      # users
        Store(strats[Message], Message),                # messages
        Dict(),              # presences
        Dict(),              # members
        Base.Semaphore(1),   # sem
        strats,              # strats
    )
end

Store(s::State, T::Type) = Store(get(s.strats, T, CacheForever()), T)

# Base.get retrieves a value of a given type from the cache, or returns nothing.

Base.get(s::State, ::Type; kwargs...) = nothing
Base.get(s::State, ::Type{User}; kwargs...) = get(s.users, kwargs[:user], nothing)
Base.get(s::State, ::Type{Message}; kwargs...) = get(s.messages, kwargs[:message], nothing)

# Get a single channel.
function Base.get(s::State, ::Type{DiscordChannel}; kwargs...)
    return get(s.channels, kwargs[:channel], nothing)
end

# Get all the channels of a guild.
function Base.get(s::State, ::Type{Vector{DiscordChannel}}; kwargs...)
    guild = kwargs[:guild]
    haskey(s.guilds, guild) || return nothing

    channels = map(
        i -> s.channels[i],
        Iterators.filter(i -> haskey(s.channels, i), collect(s.guilds[guild].djl_channels)),
    )
    return isempty(channels) ? nothing : channels
end

function Base.get(s::State, ::Type{Presence}; kwargs...)
    guild = kwargs[:guild]
    haskey(s.presences, guild) || return nothing
    return get(s.presences[guild], kwargs[:user], nothing)
end

function Base.get(s::State, ::Type{Guild}; kwargs...)
    haskey(s.guilds, kwargs[:guild]) || return nothing
    g = s.guilds[kwargs[:guild]]

    # Guilds are stored with missing channels, members, and presences.
    g = @set g.channels = map(
        ch -> s.channels[ch],
        Iterators.filter(ch -> haskey(s.channels, ch), collect(g.djl_channels)),
    )
    g = @set g.djl_channels = missing
    ms = get(s.members, g.id, Dict())
    g = @set g.members = map(
        i -> get(s, Member; guild=g.id, user=i),
        Iterators.filter(i -> haskey(ms, i), collect(coalesce(g.djl_users, Member[]))),
    )
    ps = get(s.presences, g.id, Dict())
    g = @set g.presences = map(
        i -> get(s, Presence; guild=g.id, user=i),
        Iterators.filter(i -> haskey(ps, i), collect(coalesce(g.djl_users, Presence[]))),
    )
    g = @set g.djl_users = missing

    return g
end

function Base.get(s::State, ::Type{Member}; kwargs...)
    # Members are stored with missing user.
    haskey(s.members, kwargs[:guild]) || return nothing
    guild = s.members[kwargs[:guild]]

    haskey(guild, kwargs[:user]) || return nothing
    member = guild[kwargs[:user]]

    haskey(s.users, kwargs[:user]) || return member  # With a missing user field.
    user = s.users[kwargs[:user]]
    return @set member.user = user
end

function Base.get(s::State, ::Type{Role}; kwargs...)
    haskey(s.guilds, kwargs[:guild]) || return nothing
    roles = coalesce(s.guilds[kwargs[:guild]].roles, Role[])
    idx = findfirst(r -> r.id == kwargs[:role], roles)
    return idx === nothing ? nothing : roles[idx]
end

# Base.put! inserts a value into the cache, and returns the updated value.

Base.put!(s::State, val; kwargs...) = val
Base.put!(s::State, g::UnavailableGuild; kwargs...) = insert_or_update!(s.guilds, g)
Base.put!(s::State, ms::Vector{Member}; kwargs...) = map(m -> put!(s, m; kwargs...), ms)
Base.put!(s::State, u::User; kwargs...) = insert_or_update!(s.users, u)

function Base.put!(s::State, m::Message; kwargs...)
    if ismissing(m.guild_id) && haskey(s.channels, m.channel_id)
        m = @set m.guild_id = s.channels[m.channel_id].guild_id
    end

    insert_or_update!(s.messages, m)
    touch(s.channels, m.channel_id)
    touch(s.guilds, m.guild_id)

