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QCaml/Basis/TwoElectronRRVectorized.ml
2018-02-11 02:41:55 +01:00

730 lines
25 KiB
OCaml

open Util
open Lacaml.D
open Bigarray
let cutoff = Constants.cutoff
let cutoff2 = cutoff *. cutoff
exception NullQuartet
exception Found
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)
(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
(maxm, zero_m_array)
(expo_b, expo_d)
(expo_inv_p, expo_inv_q)
(center_ab, center_cd, center_pq)
map_1d map_2d np nq
=
let totAngMom_a = Angular_momentum.to_int totAngMom_a
and totAngMom_b = Angular_momentum.to_int totAngMom_b
and totAngMom_c = Angular_momentum.to_int totAngMom_c
and totAngMom_d = Angular_momentum.to_int totAngMom_d
in
(** Vertical recurrence relations *)
let rec vrr0_v m angMom_a = function
| 0 -> Some zero_m_array.(m)
| totAngMom_a ->
let key = Zkey.of_int_tuple (Zkey.Three angMom_a)
in
try Zmap.find map_1d.(m) key with
| Not_found ->
let result =
let am, amm, amxyz, xyz =
match angMom_a with
| (x,0,0) -> (x-1,0,0),(x-2,0,0), x-1, 0
| (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1
| (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2
in
if amxyz < 0 then
None
else
begin
let cab = Coordinate.coord center_ab xyz in
let v1_top, p1_top =
if abs_float cab < cutoff then
None,
vrr0_v (m+1) am (totAngMom_a-1)
else
vrr0_v m am (totAngMom_a-1),
vrr0_v (m+1) am (totAngMom_a-1)
in
let v1_top2, p1_top2 =
if amxyz < 1 then (None,None) else
vrr0_v m amm (totAngMom_a-2),
vrr0_v (m+1) amm (totAngMom_a-2)
in
let result = Array.make_matrix np nq 0. in
if amxyz < 1 then
begin
let p0 =
match p1_top with
| Some p1_top -> p1_top
| _ -> assert false
in
begin
match v1_top with
| None -> ()
| Some v0 ->
for l=0 to np-1 do
let f0 =
-. expo_b.(l) *. expo_inv_p.(l) *. cab
in
for k=0 to nq-1 do
result.(l).(k) <- v0.(l).(k) *. f0
done
done
end;
for l=0 to np-1 do
for k=0 to nq-1 do
result.(l).(k) <- result.(l).(k)
+. expo_inv_p.(l) *. center_pq.(xyz).(l).(k) *. p0.(l).(k)
done
done
end
else
begin
let p0 =
match p1_top with
| Some p1_top -> p1_top
| _ -> assert false
in
begin
match v1_top with
| None -> ()
| Some v0 ->
for l=0 to np-1 do
let f0 = -. expo_b.(l) *. expo_inv_p.(l) *. cab in
for k=0 to nq-1 do
result.(l).(k) <- v0.(l).(k) *. f0
done
done
end;
let v1 =
match v1_top2 with
| Some v1_top2 -> v1_top2
| None -> assert false
in
let v2 =
match p1_top2 with
| Some p1_top2 -> p1_top2
| None -> assert false
in
for l=0 to np-1 do
let f = (float_of_int amxyz) *. expo_inv_p.(l) *. 0.5 in
for k=0 to nq-1
do
result.(l).(k) <- result.(l).(k) +.
expo_inv_p.(l) *. center_pq.(xyz).(l).(k) *. p0.(l).(k) +.
f *. (v1.(l).(k) +. v2.(l).(k) *. expo_inv_p.(l))
done
done
end;
Some result
end
in
Zmap.add map_1d.(m) key result;
result
and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =
match (totAngMom_a, totAngMom_c) with
| (i,0) -> vrr0_v m angMom_a totAngMom_a
| (_,_) ->
let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c))
in
try Zmap.find map_2d.(m) key with
| Not_found ->
let result =
begin
let am, cm, cmm, axyz, cxyz, xyz =
let (aax, aay, aaz) = angMom_a
and (acx, acy, acz) = angMom_c in
if (acz > 0) then
(aax, aay, aaz-1),
(acx, acy, acz-1),
(acx, acy, acz-2),
aaz, acz, 2
else if (acy > 0) then
(aax, aay-1,aaz),
(acx, acy-1,acz),
(acx, acy-2,acz),
aay,acy, 1
else
(aax-1,aay,aaz),
(acx-1,acy,acz),
(acx-2,acy,acz),
aax,acx, 0
in
(*
let result = Array.make_matrix np nq 0. in
*)
let do_compute = ref false in
let v1 =
let f = -. (Coordinate.coord center_cd xyz) 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 totAngMom_a (totAngMom_c-1) with
| None -> None
| Some v1 ->
begin
let result = Array.make_matrix np nq 0. in
for l=0 to np-1 do
for k=0 to nq-1 do
result.(l).(k) <- v1.(l).(k) *. f1.(k)
done
done;
Some result
end
else None
in
let v2 =
let f2 =
Array.init np (fun l ->
Array.init nq (fun k ->
let x = expo_inv_q.(k) *. center_pq.(xyz).(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 totAngMom_a (totAngMom_c-1) with
| None -> None
| Some v2 ->
begin
for l=0 to np-1 do
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
for k=0 to nq-1 do
v2.(l).(k) <- v2.(l).(k) +. v1.(l).(k)
done
done;
Some v2
end
in
let p2 =
if cxyz < 2 then p1 else
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 totAngMom_a (totAngMom_c-2) with
| None -> None
| Some v1 ->
begin
let result = Array.make_matrix np nq 0. in
for l=0 to np-1 do
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 totAngMom_a (totAngMom_c-2) with
| None -> None
| Some v3 ->
begin
let result = Array.make_matrix np nq 0. in
for l=0 to np-1 do
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
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
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
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
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 v =
vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
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
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
(** Horizontal recurrence relations *)
and hrr0_v angMom_a angMom_b angMom_c
totAngMom_a totAngMom_b totAngMom_c =
match totAngMom_b with
| 0 ->
begin
match (totAngMom_a, totAngMom_c) with
| (0,0) -> Array.fold_left (fun accu c ->
accu +. Array.fold_left (+.) 0. c) 0. zero_m_array.(0)
| (_,_) ->
begin
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
| None -> 0.
