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https://gitlab.com/scemama/QCaml.git
synced 2024-11-15 18:43:40 +01:00
881 lines
29 KiB
OCaml
881 lines
29 KiB
OCaml
open Util
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open Lacaml.D
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open Bigarray
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module Am = AngularMomentum
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module Co = Coordinate
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module Cs = ContractedShell
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module Csp = ContractedShellPair
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module Po = Powers
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module Psp = PrimitiveShellPair
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module Ps = PrimitiveShell
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exception NullQuartet
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exception Found
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let cutoff = Constants.integrals_cutoff
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let cutoff2 = cutoff *. cutoff
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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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(center_pa, center_qc)
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map_1d map_2d np nq
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=
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let maxm = Array.length zero_m_array - 1 in
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let get_xyz angMom =
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match angMom with
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| { Po.y=0 ; z=0 ; _ } -> Co.X
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| { z=0 ; _ } -> Co.Y
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| _ -> Co.Z
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in
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(** Vertical recurrence relations *)
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let rec vrr0_v angMom_a =
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match angMom_a.Po.tot with
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| 0 -> zero_m_array
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| _ ->
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let key = Zkey.of_powers_three angMom_a
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in
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try Zmap.find map_1d 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 = Po.decr xyz angMom_a in
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let cab = Co.get xyz center_ab in
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let result = Array.init (maxm+1-angMom_a.Po.tot) (fun _ -> Array.make_matrix np nq 0.) in
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let v_am= vrr0_v am in
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begin
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if abs_float cab >= cutoff then
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Array.iteri (fun m result_m ->
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let v0 = v_am.(m) in
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Array.iteri (fun l result_ml ->
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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_ml.(k) <- v0_lk *. f0) v0_l
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) result_m
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) result
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end;
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let amxyz = Po.get xyz am in
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if amxyz < 1 then
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Array.iteri (fun l expo_inv_p_l ->
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let center_pq_xyz_l = (center_pq xyz).(l) in
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Array.iteri (fun m result_m ->
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let result_ml = result_m.(l) in
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let p0 = v_am.(m+1) in
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let p0_l = p0.(l)
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in
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Array.iteri (fun k p0_lk ->
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result_ml.(k) <- result_ml.(k)
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+. expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk
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) p0_l
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) result
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) expo_inv_p
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else
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begin
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let amm = Po.decr xyz am in
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let amxyz = float_of_int amxyz in
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let v_amm = vrr0_v amm in
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Array.iteri (fun l expo_inv_p_l ->
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let f = amxyz *. expo_inv_p.(l) *. 0.5
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and center_pq_xyz_l = (center_pq xyz).(l)
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in
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Array.iteri (fun m result_m ->
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let v1 = v_amm.(m) in
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let v1_l = v1.(l) in
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let result_ml = result_m.(l) in
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let v2 = v_amm.(m+1) in
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let p0 = v_am.(m+1) in
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let v2_l = v2.(l)
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in
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Array.iteri (fun k p0_lk ->
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result_ml.(k) <- result_ml.(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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) expo_inv_p
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end;
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result
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in
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Zmap.add map_1d 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.Po.tot, angMom_c.Po.tot) with
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| (i,0) -> Some (vrr0_v angMom_a).(m)
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| (_,_) ->
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let key = Zkey.of_powers_six angMom_a angMom_c 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 = Po.decr xyz angMom_c in
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let axyz = Po.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 = -. (Co.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 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 = Po.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 = Po.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 = Po.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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(*
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and trr_v angMom_a angMom_c =
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match (angMom_a.Po.tot, angMom_c.Po.tot) with
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| (i,0) -> Some (vrr0_v angMom_a).(0)
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| (_,_) ->
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let key = Zkey.of_powers_six angMom_a angMom_c in
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try Zmap.find map_2d.(0) key with
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| Not_found ->
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let xyz = get_xyz angMom_c in
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let axyz = Po.get xyz angMom_a in
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let cm = Po.decr xyz angMom_c in
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let cmxyz = Po.get xyz cm in
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let expo_inv_q_over_p =
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Array.mapi (fun l expo_inv_p_l ->
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let expo_p_l = 1./.expo_inv_p_l in
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Array.mapi (fun k expo_inv_q_k ->
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expo_inv_q_k *. expo_p_l) expo_inv_q ) expo_inv_p
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in
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let result = None in
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let result =
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if cmxyz < 1 then result else
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begin
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let f = 0.5 *. (float_of_int cmxyz) in
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let cmm = Po.decr xyz cm in
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match result, trr_v angMom_a cmm with
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| None, None -> None
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| None, Some v3 ->
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Some (Array.init np (fun l ->
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let v3_l = v3.(l) in
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Array.mapi (fun k v3_lk ->
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expo_inv_q.(k) *. f *. v3_lk) v3_l
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) )
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| Some result, None -> Some result
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| Some result, Some v3 ->
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(Array.iteri (fun l v3_l ->
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let result_l = result.(l) in
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Array.iteri (fun k v3_lk ->
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result_l.(k) <- result_l.(k) +.