    return m
end

function Base.put!(s::State, g::Guild; kwargs...)
    # Replace members and presences with IDs that can be looked up later.
    ms = coalesce(g.members, Member[])
    ps = coalesce(g.presences, Presence[])
    users = map(m -> m.user.id, Iterators.filter(m -> m.user !== nothing, ms))
    unique!(append!(users, map(p -> p.user.id, ps)))
    g = @set g.members = missing
    g = @set g.presences = missing
    g = @set g.djl_users = Set(users)
    chs = coalesce(g.channels, DiscordChannel[])
    channels = map(ch -> ch.id, chs)
    g = @set g.djl_channels = Set(channels)
    g = @set g.channels = missing

    insert_or_update!(s.guilds, g)
    put!(s, chs; kwargs..., guild=g.id)
    foreach(m -> put!(s, m; kwargs..., guild=g.id), ms)
    foreach(p -> put!(s, p; kwargs..., guild=g.id), ps)

    return get(s, Guild; guild=g.id)
end

function Base.put!(s::State, ms::Vector{Message}; kwargs...)
    return map(m -> put!(s, m; kwargs...), ms)
end

function Base.put!(s::State, ch::DiscordChannel; kwargs...)
    if ismissing(ch.guild_id) && get(kwargs, :guild, nothing) !== nothing
        ch = @set ch.guild_id = kwargs[:guild]
    end

    foreach(u -> put!(s, u; kwargs...), coalesce(ch.recipients, User[]))
    haskey(s.guilds, ch.guild_id) && push!(s.guilds[ch.guild_id].djl_channels, ch.id)

    return insert_or_update!(s.channels, ch)
end

function Base.put!(s::State, chs::Vector{DiscordChannel}; kwargs...)
    return map(ch -> put!(s, ch; kwargs...), chs)
end

function Base.put!(s::State, p::Presence; kwargs...)
    guild = coalesce(get(kwargs, :guild, missing), p.guild_id)
    ismissing(guild) && return p

    if haskey(s.guilds, guild)
        g = s.guilds[guild]
        g isa Guild && push!(g.djl_users, p.user.id)
    end

    haskey(s.presences, guild) || (s.presences[guild] = Store(s, Presence))
    return insert_or_update!(s.presences[guild], p.user.id, p)
end

function Base.put!(s::State, m::Member; kwargs...)
    ismissing(m.user) && return m
    guild = kwargs[:guild]

    # Members are stored with a missing user field to save memory.
    user = m.user
    m = @set m.user = missing

    # This is a bit ugly, but basically we're updating the member as usual but then
    # filling in its user field at the same time as the user sync.
    haskey(s.members, guild) || (s.members[guild] = Store(s, Member))
    m = insert_or_update!(s.members[guild], user.id, m)
    m = @set m.user = insert_or_update!(s.users, user)

    if haskey(s.guilds, guild)
        g = s.guilds[guild]
        g isa Guild && push!(g.djl_users, user.id)
    end

    return m
end

function Base.put!(s::State, r::Role; kwargs...)
    guild = kwargs[:guild]
    haskey(s.guilds, guild) || return r
    g = s.guilds[guild]
    g isa Guild || return r

    return if ismissing(g.roles)
        s.guilds[guild] = @set g.roles = [r]
        r
    else
        insert_or_update!(g.roles, r)
    end
end

# This handles emojis being added to a guild.
function Base.put!(s::State, es::Vector{Emoji}; kwargs...)
    guild = kwargs[:guild]
    haskey(s.guilds, guild) || return es
    g = s.guilds[guild]
    g isa Guild || return es

    s.guilds[guild] = @set g.emojis = es
    return es
end

# This handles a single emoji being added as a reaction.
function Base.put!(s::State, e::Emoji; kwargs...)
    message = kwargs[:message]
    user = kwargs[:user]
    haskey(s.messages, message) || return e

