text:
############################################################################################
"""
$(TYPEDEF)

Objective struct with additional information about AD backend and configuration.

# Fields
$(TYPEDFIELDS)
"""
struct DiffObjective{O<:Objective,T<:AbstractDifferentiableTune}
    "Objective as function of a parameter vector in unconstrained space."
    objective::O
    "Automatic Differentiation configurations."
    tune::T
end

############################################################################################
function _log_density(diff::DiffObjective, θᵤ::AbstractVector{T}) where {T<:Real}
    return diff.objective(θᵤ)
end
function _log_density_and_gradient(
    diff::DiffObjective, θᵤ::AbstractVector{T}
) where {T<:Real}
    return _log_density_and_gradient(diff.objective, diff.tune, θᵤ)
end

############################################################################################
#export
export DiffObjective


text:
module LineRegression
import ..AbstractOperator.get_misfit
using ..AbstractOperator, ..CommonToAll
using PyPlot, LinearAlgebra, StatsBase

import ..Model, ..Options

export Line, makehist

mutable struct Line<:Operator1D
    d      :: Array{Float64, 1}
    useML  :: Bool
    σ      :: Union{Array{Float64, 1}, Float64}
    select :: Array{Bool, 1}
end

function Line(d::Array{Float64, 1} ;useML=false, σ=1.0)
    if isa(σ, Array)
        @assert length(d) == length(σ)
    else
        σ = σ*ones(length(d))
    end
    select = .!isnan.(d[:])
    Line(d, useML, σ, select)
end

function get_misfit(m::Model, opt::Options, line::Line)
    chi2by2 = 0.0
    if !opt.debug
        d, σ, select = line.d, line.σ, line.select
        r = (m.fstar[:][select] - d[select])./σ[select]
        chi2 = r'*r
        if line.useML
            N = sum(select)
            chi2by2 = 0.5*N*log(chi2)
        else
            chi2by2 = 0.5*chi2
        end
    end
    return chi2by2
end

function makehist(line::Line, opt::Options;
    nbins=100, burninfrac=0.5, temperaturenum=1)
    linidx = findall(.!isnan.(line.d))
    M = assembleTat1(opt, :fstar,
        temperaturenum=temperaturenum, burninfrac=burninfrac)
    resids = similar(M)
    for (im, m) in enumerate(M)
        resids[im] = m[sort(linidx)] - line.d[sort(linidx)]
    end
    resids = permutedims(hcat(resids...))
    mmin, mmax = extrema(resids)
    edges = LinRange(mmin, mmax, nbins+1)
    himage = zeros(Float64, nbins,length(linidx))
    for ilayer=1:length(linidx)
        himage[:,ilayer] = fit(Histogram, resids[:,ilayer], edges).weights
        himage[:,ilayer] = himage[:,ilayer]/sum(himage[:,ilayer])/(diff(edges)[1])
    end
    himage, edges
end

end

ext: jl

max_stars_repo_name: GeoscienceAustralia/HiQGA

max_issues_repo_name: GeoscienceAustralia/HiQGA


text:
#
#  Split - Apply - Combine operations
#

function groupsort_indexer(x::AbstractVector, ngroups::Int)
    ## translated from Wes McKinney's groupsort_indexer in pandas (file: src/groupby.pyx).

    ## count group sizes, location 0 for NA
    n = length(x)
    ## counts = x.pool
    counts = fill(0, ngroups + 1)
    for i = 1:n
        counts[x[i] + 1] += 1
    end

    ## mark the start of each contiguous group of like-indexed data
    where = fill(1, ngroups + 1)
    for i = 2:ngroups+1
        where[i] = where[i - 1] + counts[i - 1]
    end

    ## this is our indexer
    result = fill(0, n)
    for i = 1:n
        label = x[i] + 1
        result[where[label]] = i
        where[label] += 1
    end
    result, where, counts
end
groupsort_indexer(pv::PooledDataVector) = groupsort_indexer(pv.refs, length(pv.pool))

##############################################################################
##
## GroupedDataFrame...
##
##############################################################################

type GroupedDataFrame
    parent::AbstractDataFrame
    cols::Vector         # columns used for sorting
    idx::Vector{Int}     # indexing vector when sorted by the given columns
    starts::Vector{Int}  # starts of groups
    ends::Vector{Int}    # ends of groups
end

#
# Split
#
function groupby{T}(df::AbstractDataFrame, cols::Vector{T})
    ## a subset of Wes McKinney's algorithm here:
    ##     http://wesmckinney.com/blog/?p=489

    # use the pool trick to get a set of integer references for each unique item
    dv = PooledDataArray(df[cols[1]])
    # if there are NAs, add 1 to the refs to avoid underflows in x later
    dv_has_nas = (findfirst(dv.refs, 0) > 0 ? 1 : 0)
    x = copy(dv.refs) + dv_has_nas
    # also compute the number of groups, which is the product of the set lengths
    ngroups = length(dv.pool) + dv_has_nas
    # if there's more than 1 column, do roughly the same thing repeatedly
    for j = 2:length(cols)
        dv = PooledDataArray(df[cols[j]])
        dv_has_nas = (findfirst(dv.refs, 0) > 0 ? 1 : 0)
        for i = 1:nrow(df)
            x[i] += (dv.refs[i] + dv_has_nas- 1) * ngroups
        end
        ngroups = ngroups * (length(dv.pool) + dv_has_nas)
        # TODO if ngroups is really big, shrink it
    end
    (idx, starts) = groupsort_indexer(x, ngroups)
    # Remove zero-length groupings
    starts = _uniqueofsorted(starts)
    ends = [starts[2:end] - 1]
    GroupedDataFrame(df, cols, idx, starts[1:end-1], ends)
end
groupby(d::AbstractDataFrame, cols) = groupby(d, [cols])

# add a function curry
groupby{T}(cols::Vector{T}) = x -> groupby(x, cols)
groupby(cols) = x -> groupby(x, cols)

start(gd::GroupedDataFrame) = 1
next(gd::GroupedDataFrame, state::Int) =
    (sub(gd.parent, gd.idx[gd.starts[state]:gd.ends[state]]),
     state + 1)
done(gd::GroupedDataFrame, state::Int) = state > length(gd.starts)
length(gd::GroupedDataFrame) = length(gd.starts)
ref(gd::GroupedDataFrame, idx::Int) = sub(gd.parent, gd.idx[gd.starts[idx]:gd.ends[idx]])

function show(io::IO, gd::GroupedDataFrame)
    N = length(gd)
    println(io, "$(typeof(gd))  $N groups with keys: $(gd.cols)")
    println(io, "First Group:")
    show(io, gd[1])
    if N > 1
        println(io, "       :")
        println(io, "       :")
        println(io, "Last Group:")
        show(io, gd[N])
    end
end

##############################################################################
##
## GroupApplied...
##    the result of a split-apply operation
##    TODOs:
##      - better name?
##      - ref
##      - keys, vals
##      - length
##      - start, next, done -- should this return (k,v) or just v?
##      - make it a real associative type? Is there a need to look up key columns?
##
##############################################################################

type GroupApplied
    keys
    vals
end

#
# Apply / map
#

# map() sweeps along groups
function map(f::Function, gd::GroupedDataFrame)
    ## [d[1,gd.cols] => f(d) for d in gd]
    ## [f(g) for g in gd]
    keys = [d[1,gd.cols] for d in gd]
    vals = [f(d) for d in gd]
    GroupApplied(keys,vals)
end

with(x::GroupApplied, e::Expr) = GroupApplied(x.keys, map(with(e), x.vals))
map(f::Function, x::GroupApplied) = GroupApplied(x.keys, map(f, x.vals))

## function map(f::Function, gd::GroupedDataFrame)
##     # preallocate based on the results on the first one
##     x = f(gd[1])
##     res = Array(typeof(x), length(gd))
##     res[1] = x
##     for idx in 2:length(gd)
##         res[idx] = f(gd[idx])
##     end
##     res
## end

# with() sweeps along groups and applies with to each group
function with(gd::GroupedDataFrame, e::Expr)
    keys = [d[1,gd.cols] for d in gd]
    vals = {with(d, e) for d in gd}
    GroupApplied(keys,vals)
end

function combine(x)   # expecting (keys,vals) with keys to be DataFrames and values are what are to be combined
    keys = copy(x.keys)
    vals = map(DataFrame, x.vals)
    for i in 1:length(keys)
        keys[i] = rbind(fill(copy(keys[i]), nrow(vals[i])))
    end
    cbind(rbind(keys), rbind(vals))
end

