Computing Real-Valued Vector l2-norm in OCaml Example

Recall that the $l^2$-norm of a real-valued vector $\mathbf{x}$ is

$$\left|\mathbf{x}\right|=\sqrt{\sum _{k=1}^n{x}_k^2}.$$

where $x_k$ is the $k$-th component of $\mathbf{x}$. Implement an OCaml function l2_norm : float list -> float such that l2_norm x is the $l^2$-norm of x.

Solution

To solve this problem, we need a way to compute the iterated sum ${\sum }_{k=1}^n{x}_k^2$ and then pass the result to the standard library's Float.sqrt : float -> float function. We can use the higher-order function List.fold_left : ('b -> 'a -> 'b) -> 'b -> 'a list -> 'b to traverse the list from left to right while accumulating the sum of squares.

let l2_norm : float list -> float =
  fun x ->
    Float.sqrt (List.fold_left (fun acc comp -> acc +. comp *. comp) 0. x)