Add line fitting example.

examples.md

@@ -78,6 +78,7 @@ for plotting or rendering graphics.
 -   [Variance](examples/variance.html)
 -   [Matching parentheses](examples/parens.html)
 -   [Evaluating polynomials](examples/polynomials.html)
+-   [Line fitting](examples/line-fitting.html)
 
 # Automatic differentiation
 

examples/line-fitting.fut

@@ -0,0 +1,20 @@
+-- # Line fitting
+--
+-- The following function uses [linear least
+-- squares](https://en.wikipedia.org/wiki/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]