open Util
open Constants

type shell_contracted = {
  expo      : float array;
  coef      : float array;
  center    : Coordinate.t;
  totAngMom : Angular_momentum.t;
  size      : int;
  norm_coef : float array;
  norm_coef_scale : float array;
  index    : int;
  powers   : Zkey.t array;
}

type t = shell_contracted 

(** Normalization coefficient of contracted function i, which depends on the
    exponent and the angular momentum. Two conventions can be chosen : a single
    normalisation factor for all functions of the class, or a coefficient which
    depends on the powers of x,y and z.
    Returns, for each contracted function, an array of functions taking as
    argument the [|x;y;z|] powers.
*)
let compute_norm_coef expo totAngMom =
  let atot =
    Angular_momentum.to_int totAngMom
  in
  let factor int_array = 
       let dfa = Array.map (fun j ->
           ( float_of_int (1 lsl j) *. fact j) /. fact (j+j) 
         ) int_array
       in
       sqrt (dfa.(0) *.dfa.(1) *. dfa.(2))
  in
  let expo = 
    if atot mod 2 = 0 then
      Array.map (fun alpha ->
        let alpha_2 = alpha +. alpha in
        (alpha_2 *. pi_inv)**(0.75) *. (pow (alpha_2 +. alpha_2) (atot/2))
      ) expo
    else
      Array.map (fun alpha ->
        let alpha_2 = alpha +. alpha in
        (alpha_2 *. pi_inv)**(0.75) *. sqrt (pow (alpha_2 +. alpha_2) atot)
      ) expo
  in
  Array.map (fun x -> let f a = x *. (factor a) in f) expo


let make ~index ~expo ~coef ~center ~totAngMom =
  assert (Array.length expo = Array.length coef);
  assert (Array.length expo > 0);
  let norm_coef_func =
    compute_norm_coef expo totAngMom
  in
  let powers =
    Angular_momentum.zkey_array (Angular_momentum.Singlet totAngMom) 
  in
  let norm_coef =
    Array.map (fun f -> f [| Angular_momentum.to_int totAngMom ; 0 ; 0 |])  norm_coef_func
  in
  let norm_coef_scale = 
    Array.map (fun a ->
      (norm_coef_func.(0) (Zkey.to_int_array ~kind:Zkey.Kind_3 a)) /. norm_coef.(0)
    ) powers
  in
  { index ; expo ; coef ; center ; totAngMom ; size=Array.length expo ; norm_coef ;
    norm_coef_scale ; powers }


let with_index a i = { a with index = i }