text:
using JuMP, EAGO

                     m = Model()

                     EAGO.register_eago_operators!(m)

                     @variable(m, -1 <= x[i=1:3] <= 1)

                     @variable(m, -87.82140256746152 <= q <= 82.66761573703552)

                     add_NL_constraint(m, :(swish(0.568996230261511 + -0.6444045388073083*swish(0.8247395355426832 + -0.2815589970674197*swish(-0.8472674884857732 + 0.12673262140718844*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.22924863555513264*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + -0.14343275408487788*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + 0.38193743952568937*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.7470214568022899*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.3907345794847368*swish(-0.8374168336432568 + -0.5200290789256532*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.22613086714596653*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.5211815007242757*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + -0.3005041955394576*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.6833233841804214*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.23961509129748304*swish(-0.8184816952777028 + 0.16489767969630487*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.5218375475900632*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.06864645713679662*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + -0.3485834116426605*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.9488444237137803*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.657728996110658*swish(0.09567841002846222 + 0.9766053202311835*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + -0.8095561798136077*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + -0.7033837991140013*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + 0.521625940127187*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.5267419118939665*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.8462058798889074*swish(-0.9217298157598419 + -0.1303173404119562*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.9725817523240283*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.7227834995135853*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + -0.020291466895306698*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.7019902602324835*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3])))) + 0.7561672748084076*swish(-0.36205575684029867 + -0.9193089390218732*swish(-0.8472674884857732 + 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-0.1303173404119562*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.9725817523240283*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.7227834995135853*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + -0.020291466895306698*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.7019902602324835*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3])))) + -0.2179697474351241*swish(0.022418445234321904 + -0.34474228728421163*swish(-0.8472674884857732 + 0.12673262140718844*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.22924863555513264*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + -0.14343275408487788*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + 0.38193743952568937*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.7470214568022899*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + -0.7874468802412049*swish(-0.8374168336432568 + -0.5200290789256532*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.22613086714596653*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.5211815007242757*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + 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0.03773489408284192*$(x[3]))) + -0.8484024638349421*swish(0.09567841002846222 + 0.9766053202311835*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + -0.8095561798136077*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + -0.7033837991140013*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + 0.521625940127187*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.5267419118939665*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.686993637902853*swish(-0.9217298157598419 + -0.1303173404119562*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.9725817523240283*swish(-0.5206002646111196 + 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0.6833233841804214*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.8405927936757611*swish(-0.8184816952777028 + 0.16489767969630487*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.5218375475900632*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.06864645713679662*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + -0.3485834116426605*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.9488444237137803*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + 0.5554428522774222*swish(0.09567841002846222 + 0.9766053202311835*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + -0.8095561798136077*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + -0.7033837991140013*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + 0.521625940127187*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.5267419118939665*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))) + -0.9816855534058186*swish(-0.9217298157598419 + -0.1303173404119562*swish(0.8408524421985439 + -0.03850956721592169*$(x[1]) + 0.8346333861274338*$(x[2]) + 0.3435557949935637*$(x[3])) + 0.9725817523240283*swish(-0.5206002646111196 + -0.6929418480784393*$(x[1]) + -0.02820767391072332*$(x[2]) + -0.04938482127984356*$(x[3])) + 0.7227834995135853*swish(0.8250363611878835 + 0.8304207310240672*$(x[1]) + -0.20133411435535464*$(x[2]) + -0.29584435518282115*$(x[3])) + -0.020291466895306698*swish(0.6278046914235738 + -0.6443229282211105*$(x[1]) + -0.7841344946232534*$(x[2]) + -0.16775025966863577*$(x[3])) + 0.7019902602324835*swish(0.7249142640471629 + 0.8062020364864311*$(x[1]) + 0.680231814161814*$(x[2]) + 0.03773489408284192*$(x[3]))))) - $q <= 0.0))

                     @objective(m, Min, q)

                     return m

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text:
using Random
using JuMP
using DecisionProgramming

include("min_expected_value.jl")

rng = MersenneTwister(22)

S = States([2, 3])
C = [ChanceNode(2, Node[1])]
D = [DecisionNode(1, Node[])]
V = [ValueNode(3, Node[1, 2])]
X = [Probabilities(rng, c, S) for c in C]
Y = [Consequences(rng, v, S) for v in V]

validate_influence_diagram(S, C, D, V)
sort!.((C, D, V, X, Y), by = x -> x.j)

