sidef-scripts/Math/arithmetic-geometric-harmonic_mean.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 17 March 2018
# https://github.com/trizen

# Arithmetic-geometric-harmonic mean (AGHM) for a list of three values.

# Extension of the arithmetic-geometric mean (AGM).

func A(*a) { a.sum / a.len }
func G(*a) { a.prod.root(a.len) }
func H(*a) { a.len / a.map{.inv}.sum }

func AGHM(a, g, h, p=100) {
    loop {
        var a1 = A(a, g, h)
        var g1 = G(a, g, h)
        var h1 = H(a, g, h)

        if (
            (a1.round(-p) == a.round(-p)) &&
            (g1.round(-p) == g.round(-p)) &&
            (h1.round(-p) == h.round(-p))
        ) {
            return a
        }

        (a, g, h) = (a1, g1, h1)
    }
}

say AGHM(1, 2, 3)                     #=> 1.81174228573045668252604274570860756877576751416
say AGHM(1, 1/2, 1/3)                 #=> 0.551954882256789004514874128479233200903459376603
say AGHM(5, 1/sqrt(2), 1/sqrt(3))     #=> 1.33688849807307128479412972909072330610099261518