open Util open Lacaml.D open Bigarray module Am = AngularMomentum module Co = Coordinate module Cs = ContractedShell module Csp = ContractedShellPair module Sp = ShellPair module Po = Powers exception NullQuartet exception Found let cutoff = Constants.integrals_cutoff let cutoff2 = cutoff *. cutoff let at_least_one_valid arr = try Array.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false with Found -> true (** Horizontal and Vertical Recurrence Relations (HVRR) *) let 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) (center_ab, center_cd, center_pq) (center_pa, center_qc) map_1d map_2d np nq = let maxm = Array.length zero_m_array - 1 in let get_xyz angMom = match angMom with | { Po.y=0 ; z=0 ; _ } -> Co.X | { z=0 ; _ } -> Co.Y | _ -> Co.Z in (** Vertical recurrence relations *) let rec vrr0_v angMom_a = match angMom_a.Po.tot with | 0 -> zero_m_array | _ -> let key = Zkey.of_powers_three angMom_a in try Zmap.find map_1d key with | Not_found -> let result = let xyz = get_xyz angMom_a in let am = Po.decr xyz angMom_a in let cab = Co.get xyz center_ab in let result = Array.init (maxm+1-angMom_a.Po.tot) (fun _ -> Array.make_matrix np nq 0.) in let v_am= vrr0_v am in begin if abs_float cab >= cutoff then Array.iteri (fun m result_m -> let v0 = v_am.(m) in Array.iteri (fun l result_ml -> let f0 = -. expo_b.(l) *. expo_inv_p.(l) *. cab and v0_l = v0.(l) in Array.iteri (fun k v0_lk -> result_ml.(k) <- v0_lk *. f0) v0_l ) result_m ) result end; let amxyz = Po.get xyz am in if amxyz < 1 then Array.iteri (fun l expo_inv_p_l -> let center_pq_xyz_l = (center_pq xyz).(l) in Array.iteri (fun m result_m -> let result_ml = result_m.(l) in let p0 = v_am.(m+1) in let p0_l = p0.(l) in Array.iteri (fun k p0_lk -> result_ml.(k) <- result_ml.(k) +. expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk ) p0_l ) result ) expo_inv_p else begin let amm = Po.decr xyz am in let amxyz = float_of_int amxyz in let v_amm = vrr0_v amm in Array.iteri (fun l expo_inv_p_l -> let f = amxyz *. expo_inv_p.(l) *. 0.5 and center_pq_xyz_l = (center_pq xyz).(l) in Array.iteri (fun m result_m -> let v1 = v_amm.(m) in let v1_l = v1.(l) in let result_ml = result_m.(l) in let v2 = v_amm.(m+1) in let p0 = v_am.(m+1) in let v2_l = v2.(l) in Array.iteri (fun k p0_lk -> result_ml.(k) <- result_ml.(k) +. expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk +. f *. (v1_l.(k) +. v2_l.(k) *. expo_inv_p_l) ) p0.(l) ) result ) expo_inv_p end; result in Zmap.add map_1d key result; result and vrr_v m angMom_a angMom_c = match (angMom_a.Po.tot, angMom_c.Po.tot) with | (i,0) -> Some (vrr0_v angMom_a).(m) | (_,_) -> let key = Zkey.of_powers_six angMom_a angMom_c in try Zmap.find map_2d.(m) key with | Not_found -> let result = begin let xyz = get_xyz angMom_c in let cm = Po.decr xyz angMom_c in let axyz = Po.get xyz angMom_a in let do_compute = ref false in let v1 = let f = -. (Co.get xyz center_cd) in let f1 = Array.init nq (fun k -> let x = expo_d.(k) *. expo_inv_q.(k) *. f in if ( (not !do_compute) && (abs_float x > cutoff) ) then do_compute := true; x) in if (!do_compute) then match vrr_v m angMom_a cm with | None -> None | Some v1 -> begin Some (Array.init np (fun l -> let v1_l = v1.(l) in Array.mapi (fun k f1k -> v1_l.(k) *. f1k) f1 ) ) end else None in let v2 = let f2 = Array.init np (fun l -> let cpq_l = (center_pq xyz).(l) in Array.init nq (fun k -> let x = expo_inv_q.(k) *. cpq_l.(k) in if (!do_compute) then x else (if abs_float x > cutoff then do_compute := true ; x) ) ) in if (!do_compute) then match vrr_v (m+1) angMom_a cm with | None -> None | Some v2 -> begin for l=0 to np-1 do let f2_l = f2.(l) and v2_l = v2.(l) in for k=0 to nq-1 do f2_l.(k) <- -. v2_l.(k) *. f2_l.(k) done done; Some f2 end else None in let p1 = match v1, v2 with | None, None -> None | None, Some v2 -> Some v2 | Some v1, None -> Some v1 | Some v1, Some v2 -> begin for l=0 to np-1 do let v1_l = v1.