# within() sweeps along groups and applies within to each group
function within!(gd::GroupedDataFrame, e::Expr)
    x = [within!(d[:,:], e) for d in gd]
    rbind(x...)
end

within!(x::SubDataFrame, e::Expr) = within!(x[:,:], e)

function within(gd::GroupedDataFrame, e::Expr)
    x = [within(d, e) for d in gd]
    rbind(x...)
end

within(x::SubDataFrame, e::Expr) = within(x[:,:], e)

# based_on() sweeps along groups and applies based_on to each group
function based_on(gd::GroupedDataFrame, ex::Expr)
    f = based_on_f(gd.parent, ex)
    x = {f(d) for d in gd}
    idx = fill([1:length(x)], convert(Vector{Int}, map(nrow, x)))
    keydf = gd.parent[gd.idx[gd.starts[idx]], gd.cols]
    resdf = rbind(x)
    cbind(keydf, resdf)
end

function based_on(gd::GroupedDataFrame, f::Function)
    x = {DataFrame(f(d)) for d in gd}
    idx = fill([1:length(x)], convert(Vector{Int}, map(nrow, x)))
    keydf = gd.parent[gd.idx[gd.starts[idx]], gd.cols]
    resdf = rbind(x)
    cbind(keydf, resdf)
end

# default pipelines:
map(f::Function, x::SubDataFrame) = f(x)
(|)(x::GroupedDataFrame, e::Expr) = based_on(x, e)
(|)(x::GroupApplied, e::Expr) = with(x, e)
## (|)(x::GroupedDataFrame, f::Function) = map(f, x)

# apply a function to each column in a DataFrame
colwise(f::Function, d::AbstractDataFrame) = [f(d[idx]) for idx in 1:ncol(d)]
colwise(f::Function, d::GroupedDataFrame) = map(colwise(f), d)
colwise(f::Function) = x -> colwise(f, x)
colwise(f) = x -> colwise(f, x)
# apply several functions to each column in a DataFrame
colwise(fns::Vector{Function}, d::AbstractDataFrame) = [f(d[idx]) for f in fns, idx in 1:ncol(d)][:]
colwise(fns::Vector{Function}, d::GroupedDataFrame) = map(colwise(fns), d)
colwise(fns::Vector{Function}, d::GroupedDataFrame, cn::Vector{String}) = map(colwise(fns), d)
colwise(fns::Vector{Function}) = x -> colwise(fns, x)

function colwise(d::AbstractDataFrame, s::Vector{Symbol}, cn::Vector)
    header = [s2 * "_" * string(s1) for s1 in s, s2 in cn][:]
    payload = colwise(map(eval, s), d)
    df = DataFrame()
    # TODO fix this to assign the longest column first or preallocate
    # based on the maximum length.
    for i in 1:length(header)
        df[header[i]] = payload[i]
    end
    df
end
## function colwise(d::AbstractDataFrame, s::Vector{Symbol}, cn::Vector)
##     header = [s2 * "_" * string(s1) for s1 in s, s2 in cn][:]
##     payload = colwise(map(eval, s), d)
##     DataFrame(payload, header)
## end
colwise(d::AbstractDataFrame, s::Symbol, x) = colwise(d, [s], x)
colwise(d::AbstractDataFrame, s::Vector{Symbol}, x::String) = colwise(d, s, [x])
colwise(d::AbstractDataFrame, s::Symbol) = colwise(d, [s], colnames(d))
colwise(d::AbstractDataFrame, s::Vector{Symbol}) = colwise(d, s, colnames(d))

# TODO make this faster by applying the header just once.
# BUG zero-rowed groupings cause problems here, because a sum of a zero-length
# DataVector is 0 (not 0.0).
colwise(d::GroupedDataFrame, s::Vector{Symbol}) = rbind(map(x -> colwise(without(x, d.cols),s), d)...)
function colwise(gd::GroupedDataFrame, s::Vector{Symbol})
    x = map(x -> colwise(without(x, gd.cols),s), gd)
    cbind(rbind(x.keys), rbind(x.vals))
end
colwise(d::GroupedDataFrame, s::Symbol, x) = colwise(d, [s], x)
colwise(d::GroupedDataFrame, s::Vector{Symbol}, x::String) = colwise(d, s, [x])
colwise(d::GroupedDataFrame, s::Symbol) = colwise(d, [s])
(|)(d::GroupedDataFrame, s::Vector{Symbol}) = colwise(d, s)
(|)(d::GroupedDataFrame, s::Symbol) = colwise(d, [s])
colnames(d::GroupedDataFrame) = colnames(d.parent)

# by() convenience function
by(d::AbstractDataFrame, cols, f::Function) = based_on(groupby(d, cols), f)
by(d::AbstractDataFrame, cols, e::Expr) = based_on(groupby(d, cols), e)
by(d::AbstractDataFrame, cols, s::Vector{Symbol}) = colwise(groupby(d, cols), s)
by(d::AbstractDataFrame, cols, s::Symbol) = colwise(groupby(d, cols), s)
function by(d, x::Union(Function,Expr)...)
    res = d
    for e in x
        if isa(e, Function)
            res = e(res)
        else
            res = with(res, e)
        end
    end
    res
end


text:
# Insert graph data into an adjacency table.
using JLD

# Iterate through files
(@isdefined Nfile) || (Nfile = 8)
for i = 1:Nfile
    inserttime = @elapsed begin

        # Create filename
        fname = joinpath(Base.source_dir(),"data", string(i))
        println("On file: "*string(i))

        # Load associative array.
        #E = loadassoc(fname*".E.jld")
        E = load(fname*".E.jld")["E"]

        # Insert associative array.
        put(Tedge,E)

        #Compute in and out degree.
        Edeg = putCol(sum(E,1)',"Degree,")

        # Accumulate in and out degrees.
        put(TedgeDeg,Edeg)

    end

    println("Time: "*string(inserttime)*", Edges/sec: "*string((2*nnz(E)+nnz(Edeg))./inserttime))
end

println("Table entries: "*string(nnz(Tedge)));


text:
# # Springpot
#md # [![](https://mybinder.org/badge_logo.svg)](@__BINDER_ROOT_URL__/notebooks/model_elements.ipynb)
#md # [![](https://img.shields.io/badge/show-nbviewer-579ACA.svg)](@__NBVIEWER_ROOT_URL__/notebooks/model_elements.ipynb)

using RHEOS
## include a helper function for plotting
include("assets/plothelper.jl");
#-

# By typing the name of the model, it is possible to visualise its graphical representation and its parameters.

Springpot

# #### Constitutive Equation
# ```math
# \sigma(t) = c_{\beta} \frac{d^\beta \epsilon(t)}{dt^\beta}
# ```

# ```math
# \text{for}\; \ 0 \leq \beta \leq 1
# ```

# #### Relaxation Modulus
# ```math
# G(t) = \frac{c_{\beta} }{\Gamma(1-\beta)} t^{-\beta}
# ```

# #### Creep Modulus
# ```math
# J(t) = \frac{1}{c_\beta \Gamma(1+\beta)}t^\beta
# ```

# #### Storage Modulus
# ```math
# G^{\prime}(\omega) = c_\beta \omega^\beta \cos(\frac{\pi}{2}\beta)
# ```

# #### Loss Modulus
# ```math
# G^{\prime\prime}(\omega) = c_\beta \omega^\beta \sin(\frac{\pi}{2}\beta)
# ```

# # Spring

# When β = 0 the springpot specialises to a spring.

Spring

# # Dashpot

# When β = 1 the springpot specialises to a dashpot.

Dashpot

# ## Qualitative Behaviours of the Moduli

models = Vector{RheoModel}()

## Spring
push!(models, RheoModel(Spring, k = 1.0))

## plot moduli for varying β
for beta in [0.2, 0.5, 0.8]

    push!(models, RheoModel(Springpot, cᵦ = 1.0, β = beta))

end

## Dashpot
push!(models, RheoModel(Dashpot, η = 1.0))

plotmodel(models, ymaxG = 2.0)


text:
using LinearAlgebra
using Random
using Rimu
using Rimu.DictVectors
using Rimu.StochasticStyles: IsStochastic2Pop
using StaticArrays
using Suppressor
using Test
using ThreadsX

function test_dvec_interface(type, keys, vals, cap)
    K = eltype(keys)
    V = eltype(vals)
    pairs = [k => v for (k, v) in zip(keys, vals)]

    @testset "$type{$K,$V}" begin
        @testset "constructors" begin
            dvec1 = type(pairs...; capacity=cap)
            dvec2 = type(Dict(pairs...))
            for (k, v) in pairs
                @test dvec1[k] == dvec2[k] == v
            end
            @test dvec1 == dvec2

            dvec3 = type(Dict{K,V}(); capacity=cap)
            dvec4 = type{K,V}()

