open Util open Lacaml.D open Bigarray module Am = AngularMomentum module Co = Coordinate module Cs = ContractedShell module Csp = ContractedShellPair module Cspc = ContractedShellPairCouple module Po = Powers module Psp = PrimitiveShellPair module Ps = PrimitiveShell module Zp = Zero_m_parameters exception NullQuartet exception Found let cutoff = Constants.integrals_cutoff let cutoff2 = cutoff *. cutoff let empty = Zmap.create 0 let at_least_one_valid arr = try Array.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false with Found -> true type four_idx_intermediate = { expo_b : float array; expo_d : float array; expo_p_inv : float array; expo_q_inv : float array; center_ab : Co.t ; center_cd : Co.t ; center_pq : Co.axis -> float array array; center_pa : Co.axis -> float array; center_qc : Co.axis -> float array; zero_m_array : float array array array; } (** Horizontal and Vertical Recurrence Relations (HVRR) *) let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d) abcd map_1d map_2d np nq = let expo_p_inv = abcd.expo_p_inv and expo_q_inv = abcd.expo_q_inv and center_ab = abcd.center_ab and center_cd = abcd.center_cd and center_pq = abcd.center_pq in let zero_m_array = abcd.zero_m_array in 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 let expo_b = abcd.expo_b in Array.iteri (fun m result_m -> let v0 = v_am.(m) in Array.iteri (fun l result_ml -> let f0 = -. expo_b.(l) *. expo_p_inv.(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_p_inv else begin let amm = Po.decr xyz am in let amxyz = float_of_int_fast amxyz in let v_amm = vrr0_v amm in Array.iteri (fun l expo_inv_p_l -> let f = amxyz *. expo_p_inv.(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_p_inv 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 | (_,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 = let expo_d = abcd.expo_d in Array.init nq (fun k -> let x = expo_d.(k) *. expo_q_inv.(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_q_inv.(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_fast (cxyz-1)) *. 0.5 in let f1 = Array.init nq (fun k -> let x = fcm *. expo_q_inv.(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_q_inv.(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_fast axyz) *. expo_p_inv.(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_q_inv.(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_q_inv ) expo_p_inv in let result = None in let result = if cmxyz < 1 then result else begin let f = 0.5 *. (float_of_int_fast 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_q_inv.(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_q_inv.(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_fast 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_q_inv.(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_q_inv.(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 ~basis ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t = let sp = Csp.shell_pairs shell_p and sq = Csp.shell_pairs shell_q and cp = Csp.coefficients shell_p and cq = Csp.coefficients shell_q in let np, nq = Array.length sp, Array.length sq in try match Cspc.make ~cutoff shell_p shell_q with | None -> raise NullQuartet | Some shell_pair_couple -> let shell_a = Cspc.shell_a shell_pair_couple and shell_c = Cspc.shell_c shell_pair_couple in let maxm = Am.to_int (Cspc.ang_mom shell_pair_couple) in (* Pre-computation of integral class indices *) let class_indices = Cspc.zkey_array shell_pair_couple in let contracted_class = Array.make (Array.length class_indices) 0.; in let monocentric = Cspc.monocentric shell_pair_couple in (* Compute all integrals in the shell for each pair of significant shell pairs *) begin match Cspc.ang_mom shell_pair_couple with | Am.S -> contracted_class.(0) <- begin try let expo_p_inv = Vec.init np (fun ab -> Psp.exponent_inv sp.(ab-1)) and expo_q_inv = 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 @@ cq) (Vec.of_array @@ cp) 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_p_inv, expo_q_inv = expo_p_inv.{i}, expo_q_inv.{j} in let center_pq = Co.(Psp.center sp.(i-1) |- Psp.center sq.(j-1)) and center_pa = Co.(Psp.center sp.(i-1) |- Cs.center shell_a) and center_qc = Co.(Psp.center sq.(i-1) |- Cs.center shell_c) in let norm_pq_sq = Co.dot center_pq center_pq in let zero = Zp.zero basis zero_m in let zero_m_array = zero_m {zero with expo_p_inv ; expo_q_inv ; norm_pq_sq ; center_pq ; center_pa ; center_qc ; } in zero_m_array.(0) with NullQuartet -> 0. ) in Mat.gemm_trace zm_array coef with (Invalid_argument _) -> 0. end | _ -> let coef = Array.init np (fun l -> Array.init nq (fun k -> cq.(k) *. cp.(l)) ) in let norm = Cspc.norm_scales shell_pair_couple in let expo_p_inv = Array.map (fun shell_ab -> Psp.exponent_inv shell_ab) sp and expo_q_inv = 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 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 let center_qc_tmp = Array.init nq (fun cd -> Coordinate.make { Coordinate. x = (center_qc Co.X).(cd) ; y = (center_qc Co.Y).(cd) ; z = (center_qc Co.Z).(cd) ; }) in Array.iteri (fun ab _shell_ab -> let center_pa = Coordinate.make { Coordinate. x = (center_pa Co.X).(ab) ; y = (center_pa Co.Y).(ab) ; z = (center_pa Co.Z).(ab) ; } in let zero_m_array_tmp = Array.mapi (fun cd _shell_cd -> if (abs_float coef.(ab).(cd) < cutoff) then empty else let expo_p_inv, expo_q_inv = expo_p_inv.(ab), expo_q_inv.(cd) in let x = (center_pq X).(ab).(cd) and y = (center_pq Y).(ab).(cd) and z = (center_pq Z).(ab).(cd) in let norm_pq_sq = x *. x +. y *. y +. z *. z in let zero = Zp.zero basis zero_m in zero_m {zero with maxm ; expo_p_inv ; expo_q_inv ; norm_pq_sq ; center_pq = Coordinate.make Coordinate.{x ; y ; z} ; center_pa ; center_qc = center_qc_tmp.(cd) ; } ) 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 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 abcd = { expo_b ; expo_d ; expo_p_inv ; expo_q_inv ; center_ab = Csp.a_minus_b shell_p; center_cd = Csp.a_minus_b shell_q ; center_pq ; center_pa ; center_qc ; zero_m_array } in let integral = hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d) abcd 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 with NullQuartet -> empty