mirror of https://gitlab.com/scemama/QCaml.git
730 lines
24 KiB
OCaml
730 lines
24 KiB
OCaml
open Util
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open Lacaml.D
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open Bigarray
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open Powers
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open Coordinate
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let cutoff = Constants.cutoff
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let cutoff2 = cutoff *. cutoff
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exception NullQuartet
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exception Found
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let at_least_one_valid arr =
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try
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Array.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false
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with Found -> true
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(** Horizontal and Vertical Recurrence Relations (HVRR) *)
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let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
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zero_m_array
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(expo_b, expo_d)
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(expo_inv_p, expo_inv_q)
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(center_ab, center_cd, center_pq)
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map_1d map_2d np nq
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=
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let get_xyz angMom =
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match angMom with
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| { y=0 ; z=0 ; _ } -> X
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| { z=0 ; _ } -> Y
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| _ -> Z
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in
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(** Vertical recurrence relations *)
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let rec vrr0_v m angMom_a =
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match angMom_a.tot with
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| 0 -> Some zero_m_array.(m)
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| _ ->
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let key = Zkey.of_powers (Zkey.Three angMom_a)
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in
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try Zmap.find map_1d.(m) key with
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| Not_found ->
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let result =
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let xyz = get_xyz angMom_a in
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let am = Powers.decr xyz angMom_a in
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let amxyz = Powers.get xyz am in
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if amxyz >= 0 then
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begin
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let cab = Coordinate.get xyz center_ab in
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let v1_top, p1_top =
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if abs_float cab < cutoff then
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None,
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vrr0_v (m+1) am
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else
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vrr0_v m am, vrr0_v (m+1) am
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in
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let v1_top2, p1_top2 =
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if amxyz < 1 then None, None else
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let amm = Powers.decr xyz am in
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vrr0_v m amm, vrr0_v (m+1) amm
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in
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let result = Array.make_matrix np nq 0. in
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let p0 =
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match p1_top with
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| Some p1_top -> p1_top
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| _ -> assert false
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in
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begin
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match v1_top with
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| None -> ()
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| Some v0 ->
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Array.iteri (fun l result_l ->
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let f0 = -. expo_b.(l) *. expo_inv_p.(l) *. cab
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and v0_l = v0.(l)
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in
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Array.iteri (fun k v0_lk ->
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result_l.(k) <- v0_lk *. f0) v0_l ) result
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end;
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let amxyz = Powers.get xyz am in
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if amxyz < 1 then
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Array.iteri (fun l result_l ->
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let expo_inv_p_l = expo_inv_p.(l)
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and center_pq_xyz_l = (center_pq xyz).(l)
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and result_l = result.(l)
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and p0_l = p0.(l)
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in
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Array.iteri (fun k p0_lk ->
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result_l.(k) <- result_l.(k)
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+. expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk
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) p0_l ) result
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else
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begin
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let v1 =
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match v1_top2 with
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| Some v1_top2 -> v1_top2
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| None -> assert false
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in
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let v2 =
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match p1_top2 with
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| Some p1_top2 -> p1_top2
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| None -> assert false
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in
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Array.iteri (fun l result_l ->
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let f = float_of_int amxyz *. expo_inv_p.(l) *. 0.5
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and expo_inv_p_l = expo_inv_p.(l)
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and center_pq_xyz_l = (center_pq xyz).(l)
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and v1_l = v1.(l)
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and v2_l = v2.(l)
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and result_l = result.(l)
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in
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Array.iteri (fun k p0_lk ->
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result_l.(k) <- result_l.(k) +.
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expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk +.