            @test isempty(dvec4)
            for (k, _) in pairs
                @test dvec3[k] == dvec4[k] == zero(V)
            end

            dvec5 = type(dvec2)
            @test dvec5 == dvec2

            dvec6 = type(IdDict(pairs))
            for (k, v) in pairs
                @test dvec6[k] == v
            end
        end
        @testset "empty, similar" begin
            dvec1 = type(pairs...; capacity=cap)
            dvec2 = empty(empty(empty(empty(dvec1))))
            dvec3 = similar(similar(similar(similar(dvec1))))
            @test typeof(dvec1) == typeof(dvec2) == typeof(dvec3)
            @test isempty(dvec2)
            @test isempty(dvec3)
            @test keytype(dvec1) == keytype(dvec2) == keytype(dvec3)
        end
        @testset "setindex, delete" begin
            dvec = type(pairs...; capacity=cap)
            @test length(dvec) == length(pairs)
            zero!(dvec)
            @test length(dvec) == 0
            for (k, v) in shuffle(pairs)
                dvec[k] = v
            end
            for (k, v) in shuffle(pairs)
                @test dvec[k] == v
                delete!(dvec, k)
                @test iszero(dvec[k])
            end
            @test isempty(dvec)
            for (k, v) in shuffle(pairs)
                dvec[k] += v
            end
            for (k, v) in shuffle(pairs)
                dvec[k] -= v
            end
            @test isempty(dvec)
        end
        @testset "types and traits" begin
            dvec = type(pairs...; capacity=cap)
            @test dvec isa AbstractDVec{K,V}

            @test eltype(dvec) ≡ Pair{K,V}
            @test eltype(typeof(dvec)) ≡ Pair{K,V}

            @test keytype(dvec) ≡ K
            @test keytype(typeof(dvec)) ≡ K

            @test valtype(dvec) ≡ V
            @test valtype(typeof(dvec)) ≡ V

            @test isreal(dvec) == (V <: Real)
            @test ndims(dvec) == 1
        end
        @testset "norm" begin
            dvec = type(Dict(pairs))
            for p in (1, 2, Inf)
                @test norm(dvec, p) == norm(vals, p)
            end
            @test norm(dvec) == norm(dvec, 2)
            @test_throws ErrorException norm(dvec, 3)

            @test norm(empty(dvec)) == 0
            @test norm(empty(dvec), 1) == 0
            @test norm(empty(dvec), 2) == 0
            @test norm(empty(dvec), Inf) == 0
        end
        @testset "copy" begin
            dvec1 = type(Dict(pairs))
            dvec2 = type{K,V}()

            copy!(dvec2, dvec1)
            for (k, v) in pairs
                @test dvec2[k] == v
            end

            dvec3 = copy(dvec1)
            empty!(dvec1)
            for (k, v) in pairs
                @test dvec3[k] == v
            end
        end
        @testset "mul!, *, rmul!" begin
            dvec = type(Dict(pairs))
            res1 = type{K,V}()
            mul!(res1, dvec, one(V))
            @test res1 == dvec
            mul!(res1, dvec, zero(V))
            @test isempty(res1)
            mul!(res1, dvec, V(2))
            res2 = V(2) * dvec
            res3 = dvec * V(2)
            @test res1 == res2 == res3
            for (k, v) in pairs
                @test res1[k] == 2v
            end

            rmul!(dvec, V(3))
            for (k, v) in pairs
                @test dvec[k] == 3v
            end
        end
        @testset "ThreadsX" begin
            dvec = type(Dict(pairs))
            @test ThreadsX.sum(values(dvec)) ≈ sum(values(dvec))
            @test ThreadsX.sum(last, Base.pairs(dvec)) ≈ sum(last, Base.pairs(dvec))
        end
        @testset "add!" begin
            dvec1 = type(Dict(pairs))
            dvec2 = type(Dict(pairs[1:2:end]))
            add!(dvec1, dvec2)
            for (i, (k, v)) in enumerate(pairs)
                if isodd(i)
                    @test dvec1[k] == 2v
                else
                    @test dvec1[k] == v
                end
            end

            copy!(dvec2, dvec1)
            add!(dvec1, type{K,V}())
            @test dvec1 == dvec2
        end
        @testset "axpy!" begin
            dvec1 = type(Dict(pairs))
            dvec2 = type(Dict(pairs[1:2:end]))
            axpy!(V(2), dvec1, dvec2)
            for (i, (k, v)) in enumerate(pairs)
                if isodd(i)
                    @test dvec2[k] == 3v
                else
                    @test dvec2[k] == 2v
                end
            end
        end
        @testset "axpby!" begin
            dvec1 = type(Dict(pairs))
            dvec2 = type(Dict(pairs[1:2:end]))
            axpby!(V(2), dvec1, V(3), dvec2)
            for (i, (k, v)) in enumerate(pairs)
                if isodd(i)
                    @test dvec2[k] == 5v
                else
                    @test dvec2[k] == 2v
                end
            end
        end
        @testset "dot" begin
            dvec1 = type(Dict(pairs))
            dvec2 = type(Dict(pairs[1:2:end]))
            dvec3 = type(Dict(pairs[2:2:end]))

            @test dvec1 ⋅ dvec1 ≈ norm(dvec1)^2
            @test dvec1 ⋅ dvec2 ≈ norm(dvec2)^2
            @test dot(dvec1, (dvec2, dvec3)) ≈ norm(dvec1)^2
        end
        @testset "iteration" begin
            dvec = type(Dict(pairs))

            dvec_pairs = [kv for kv in Base.pairs(dvec)]
            @test issetequal(pairs, dvec_pairs)

            dvec_keys = [k for k in Base.keys(dvec)]
            @test issetequal(dvec_keys, keys)

            dvec_vals = [k for k in Base.values(dvec)]
            @test issetequal(dvec_vals, vals)
        end
        @testset "projection" begin
            dvec = type(Dict(pairs))
            @test UniformProjector() ⋅ dvec == sum(dvec)
            @test UniformProjector()[2] == 1
            if valtype(dvec) isa AbstractFloat
                @test NormProjector() ⋅ dvec == norm(dvec, 1)
            end
            @test Norm2Projector() ⋅ dvec == norm(dvec, 2)
            @test Norm1ProjectorPPop() ⋅ dvec ==
                norm(real.(values(dvec)), 1) + im*norm(imag.(values(dvec)), 1)
            @test DictVectors.PopsProjector()⋅dvec ==
                real(collect(values(dvec))) ⋅ imag(collect(values(dvec)))
        end
        @testset "show" begin
            h, _ = displaysize()
            @test length(split(sprint(show, type(Dict(pairs))), '\n')) < h
        end
    end

    @testset "StochasticStyle" begin
        @test StochasticStyle(type(:a => 1)) isa IsStochasticInteger{Int}
        @test StochasticStyle(type(:a => 1.5; capacity=5)) isa IsDeterministic
        @test StochasticStyle(type(:a => 1 + 2im; capacity=5)) isa IsStochastic2Pop
        @test StochasticStyle(type(:a => SA[1 1; 1 1]; capacity=5)) isa StyleUnknown
    end
end

@testset "DVec" begin
    @testset "interface tests" begin
        keys1 = shuffle(1:20)
        vals1 = shuffle(1:20)
        test_dvec_interface(DVec, keys1, vals1, 100)

        keys2 = ['x', 'y', 'z', 'w', 'v']
        vals2 = [1.0 + 2.0im, 3.0 - 4.0im, 0.0 - 5.0im, -2.0 + 0.0im, 12.0 + im]
        test_dvec_interface(DVec, keys2, vals2, 200)
    end

    @testset "Stochastic styles convert eltype" begin
        dvec1 = DVec(:a => 0f0)
        @test valtype(dvec1) === Float32
        @test StochasticStyle(dvec1) == IsDeterministic{Float32}()

        dvec2 = DVec(:a => 1, style=IsDynamicSemistochastic())
        @test dvec2[:a] isa Float64

        dvec3 = DVec(:a => 1.0, style=IsStochasticInteger())
        @test dvec3 isa DVec{Symbol,Int}

        dvec4 = DVec(:a => 1.0, style=IsStochastic2Pop())
        @test !isreal(dvec4)
    end
end

@testset "InitiatorDVec" begin
    @testset "interface tests" begin
        keys1 = shuffle(1:20)
        vals1 = shuffle(1:20)
        test_dvec_interface(InitiatorDVec, keys1, vals1, 100)

        keys2 = ['x', 'y', 'z', 'w', 'v']
        vals2 = [1.0 + 2.0im, 3.0 - 4.0im, 0.0 - 5.0im, -2.0 + 0.0im, 12.0 + im]
        test_dvec_interface(InitiatorDVec, keys2, vals2, 200)
    end

