(** Contains the conventions relative to the program.

  The phase convention is given by:
  {% $\sum_i c_i > 0$ %} or {% $\min_i c_i \ge  0$ %}

*)

open Lacaml.D

let in_phase vec =
  let s = Vec.sum vec in
  if s = 0. then 
    let rec first_non_zero k =
      if k > Vec.dim vec then
        k-1
      else if vec.{k} = 0. then
        first_non_zero (k+1)
      else k
    in
    let k = first_non_zero 1 in
    vec.{k} >= 0.
  else
    s > 0.


let rephase mat  =
  Mat.to_col_vecs mat
  |> Array.map (fun v -> if in_phase v then v else Vec.neg v)
  |> Mat.of_col_vecs