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f *. (v1_l.(k) +. v2_l.(k) *. expo_inv_p_l)
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) p0.(l)
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) result
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end;
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Some result
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end
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else
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None
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in
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Zmap.add map_1d.(m) key result;
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result
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and vrr_v m angMom_a angMom_c =
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match (angMom_a.tot, angMom_c.tot) with
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| (i,0) -> vrr0_v m angMom_a
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| (_,_) ->
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let key = Zkey.of_powers (Zkey.Six (angMom_a, angMom_c))
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in
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try Zmap.find map_2d.(m) key with
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| Not_found ->
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let result =
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begin
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let xyz = get_xyz angMom_c in
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let cm = Powers.decr xyz angMom_c in
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let axyz = Powers.get xyz angMom_a in
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let do_compute = ref false in
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let v1 =
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let f = -. (Coordinate.get xyz center_cd) in
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let f1 =
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Array.init nq (fun k ->
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let x = expo_d.(k) *. expo_inv_q.(k) *. f in
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if ( (not !do_compute) && (abs_float x > cutoff) ) then
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do_compute := true;
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x)
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in
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if (!do_compute) then
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match vrr_v m angMom_a cm with
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| None -> None
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| Some v1 ->
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begin
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Some (Array.init np (fun l ->
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let v1_l = v1.(l) in
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Array.mapi (fun k f1k -> v1_l.(k) *. f1k) f1
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) )
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end
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else None
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in
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let v2 =
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let f2 =
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Array.init np (fun l ->
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let cpq_l = (center_pq xyz).(l) in
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Array.init nq (fun k ->
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let x = expo_inv_q.(k) *. cpq_l.(k) in
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if (!do_compute) then x
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else (if abs_float x > cutoff then do_compute := true ; x)
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) )
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in
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if (!do_compute) then
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match vrr_v (m+1) angMom_a cm with
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| None -> None
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| Some v2 ->
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begin
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for l=0 to np-1 do
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let f2_l = f2.(l)
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and v2_l = v2.(l)
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in
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for k=0 to nq-1 do
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f2_l.(k) <- -. v2_l.(k) *. f2_l.(k)
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done
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done;
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Some f2
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end
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else
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None
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in
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let p1 =
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match v1, v2 with
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| None, None -> None
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| None, Some v2 -> Some v2
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| Some v1, None -> Some v1
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| Some v1, Some v2 ->
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begin
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for l=0 to np-1 do
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let v1_l = v1.(l)
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and v2_l = v2.(l)
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in
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for k=0 to nq-1 do
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v2_l.(k) <- v2_l.(k) +. v1_l.(k)
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done
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done;
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Some v2
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end
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in
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let cxyz = Powers.get xyz angMom_c in
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let p2 =
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if cxyz < 2 then p1 else
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let cmm = Powers.decr xyz cm in
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let fcm = (float_of_int (cxyz-1)) *. 0.5 in
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let f1 =
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Array.init nq (fun k ->
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let x = fcm *. expo_inv_q.(k) in
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if (!do_compute) then x
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else (if abs_float x > cutoff then do_compute := true ; x)
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)
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in
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let v1 =
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if (!do_compute) then
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match vrr_v m angMom_a cmm with
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| None -> None
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| Some v1 ->
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begin
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let result = Array.make_matrix np nq 0. in
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for l=0 to np-1 do
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let v1_l = v1.(l)
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and result_l = result.(l)
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in
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for k=0 to nq-1 do
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result_l.(k) <- v1_l.(k) *. f1.(k)
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done;
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done;
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Some result
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end
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else None
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in
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let v3 =
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let f2 =
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Array.init nq (fun k ->
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let x = expo_inv_q.(k) *. f1.(k) in
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if (!do_compute) then x
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else (if abs_float x > cutoff then do_compute := true ; x)
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)
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in
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if (!do_compute) then
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match vrr_v (m+1) angMom_a cmm with
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| None -> None
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| Some v3 ->
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begin
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let result = Array.make_matrix np nq 0. in
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for l=0 to np-1 do
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let v3_l = v3.(l)
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and result_l = result.(l)
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in
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for k=0 to nq-1 do
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result_l.(k) <- v3_l.(k) *. f2.(k)
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done