    @testset "Stochastic styles convert eltype" begin
        dvec1 = InitiatorDVec(:a => 0f0)
        @test valtype(dvec1) === Float32
        @test StochasticStyle(dvec1) == IsDeterministic{Float32}()

        dvec2 = InitiatorDVec(:a => 1, style=IsDynamicSemistochastic())
        @test dvec2[:a] isa Float64

        dvec3 = InitiatorDVec(:a => 1.0, style=IsStochasticInteger())
        @test dvec3 isa InitiatorDVec{Symbol,Int}

        dvec4 = InitiatorDVec(:a => 1.0, style=IsStochastic2Pop())
        @test !isreal(dvec4)
    end
end


text:
function estimationPlot(x, xLocs, bootArray; scaleKDE=2, xticks=false, kwargs...)
    kArray = kde.([b.boot for b in bootArray])
    lbs = [b.ci.low for b in bootArray]
    ubs = [b.ci.high for b in bootArray]
    lBArray = lbs .- 0.15 .* (ubs .- lbs)
    uBArray = ubs .+ 0.15 .* (ubs .- lbs)
    shapes = []

    scaleFactor = scaleKDE*maximum(vcat([k.density for k in kArray]...))
    xLocs = scaleFactor.*xLocs .- 0.5 * scaleFactor
    nBreaks = length(unique(x))

    for i in 1:length(kArray)
        subset = findall(x -> x >= lBArray[i] && x <= uBArray[i],
            kArray[i].x)
        subX = kArray[i].x[subset]
        subY = kArray[i].density[subset]
        kdeShape = Shape(vcat([0], subY, [0]),
            vcat(minimum(subX), subX, maximum(subX)))
        kdeShape.x .+= xLocs[i]
        push!(shapes, kdeShape)
    end

    plt = plot(shapes[1]; kwargs...)

    for i in 1:length(shapes)
        if i > 1
            plot!(shapes[i]; kwargs...)
        end

        if xticks != false
            plot!([xLocs[i],xLocs[i]], [lbs[i], ubs[i]],
                xticks=(collect(1:1:nBreaks).*scaleFactor .- 0.5*scaleFactor, xticks),
                color=:black, linewidth=2, dpi=300, legend=false,
                xlim=(0,nBreaks*scaleFactor))
        else
            plot!([xLocs[i],xLocs[i]], [lbs[i], ubs[i]], xticks=false,
                color=:black, linewidth=2, dpi=300, legend=false,
                xlim=(0,nBreaks*scaleFactor))
        end
        scatter!([xLocs[i]],
            [mean(bootArray[i].boot)], markersize=4, color=:white,
        markerstrokewidth=1, dpi=300)
    end
    hline!([0], color=:black, linewidth=1, linestyle=:dash)

    return plt
end


text:
include("AWSCorePrototype.jl")

# This is a little bit gross
using .AWSCorePrototype: @service
using Random
using Test
using UUIDs
using SymDict

@service S3
@service EC2
@service ECS
@service Robomaker
using .S3
using .EC2
using .ECS
using .Robomaker

macro no_error(ex)
    quote
        try
            $(esc(ex))
            true
        catch
            false
        end
    end
end

@test_skip @testset "Rest-XML" begin
    rng = MersenneTwister(1)
    bucket_name = "mattbr-" * string(uuid1(rng))

    @testset "Required Arguments" begin
        @test @no_error S3.CreateBucket(bucket_name)
        S3.DeleteBucket(bucket_name)
    end

    @testset "Optional Arguments" begin
        @test @no_error S3.CreateBucket(
            bucket_name;
            content="""
            <CreateBucketConfiguration>
                <LocationConstraint>us-east-2</LocationConstraint>
            </CreateBucketConfiguration>
            """
        )
        S3.DeleteBucket(bucket_name)
    end

    @testset "Header, URI, and QueryString Parameters" begin
        # DeleteObject

        S3.CreateBucket(bucket_name)
        S3.PutObject(bucket_name)
    end
end

@test_skip @testset "Query" begin
    EC2.CreateSecurityGroup(
        [
            "GroupDescription"=>"Test-Description",
            "GroupName"=>"Test-Name"
        ]
    )

    groups = EC2.DescribeSecurityGroups()
    println(groups)
end

@test_skip @testset "Rest-JSON" begin
    query = @SymDict(
        application = "arn:aws:robomaker:us-east-1:351396300852:robot-application/AWSRoboMakerHelloWorld-1581109006927_Ng9NYnJq/1581109093830"
    )

    robots = Robomaker.DescribeRobotApplication("poop", query)
    println(robots)
end

@testset "JSON" begin
    capacity_providers = ECS.ListServices(
        [
            "cluster"=>"test"
        ]
    )

    println(capacity_providers)
end

max_stars_repo_name: mattBrzezinski/Julia-AWS-Status

max_issues_repo_name: mattBrzezinski/Julia-AWS-Status

max_forks_repo_name: mattBrzezinski/Julia-AWS-Status


text:
# Utility functions for common algebraic operations.

"""
    rotateTensorToVectorZ(tensor, vector)

Rotate `tensor` with a rotation matrix that aligns the 3rd direction with `vector`, which is
equivalent to change the basis from (i,j,k) to (i′,j′,k′) where k′ ∥ vector.
Reference: [Tensor rotation](https://math.stackexchange.com/questions/2303869/tensor-rotation)
"""
function rotateTensorToVectorZ(tensor::AbstractMatrix{T}, v::AbstractVector{T}) where T
   k = SVector{3, T}(0.0, 0.0, 1.0)
   axis = v × k::SVector{3, T}
   if axis[1] == axis[2] == 0
      return tensor
   else
      normalize!(axis)
      angle = acos(v ⋅ k / hypot(v[1], v[2], v[3]))
      R = getRotationMatrix(axis, angle)
      return R * tensor * R'
   end
end

"""
    getRotationMatrix(axis::AbstractVector, angle) --> SMatrix{3,3}

Create a rotation matrix for rotating a 3D vector around a unit `axis` by an `angle` in
radians.
Reference: [Rotation matrix from axis and angle](https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle)

# Example

```julia
using LinearAlgebra
v = [-0.5, 1.0, 1.0]
v̂ = normalize(v)
angle = deg2rad(-74)
R = getRotationMatrix(v̂, angle)
```
"""
function getRotationMatrix(v::AbstractVector{<:AbstractFloat}, θ)
   sinθ, cosθ = sincos(eltype(v)(θ))
   tmp = 1 - cosθ
   m =  @SMatrix [
        cosθ+v[1]^2*tmp         v[1]*v[2]*tmp-v[3]*sinθ v[1]*v[3]*tmp+v[2]*sinθ;
        v[1]*v[2]*tmp+v[3]*sinθ cosθ+v[2]^2*tmp         v[2]*v[3]*tmp-v[1]*sinθ;
        v[1]*v[3]*tmp-v[2]*sinθ v[3]*v[2]*tmp+v[1]*sinθ cosθ+v[3]^2*tmp]
end

"""
    getRotationMatrix(e1::Matrix, e2::Matrix) --> SMatrix{3,3}

Obtain the rotation matrix from orthgonal base vectors `e1` to `e2`, such that a vector
``\\mathbf{u}_1`` in `e1` can be expressed as ``\\mathbf{u}_1 = M\\cdot \\mathbf{u}_2``,
where ``M`` is the rotation matrix and ``\\mathbf{u}_2`` is the same vector in `e2`.