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expo_inv_q.(k) *. f *. v3_lk) v3_l
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) v3 ; Some result)
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end
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in
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let result =
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begin
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match result, trr_v angMom_a cm with
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| Some result, None -> Some result
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| Some result, Some v1 ->
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(Array.iteri (fun l v1_l ->
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let cpa = (center_pa xyz).(l)
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and result_l = result.(l)
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and expo_inv_q_over_p_l = expo_inv_q_over_p.(l)
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in
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Array.iteri (fun k v1_lk ->
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let cqc = (center_qc xyz).(k) in
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result_l.(k) <- result_l.(k) +.
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(cqc +. expo_inv_q_over_p_l.(k) *. cpa) *. v1_lk
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) v1_l
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) v1 ; Some result)
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| None, None -> None
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| None, Some v1 ->
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Some (Array.init np (fun l ->
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let v1_l = v1.(l)
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and cpa = (center_pa xyz).(l)
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and expo_inv_q_over_p_l = expo_inv_q_over_p.(l)
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in
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Array.mapi (fun k v1_lk ->
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let cqc = (center_qc xyz).(k) in
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(cqc +. expo_inv_q_over_p_l.(k) *. cpa) *. v1_lk
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) v1_l
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) )
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end
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in
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let result =
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if cmxyz < 0 then result else
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begin
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let ap = Po.incr xyz angMom_a in
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match result, trr_v ap cm with
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| Some result, None -> Some result
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| Some result, Some v4 ->
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(Array.iteri (fun l v4_l ->
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let result_l = result.(l) in
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Array.iteri (fun k v4_lk ->
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let expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in
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result_l.(k) <- result_l.(k)
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-. expo_inv_q_over_p_l.(k) *. v4_lk) v4_l
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) v4 ; Some result)
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| None, None -> None
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| None, Some v4 ->
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Some (Array.init np (fun l ->
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let v4_l = v4.(l) in
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let expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in
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Array.mapi (fun k v4_lk ->
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-. expo_inv_q_over_p_l.(k) *. v4_lk) v4_l
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) )
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end
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in
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let result =
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if axyz < 1 then result else
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begin
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let f = 0.5 *. (float_of_int axyz) in
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let am = Po.decr xyz angMom_a in
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match result, trr_v am cm with
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| Some result, None -> Some result
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| Some result, Some v2 ->
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(Array.iteri (fun l v2_l ->
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let result_l = result.(l) in
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Array.iteri (fun k v2_lk ->
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result_l.(k) <- result_l.(k) +.
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expo_inv_q.(k) *. f *. v2_lk) v2_l
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) v2; Some result)
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| None, None -> None
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| None, Some v2 ->
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Some (Array.init np (fun l ->
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let v2_l = v2.(l) in
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Array.mapi (fun k v2_lk ->
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expo_inv_q.(k) *. f *. v2_lk) v2_l
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) )
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end
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in
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Zmap.add map_2d.(0) key result;
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result
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*)
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in
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let sum matrix =
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Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
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in
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let vrr_v a c =
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let v =
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(*
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if c.Po.tot <> 0 then
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vrr_v 0 a c
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else trr_v a c
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*)
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vrr_v 0 a c
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in
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match v with
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| Some matrix -> sum matrix
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| None -> 0.
