// MeanDist computes the mean (μ) and the standard deviation (σ)
// of the spherical distances between point q and points p₀,p₁,...
// on the unit sphere S². This function panics if len(p) ≤ 1.
func MeanDist(q Geo, p []Geo) (μ, σ float64) {
n := len(p)
if n < 2 {
panic("MeanDist: len(p) ≤ 1")
}
var sum acc.Accum
var sum2 acc.Accum2
for _, t := range p {
dist := q.Dist(t)
sum.Add(dist)
sum2.Add2(dist)
}
μ = sum.Value() / float64(n)
σ = (sum2.Value() - float64(n)*μ*μ) / float64(n-1)
σ = math.Sqrt(plus(σ))
return
}
// MeanGeo computes the mean direction (m) and the mean resultant length (r)
// of points p₀,p₁,... on the unit sphere S². This function panics if len(p) = 0.
func MeanGeo(p []Geo) (m Geo, r float64) {
n := len(p)
if n == 0 {
panic("MeanGeo: len(p) = 0")
}
var accx, accy, accz acc.Accum
for _, t := range p {
c := t.c()
accx.Add(c[0])
accy.Add(c[1])
accz.Add(c[2])
}
u := vec{accx.Value(), accy.Value(), accz.Value()}
m = Geo{u.hat()}
r = u.div(float64(n)).abs()
if r > 1 {
r = 1
}
return
}