# Example

```julia
e1 = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]
e2 = [0.0 1.0 0.0; 1.0 0.0 0.0; 0.0 0.0 1.0]
R = getRotationMatrix(e1, e2)
```
"""
function getRotationMatrix(e1::AbstractMatrix, e2::AbstractMatrix)
   @views begin
      r11 = e1[:,1] ⋅ e2[:,1]
      r12 = e1[:,1] ⋅ e2[:,2]
      r13 = e1[:,1] ⋅ e2[:,3]
      r21 = e1[:,2] ⋅ e2[:,1]
      r22 = e1[:,2] ⋅ e2[:,2]
      r23 = e1[:,2] ⋅ e2[:,3]
      r31 = e1[:,3] ⋅ e2[:,1]
      r32 = e1[:,3] ⋅ e2[:,2]
      r33 = e1[:,3] ⋅ e2[:,3]
   end
   R = @SMatrix [r11 r12 r13; r21 r22 r23; r31 r32 r33]
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

# ╔═╡ a22bf9fc-7b28-11eb-30c1-0fa6d84c74d1

begin
	#try
		using PlutoUI
		using Plots
		using Plots.PlotMeasures
		using LaTeXStrings
		using Markdown
		using Images
		#using LinearAlgebra
		#using SparseArrays
		#using SpecialFunctions
		#using StatsBase
		#using Random
		#using Distributions
		md"""
		### Packages

		All needed Packages available :) """
	#=catch
		using Pkg;
		Pkg.activate(mktempdir())
		Pkg.add("PlutoUI")
		Pkg.add("Plots")
		Pkg.add("LaTeXStrings")
		Pkg.add("Markdown")
		Pkg.add("Images")
		#Pkg.add("LinearAlgebra")
		#Pkg.add("SparseArrays")
		#Pkg.add("SpecialFunctions")
		#Pkg.add("StatsBase")
		#Pkg.add("Distributions")
		using PlutoUI, Plots, LaTeXStrings, Markdown, Images, Plots.PlotMeasures
		#using LinearAlgebra
		#using SparseArrays
		#using StatsBase
		#using Random
		md"""
		### Packages

		Some Package sources not added, this will take approx. 3 minutes"""
	end
	# TODO: make it more generally, so one understands how to compare rating
	# maybe make to diagrams next to each other to make them compareable
	=#
end

# ╔═╡ 9428fba4-67b3-4d2f-a09f-7dc5f28deadd
TableOfContents(aside=true)

# ╔═╡ 5210a326-7b34-11eb-0d14-67f67a882d68
md"""
# The starfish rating problem ⭐⭐⭐⭐⭐
## MaxEnt probabilities, given the true  mean
 Here we use Maximum entropy to determine the rating probabilities given the normalization constraint and the instrinsic mean $\mu = \langle R \rangle$ with $R$ $\in$ $\{1,2,3,4,5\}$.
"""

# ╔═╡ 852d6e36-7b31-11eb-0653-61bcf655249d
md"
choose intrinsic mean rating $\mu$  between 1 and 5:    $(@bind μ_r Slider(1.00:0.001:4.999, show_value=true,default=2.0))
"

# ╔═╡ 8240f678-7b35-11eb-1a68-bb2b66ce0d04
begin
	# images
	grey_starfish_url = "https://raw.githubusercontent.com/Captain-Bayes/images/main/starfish_grey_five.png"
	red_starfish_url = "https://raw.githubusercontent.com/Captain-Bayes/images/main/starfish_red_five.png"
	grey_starfish_local = download(grey_starfish_url)
	red_starfish_local = download(red_starfish_url)
	grey_starfish = load(grey_starfish_local)
	red_starfish = load(red_starfish_local)

	ir = Int64(round(μ_r))
	L_stars = ["⭐","⭐⭐","⭐⭐⭐","⭐⭐⭐⭐","⭐⭐⭐⭐⭐","★★★★★"]
md"""
	$(L_stars[ir])
	"""

	[red_starfish[:,1:Int(ceil(μ_r/5*size(red_starfish,2)))] grey_starfish[:,(Int(ceil(μ_r/5*size(red_starfish,2)))):end]]
end

# ╔═╡ 0649912d-5164-4709-ad64-ca79b5256bf3
md"""
## Probability for the true mean, given the sample mean  of $\mathcal{N}$ votes
Here we use Bayesian probability theorem to determine the probability
$P(\mu \mid \overline{\boldsymbol{R}},\mathcal{N})$ for the intrinsic mean $\mu$ given the average rating $\overline{\boldsymbol{R}}$  based on $\mathcal{N}$ votes.

"""

# ╔═╡ f1646630-8507-4967-beab-a61c2f26bd17
md"""
### Bayesian theory

Eager to see the theory ? 🤓🧐😋😃👏  _click here_ 👉$(@bind show_Bayes CheckBox())

"""

# ╔═╡ d22311d9-c2c5-4dbd-be38-a377c6b19c37
if show_Bayes
md"""
- we seek: $P(\mu \mid \mathcal{\boldsymbol{R}}, \mathcal{N})$, where $\mathcal{\boldsymbol{R}}$ is the sum of the $ \mathcal{N}$ votes

- Bayes' theorem gives: $P(\mu\mid \mathcal{\boldsymbol{R}}, \mathcal{N}) \propto P(\mathcal{\boldsymbol{R}}\mid \mu , \mathcal{N}) \; P(\mu)$

- We marginalize over the unknown ratings $\boldsymbol{R}_{\nu}$ of the $\mathcal{N}$ voters
$P(\mathcal{\boldsymbol{R}}\mid \mu , \mathcal{N})  = \sum_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}=1}^{5}
P(\mathcal{\boldsymbol{R}}\mid  \boldsymbol{R},\mu , \mathcal{N})\;  \prod_{\nu}  P(R = \boldsymbol{R}_{\nu}\mid \mu)$

- the terms $P(R_{i}\mid \mu)$ have been computed in the MaxEnt section

- the remaining probability for the total rating $\boldsymbol{\mathcal{R}}$ given the individual ratings is
$P(\boldsymbol{\mathcal{R}}\mid \boldsymbol{R})
=
\begin{cases}
	1 & \text{if }\sum_{\nu} \boldsymbol{R}_{\nu} = \boldsymbol{\mathcal{R}}\\
	0 & \text{otherwise}
\end{cases}$

- which simply leads to a restricted sum
$P(\mu\mid \mathcal{\boldsymbol{R}},\mathcal{N}) \propto
\sum^{\sum_{\nu}\boldsymbol{R}_\nu = \boldsymbol{\mathcal{R}}}_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}}\;
\prod_{\nu}\frac{e^{\lambda(\mu) \boldsymbol{R}_{\nu}}}{Z(\mu)}
\propto
\sum^{\sum_{\nu}\boldsymbol{R}_\nu = \boldsymbol{\mathcal{R}}}_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}}  \;
\; \frac{e^{\lambda(\mu) \sum_{\nu}\boldsymbol{R}_{\nu}}}{(Z(\mu))^{\mathcal{N}}}
\propto
\bigg[\sum^{\sum_{\nu}\boldsymbol{R}_\nu = \boldsymbol{\mathcal{R}}}_{\boldsymbol{R}_{1},\ldots \boldsymbol{R}_{\mathcal{N}}} 1\bigg] \;
\frac{e^{\lambda(\mu) \mathcal{\boldsymbol{R}}}}{(Z(\mu))^{\mathcal{N}}}$

- final result:
$P(\mu\mid \overline{\boldsymbol{R}},\mathcal{N})  =\frac{1}{Z}
\frac{e^{\lambda(\mu) \mathcal{\boldsymbol{R}}}}{(Z(\mu))^{\mathcal{N}}}\;P(\mu)$

"""
end

# ╔═╡ f6a34d0c-2591-45f9-baac-f58fd5eace8b
md"""
### Prior
"""

# ╔═╡ 74a7a904-f043-4a69-93ea-2483d9eb0826
begin

	image_claire = "https://raw.githubusercontent.com/Captain-Bayes/images/main/claire_100px.gif"
	tin_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Tin_pot.png"
	iron_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Iron_pot.png"
	brass_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Brass_pot.png"
	copper_pot = "https://raw.githubusercontent.com/Captain-Bayes/images/main/Copper_pot.png"

	md"""
	The pot ratings of Claire's pottery store
	 were the following:

	- Tin pot: ``\overline{\boldsymbol{R}} = 3.9,\, \mathcal{N} = 250``
	- Brass pot: ``\overline{\boldsymbol{R}} = 4.2,\, \mathcal{N} = 80``
	- Iron pot: ``\overline{\boldsymbol{R}} = 5,\, \mathcal{N} = 2``
	- Copper pot: ``\overline{\boldsymbol{R}} = 4.5,\, \mathcal{N} = 15``
	$(Resource(image_claire, :width=> 200))
	$(Resource(tin_pot, :width=> 80))
	$(Resource(brass_pot, :width=> 100))
	$(Resource(iron_pot, :width=> 130))
	$(Resource(copper_pot, :width=> 100))
	"""
end

# ╔═╡ 44ea4b68-20d0-4f67-95d6-4228c9174c2b
md"""
## Some nice large plots
"""

# ╔═╡ 8102cbf7-e2ad-4492-9756-278fb8d072e7
begin
	Q = [0.000001;0.01:0.01:1]
	ll = -Q.*log.(Q)

	plot(Q, ll,
	size = (600,400),
	xlabel = latexstring("Q_i"),
	ylabel = latexstring("S(Q_i)"),
	labelfontsize = 20,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,
	linewidth = 3,
	label = :none,
		title= "Entropy",
	titlefontsize = 20,
	#foreground_color_grid = :black,
	#foreground_color_xticks = :black,
	background_color = :transparent,
	#foreground_color_axis = :black,
	#foreground_color_text = :black,
	#foreground_color_border = :black,
	foreground_color = :black,
	fontfamily="Computer Modern"
	)

