Line fitting
The following function uses linear least
squares to
determine constants a, b for a function f(x)=b*x+a given a
collection of observations.
let line_fit [n] (x: [n]f64) (y: [n]f64) =
let n = f64.i64 n
let xa = f64.sum x / n
let ya = f64.sum y / n
let Stt = f64.sum (map (**2) (map (\x' -> x' - xa) x))
let b = f64.sum (map2 (*) (map (\x' -> x' - xa) x) y) / Stt
let a = ya - xa*b
let chi2 = f64.sum(map2 (\x' y' -> (y'-a-b*x')**2) x y)
let siga = f64.sqrt((1/n + xa**2/Stt)*chi2/n)
let sigb = f64.sqrt((1/Stt)*(chi2/n))
in (a, b, siga, sigb)> line_fit [0.0, 1.0, 2.0, 3.0, 4.0] [2.75, 5.0, 7.0, 9.0, 11.0](2.8500000000000005f64, 2.05f64, 5.477225575051671e-2f64, 2.2360679774997935e-2f64)