    withsem(s.sem) do
        m = s.messages[message]
        isclient = !ismissing(s.user) && s.user.id == user
        if ismissing(m.reactions)
            s.messages[message] = @set m.reactions = [Reaction(1, isclient, e)]
        else
            idx = findfirst(r -> r.emoji.name == e.name, m.reactions)
            if idx === nothing
                push!(m.reactions, Reaction(1, isclient, e))
            else
                r = m.reactions[idx]
                r = @set r.count += 1
                r = @set r.me |= isclient
                r = @set r.emoji = merge(r.emoji, e)
                m.reactions[idx] = r
            end
        end
    end

    return e
end

# Insert or update a value in the cache.
insert_or_update!(d, k, v; kwargs...) = d[k] = haskey(d, k) ? merge(d[k], v) : v
function insert_or_update!(d::Vector, k, v; key::Function=x -> x.id)
    idx = findfirst(x -> key(x) == k, d)
    return if idx === nothing
        push!(d, v)
        v
    else
        d[idx] = merge(d[idx], v)
    end
end
function insert_or_update!(d, v; key::Function=x -> x.id)
    insert_or_update!(d, key(v), v; key=key)
end


text:
@testset "time_based_sample_model" begin
    m = TimeBasedSampleModel(2, 1.0)

    update!(m, (1, 1, 1.0, false, 2))
    update!(m, (2, 1, 1.0, false, 3))

    @test m.experiences[1][1] == (reward = 1.0, terminal = false, nextstate = 2)
    @test m.experiences[2][1] == (reward = 1.0, terminal = false, nextstate = 3)
    @test m.last_visit[(1, 1)] == 1
    @test m.last_visit[(2, 1)] == 2
end


text:
### A Pluto.jl notebook ###
# v0.17.2

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)
    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
end

# ╔═╡ 8d4298e0-6c44-11eb-3406-31a39340d1aa
begin
	#try
		using PlutoUI
		using Plots
		using LinearAlgebra
		using SparseArrays
		using SpecialFunctions
		using StatsBase

		using Random
		md"""
		# Packages

		All needed Packages available :) """
	#=catch
		using Pkg;
		Pkg.activate(mktempdir())
		Pkg.add("PlutoUI")
		Pkg.add("Plots")
		#Pkg.add("LinearAlgebra")
		#Pkg.add("SparseArrays")
		Pkg.add("SpecialFunctions")
		Pkg.add("StatsBase")
		using PlutoUI
		using Plots
		using LinearAlgebra
		using SparseArrays
		using SpecialFunctions
		using StatsBase

		using Random
		md"""
		# Packages

		Some Package sources not added, this will take approx. 3 minutes"""
	end
	=#
	# TODO: add a GIF of the golden Nautilus wheel spinning and maybe a link to the derivation of the proabilities and to the video
end

# ╔═╡ 9637fe40-6c44-11eb-1df3-eb0b0d36db34
md"""

# **The golden Nautilus wheel** - _Distributions and the law of large numbers_

As you can watch in video below 👇, Captain Venn wants to find out the chances for the four tasks of the day. Help him with doing the experiments, press **_START_** and count the results in the **histogram** below. The red bullets 📍 indicate the intrinsic probabilities times the number of experiments $P_i \cdot \mathcal{N}$.

"""

# ╔═╡ f3f80e2e-51d2-4fce-b7df-b2cdd3a0cad5
html"""

"""

# ╔═╡ e03eeec0-8299-11eb-119b-5dfd576a2811
md"""
Choose the **random seed** $\,\,$ 👉 $(@bind seed Slider(1:100, default=1, show_value = true))
"""

# ╔═╡ 8d180f60-829e-11eb-36a3-6fb2eab9c846
md"""
Start the **measurements** (don't forget to stop the clock at some point!):  $(@bind n_sample_size Clock(0.2,true,false))
"""

#md"""
#Change the number of measurements 👉 $\mathcal{N} =$ $(@bind n_sample_size #Scrubbable(1:1:200, default=10))  (*drag the red number with the mouse* 🖱)
#"""

# ╔═╡ 32d0d060-82b1-11eb-37a0-4bcd4881e6e1
md"""
##### Wages
Captain Venn trusts you a lot, you can even **change the wages** Captain Venn pays for the four tasks (just drag the numbers with the mouse).