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done;
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Some result
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end
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else None
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in
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match p1, v1, v3 with
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| None, None, None -> None
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| Some p1, None, None -> Some p1
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| None, Some v1, None -> Some v1
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| None, None, Some v3 -> Some v3
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| Some p1, Some v1, Some v3 ->
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begin
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for l=0 to np-1 do
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let v3_l = v3.(l)
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and v1_l = v1.(l)
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and p1_l = p1.(l)
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in
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for k=0 to nq-1 do
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v3_l.(k) <- p1_l.(k) +. v1_l.(k) +. v3_l.(k)
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done
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done;
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Some v3
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end
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| Some p1, Some v1, None ->
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begin
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for l=0 to np-1 do
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let v1_l = v1.(l)
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and p1_l = p1.(l)
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in
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for k=0 to nq-1 do
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p1_l.(k) <- v1_l.(k) +. p1_l.(k)
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done
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done;
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Some p1
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end
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| Some p1, None, Some v3 ->
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begin
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for l=0 to np-1 do
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let v3_l = v3.(l)
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and p1_l = p1.(l)
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in
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for k=0 to nq-1 do
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p1_l.(k) <- p1_l.(k) +. v3_l.(k)
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done
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done;
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Some p1
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end
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| None , Some v1, Some v3 ->
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begin
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for l=0 to np-1 do
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let v3_l = v3.(l)
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and v1_l = v1.(l)
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in
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for k=0 to nq-1 do
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v3_l.(k) <- v1_l.(k) +. v3_l.(k)
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done
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done;
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Some v3
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end
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in
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if (axyz < 1) || (cxyz < 1) then p2 else
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let am = Powers.decr xyz angMom_a in
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let v =
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vrr_v (m+1) am cm
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in
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match (p2, v) with
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| None, None -> None
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| Some p2, None -> Some p2
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| _, Some v ->
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begin
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let p2 =
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match p2 with
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| None -> Array.make_matrix np nq 0.
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| Some p2 -> p2
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in
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for l=0 to np-1 do
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let fa = (float_of_int axyz) *. expo_inv_p.(l) *. 0.5 in
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let p2_l = p2.(l)
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and v_l = v.(l)
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in
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for k=0 to nq-1 do
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p2_l.(k) <- p2_l.(k) -. fa *. expo_inv_q.(k) *. v_l.(k)
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done
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done;
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Some p2
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end
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end
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in Zmap.add map_2d.(m) key result;
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result
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(** Horizontal recurrence relations *)
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and hrr0_v angMom_a angMom_b angMom_c =
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match angMom_b.tot with
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| 0 ->
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begin
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match (angMom_a.tot, angMom_c.tot) with
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| (0,0) -> Array.fold_left (fun accu c ->
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accu +. Array.fold_left (+.) 0. c) 0. zero_m_array.(0)
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| (_,_) ->
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begin
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match vrr_v 0 angMom_a angMom_c with
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| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
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| None -> 0.
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end
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end
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| 1 ->
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let xyz = get_xyz angMom_b in
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let ap = Powers.incr xyz angMom_a in
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let f = Coordinate.get xyz center_ab in
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let v1 =
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match vrr_v 0 ap angMom_c with
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| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
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| None -> 0.
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in
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if (abs_float f < cutoff) then v1 else
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let v2 =
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match vrr_v 0 angMom_a angMom_c with
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| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
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| None -> 0.
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in
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v1 +. v2 *. f
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| _ ->
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let xyz = get_xyz angMom_b in
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let bxyz = Powers.get xyz angMom_b in
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if (bxyz < 0) then 0. else
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let ap = Powers.incr xyz angMom_a in
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let bm = Powers.decr xyz angMom_b in
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let h1 =
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hrr0_v ap bm angMom_c
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in
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let f = Coordinate.get xyz center_ab in
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if abs_float f < cutoff then h1 else
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let h2 =
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hrr0_v angMom_a bm angMom_c
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in
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h1 +. h2 *. f
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and hrr_v angMom_a angMom_b angMom_c angMom_d =
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match (angMom_b.tot, angMom_d.tot) with
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| (_,0) -> if angMom_b.tot = 0 then
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begin
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match vrr_v 0 angMom_a angMom_c with
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| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
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| None -> 0.
