ternary-search.fsx

/// Assuming f is a continuous function with a single minimum and no maximums in (lower,upper), find the minimum point.
let rec minimise f lower upper =
    let lmid = (2.0*lower+upper)/3.0
    let umid = (lower+2.0*upper)/3.0
    if lmid = lower && umid = upper then
        Seq.minBy f [lower; upper]
    else if f lmid < f umid then      
        minimise f lower umid
    else
        minimise f lmid upper

let solution = minimise Math.Cos 0.0 6.0
printf "solution: %g" solution
printf "absolute error: %g" (solution - Math.PI)

/// Binary search to find root.
let rec root f lower upper =
    let mid = (lower+upper)/2.0
    if lower = mid || mid = upper then
        Seq.minBy (f >> abs) [lower; mid; upper]
    else if f lower * f mid <= 0.0 then
        root f lower mid
    else
        root f mid upper

let solution2 = root Math.Sin 3.0 4.0
printf "solution: %g" solution2
printf "absolute error: %g" (solution2 - Math.PI)