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QCaml/Basis/TwoElectronRRVectorized.ml

825 lines
28 KiB
OCaml

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
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
(** 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 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_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 @@ 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_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 =
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_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 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 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.a_minus_b shell_p,
Csp.a_minus_b 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
with NullQuartet -> empty