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end
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else
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hrr0_v angMom_a angMom_b angMom_c
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| (_,_) ->
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let xyz = get_xyz angMom_d in
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let cp = Powers.incr xyz angMom_c in
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let dm = Powers.decr xyz angMom_d in
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let h1 =
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hrr_v angMom_a angMom_b cp dm
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in
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let f = Coordinate.get xyz center_cd in
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if abs_float f < cutoff then
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h1
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else
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let h2 =
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hrr_v angMom_a angMom_b angMom_c dm
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in h1 +. f *. h2
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in
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hrr_v angMom_a angMom_b angMom_c angMom_d
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let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
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let shell_a = shell_p.ContractedShellPair.shell_a
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and shell_b = shell_p.ContractedShellPair.shell_b
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and shell_c = shell_q.ContractedShellPair.shell_a
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and shell_d = shell_q.ContractedShellPair.shell_b
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and sp = shell_p.ContractedShellPair.shell_pairs
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and sq = shell_q.ContractedShellPair.shell_pairs
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in
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let maxm =
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shell_p.ContractedShellPair.totAngMomInt +
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shell_q.ContractedShellPair.totAngMomInt
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in
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(* Pre-computation of integral class indices *)
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let class_indices =
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Angular_momentum.zkey_array
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(Angular_momentum.Quartet
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Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d))
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in
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let contracted_class =
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Array.make (Array.length class_indices) 0.;
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in
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let monocentric =
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shell_p.ContractedShellPair.monocentric &&
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shell_q.ContractedShellPair.monocentric &&
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Contracted_shell.center shell_p.ContractedShellPair.shell_a =
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Contracted_shell.center shell_q.ContractedShellPair.shell_a
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in
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(** Screening on the product of coefficients *)
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let coef_max_p =
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Array.fold_left (fun accu x ->
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if (abs_float x) > accu then (abs_float x) else accu)
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0. shell_p.ContractedShellPair.coef
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and coef_max_q =
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Array.fold_left (fun accu x ->
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if (abs_float x) > accu then (abs_float x) else accu)
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0. shell_q.ContractedShellPair.coef
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in
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let rec build_list cutoff vec accu = function
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| -1 -> Array.of_list accu
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| k -> build_list cutoff vec (
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if (abs_float vec.(k) > cutoff) then (k::accu)
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else accu ) (k-1)
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in
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let p_list =
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let vec = shell_p.ContractedShellPair.coef in
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build_list (cutoff /. coef_max_q) vec [] (Array.length vec - 1)
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and q_list =
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let vec = shell_q.ContractedShellPair.coef in
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build_list (cutoff /. coef_max_p) vec [] (Array.length vec - 1)
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in
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let np, nq =
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Array.length p_list,
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Array.length q_list
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in
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let filter_p vec = Array.init np (fun k -> vec.(p_list.(k)))
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and filter_q vec = Array.init nq (fun k -> vec.(q_list.(k)))
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in
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let sp = filter_p sp
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and sq = filter_q sq
|
|
in
|
|
|
|
|
|
(* Compute all integrals in the shell for each pair of significant shell pairs *)
|
|
|
|
begin
|
|
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
|
|
totAngMom shell_c, totAngMom shell_d) with
|
|
| Angular_momentum.(S,S,S,S) ->
|
|
contracted_class.(0) <-
|
|
begin
|
|
try
|
|
let expo_inv_p =
|
|
Vec.init np (fun ab -> sp.(ab-1).ShellPair.expo_inv)
|
|
and expo_inv_q =
|
|
Vec.init nq (fun cd -> sq.(cd-1).ShellPair.expo_inv)
|
|
in
|
|
|
|
let coef =
|
|
let result = Mat.make0 nq np in
|
|
Lacaml.D.ger
|
|
(Vec.of_array @@ filter_q shell_q.ContractedShellPair.coef)
|
|
(Vec.of_array @@ filter_p shell_p.ContractedShellPair.coef)
|
|
result;
|
|
result
|
|
in
|
|
let zm_array = Mat.init_cols np nq (fun i j ->
|
|
try
|
|
if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then
|
|
raise NullQuartet;
|
|
|
|
let expo_pq_inv =
|
|
expo_inv_p.{i} +. expo_inv_q.{j}
|
|
in
|
|
|
|
let center_pq =
|
|
sp.(i-1).ShellPair.center |- sq.(j-1).ShellPair.center
|
|
in
|
|
let norm_pq_sq =
|
|
Coordinate.dot center_pq center_pq
|
|
in
|
|
|
|
let zero_m_array =
|
|
zero_m ~maxm:0 ~expo_pq_inv ~norm_pq_sq
|
|
in
|
|
zero_m_array.(0)
|
|
with NullQuartet -> 0.