	#	savefig("C://Lehre//Bayes MOOC//Lesson 6//Images//entropy")

end

# ╔═╡ 9345ab4c-69f9-47b2-a1a4-388adeb4f74c
begin
	Rat = 1:5
	lam = -5:0.01:5

	normierung = sum(exp.(lam'.*Rat),dims=1)
	mean_value = sum(Rat.*exp.(lam'.*Rat)./normierung, dims = 1)

	plot(lam, mean_value',
	size = (600,400),
	xlabel = latexstring("\\lambda"),
	ylabel = latexstring("\\mu(\\lambda)"),
	labelfontsize = 20,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,
	linewidth = 3,
	label = :none,
	titlefontsize = 20,
		title = "Lagrange paramter and mean value",
	#foreground_color_grid = :black,
	#foreground_color_xticks = :black,
	background_color = :transparent,
	#foreground_color_axis = :black,
	#foreground_color_text = :black,
	#foreground_color_border = :black,
	foreground_color = :black,
	fontfamily="Computer Modern"
	)

	#	savefig("C://Lehre//Bayes MOOC//Lesson 6//Images//lagrange")

end

# ╔═╡ 033db041-4b66-4a4f-a063-1b7d310c232c
md"""
## Program code
"""

# ╔═╡ 248a131d-49c7-45cd-8e30-527386e317f5
begin
	L_r = [1:5;]

	function Newton(L_r,μ_r; max_iter = 10000, ε = 1.e-8)
		#=
			for given true mean μ_r compute
			Z(μ_r) und λ(μ_r) of Maxent solution for
			probability q_r = P(r| μ_r)   = exp(λ r)/Z
		=#

		λ = 0.0
		Z = 0.0
		q_r = zeros(size(L_r))
		for i_step = 1: max_iter
			𝜌_r = exp.(λ .* L_r)
			Z   = sum(𝜌_r)
			q_r = 𝜌_r ./ Z
			avg_r = sum(L_r .* q_r)
			var_r = sum(L_r.^2 .* q_r) - avg_r^2
			𝛷 = avg_r - μ_r
			𝛥𝜆 = 𝛷 / var_r
			λ  = λ - 𝛥𝜆
			if abs(𝛥𝜆) < ε
				break
			end
		end

		return Z,λ,q_r
	end
	md" ### Newton Raphson"
end

# ╔═╡ b033b45c-7b28-11eb-1216-5703dc0e7792
begin
	aux1,𝜆_ME,q_r = Newton(L_r,μ_r; max_iter = 10000, ε = 1.e-3)

	txt2 = latexstring("\\mathrm{MaxEnt\\, probability\\,  for\\, given \\, true\\, mean\\, \\mu }")
	col_pal = palette(:default) # color palette

	plot(L_r,q_r,
		line= (0.0 , 2.0 , :bar),
		bar_width = 0.05,
		title = txt2,
		ylim = (0.0, 1.1),
		xlabel = latexstring("R"),
		ylabel = latexstring("P\\,(R\\,|\\mu)"),
		label = false
	)
	plot!(L_r,q_r,size=[500,300],
		line = ( 1, 0., :path),
		marker = (5, 1., :o),
		markerstrokewidth = 1.,
    	color = col_pal[1],
		label = false
	)

end

# ╔═╡ a0e51c0c-7b2f-11eb-2c1c-a77cfaf645f7
md"
 **The corresponding Lagrange parameter is**: $\lambda$ = $(round(𝜆_ME,digits=4))
"

# ╔═╡ 3bcf9ac2-213d-44fe-b8b5-8b54695c3029
begin
	N_iter_max = 10000
	eps_lagr = 1.e-8
	μ_Delta = 0.01
	L_μ = [1.01:μ_Delta:4.99;]
	L_𝜆 = zeros(length(L_μ))
	L_Z = zeros(length(L_μ))

	for (i,μ_r) in enumerate(L_μ)
		Z,λ,aux2  = Newton(L_r,μ_r; max_iter = 10000, ε = 1.e-8)
		L_𝜆[i]   = λ
		L_Z[i]   = Z
	end

	md"""
	 ### determine auxiliary Maxent functions
	 $\lambda(\mu)$  and $Z(\mu)$
	"""
end

# ╔═╡ 4c48af3c-dac8-43d4-9a57-7fed5052300a
begin
	slider_α = @bind 	α 	Scrubbable(0:.1:5, default=2.0)
	slider_β = @bind 	β   Scrubbable(0:.1:5, default=3.0)
	md"### sliders "
end

# ╔═╡ cdf3d720-bc21-44f5-976e-87fb5d8ed64b
md"""
  We still need to choose the prior probability $P(\mu)$ that encode our prior knowledge/ expectation about the true rating-mean $\mu$

We seek a function of $\mu \in [1,5]$, that (depending on some paramerters) is flexble enough to cover all conceivable shapes a prior probability  distribution my have.

Such a function is given by an adjusted Beta distribution

$P(\mu) \propto (\mu-1)^{\alpha-1}  (5-\mu)^{\beta-1}$

which depends only on two parameters.

---------------
_Choose the paramters_ $\alpha$ and $\beta$ and try to match your prior expectations

🔊 **to change the values, click and pull the numbers**

α:    $slider_α
β:    $slider_β
"""

# ╔═╡ 53365c4a-b00a-4bdf-8314-9ab9dbd19db6
begin
	Prior = (L_μ .- 1).^(α-1)  .* (5 .- L_μ).^(β-1)
	Prior = Prior ./ (sum(Prior)*(L_μ[2]-L_μ[1]))

	plot1 = plot(L_μ,Prior,
	xlim = (1,5), ylim = (0, 1),
	label = false,
	xlabel = latexstring("\\mu"),
	ylabel = latexstring("P\\,(\\mu)"),
	title = "Prior probabilities"
	)
	plot!(size=(400,200))
end

# ╔═╡ 4b6c15b2-7ac8-42cf-8c6b-070ae19405bd
md"""
### Posterior
_now you can study how the posterior probability_ $P(\mu\;| \overline{\boldsymbol{R}}, \mathcal{N} )$
depends on the sample rating-mean $\overline{\boldsymbol{R}}$, the sample size (# of votes) $\mathcal{N}$
and your prior choice
(_remember_  $\boldsymbol{\mathcal{R}} = \mathcal{N}\overline{\boldsymbol{R}}$)

-------------

rating $\overline{\boldsymbol{R}}$:    $(@bind 	mean_r Scrubbable(1.0:0.05:5, default=4.5))

number of votes $\mathcal{N}$: $(@bind 	N Slider(1:250, show_value=true,default=80))

Parameters for prior probability (flat prior: ``\alpha = \beta = 1``):

 ``\alpha``:    $slider_α
 ``\beta``:    $slider_β
      (_to change the values, click and pull the numbers_)
"""

# ╔═╡ 1b9848f0-7a4a-4916-b7df-ffcd61c39415
begin
	# compute posterior
	R       = N * mean_r
	L_ln_P 	= R * L_𝜆 .- N * log.(L_Z) .- log.(Prior)
	L_ln_P  = L_ln_P .- maximum(L_ln_P)
	L_P     = exp.(L_ln_P)
	L_P     = L_P/(sum(L_P)*μ_Delta)
    md"### compute posterior "
end

# ╔═╡ 7cde88e1-a4c0-4541-aa8d-61845b479192
begin
    # plot posterior
	txt    = "Posterior probability "
	plot2  = plot(L_μ,L_P,
	label  = false,
	xlabel = latexstring("\\mu"),
	ylabel = latexstring("P\\, (\\mu |  \\textbf{R}, \\mathcal{N})"),
	title  = txt,
	ylim   = (0, 6)
	)
	plot(plot1,plot2,layout = (1, 2))
		plot!(size=[600,300])
end

# ╔═╡ 9096d5fe-ee6b-4842-ac4b-0fd8a421db32
begin
	mean_rating = sum(L_μ.*L_P)
	stdeviation = sqrt(sum((L_μ .-mean_rating).^2 .*L_P))
	string(round(mean_rating, digits=3))*"±"*string(round(stdeviation,digits=2))
	md"### mean rating"
end

# ╔═╡ eb0a9de2-48b4-4220-abfc-433ce87c879c
function sr(variable, dig = 2)
	# string and round - converts a variable into a string with the predifined precission - to be extended to scientific and other formats
	if dig == 0
		return string(round(Int, variable))
	else
		return string(round(variable, digits = dig))
	end
end

