using LinearAlgebra

function custom(x::Union{Nothing, Number})::Tuple{Number, Number, Number, Union{Nothing, Tuple{Number, Number}}}
    # custom 10-th degree polynomial
    # f = @(x) 91 * x^2 / 30 - 19 * x^3 / 6 - 54 * x^4 / 25 ...
    #   + 93 * x^5 / 23 - 23 * x^6 / 36 -  121 * x^7 / 93 ...
    #   + 72 * x^8 / 91 - 13 * x^9 / 74 + 9 * x^10 / 640
    #
    # f'(x)
    # (9*x^9)/64 - (117*x^8)/74 + (576*x^7)/91 - (847*x^6)/93
    # - (23*x^5)/6 + (465*x^4)/23 - (216*x^3)/25 - (19*x^2)/2 + (91*x)/15
    #
    # f''(x)
    # (81*x^8)/64 - (468*x^7)/37 + (576*x^6)/13 - (1694*x^5)/31
    # - (115*x^4)/6 + (1860*x^3)/23 - (648*x^2)/25 - 19*x + 91/15

    if x == nothing # informative call
        return (0, 0, 0, (-0.5, 3))
    else
        f(x) = 91 * x^2 / 30 - 19 * x^3 / 6 - 54 * x^4 / 25 +
               93 * x^5 / 23 - 23 * x^6 / 36 -  121 * x^7 / 93 +
               72 * x^8 / 91 - 13 * x^9 / 74 + 9 * x^10 / 640
        Df(x) = 91 * x / 15 - 19 * x^2 / 2 - 216 * x^3 / 25 + 465 * x^4 / 23 -
                23 * x^5 / 6 - 847 * x^6 / 93 + 576 * x^7 / 91 -
                117 * x^8 / 74 + 9 * x^9 / 64
        DDf(x) = 91 / 15 - 19 * x - 648 * x^2 / 25 + 1860 * x^3 / 23 -
                 115 * x^4 / 6 - 1694 * x^5 / 31 + 576 * x^6 / 13 -
                 468 * x^7 / 37 + 81 * x^8 / 64
        return (f(x), Df(x), DDf(x), nothing)
    end
end # custom



function genericquad(Q::Matrix, q::Vector, x::Nothing)::Tuple{Number, Nothing, Nothing, Tuple{Vector, Vector}}
    # generic quadratic function f(x) = x' * Q * x / 2 + q' * x
    # informative call

    if minimum(eigvals(Q)) > 1e-14
        xStar = Q \ -q
        v = 0.5 * dot(xStar', Q, xStar) + dot(q', xStar)
    else
        v = -Inf
    end
    return (v, nothing, nothing, ([-0.5, -0.5], [3, 3]))
end # genericquad

function genericquad(Q::Matrix, q::Vector, x::Vector)::Tuple{Number, Vector, Matrix, Nothing}
    # generic quadratic function f(x) = x' * Q * x / 2 + q' * x

    if !(size(x) == (2,))
        throw(ArgumentError("genericquad: x is of wrong size"))
    end
    v = 0.5 * dot(x', Q, x) + dot(q', x) # f(x)
    v2 = Q * x + q # \nabla f(x)
    v3 = Q # \nabla^2 f(x)

    return (v, v2, v3, nothing)
end # genericquad



function oneDTestFunctions()::Array{Any}
    return [custom, x -> genericquad([6 -2;-2 6], [10; 5], x)]
end