_sailing_ ⛵ $(@bind sailing Scrubbable(6)) pennies,

_fishing_ 🐬$(@bind fishing Scrubbable(4)) pennies,

_shrubbing the deck_ 🧹 $(@bind shrubbing Scrubbable(3)) pennies,

_free day_ 🏝 $(@bind free_day Scrubbable(1)) penny.
"""

# ╔═╡ b7a7b220-6c56-11eb-1e6c-6f7595f02439
md"""
In order to see the variation of the sample mean we **repeat the measurements with fixed sample size** ($\mathcal{N}$) $n$ times. This way we can **sample the distribution of the sample mean value** (which is a random variable in contrast to the intrinsic mean $\langle X \rangle$ = 0.1056. Use the slider to change the number of repeated measurements $N$ of samples of size $n$.

"""

# ╔═╡ 8b8cd540-6d86-11eb-339e-7b8a2df774f9
md"""
Choose the **number of repetitions** 👉 n =   $(@bind rep Scrubbable(100:100:2000)) of sampling samples with **sample size**
👉 N = $(@bind n_sam_size Scrubbable(500:1000:12000))
"""

# ╔═╡ b1515d9a-8039-4410-bbd2-54890804fda8
md"""
Learn more about the law of large numbers and how to evaluate the standard error in the lesson below 👇 or in the [`IMOOX course`](https://imoox.at/mooc/local/landingpage/course.php?shortname=bayes&lang=en) equipped with many quizzes."""

# ╔═╡ 936054d5-2863-4f69-9a12-c865d6dd37b0
html"""

"""

# ╔═╡ 3cc85769-13d1-44d9-acd8-20353c848829
md"""
## About the creators

This notebook was created by **Gerhard Dorn** in the context of the course **Bayesian probability theory**.

The course is a free massive open online course (MOOC) available on the platform [`IMOOX`](https://imoox.at/mooc/local/landingpage/course.php?shortname=bayes&lang=en)

$(Resource("https://raw.githubusercontent.com/Captain-Bayes/images/main/adventure_map.gif"))
"""

# ╔═╡ a2541e60-8356-11eb-1b16-6fb19948ed1c
md"""
# Some code below
In order to have a look at the code download the notebook or load it on binder (takes 6-10 minutes)

To do so, **press the binder button** in the right top corner ↗
"""

# ╔═╡ 48f7c480-6d84-11eb-1f24-e16d7f649c9c
begin
	phi = (1+sqrt(5))/2 #golden ratio
	prob = phi.^(0:3)./sum(phi.^(0:3)) # intrinsic probabilities of the four sectors
	prob_string = [string(round(prob[i]*100, digits=1)) * "%, " for i in 1:4]
md"""
##### Calculating the intrinsic probabilities of the golden Nautilus wheel

 $P$ :   [$(prob_string[:]) ]

	"""
end

# ╔═╡ 70209d20-8350-11eb-2da3-9f99a25eb4f9
begin
	rng = MersenneTwister(20)

	local sample_temp = 5 .- sum(rand(rng, 1,rep*n_sam_size) .<= cumsum(prob), dims=1)
	local sample_array = reshape(sample_temp, (n_sam_size,:))
	X = sum(sample_array .== 1,dims=1)/n_sam_size

	md"""
	##### sampling the sample means
	"""
end

# ╔═╡ 5523cb40-82b6-11eb-3e29-81d50ff29db6
begin

	histogram(X[:], nbins=20,
	xlim=[0.06, 0.15], label=:none, xlabel="Sample mean", ylabel="Frequency"
	)

	plot!([0.1, 0.1], [0, rep/6], line=(3.2, 1.0, :line), linestyle=:dash, color = :red, label="10% limit")
	plot!([0.1056, 0.1056], [0, rep/6], line=(3.2, 1.0, :line), linestyle=:dash, color = :green, label="intrinsic mean")
end

# ╔═╡ 86962d00-8449-11eb-31f9-dfb502c7e132
md"""
Captain Venn's statement of having at least 10% free days is **wrong** in **$(round(100*sum(X.<0.1)/length(X), digits=1)) %** of all $(n_sam_size) day-long sailing turns *(a contract for $(round(n_sam_size/365, digits=1)) years)*"""

