type bohr = Bohr.t
type angstrom = Angstrom.t

type t = bohr

type axis = X | Y | Z


let a_to_b a = Constants.a0_inv *. a
let b_to_a b = Constants.a0     *. b

let bohr_to_angstrom { Bohr.x ; y ; z } = 
  Angstrom.make 
  {
    Point.
    x = b_to_a x ;
    y = b_to_a y ;
    z = b_to_a z ;
  }

let angstrom_to_bohr { Angstrom.x ; y ; z } =  
  Bohr.make 
  {
    Point.
    x = a_to_b x ;
    y = a_to_b y ;
    z = a_to_b z ;
  }


let zero =
  Bohr.make { Point.x = 0. ; y = 0. ; z = 0. } 


(** Linear algebra *)
let ( |. )  s { Bohr.x ; y ; z } =
    Bohr.make {
      Point.
      x = s *. x ;
      y = s *. y ;
      z = s *. z ;
    }

let ( |+ ) { Bohr.x = x1 ; y = y1 ; z = z1 } { Bohr.x = x2 ; y = y2 ; z = z2 } =
  Bohr.make {
    Point.
    x = x1 +. x2 ;
    y = y1 +. y2 ;
    z = z1 +. z2 ;
  }


let ( |- ) { Bohr.x = x1 ; y = y1 ; z = z1 } { Bohr.x = x2 ; y = y2 ; z = z2 } =
  Bohr.make {
    Point.
    x = x1 -. x2 ;
    y = y1 -. y2 ;
    z = z1 -. z2 ;
  }


let neg a = -1. |. a


let dot { Bohr.x = x1 ; y = y1 ; z = z1 } { Bohr.x = x2 ; y = y2 ; z = z2 } =
  x1 *. x2 +. y1 *. y2 +. z1 *. z2


let norm u =
  sqrt ( dot u u )


let get axis { Bohr.x ; y ; z } = 
  match axis with
  | X -> x 
  | Y -> y 
  | Z -> z