# ╔═╡ 43389709-7d95-4d06-a284-a532b3d23dee
begin

	#plotting for video
	title_mu_plots = latexstring("\\overline{\\boldsymbol{R}} = " * string(round(mean_r,digits=2)) * ",\\, \\mathcal{N} = "*string(round(Int,N)))

	plot(plot2,size=(600,400),
	xlabel = latexstring("\\mu_{\\textrm{copper}}"),
	labelfontsize = 20,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,
		linewidth = 3,
	#title = title_mu_plots,
	titlefontsize = 20,
	background_color = :transparent,
	fontfamily="Computer Modern",
		ylim = [0,2],
		label=latexstring("\\overline{\\mathbf{R}} = "* sr(mean_r,2) * ", \\mathcal{N} = "* sr(N,0) ),
		legendfontsize = 15,
		leg = :topleft,

	)
	#savefig("C://Lehre//Bayes MOOC//Lesson 6//Images//posterior_copper")

	# copper:

end

# ╔═╡ f1586893-5fe6-4202-801b-80fda48511bc
begin
bind_prior = @bind rr Slider(1.00:0.001:4.999, default=2.0)
	nothing
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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[[Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
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[[HypertextLiteral]]
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[[IOCapture]]
deps = ["Logging", "Random"]
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[[IfElse]]
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[[ImageAxes]]
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git-tree-sha1 = "c54b581a83008dc7f292e205f4c409ab5caa0f04"
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[[ImageBase]]
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git-tree-sha1 = "b51bb8cae22c66d0f6357e3bcb6363145ef20835"
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[[ImageContrastAdjustment]]
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git-tree-sha1 = "0d75cafa80cf22026cea21a8e6cf965295003edc"
uuid = "f332f351-ec65-5f6a-b3d1-319c6670881a"
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[[ImageCore]]
deps = ["AbstractFFTs", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Graphics", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "Reexport"]
git-tree-sha1 = "9a5c62f231e5bba35695a20988fc7cd6de7eeb5a"
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[[ImageDistances]]
deps = ["Distances", "ImageCore", "ImageMorphology", "LinearAlgebra", "Statistics"]
git-tree-sha1 = "7a20463713d239a19cbad3f6991e404aca876bda"
uuid = "51556ac3-7006-55f5-8cb3-34580c88182d"
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[[ImageFiltering]]
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git-tree-sha1 = "15bd05c1c0d5dbb32a9a3d7e0ad2d50dd6167189"
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[[ImageIO]]
deps = ["FileIO", "Netpbm", "OpenEXR", "PNGFiles", "TiffImages", "UUIDs"]
git-tree-sha1 = "a2951c93684551467265e0e32b577914f69532be"
uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
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[[ImageMagick]]
deps = ["FileIO", "ImageCore", "ImageMagick_jll", "InteractiveUtils", "Libdl", "Pkg", "Random"]
git-tree-sha1 = "5bc1cb62e0c5f1005868358db0692c994c3a13c6"
uuid = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
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[[ImageMagick_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "ea2b6fd947cdfc43c6b8c15cff982533ec1f72cd"
uuid = "c73af94c-d91f-53ed-93a7-00f77d67a9d7"
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[[ImageMetadata]]
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git-tree-sha1 = "36cbaebed194b292590cba2593da27b34763804a"
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[[ImageMorphology]]
deps = ["ImageCore", "LinearAlgebra", "Requires", "TiledIteration"]
git-tree-sha1 = "5581e18a74a5838bd919294a7138c2663d065238"
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[[ImageQualityIndexes]]
deps = ["ImageContrastAdjustment", "ImageCore", "ImageDistances", "ImageFiltering", "OffsetArrays", "Statistics"]
git-tree-sha1 = "1d2d73b14198d10f7f12bf7f8481fd4b3ff5cd61"
uuid = "2996bd0c-7a13-11e9-2da2-2f5ce47296a9"
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[[ImageSegmentation]]
deps = ["Clustering", "DataStructures", "Distances", "Graphs", "ImageCore", "ImageFiltering", "ImageMorphology", "LinearAlgebra", "MetaGraphs", "RegionTrees", "SimpleWeightedGraphs", "StaticArrays", "Statistics"]
git-tree-sha1 = "36832067ea220818d105d718527d6ed02385bf22"
uuid = "80713f31-8817-5129-9cf8-209ff8fb23e1"
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[[ImageShow]]
deps = ["Base64", "FileIO", "ImageBase", "ImageCore", "OffsetArrays", "StackViews"]
git-tree-sha1 = "d0ac64c9bee0aed6fdbb2bc0e5dfa9a3a78e3acc"
uuid = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
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[[ImageTransformations]]
deps = ["AxisAlgorithms", "ColorVectorSpace", "CoordinateTransformations", "ImageBase", "ImageCore", "Interpolations", "OffsetArrays", "Rotations", "StaticArrays"]
git-tree-sha1 = "b4b161abc8252d68b13c5cc4a5f2ba711b61fec5"
uuid = "02fcd773-0e25-5acc-982a-7f6622650795"
version = "0.9.3"

[[Images]]
deps = ["Base64", "FileIO", "Graphics", "ImageAxes", "ImageBase", "ImageContrastAdjustment", "ImageCore", "ImageDistances", "ImageFiltering", "ImageIO", "ImageMagick", "ImageMetadata", "ImageMorphology", "ImageQualityIndexes", "ImageSegmentation", "ImageShow", "ImageTransformations", "IndirectArrays", "IntegralArrays", "Random", "Reexport", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "TiledIteration"]
git-tree-sha1 = "35dc1cd115c57ad705c7db9f6ef5cc14412e8f00"
uuid = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
version = "0.25.0"

[[Imath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "87f7662e03a649cffa2e05bf19c303e168732d3e"
uuid = "905a6f67-0a94-5f89-b386-d35d92009cd1"
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[[IndirectArrays]]
git-tree-sha1 = "012e604e1c7458645cb8b436f8fba789a51b257f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
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[[Inflate]]
git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
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[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[IntegralArrays]]
deps = ["IntervalSets"]
git-tree-sha1 = "26c4df96fdf6127a92d53cb8ffb577104617adca"
uuid = "1d092043-8f09-5a30-832f-7509e371ab51"
version = "0.1.0"

[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2018.0.3+2"

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

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "61aa005707ea2cebf47c8d780da8dc9bc4e0c512"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.13.4"

[[IntervalSets]]
deps = ["Dates", "EllipsisNotation", "Statistics"]
git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.5.3"

[[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]]
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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"

[[JLD2]]
deps = ["DataStructures", "FileIO", "MacroTools", "Mmap", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
git-tree-sha1 = "46b7834ec8165c541b0b5d1c8ba63ec940723ffb"
uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
version = "0.4.15"

[[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]]
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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"

[[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"

[[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"

[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "5455aef09b40e5020e1520f551fa3135040d4ed0"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+2"

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

[[MappedArrays]]
git-tree-sha1 = "e8b359ef06ec72e8c030463fe02efe5527ee5142"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.1"

[[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"

[[MetaGraphs]]
deps = ["Graphs", "JLD2", "Random"]
git-tree-sha1 = "2af69ff3c024d13bde52b34a2a7d6887d4e7b438"
uuid = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
version = "0.7.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MosaicViews]]
deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"]
git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d"
uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.3"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

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

[[NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "16baacfdc8758bc374882566c9187e785e85c2f0"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.9"

[[Netpbm]]
deps = ["FileIO", "ImageCore"]
git-tree-sha1 = "18efc06f6ec36a8b801b23f076e3c6ac7c3bf153"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.0.2"

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

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "043017e0bdeff61cfbb7afeb558ab29536bbb5ed"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.8"

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

[[OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
version = "0.3.2"

[[OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "923319661e9a22712f24596ce81c54fc0366f304"
uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
version = "3.1.1+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]]
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[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "6d105d40e30b635cfed9d52ec29cf456e27d38f8"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
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[[PaddedViews]]
deps = ["OffsetArrays"]
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uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.10"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
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[[Parsers]]
deps = ["Dates"]
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uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
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[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
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uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
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[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
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[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
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[[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]]
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git-tree-sha1 = "1e0cb51e0ccef0afc01aab41dc51a3e7f781e8cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
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[[Preferences]]
deps = ["TOML"]
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[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
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[[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"
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[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

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

[[RangeArrays]]
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uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
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[[Ratios]]
deps = ["Requires"]
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uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
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[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
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[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
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[[Reexport]]
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[[RegionTrees]]
deps = ["IterTools", "LinearAlgebra", "StaticArrays"]
git-tree-sha1 = "4618ed0da7a251c7f92e869ae1a19c74a7d2a7f9"
uuid = "dee08c22-ab7f-5625-9660-a9af2021b33f"
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[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
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[[Rotations]]
deps = ["LinearAlgebra", "Random", "StaticArrays", "Statistics"]
git-tree-sha1 = "6a23472b6b097d66da87785b61137142ac104f94"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.4"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
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[[Serialization]]
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[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
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[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
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[[SimpleWeightedGraphs]]
deps = ["Graphs", "LinearAlgebra", "Markdown", "SparseArrays", "Test"]
git-tree-sha1 = "a6f404cc44d3d3b28c793ec0eb59af709d827e4e"
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[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
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[[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"