# ╔═╡ 8cc9f417-ad45-48d2-8960-6a8d465cb9a5
begin

		bayes = "https://raw.githubusercontent.com/Captain-Bayes/images/main/bayes_50px.gif"
	bernoulli = "https://raw.githubusercontent.com/Captain-Bayes/images/main/bernoulli_50px.gif"

	venn = "https://raw.githubusercontent.com/Captain-Bayes/images/main/venn_50px1.gif"

	md"""Images"""
end

# ╔═╡ 67f01600-82ae-11eb-2c1a-c906e8a6a892
begin
md"""
$(Resource(bayes, :width=>180))
$(Resource(venn, :width=>180))

**Captain Bayes and Captain Venn** are investigating the **golden Nautilus wheel** and are wondering how one can make reliable predictions about the minimum free days ratio.

A **rough rule of thumb** says that for most distributions the standard deviation can be used as a measure of how much probability mass is **spread around the mean value**, namely that within the following intervals one can find:

``P(X \in [μ - σ, μ + σ])  ≈ 67\%,``

``P(X ∈ [μ - 2σ, μ + 2σ]) ≈ 95\%,``

``P(X ∈ [μ - 3σ, μ + 3σ]) ≈ 99\%.``

We examine the standard error which is the standard deviation of the sample mean 	(since we want to find an estimate for the sample mean ``\overline{\boldsymbol{X}}``).

"""

end

# ╔═╡ 59607242-82b0-11eb-35cf-cb7b33cddf21
x_rand_var = [free_day, shrubbing, fishing, sailing]

# ╔═╡ d6519370-825a-11eb-1ae5-ed41bc0c343f
begin
	function take_sample(N_sample_size, seed)
	rng = MersenneTwister(seed)
	sample = 5 .- sum(rand(rng, 1,N_sample_size) .<= cumsum(prob), dims=1)
	return sample
	end

	md"""
	##### Function for taking a sample of size N using a seed
	"""
end

# ╔═╡ 5e0bfb10-6d8a-11eb-06ef-9335eb90064c
begin
	n_size = minimum([n_sample_size, 200])
	sample_1 = take_sample(n_size, seed)
	sample_count = [count(==(i), sample_1) for i = 1:4]

	plot(x_rand_var, sample_count,
    line = (1.0 , 2.0 , :bar),
    normalize = false,
	bar_width = 0.6,
    marker = (6, 0.5, :none),
    markerstrokewidth = 5.,
    color = :steelblue,
    fill = 0.9,
    orientation = :v,
    title = "Histogram with total sample size: " * string(n_size),
	ylabel = "frequency N",
	xlabel = "Pennies (random variable X)",
	label = :none,
	ylim =[0,maximum([20,n_size/2])])

	plot!(
    x_rand_var,prob.*n_size,
    line = ( 1, 0., :path),
    normalize = false,
    marker = (5, 1.0, :o),
    markerstrokewidth = 3.,
    color = :red,
    fill = 0.,
    orientation = :v,
	label = "expected value",
	legend = :topleft
	)
end

# ╔═╡ 4171c850-82a6-11eb-1031-73a99aff7207
begin

	free_days = [(i>1) ? md"🔴" : md"🟢" for i in sample_1]
	free_days_table = reshape([free_days [md"" for i in 1:1, j in (1:(7-Integer(length(free_days)- floor(length(free_days)/7)*7)))]], (7,:))
	fd_table = permutedims(free_days_table, [2,1])
md"""
#### Working days:
 $(Resource(bernoulli, :width=>180))

	Bernoulli made a calender 📅 of all working 🔴 and free 🟢 days:

	"""

end

# ╔═╡ 3f47bb1e-8350-11eb-2cca-cb42ea1105d2
	fd_table

# ╔═╡ 26395db0-82b4-11eb-3c44-d18d737d9e53
md"""
The estimated free days ratio from the data is: $(round(100*sum(sample_1 .==1)/length(sample_1))) %
"""