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in
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|
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|
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(** Horizontal recurrence relations *)
|
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let rec hrr0_v angMom_a angMom_b angMom_c =
|
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|
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match angMom_b.Po.tot with
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| 0 ->
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begin
|
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match (angMom_a.Po.tot, angMom_c.Po.tot) with
|
|
| (0,0) -> sum zero_m_array.(0)
|
|
| (_,_) -> vrr_v angMom_a angMom_c
|
|
end
|
|
| 1 ->
|
|
let xyz = get_xyz angMom_b in
|
|
let ap = Po.incr xyz angMom_a in
|
|
let f = Co.get xyz center_ab in
|
|
let v1 = vrr_v ap angMom_c in
|
|
if (abs_float f < cutoff) then v1 else
|
|
let v2 = vrr_v angMom_a angMom_c in
|
|
v1 +. v2 *. f
|
|
| _ ->
|
|
let xyz = get_xyz angMom_b in
|
|
let bxyz = Po.get xyz angMom_b in
|
|
if (bxyz < 0) then 0. else
|
|
let ap = Po.incr xyz angMom_a in
|
|
let bm = Po.decr xyz angMom_b in
|
|
let h1 = hrr0_v ap bm angMom_c in
|
|
let f = Co.get xyz center_ab in
|
|
if abs_float f < cutoff then h1 else
|
|
let h2 = hrr0_v angMom_a bm angMom_c in
|
|
h1 +. h2 *. f
|
|
|
|
and hrr_v angMom_a angMom_b angMom_c angMom_d =
|
|
|
|
match (angMom_b.Po.tot, angMom_d.Po.tot) with
|
|
| (_,0) -> if angMom_b.Po.tot = 0 then
|
|
vrr_v angMom_a angMom_c
|
|
else
|
|
hrr0_v angMom_a angMom_b angMom_c
|
|
| (_,_) ->
|
|
let xyz = get_xyz angMom_d in
|
|
let cp = Po.incr xyz angMom_c in
|
|
let dm = Po.decr xyz angMom_d in
|
|
let h1 =
|
|
hrr_v angMom_a angMom_b cp dm
|
|
in
|
|
let f = Co.get xyz center_cd in
|
|
if abs_float f < cutoff then
|
|
h1
|
|
else
|
|
let h2 =
|
|
hrr_v angMom_a angMom_b angMom_c dm
|
|
in h1 +. f *. h2
|
|
in
|
|
hrr_v angMom_a angMom_b angMom_c angMom_d
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
|
|
|
|
let shell_a = Csp.shell_a shell_p
|
|
and shell_b = Csp.shell_b shell_p
|
|
and shell_c = Csp.shell_a shell_q
|
|
and shell_d = Csp.shell_b shell_q
|
|
and sp = Csp.shell_pairs shell_p
|
|
and sq = Csp.shell_pairs shell_q
|
|
in
|
|
let maxm =
|
|
Am.(Csp.totAngMom shell_p + Csp.totAngMom shell_q |> to_int)
|
|
in
|
|
|
|
(* Pre-computation of integral class indices *)
|
|
let class_indices =
|
|
Am.zkey_array (Am.Quartet
|
|
Cs.(totAngMom shell_a, totAngMom shell_b,
|
|
totAngMom shell_c, totAngMom shell_d))
|
|
in
|
|
|
|
let contracted_class =
|
|
Array.make (Array.length class_indices) 0.;
|
|
in
|
|
|
|
let monocentric =
|
|
Csp.monocentric shell_p && Csp.monocentric shell_q &&
|
|
Cs.center (Csp.shell_a shell_p) =
|
|
Cs.center (Csp.shell_a shell_q)
|
|
in
|
|
|
|
(** Screening on the product of coefficients *)
|
|
let coef_max_p =
|
|
Array.fold_left (fun accu x ->
|
|
if (abs_float x) > accu then (abs_float x) else accu)
|
|
0. (Csp.coefficients shell_p)
|
|
and coef_max_q =
|
|
Array.fold_left (fun accu x ->
|
|
if (abs_float x) > accu then (abs_float x) else accu)
|
|
0. (Csp.coefficients shell_q)
|
|
in
|
|
|
|
let rec build_list cutoff vec accu = function
|
|
| -1 -> Array.of_list accu
|
|
| k -> build_list cutoff vec (
|
|
if (abs_float vec.(k) > cutoff) then (k::accu)
|
|
else accu ) (k-1)
|
|
in
|
|
let p_list =
|
|
let vec = (Csp.coefficients shell_p) in
|
|
build_list (cutoff /. coef_max_q) vec [] (Array.length vec - 1)
|
|
and q_list =
|
|
let vec = (Csp.coefficients shell_q) in
|
|
build_list (cutoff /. coef_max_p) vec [] (Array.length vec - 1)