|
|
) in
|
|
Mat.gemm_trace zm_array coef
|
|
with (Invalid_argument _) -> 0.
|
|
end
|
|
| _ ->
|
|
|
|
let coef =
|
|
let cp = filter_p shell_p.ContractedShellPair.coef
|
|
and cq = filter_q shell_q.ContractedShellPair.coef
|
|
in
|
|
Array.init np (fun l -> Array.init nq (fun k -> cq.(k) *. cp.(l)) )
|
|
in
|
|
|
|
let expo_inv_p =
|
|
Array.map (fun shell_ab -> shell_ab.ShellPair.expo_inv) sp
|
|
and expo_inv_q =
|
|
Array.map (fun shell_cd -> shell_cd.ShellPair.expo_inv) sq
|
|
in
|
|
|
|
let expo_b =
|
|
Array.map (fun shell_ab -> Contracted_shell.expo shell_b shell_ab.ShellPair.j) sp
|
|
and expo_d =
|
|
Array.map (fun shell_cd -> Contracted_shell.expo shell_d shell_cd.ShellPair.j) sq
|
|
in
|
|
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
|
|
|
|
let center_pq =
|
|
let result =
|
|
Array.init 3 (fun xyz ->
|
|
Array.init np (fun ab ->
|
|
let shell_ab = sp.(ab) in
|
|
Array.init nq (fun cd ->
|
|
let shell_cd = sq.(cd)
|
|
in
|
|
let cpq =
|
|
shell_ab.ShellPair.center |- shell_cd.ShellPair.center
|
|
in
|
|
match xyz with
|
|
| 0 -> Coordinate.get X cpq;
|
|
| 1 -> Coordinate.get Y cpq;
|
|
| 2 -> Coordinate.get Z cpq;
|
|
| _ -> assert false
|
|
)
|
|
)
|
|
)
|
|
in function
|
|
| X -> result.(0)
|
|
| Y -> result.(1)
|
|
| Z -> result.(2)
|
|
in
|
|
let zero_m_array =
|
|
let result =
|
|
Array.init (maxm+1) (fun _ ->
|
|
Array.init np (fun _ -> Array.make nq 0. ) )
|
|
in
|
|
let empty = Array.make (maxm+1) 0. in
|
|
Array.iteri (fun ab shell_ab ->
|
|
let zero_m_array_tmp =
|
|
Array.mapi (fun cd shell_cd ->
|
|
if (abs_float coef.(ab).(cd) < cutoff) then
|
|
empty
|
|
else
|
|
let expo_pq_inv =
|
|
expo_inv_p.(ab) +. expo_inv_q.(cd)
|
|
in
|
|
let norm_pq_sq =
|
|
let x = (center_pq X).(ab).(cd)
|
|
and y = (center_pq Y).(ab).(cd)
|
|
and z = (center_pq Z).(ab).(cd)
|
|
in
|
|
x *. x +. y *. y +. z *. z
|
|
in
|
|
|
|
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
|
|
) sq
|
|
in
|
|
(* Transpose result *)
|
|
for m=0 to maxm do
|
|
for cd=0 to nq-1 do
|
|
result.(m).(ab).(cd) <- zero_m_array_tmp.(cd).(m) *. coef.(ab).(cd)
|
|
done
|
|
done
|
|
) sp;
|
|
result
|
|
in
|
|
|
|
let norm =
|
|
let norm_coef_scale_q =
|
|
shell_q.ContractedShellPair.norm_coef_scale
|
|
in
|
|
Array.to_list norm_coef_scale_p
|
|
|> List.map (fun v1 ->
|
|