# ╔═╡ 2293a98e-d6a8-443a-9f84-47b632a199f4
TableOfContents()

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"

[compat]
Plots = "~1.24.0"
PlutoUI = "~0.7.20"
SpecialFunctions = "~2.0.0"
StatsBase = "~0.33.13"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "0bc60e3006ad95b4bb7497698dd7c6d649b9bc06"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.1"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.11.1"

[[ChangesOfVariables]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "9a1d594397670492219635b35a3d830b04730d62"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.1"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "a851fec56cb73cfdf43762999ec72eff5b86882a"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.15.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.40.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[DataAPI]]
git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.10"

[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.6"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.2.3+0"

[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.2.10+0"

[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.0+0"

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

[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+1"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.62.1"

[[GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.62.0+0"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"

[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+0"

[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.17"

[[HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+0"

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

[[HypertextLiteral]]
git-tree-sha1 = "2b078b5a615c6c0396c77810d92ee8c6f470d238"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.3"

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

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[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"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[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"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.9"

[[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"

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

[[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]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

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

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[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"

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

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

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+0"

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

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.10+0"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

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

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[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"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.15"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
git-tree-sha1 = "02a083caba3f73e42decb810b2e0740783022978"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.24.0"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "1e0cb51e0ccef0afc01aab41dc51a3e7f781e8cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.20"

[[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"

[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+0"

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

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

[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.4.1"

[[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"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

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

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[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 = "e08890d19787ec25029113e88c34ec20cac1c91e"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.0.0"

[[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 = "0f2aa8e32d511f758a2ce49208181f7733a0936a"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.1.0"

[[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"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.3"

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

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

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

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

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

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

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

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

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

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

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

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

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
# ╟─9637fe40-6c44-11eb-1df3-eb0b0d36db34
# ╟─f3f80e2e-51d2-4fce-b7df-b2cdd3a0cad5
# ╟─e03eeec0-8299-11eb-119b-5dfd576a2811
# ╟─8d180f60-829e-11eb-36a3-6fb2eab9c846
# ╟─5e0bfb10-6d8a-11eb-06ef-9335eb90064c
# ╟─32d0d060-82b1-11eb-37a0-4bcd4881e6e1
# ╟─4171c850-82a6-11eb-1031-73a99aff7207
# ╟─3f47bb1e-8350-11eb-2cca-cb42ea1105d2
# ╟─26395db0-82b4-11eb-3c44-d18d737d9e53
# ╟─67f01600-82ae-11eb-2c1a-c906e8a6a892
# ╟─b7a7b220-6c56-11eb-1e6c-6f7595f02439
# ╟─8b8cd540-6d86-11eb-339e-7b8a2df774f9
# ╟─5523cb40-82b6-11eb-3e29-81d50ff29db6
# ╟─86962d00-8449-11eb-31f9-dfb502c7e132
# ╟─b1515d9a-8039-4410-bbd2-54890804fda8
# ╟─936054d5-2863-4f69-9a12-c865d6dd37b0
# ╟─8d4298e0-6c44-11eb-3406-31a39340d1aa
# ╟─3cc85769-13d1-44d9-acd8-20353c848829
# ╟─a2541e60-8356-11eb-1b16-6fb19948ed1c
# ╟─70209d20-8350-11eb-2da3-9f99a25eb4f9
# ╟─48f7c480-6d84-11eb-1f24-e16d7f649c9c
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text:
using IterTools

cd(dirname(@__FILE__))
const lines = open("four.txt", "r") do f
    readlines(f)
end

const StringDict = Dict{String, String}

valid_set = Set(["hcl", "iyr", "eyr", "ecl", "pid", "byr", "hgt"])
valid_keys(d::StringDict) = issubset(valid_set, keys(d))

# byr (Birth Year) - four digits; at least 1920 and at most 2002.
valid_byr(s::String) = length(s) == 4 && 1920 <= parse(Int64, s) <= 2002
valid_byr(d::StringDict) = valid_byr(d["byr"])