U = DefaultPathUtility(V, Y)
U⁺ = PositivePathUtility(S, U)

k = 1
ϵ = 0.1
deviations = [
    s_I => Deviation(X[k].data[s_I..., :], ϵ) for s_I in paths(S[C[k].I_j])
]

# --- Maximize expected value ---

model = Model()
z = DecisionVariables(model, S, D)
P = DefaultPathProbability(C, X)
π_s = PathProbabilityVariables(model, z, S, P; hard_lower_bound=false)
EV = expected_value(model, π_s, U⁺)
@objective(model, Max, EV)

using SCIP
optimizer = optimizer_with_attributes(
    () -> SCIP.Optimizer()
)
set_optimizer(model, optimizer)
optimize!(model)

# --- Minimize regret ---

model = Model()
z = DecisionVariables(model, S, D)
μ = value(EV)
regret = μ - min_expected_value(deviations, model, S, C, X, U⁺, z, k)
@objective(model, Min, regret)

optimizer = optimizer_with_attributes(
    () -> SCIP.Optimizer()
)
set_optimizer(model, optimizer)
optimize!(model)

# --- Results ---

@info("Extracting results.")
Z = DecisionStrategy(z)

@info("Printing decision strategy:")
print_decision_strategy(S, Z)

ext: jl

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text:
#######################################
#
# Wrapper convert functions
#
#######################################

import Base.convert

function convert(::Type{Talairach}, l::BrainVision)

    x, y, z = conv_bv2tal(l.x, l.y, l.z)

    Talairach(x, y, z)
end

function convert(::Type{Talairach}, l::SPM)

    x, y, z = conv_spm_mni2tal(l.x, l.y, l.z)

    Talairach(x[1], y[1], z[1])
end

#######################################
#
# Convert brain vision to talairach
#
#######################################

function conv_bv2tal(
    Xbv::Union{AbstractArray,Number},
    Ybv::Union{AbstractArray,Number},
    Zbv::Union{AbstractArray,Number};
    offset::Number = 128,
)

    X = -Zbv .+ offset
    Y = -Xbv .+ offset
    Z = -Ybv .+ offset

    Logging.info("Converted $(length(Xbv)) coordinates to talairach space from BV")

    return X, Y, Z
end

#######################################
#
# Convert MNI to talairach
#
#######################################

function conv_spm_mni2tal(
    Xspm::Union{AbstractArray,Number},
    Yspm::Union{AbstractArray,Number},
    Zspm::Union{AbstractArray,Number},
)

    # Convert MNI ICMB152 coordinates as used in spm99 to talairach
    # http://onlinelibrary.wiley.com/doi/10.1002/hbm.20345/abstract
    # Port of http://www.brainmap.org/icbm2tal/icbm_spm2tal.m

    inpoints = [Xspm Yspm Zspm]'
    inpoints = [inpoints; ones(Float64, (1, size(inpoints)[2]))]

    # Transformation matrices, different for each software package
    icbm_spm = [
        0.9254 0.0024 -0.0118 -1.0207
        -0.0048 0.9316 -0.0871 -1.7667
        0.0152 0.0883 0.8924 4.0926
        0.0000 0.0000 0.0000 1.0000
    ]

    # apply the transformation matrix
    inpoints = icbm_spm * inpoints

    X = inpoints[1, :]'
    Y = inpoints[2, :]'
    Z = inpoints[3, :]'

    Logging.info("Converted $(length(X)) coordinates to talairach space from SPM MNI")

    return X, Y, Z
end

function conv_spm_mni2tal(elec::Electrode)

    x, y, z = conv_spm_mni2tal(elec.coordinate.x, elec.coordinate.y, elec.coordinate.z)

    Electrode(elec.label, Talairach(x[1], y[1], z[1]), elec.info)
end

# Euclidean distance for coordinates and dipoles

function Distances.euclidean(a::Union{Coordinate,Dipole}, b::Union{Coordinate,Dipole})
    euclidean([float(a.x), float(a.y), float(a.z)], [float(b.x), float(b.y), float(b.z)])
end

function Distances.euclidean(a::Union{Coordinate,Dipole}, b::V) where {V<:AbstractVector}
    euclidean([float(a.x), float(a.y), float(a.z)], b)
end

function Distances.euclidean(a::V, b::Union{Coordinate,Dipole}) where {V<:AbstractVector}
    euclidean(a, [float(b.x), float(b.y), float(b.z)])
end