|
|
in
|
|
|
|
let np, nq =
|
|
Array.length p_list,
|
|
Array.length q_list
|
|
in
|
|
let filter_p vec = Array.init np (fun k -> vec.(p_list.(k)))
|
|
and filter_q vec = Array.init nq (fun k -> vec.(q_list.(k)))
|
|
in
|
|
let sp = filter_p sp
|
|
and sq = filter_q sq
|
|
in
|
|
|
|
|
|
(* Compute all integrals in the shell for each pair of significant shell pairs *)
|
|
|
|
begin
|
|
match Cs.(totAngMom shell_a, totAngMom shell_b,
|
|
totAngMom shell_c, totAngMom shell_d) with
|
|
| Am.(S,S,S,S) ->
|
|
contracted_class.(0) <-
|
|
begin
|
|
try
|
|
let expo_inv_p =
|
|
Vec.init np (fun ab -> Psp.exponent_inv sp.(ab-1))
|
|
and expo_inv_q =
|
|
Vec.init nq (fun cd -> Psp.exponent_inv sq.(cd-1))
|
|
in
|
|
|
|
let coef =
|
|
let result = Mat.make0 nq np in
|
|
Lacaml.D.ger
|
|
(Vec.of_array @@ filter_q (Csp.coefficients shell_q))
|
|
(Vec.of_array @@ filter_p (Csp.coefficients shell_p))
|
|
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 =
|
|
Co.(Psp.center sp.(i-1) |- Psp.center sq.(j-1))
|
|
in
|
|
let norm_pq_sq =
|
|
Co.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 (Csp.coefficients shell_p)
|
|
and cq = filter_q (Csp.coefficients shell_q)
|
|
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 -> Psp.exponent_inv shell_ab) sp
|
|
and expo_inv_q =
|
|
Array.map (fun shell_cd -> Psp.exponent_inv shell_cd) sq
|
|
in
|
|
|
|
let expo_b =
|
|
Array.map (fun shell_ab -> Ps.exponent (Psp.shell_b shell_ab) ) sp
|
|
and expo_d =
|
|
Array.map (fun shell_cd -> Ps.exponent (Psp.shell_b shell_cd) ) sq
|
|
in
|
|
let norm_coef_scale_p = Csp.norm_scales shell_p 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 =
|
|
Co.(Psp.center shell_ab |- Psp.center shell_cd)
|
|
in
|
|
match xyz with
|
|
| 0 -> Co.get X cpq;
|
|
| 1 -> Co.get Y cpq;
|
|
| _ -> Co.get Z cpq;
|
|
)
|
|
)
|
|
)
|
|
in function
|
|
| Co.X -> result.(0)
|
|
| Co.Y -> result.(1)
|
|
| Co.Z -> result.(2)
|
|
in
|
|
let center_pa =
|
|
let result =
|
|
Array.init 3 (fun xyz ->
|
|
Array.init np (fun ab ->
|
|
let shell_ab = sp.(ab) in
|
|
let cpa =
|
|
Co.(Psp.center shell_ab |- Cs.center shell_a)
|
|
in
|
|
match xyz with
|
|
| 0 -> Co.(get X cpa);
|
|
| 1 -> Co.(get Y cpa);
|
|
| _ -> Co.(get Z cpa);
|
|
)
|
|
)
|
|
in function
|
|
| Co.X -> result.(0)
|
|
| Co.Y -> result.(1)
|
|
| Co.Z -> result.(2)
|
|
in
|
|
let center_qc =
|
|
let result =
|
|
Array.init 3 (fun xyz ->
|
|
Array.init nq (fun cd ->
|
|
let shell_cd = sq.(cd) in
|
|
let cqc =
|
|
Co.(Psp.center shell_cd |- Cs.center shell_c)
|
|
in
|
|
match xyz with
|
|
| 0 -> Co.(get X cqc);
|
|
| 1 -> Co.(get Y cqc);
|
|
| _ -> Co.(get Z cqc);
|
|
)
|
|
)
|
|
in function
|
|
| Co.X -> result.(0)
|
|
| Co.Y -> result.(1)
|
|
| Co.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 *)
|
|
let coef_ab = coef.(ab) in
|
|
for m=0 to maxm do
|
|
let result_m_ab = result.(m).(ab)
|
|
in
|
|
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 =
|
|
Csp.norm_scales shell_q
|
|
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 = 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 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_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_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)
|
|
(Csp.center_ab shell_p,
|
|
Csp.center_ab shell_q, center_pq)
|
|
(center_pa, center_qc)
|
|
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 = Csp.make ~cutoff shell_a shell_b
|
|
and shell_q = Csp.make ~cutoff shell_c shell_d
|
|
in
|
|
match shell_p, shell_q with
|
|
| Some shell_p, Some shell_q ->
|
|
contracted_class_shell_pairs ~zero_m shell_p shell_q
|
|
| _ -> Zmap.create 0
|
|
|