open Util
open Lacaml.D

type t = 
| Lowdin    of Mat.t
| Canonical of Mat.t
| Svd       of Mat.t


let make_lowdin ?(thresh=1.e-12) ~overlap =
  
  let u_vec, u_val = diagonalize_symm overlap in

  Vec.iter (fun x -> if x < thresh then
      invalid_arg "Orthonormalization.make_lowdin") u_val;

  let u_val = Vec.reci (Vec.sqrt u_val) in

  let u_vec' =
    Mat.init_cols (Mat.dim1 u_vec) (Mat.dim2 u_vec) (fun i j -> u_vec.{i,j} *. u_val.{j})
  in
  let result = 
    gemm u_vec' ~transb:`T u_vec
  in

  Lowdin result
     

let make = make_lowdin