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q)
|
|
|> Array.concat
|
|
in
|
|
|
|
let map_1d = Array.init (maxm+1) (fun _ -> Zmap.create (4*maxm))
|
|
and map_2d = Array.init (maxm+1) (fun _ -> Zmap.create (Array.length class_indices))
|
|
in
|
|
(* Compute the integral class from the primitive shell quartet *)
|
|
Array.iteri (fun i key ->
|
|
let (angMom_a,angMom_b,angMom_c,angMom_d) =
|
|
match Zkey.to_powers ~kind:Zkey.Kind_12 key with
|
|
| Zkey.Twelve x -> x
|
|
| _ -> assert false
|
|
in
|
|
try
|
|
if monocentric then
|
|
begin
|
|
if ( ((1 land angMom_a.x + angMom_b.x + angMom_c.x + angMom_d.x) =1) ||
|
|
((1 land angMom_a.y + angMom_b.y + angMom_c.y + angMom_d.y) =1) ||
|
|
((1 land angMom_a.z + angMom_b.z + angMom_c.z + angMom_d.z) =1)
|
|
) then
|
|
raise NullQuartet
|
|
end;
|
|
|
|
(* Schwartz screening *)
|
|
if (np+nq> 24) then
|
|
(
|
|
let schwartz_p =
|
|
let key = Zkey.of_powers (Zkey.Twelve
|
|
(angMom_a, angMom_b, angMom_a, angMom_b) )
|
|
in
|
|
match schwartz_p with
|
|
| None -> 1.
|
|
| Some schwartz_p -> Zmap.find schwartz_p key
|
|
in
|
|
if schwartz_p < cutoff then raise NullQuartet;
|
|
let schwartz_q =
|
|
let key = Zkey.of_powers (Zkey.Twelve
|
|
(angMom_c, angMom_d, angMom_c, angMom_d) )
|
|
in
|
|
match schwartz_q with
|
|
| None -> 1.
|
|
| Some schwartz_q -> Zmap.find schwartz_q key
|
|
in
|
|
if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet;
|
|
);
|
|
|
|
let integral =
|
|
hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
|
|
zero_m_array
|
|
(expo_b, expo_d)
|
|
(expo_inv_p, expo_inv_q)
|
|
(shell_p.ContractedShellPair.center_ab,
|
|
shell_q.ContractedShellPair.center_ab, center_pq)
|
|
map_1d map_2d np nq
|
|
in
|
|
contracted_class.(i) <- contracted_class.(i) +. integral *. norm.(i)
|
|
with NullQuartet -> ()
|
|
) class_indices
|
|
|
|
end;
|
|
|
|
let result =
|
|
Zmap.create (Array.length contracted_class)
|
|
in
|
|
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
|
|
result
|
|
|
|
|
|
|
|
(** Computes all the two-electron integrals of the contracted shell quartet *)
|
|
let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
|
|
|
|
let shell_p = ContractedShellPair.create ~cutoff shell_a shell_b
|
|
and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d
|
|
in
|
|
contracted_class_shell_pairs ~zero_m shell_p shell_q
|
|
|