QCaml/Basis/ERI.ml

(** Electron-electron repulsion integrals *)

open Util
open Constants

type t = FourIdxStorage.t


module Am  = AngularMomentum
module As  = AtomicShell
module Asp = AtomicShellPair
module Bs  = Basis
module Cs  = ContractedShell
module Csp = ContractedShellPair
module Cspc = ContractedShellPairCouple
module Fis = FourIdxStorage


let get_chem = Fis.get_chem
let get_phys = Fis.get_phys

let set_chem = Fis.set_chem
let set_phys = Fis.set_phys

let to_file = Fis.to_file

let cutoff = integrals_cutoff


(** (00|00)^m : Fundamental electron repulsion integral
    $ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $

    maxm        : Maximum total angular momentum
    expo_pq_inv : $1./p + 1./q$ where $p$ and $q$ are the exponents of
                $\phi_p$ and $\phi_q$
    norm_pq_sq  : square of the distance between the centers of $\phi_p$
                and $\phi_q$
*)

let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
  let exp_pq = 1. /. expo_pq_inv in
  let t = norm_pq_sq *. exp_pq in
  let f = two_over_sq_pi *. (sqrt exp_pq) in
  let result = boys_function ~maxm t in
  let rec aux accu k = function
    | 0 -> result.(k) <- result.(k) *. accu
    | l -> 
      begin
        result.(k) <- result.(k) *. accu;
        let new_accu = -. accu *. exp_pq in
        aux new_accu (k+1) (l-1)
      end
  in
  aux f 0 maxm;
  result





let class_of_contracted_shell_pair_couple shell_pair_couple = 
  let shell_p = Cspc.shell_pair_p shell_pair_couple
  and shell_q = Cspc.shell_pair_q shell_pair_couple
  in
  if Array.length (Csp.shell_pairs shell_p) + (Array.length (Csp.shell_pairs shell_q))  < 4 then 
    TwoElectronRR.contracted_class_shell_pair_couple ~zero_m shell_pair_couple
  else
    TwoElectronRRVectorized.contracted_class_shell_pairs ~zero_m shell_p shell_q





let filter_contracted_shell_pairs ?(cutoff=integrals_cutoff) shell_pairs = 
  List.map (fun pair -> 
        match Cspc.make ~cutoff pair pair with
        | Some cspc -> 
          let cls = class_of_contracted_shell_pair_couple cspc in
          (pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
          (* TODO \sum_k |coef_k * integral_k| *)
        | None -> (pair, -1.) 
    ) shell_pairs
  |> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff)
  |> List.map fst


(*  TODO
let filter_contracted_shell_pair_couples ?(cutoff=integrals_cutoff) shell_pair_couples = 
  List.map (fun pair -> 
      let cls = 
        class_of_contracted_shell_pairs pair pair
      in
      (pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. )
    ) shell_pairs
  |> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff)
  |> List.map fst

*)


let store_class ?(cutoff=integrals_cutoff) data contracted_shell_pair_couple cls = 
  let to_powers x = 
      let open Zkey in
      match to_powers x with
      | Three x -> x
      | _ -> assert false
  in

  let shell_p = Cspc.shell_pair_p contracted_shell_pair_couple
  and shell_q = Cspc.shell_pair_q contracted_shell_pair_couple
  in

  Array.iteri (fun i_c powers_i ->
      let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in
      let xi = to_powers powers_i in
      Array.iteri (fun j_c powers_j ->
          let j_c = Cs.index (Csp.shell_b shell_p) + j_c + 1 in
          let xj = to_powers powers_j in
          Array.iteri (fun k_c powers_k ->
              let k_c = Cs.index (Csp.shell_a shell_q) + k_c + 1 in 
              let xk = to_powers powers_k in
              Array.iteri (fun l_c powers_l ->
                  let l_c = Cs.index (Csp.shell_b shell_q) + l_c + 1 in
                  let xl = to_powers powers_l in
                  let key = Zkey.of_powers_twelve  xi xj xk xl in
                  let value = Zmap.find cls key in
                  set_chem data i_c j_c k_c l_c value;
                ) (Cs.zkey_array (Csp.shell_b shell_q))
            ) (Cs.zkey_array (Csp.shell_a shell_q))
        ) (Cs.zkey_array (Csp.shell_b shell_p))
    ) (Cs.zkey_array (Csp.shell_a shell_p))






let of_basis basis = 

  let n = Bs.size basis
  and shell = Bs.contracted_shells basis
  in

  let eri_array = 
    Fis.create ~size:n `Dense
(*
    Fis.create ~size:n `Sparse
*)
  in

  let t0 = Unix.gettimeofday () in

  let shell_pairs =
    Csp.of_contracted_shell_array shell
    |> filter_contracted_shell_pairs ~cutoff
  in

  Printf.printf "%d significant shell pairs computed in %f seconds\n"
    (List.length shell_pairs) (Unix.gettimeofday () -. t0);


  let t0 = Unix.gettimeofday () in
  let ishell = ref 0 in

  List.iter (fun shell_p ->
      let () = 
        if (Cs.index (Csp.shell_a shell_p) > !ishell) then
          (ishell := Cs.index (Csp.shell_a shell_p) ; print_int !ishell ; print_newline ())
      in

      let sp =
        Csp.shell_pairs shell_p
      in

      try
        List.iter (fun shell_q ->
            let () = 
              if  Cs.index (Csp.shell_a shell_q) >
                  Cs.index (Csp.shell_a shell_p) then
                raise Exit
            in
            let sq = Csp.shell_pairs shell_q in
            let cspc = 
              if Array.length sp < Array.length sq then
                Cspc.make ~cutoff shell_p shell_q
              else
                Cspc.make ~cutoff shell_q shell_p
            in

            match cspc with
            | Some cspc -> let cls = class_of_contracted_shell_pair_couple cspc in
                           store_class ~cutoff eri_array cspc cls
            | None -> ()
          ) shell_pairs
      with Exit -> ()
    ) shell_pairs ;
  Printf.printf "Computed ERIs in %f seconds\n%!" (Unix.gettimeofday () -. t0);
  eri_array