Question

Continuing my F# learning today by attempting to recreate a simple bisection method using recursion, here I am using the MathNet library to inherit from the Beta distribution.

I receive errors on the function ‘search’ (binary search method) saying the value is not a function and cannot be applied.

//Beta class inheriting from MathNet Beta distribution
//Extends the class by implementing an InverseCDF function

type newBeta(alpha:double, beta:double) =
    inherit MathNet.Numerics.Distributions.Beta(alpha, beta)

member this.InverseCDF(p: float) =
    let rec search (min: float, max: float, acc: uint32) = 
        let x = (min + max) / 2.0
        let error = 0.001
        let maxiters : uint32 = 1000u
        let cdf = this.CumulativeDistribution(x)

        match cdf, (Math.Abs(cdf - p) < error || acc > maxiters) with   //while statement
        | _ , true                  -> cdf      //auto match cdf and if while statement evaluates true then break and return cdf result
        | p , _                     -> cdf      //if exactly matches p then break and return cdf result
        | p , false when p > cdf    -> search (min) (x) (acc + 1)   //if p > cdf then set max = x and increment then call func with new params
        | p , false when p < cdf    -> search (x) (max) (acc + 1)   //if p < cdf then set min = x and increment then call func with new params

    search (0.0) (1.0) (0)  //Call the bisection method with initial parameters

Can anyone help? Also obviously any input on how to make this more ‘functional’ would be cool. Havn’t been able to run this yet to test due to the error though. My first 2 match patterns look suspect given I’m trying to return the current value of cdf.

Answer 1

As @John said, your fundamental error is that you declared the function in the tuple form but used it in the curried form.

I notice that you pattern-matched cdf with p. The new value p will shadow parameter p of this.InverseCDF; therefore, that parameter isn’t available for comparison anymore. You actually compared cdf with cdf itself and two when guards are always false, which you do not want at all.

A few corrections:

1. Remove cdf from pattern matching since you only want to compare its value with p, not match with specific literals.
2. Move two when guards up. The last pattern shouldn’t be a when guard; the compiler will complain about incomplete pattern matching in that case.
3. Use suffix u for any arithmetic operation on acc (which is of type unint32).

The new search function:

let rec search (min: float) (max: float) (acc: uint32) = 
    let x = (min + max) / 2.0
    let error = 0.001
    let maxiters : uint32 = 1000u
    let cdf = this.CumulativeDistribution(x)

    match abs(cdf - p) < error || acc > maxiters with   // while statement
    | false when p > cdf    -> search min x (acc + 1u)   // if p > cdf then set max = x and increment then call func with new params
    | false when p < cdf    -> search x max (acc + 1u)   // if p < cdf then set min = x and increment then call func with new params 
    | _                     -> cdf      // if exactly matches p or returns true then break and return cdf result

search 0.0 1.0 0u  // call the bisection method with initial parameters