(l) and v2_l = v2.(l) in for k=0 to nq-1 do v2_l.(k) <- v2_l.(k) +. v1_l.(k) done done; Some v2 end in let cxyz = Po.get xyz angMom_c in let p2 = if cxyz < 2 then p1 else let cmm = Po.decr xyz cm in let fcm = (float_of_int (cxyz-1)) *. 0.5 in let f1 = Array.init nq (fun k -> let x = fcm *. expo_inv_q.(k) in if (!do_compute) then x else (if abs_float x > cutoff then do_compute := true ; x) ) in let v1 = if (!do_compute) then match vrr_v m angMom_a cmm with | None -> None | Some v1 -> begin let result = Array.make_matrix np nq 0. in for l=0 to np-1 do let v1_l = v1.(l) and result_l = result.(l) in for k=0 to nq-1 do result_l.(k) <- v1_l.(k) *. f1.(k) done; done; Some result end else None in let v3 = let f2 = Array.init nq (fun k -> let x = expo_inv_q.(k) *. f1.(k) in if (!do_compute) then x else (if abs_float x > cutoff then do_compute := true ; x) ) in if (!do_compute) then match vrr_v (m+1) angMom_a cmm with | None -> None | Some v3 -> begin let result = Array.make_matrix np nq 0. in for l=0 to np-1 do let v3_l = v3.(l) and result_l = result.(l) in for k=0 to nq-1 do result_l.(k) <- v3_l.(k) *. f2.(k) done done; Some result end else None in match p1, v1, v3 with | None, None, None -> None | Some p1, None, None -> Some p1 | None, Some v1, None -> Some v1 | None, None, Some v3 -> Some v3 | Some p1, Some v1, Some v3 -> begin for l=0 to np-1 do let v3_l = v3.(l) and v1_l = v1.(l) and p1_l = p1.(l) in for k=0 to nq-1 do v3_l.(k) <- p1_l.(k) +. v1_l.(k) +. v3_l.(k) done done; Some v3 end | Some p1, Some v1, None -> begin for l=0 to np-1 do let v1_l = v1.(l) and p1_l = p1.(l) in for k=0 to nq-1 do p1_l.(k) <- v1_l.(k) +. p1_l.(k) done done; Some p1 end | Some p1, None, Some v3 -> begin for l=0 to np-1 do let v3_l = v3.(l) and p1_l = p1.(l) in for k=0 to nq-1 do p1_l.(k) <- p1_l.(k) +. v3_l.(k) done done; Some p1 end | None , Some v1, Some v3 -> begin for l=0 to np-1 do let v3_l = v3.(l) and v1_l = v1.(l) in for k=0 to nq-1 do v3_l.(k) <- v1_l.(k) +. v3_l.(k) done done; Some v3 end in if (axyz < 1) || (cxyz < 1) then p2 else let am = Po.decr xyz angMom_a in let v = vrr_v (m+1) am cm in match (p2, v) with | None, None -> None | Some p2, None -> Some p2 | _, Some v -> begin let p2 = match p2 with | None -> Array.make_matrix np nq 0. | Some p2 -> p2 in for l=0 to np-1 do let fa = (float_of_int axyz) *. expo_inv_p.(l) *. 0.5 in let p2_l = p2.(l) and v_l = v.(l) in for k=0 to nq-1 do p2_l.(k) <- p2_l.(k) -. fa *. expo_inv_q.(k) *. v_l.(k) done done; Some p2 end end in Zmap.add map_2d.(m) key result; result (* and trr_v angMom_a angMom_c = match (angMom_a.Po.tot, angMom_c.Po.tot) with | (i,0) -> Some (vrr0_v angMom_a).(0) | (_,_) -> let key = Zkey.of_powers_six angMom_a angMom_c in try Zmap.find map_2d.(0) key with | Not_found -> let xyz = get_xyz angMom_c in let axyz = Po.get xyz angMom_a in let cm = Po.decr xyz angMom_c in let cmxyz = Po.get xyz cm in let expo_inv_q_over_p = Array.mapi (fun l expo_inv_p_l -> let expo_p_l = 1./.expo_inv_p_l in Array.mapi (fun k expo_inv_q_k -> expo_inv_q_k *. expo_p_l) expo_inv_q ) expo_inv_p in let result = None in let result = if cmxyz < 1 then result else begin let f = 0.5 *. (float_of_int cmxyz) in let cmm = Po.decr xyz cm in match result, trr_v angMom_a cmm with | None, None -> None | None, Some v3 -> Some (Array.init np (fun l -> let v3_l = v3.(l) in Array.mapi (fun k v3_lk -> expo_inv_q.(k) *. f *. v3_lk) v3_l ) ) | Some result, None -> Some result | Some result, Some v3 -> (Array.iteri (fun l v3_l -> let result_l = result.(l) in Array.iteri (fun k v3_lk -> result_l.(k) <- result_l.(k) +. expo_inv_q.(k) *. f *. v3_lk) v3_l ) v3 ; Some result) end in let result = begin match result, trr_v angMom_a cm with | Some result, None -> Some result | Some result, Some v1 -> (Array.iteri (fun l v1_l -> let cpa = (center_pa xyz).(l) and result_l = result.