# iyr (Issue Year) - four digits; at least 2010 and at most 2020.
valid_iyr(s) = length(s) == 4 && 2010 <= parse(Int64, s) <= 2020
valid_iyr(d::StringDict) = valid_iyr(d["iyr"])

# eyr (Expiration Year) - four digits; at least 2020 and at most 2030.
valid_eyr(s) = length(s) == 4 && 2020 <= parse(Int64, s) <= 2030
valid_eyr(d::StringDict) = valid_eyr(d["eyr"])

# hgt (Height) - a number followed by either cm or in:
# If cm, the number must be at least 150 and at most 193.
# If in, the number must be at least 59 and at most 76.
valid_hgt(s::String) = begin
    m = match(r"^([0-9]{2,3})(in|cm)$", s)
    if m !== nothing
        v,u = m.captures
        h = parse(Int64,v)
        if u == "cm"
            150 <= h <= 193
        else # must be "in"
            59 <= h <= 76
        end
    else
        false
    end
end
valid_hgt(d::StringDict) = valid_hgt(d["hgt"])

# hcl (Hair Color) - a # followed by exactly six characters 0-9 or a-f.
valid_hcl(s::String) = nothing !== match(r"^#[a-f,0-9]{6}$", s)
valid_hcl(d::StringDict) = valid_hcl(d["hcl"])

# ecl (Eye Color) - exactly one of: amb blu brn gry grn hzl oth.
ecls = Set(["amb" "blu" "brn" "gry" "grn" "hzl" "oth"])
valid_ecl(s::String) = s in ecls
valid_ecl(d::StringDict) = valid_ecl(d["ecl"])

# pid (Passport ID) - a nine-digit number, including leading zeroes.
valid_pid(s::String) = nothing !== match(r"^[0-9]{9}$", s)
valid_pid(d::StringDict) = valid_pid(d["pid"])

is_valid(d::StringDict) = (
    valid_keys(d)
    && valid_byr(d)
    && valid_iyr(d)
    && valid_eyr(d)
    && valid_hgt(d)
    && valid_hcl(d)
    && valid_ecl(d)
    && valid_pid(d)
)

parse_line(l::String)::Dict{String,String} =
    Dict(split(s,":") for s in split(l))

join_by_space(l) = join(l, " ")

n = (groupby(!isempty, lines)
    |> l -> map(join_by_space, l)
    |> l -> filter(!isempty, l)
    |> l -> map(parse_line, l)
    |> s -> map(is_valid, s)
    |> sum)

println(n)


text:
"""
    compute_ddf(date, ddf_min, ddf_max)

Compute a time-varying degree-day factor depending on the date and a minimum
`ddf_min` and maximum `ddf_max` degree-day factor.
"""
function compute_ddf(date::DateTime, ddf_min::Float64, ddf_max::Float64)

    doy = Dates.dayofyear(date)

    ddf = (ddf_max - ddf_min) * (0.5*sin(2.0*pi*(doy - 80)/366) + 0.5) + ddf_min

    return ddf

end

"""
    split_prec(prec, tair, tth_phase = 0.0; m_phase = 0.5)

Split precipitation into solid and liquid precipitation from precipitation
`prec` and air temperature `tair` using temperature threshold parameter
`tth_phase` and smoothing parameter `m_phase` which needs to be greater
than zero.
"""
function split_prec(prec, tair, tth_phase = 0.0; m_phase = 0.5)

    frac_snowfall = 1. / (1. + exp( (tair - tth_phase) / m_phase ))

    psolid = prec * frac_snowfall
    pliquid = prec - psolid

    return psolid, pliquid

end

"""
    pot_melt(tair, ddf = 3.0, tth_melt = 0.0; m_melt = 0.5)

Compute potential snowmelt from air temperature `tair` using a degree-day factor
`ddf`, a temperature threshold `tth_melt`, and a smoothing parameter `m_melt`
which needs to be greater than zero.
"""
function pot_melt(tair, ddf = 3.0, tth_melt = 0.0; m_melt = 0.5)

    t_m = (tair - tth_melt) / m_melt
    pot_melt = ddf * m_melt * (t_m + log(1. + exp(-t_m)))

    return pot_melt

end

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