[[StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
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[[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"
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[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
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uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
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[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
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[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
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[[TOML]]
deps = ["Dates"]
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[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
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[[Tables]]
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[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

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

[[TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "c342ae2abf4902d65a0b0bf59b28506a6e17078a"
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[[TiledIteration]]
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[[TranscodingStreams]]
deps = ["Random", "Test"]
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[[URIs]]
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[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
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uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
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[[Unicode]]
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[[UnicodeFun]]
deps = ["REPL"]
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[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
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[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
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[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
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[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
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[[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"
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[[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"
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[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
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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"
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max_stars_repo_name: moserjo/bayes-imoox

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text:
#jl #! format: off
# # PTDF with [PowerSimulations.jl](https://github.com/NREL-SIIP/PowerSimulations.jl)

# **Originally Contributed by**: Sourabh Dalvi

# ## Introduction

# PowerSimulations.jl supports linear PTDF optimal power flow formulation. This example shows a
# single multi-period optimization of economic dispatch with a linearized DC-OPF representation of
# using PTDF power flow and how to extract duals values or locational marginal prices for energy.

# ## Dependencies
using SIIPExamples
using PowerSystems
using PowerSimulations
const PSI = PowerSimulations
using PowerSystemCaseBuilder
using DataFrames

# Since we'll be retrieving duals, we need a solver that returns duals values
# here we use HiGHS.
using HiGHS # mip solver
solver = optimizer_with_attributes(HiGHS.Optimizer, "mip_rel_gap" => 0.05)

# We can use the same RTS data and some of the initialization as in
# [OperationsProblem example](https://nbviewer.jupyter.org/github/NREL-SIIP/SIIPExamples.jl/blob/master/notebook/3_PowerSimulations_examples/01_operations_problems.ipynb)
sys = build_system(PSITestSystems, "modified_RTS_GMLC_DA_sys")

# Here, we want do define an economic dispatch (linear generation decisions) with
# linear DC-OPF using PTDF network representation.
# So, starting with the network, we can select from _almost_ any of the endpoints on this
# tree:
print_tree(PowerSimulations.PM.AbstractPowerModel)

# Calculate the PTDF matrix.
PTDF_matrix = PTDF(sys)

# For now, let's just choose a standard PTDF formulation.
template = template_unit_commitment(
    network = NetworkModel(
        StandardPTDFModel,
        PTDF = PTDF_matrix,
        duals = [CopperPlateBalanceConstraint],
        use_slacks = false,
    ),
    use_slacks = true,
)
for (k, v) in template.branches
    v.duals = [NetworkFlowConstraint]
end

# Now we can build a 4-hour economic dispatch / OPF problem with the RTS data.
# Here, we have to pass the keyword argument `constraint_duals` to OperationsProblem
# with the name of the constraint for which duals are required for them to be returned in the results.
problem = DecisionModel(template, sys, horizon = 24, optimizer = solver)
build!(problem, output_dir = mktempdir())

# And solve the problem and collect the results
solve!(problem)

# Here we collect the dual values from the results for the `:CopperPlateBalance` and `:network_flow`
# constraints. In the case of PTDF network formulation we need to compute the final LMP for each bus in the system by
# subtracting the duals (μ) of `:network_flow` constraints multiplied by the PTDF matrix
# from the  dual (λ) of `:CopperPlateBalance` constraint.
res = ProblemResults(problem)
duals = Dict([
    k => read_dual(res, k) for
    k in list_dual_keys(res) if PSI.get_entry_type(k) == NetworkFlowConstraint
])
λ = read_dual(res, "CopperPlateBalanceConstraint__System")[:, 2]
flow_duals = outerjoin(values(duals)..., on = :DateTime)
μ = Matrix(flow_duals[:, PTDF_matrix.axes[1]])

# Here we calculate LMP as λ + congestion component of the LMP which is a product of μ and the PTDF matrix.
LMP = flow_duals[:, [:DateTime]]
for bus in get_components(Bus, sys)
    LMP[:, get_name(bus)] = λ .+ μ * PTDF_matrix[:, get_number(bus)]
end

# Finally here we have the LMPs
LMP

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text:
export zoo_spn, zoo_spn_file,
    SpnFormat, SpnVtreeFormat

struct SpnFormat <: FileFormat end

##############################################
# Read SPN format (some dialect of the Libra AC format?)
##############################################

zoo_spn_file(name) =
    artifact"circuit_model_zoo" * zoo_version * "/spns/$name"

"""
    zoo_spn(name)

Loads SPN file with given name from model zoo. See https://github.com/UCLA-StarAI/Circuit-Model-Zoo.
"""
zoo_spn(name) =
    read(zoo_spn_file(name), ProbCircuit, SpnFormat())

const spn_grammar = raw"""
    start : domains (_NL node)+ _NL "EOF" _NL?

    domains : "(2" (_WS "2")* ")"

    node : "v" _WS INT _WS INT -> literal_node
         | "*" (_WS INT)+ -> prod_node
         | "+" (_WS INT _WS LOGPROB)+ -> sum_node

    %import common.INT
    %import common.SIGNED_NUMBER -> LOGPROB
    %import common.WS_INLINE -> _WS
    %import common.NEWLINE -> _NL
    """

const spn_parser = Lark(spn_grammar)

struct SpnParse <: JuiceTransformer
    nodes::Vector{PlainProbCircuit}
    SpnParse() = new(PlainProbCircuit[])
end

@rule start(t::SpnParse, x) =
    t.nodes[end]

@inline domains(t::SpnParse, x) = begin
    d = Base.parse.(Int,x)
    @assert d .== 2 "Only Boolean domains are currently supported, not $d in SPN format"
    d
end

@rule literal_node(t::SpnParse, x) = begin
    v = Base.parse(Var,x[1]) + 1
    @assert x[2] == "0" || x[2] == "1" "Boolean domains only."
    l = (x[2] == "1") ? Lit(v) : -Lit(v)
    push!(t.nodes, PlainProbLiteralNode(l))
end

@rule prod_node(t::SpnParse,x) = begin
    child_i = Base.parse.(Int,x) .+ 1
    children = t.nodes[child_i]
    push!(t.nodes, PlainMulNode(children))
end

@rule sum_node(t::SpnParse,x) = begin
    child_i = Base.parse.(Int,x[1:2:end]) .+ 1
    children = t.nodes[child_i]
    log_probs = Base.parse.(Float64,x[2:2:end])
    push!(t.nodes, PlainSumNode(children, log_probs))
end

function Base.parse(::Type{PlainProbCircuit}, str, ::SpnFormat)
    ast = Lerche.parse(spn_parser, str)
    Lerche.transform(SpnParse(), ast)
end

Base.read(io::IO, ::Type{PlainProbCircuit}, ::SpnFormat) =
    parse(PlainProbCircuit, read(io, String), SpnFormat())

##############################################
# Write SPNs
##############################################

function Base.write(io::IO, circuit::ProbCircuit, ::SpnFormat)

    labeling = label_nodes(circuit)
    map!(x -> x-1, values(labeling)) # nodes are 0-based indexed

    println(io, "(2" * " 2"^(num_variables(circuit)-1) * ")")
    foreach(circuit) do n
        if isliteralgate(n)
            state = ispositive(n) ? "1" : "0"
            println(io, "v $(variable(n)-1) $state")
        else
            print(io, is⋀gate(n) ? "*" : "+")
            if is⋀gate(n)
                for child in children(n)
                    print(io, " $(labeling[child])")
                end
            else
                @assert is⋁gate(n)
                for (child, logp) in zip(children(n), n.log_probs)
                    print(io, " $(labeling[child]) $logp")
                end
            end
            println(io)
        end
    end
    println(io, "EOF")
    nothing
end


text:
module PlmDCA
using GaussDCA
using Distributed
using Printf
using LinearAlgebra
using SharedArrays
using Statistics: mean

using NLopt

export PlmOut, plmdca, plmdcasym, mutualinfo

include("types.jl")
include("utils.jl")
include("plmdca_asym.jl")
#include("decimation_asym.jl")
include("plmdca_sym.jl")
include("decimation_sym.jl")
include("mi.jl")
end

max_stars_repo_name: YoshitakaMo/PlmDCA

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text:
using AreumAI
using Test

@testset "AreumAI.jl" begin
    # Write your tests here.
end

max_stars_repo_name: areumict/AreumAI

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