(l) and expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in Array.iteri (fun k v1_lk -> let cqc = (center_qc xyz).(k) in result_l.(k) <- result_l.(k) +. (cqc +. expo_inv_q_over_p_l.(k) *. cpa) *. v1_lk ) v1_l ) v1 ; Some result) | None, None -> None | None, Some v1 -> Some (Array.init np (fun l -> let v1_l = v1.(l) and cpa = (center_pa xyz).(l) and expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in Array.mapi (fun k v1_lk -> let cqc = (center_qc xyz).(k) in (cqc +. expo_inv_q_over_p_l.(k) *. cpa) *. v1_lk ) v1_l ) ) end in let result = if cmxyz < 0 then result else begin let ap = Po.incr xyz angMom_a in match result, trr_v ap cm with | Some result, None -> Some result | Some result, Some v4 -> (Array.iteri (fun l v4_l -> let result_l = result.(l) in Array.iteri (fun k v4_lk -> let expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in result_l.(k) <- result_l.(k) -. expo_inv_q_over_p_l.(k) *. v4_lk) v4_l ) v4 ; Some result) | None, None -> None | None, Some v4 -> Some (Array.init np (fun l -> let v4_l = v4.(l) in let expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in Array.mapi (fun k v4_lk -> -. expo_inv_q_over_p_l.(k) *. v4_lk) v4_l ) ) end in let result = if axyz < 1 then result else begin let f = 0.5 *. (float_of_int axyz) in let am = Po.decr xyz angMom_a in match result, trr_v am cm with | Some result, None -> Some result | Some result, Some v2 -> (Array.iteri (fun l v2_l -> let result_l = result.(l) in Array.iteri (fun k v2_lk -> result_l.(k) <- result_l.(k) +. expo_inv_q.(k) *. f *. v2_lk) v2_l ) v2; Some result) | None, None -> None | None, Some v2 -> Some (Array.init np (fun l -> let v2_l = v2.(l) in Array.mapi (fun k v2_lk -> expo_inv_q.(k) *. f *. v2_lk) v2_l ) ) end in Zmap.add map_2d.(0) key result; result *) in let sum matrix = Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix in let vrr_v a c = let v = (* if c.Po.tot <> 0 then vrr_v 0 a c else trr_v a c *) vrr_v 0 a c in match v with | Some matrix -> sum matrix | None -> 0. in (** Horizontal recurrence relations *) let rec hrr0_v angMom_a angMom_b angMom_c = match angMom_b.Po.tot with | 0 -> begin 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 = Csp.totAngMomInt shell_p + Csp.totAngMomInt shell_q 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.coef 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.coef 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.coef shell_p) in build_list (cutoff /. coef_max_q) vec [] (Array.length vec - 1) and q_list = let vec = (Csp.coef 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 -> sp.(ab-1).Sp.expo_inv) and expo_inv_q = Vec.init nq (fun cd -> sq.(cd-1).Sp.expo_inv) in let coef = let result = Mat.make0 nq np in Lacaml.D.ger (Vec.of_array @@ filter_q (Csp.coef shell_q)) (Vec.of_array @@ filter_p (Csp.coef 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.(sp.(i-1).Sp.center |- sq.(j-1).Sp.center) 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.coef shell_p) and cq = filter_q (Csp.coef 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 -> shell_ab.Sp.expo_inv) sp and expo_inv_q = Array.map (fun shell_cd -> shell_cd.Sp.expo_inv) sq in let expo_b = Array.map (fun shell_ab -> (Cs.expo shell_b).(shell_ab.Sp.j)) sp and expo_d = Array.map (fun shell_cd -> (Cs.expo shell_d).(shell_cd.Sp.j)) sq in let norm_coef_scale_p = Csp.norm_coef_scale 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.(shell_ab.Sp.center |- shell_cd.Sp.center) 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.(shell_ab.Sp.center |- 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.(shell_cd.Sp.center |- 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_coef_scale 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.create ~cutoff shell_a shell_b and shell_q = Csp.create ~cutoff shell_c shell_d in contracted_class_shell_pairs ~zero_m shell_p shell_q