end
end
| 1 ->
let (aax, aay, aaz) = angMom_a in
let ap, xyz =
match angMom_b with
| (_,_,1) -> (aax,aay,aaz+1), 2
| (_,1,_) -> (aax,aay+1,aaz), 1
| (_,_,_) -> (aax+1,aay,aaz), 0
in
let f = Coordinate.coord center_ab xyz in
let v1 =
match vrr_v 0 ap angMom_c (totAngMom_a+1) totAngMom_c with
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
| None -> 0.
in
if (abs_float f < cutoff) then v1 else
let v2 =
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
| None -> 0.
in
v1 +. v2 *. f
| _ ->
let (aax, aay, aaz) = angMom_a
and (abx, aby, abz) = angMom_b in
let bxyz, xyz =
match angMom_b with
| (0,0,_) -> abz, 2
| (0,_,_) -> aby, 1
| _ -> abx, 0
in
if (bxyz < 1) then 0. else
let ap, bm =
match xyz with
| 0 -> (aax+1,aay,aaz),(abx-1,aby,abz)
| 1 -> (aax,aay+1,aaz),(abx,aby-1,abz)
| _ -> (aax,aay,aaz+1),(abx,aby,abz-1)
in
let h1 =
hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
in
let f = (Coordinate.coord center_ab xyz) in
if (abs_float f < cutoff) then h1 else
let h2 =
hrr0_v angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
in
h1 +. h2 *. f
and hrr_v angMom_a angMom_b angMom_c angMom_d
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
match (totAngMom_b, totAngMom_d) with
| (_,0) -> if (totAngMom_b = 0) then
begin
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
| None -> 0.
end
else
hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
| (_,_) ->
let (acx, acy, acz) = angMom_c
and (adx, ady, adz) = angMom_d in
let cp, dm, xyz =
match angMom_d with
| (_,0,0) -> (acx+1, acy, acz), (adx-1, ady, adz), 0
| (_,_,0) -> (acx, acy+1, acz), (adx, ady-1, adz), 1
| _ -> (acx, acy, acz+1), (adx, ady, adz-1), 2
in
let h1 =
hrr_v angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
in
let f = (Coordinate.coord center_cd xyz) in
if (abs_float f < cutoff) then
h1
else
let h2 =
hrr_v angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
in h1 +. f *. h2
in
hrr_v
(angMom_a.(0),angMom_a.(1),angMom_a.(2))
(angMom_b.(0),angMom_b.(1),angMom_b.(2))
(angMom_c.(0),angMom_c.(1),angMom_c.(2))
(angMom_d.(0),angMom_d.(1),angMom_d.(2))
totAngMom_a totAngMom_b totAngMom_c totAngMom_d
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
let shell_a = shell_p.ContractedShellPair.shell_a
and shell_b = shell_p.ContractedShellPair.shell_b
and shell_c = shell_q.ContractedShellPair.shell_a
and shell_d = shell_q.ContractedShellPair.shell_b
and sp = shell_p.ContractedShellPair.shell_pairs
and sq = shell_q.ContractedShellPair.shell_pairs
in
let maxm =
shell_p.ContractedShellPair.totAngMomInt +
shell_q.ContractedShellPair.totAngMomInt
in
(* Pre-computation of integral class indices *)
let class_indices =
Angular_momentum.zkey_array
(Angular_momentum.Quartet
Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d))
in
let contracted_class =
Array.make (Array.length class_indices) 0.;
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. shell_p.ContractedShellPair.coef
and coef_max_q =
Array.fold_left (fun accu x ->
if (abs_float x) > accu then (abs_float x) else accu)
0. shell_q.ContractedShellPair.coef
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 = shell_p.ContractedShellPair.coef in
build_list (cutoff /. coef_max_q) vec [] (Array.length vec - 1)
and q_list =
let vec = shell_q.ContractedShellPair.coef in
build_list (cutoff /. coef_max_p) vec [] (Array.length vec - 1)
in
(*
if (Array.length p_list) < (Array.length shell_p.ContractedShellPair.coef) then
begin
Printf.printf "Reduced p from %d to %d:\n" (Array.length
shell_p.ContractedShellPair.coef) (Array.length p_list);
Array.iter (fun k -> Printf.printf "%d " k) p_list; print_newline ();
Printf.printf "\n%!"
end;
if (Array.length q_list) < (Array.length shell_q.ContractedShellPair.coef) then
begin
Printf.printf "Reduced q from %d to %d:\n" (Array.length
shell_q.ContractedShellPair.coef) (Array.length q_list);
Array.iter (fun k -> Printf.printf "%d " k) q_list; print_newline ();
Printf.printf "\n%!"
end;
*)
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 Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d) with
| Angular_momentum.(S,S,S,S) ->
contracted_class.(0) <-
begin
try
let expo_inv_p =
Vec.init np (fun ab -> sp.(ab-1).ShellPair.expo_inv)
and expo_inv_q =
Vec.init nq (fun cd -> sq.(cd-1).ShellPair.expo_inv)
in
let coef =
let result = Mat.make0 nq np in
Lacaml.D.ger
(Vec.of_array @@ filter_q shell_q.ContractedShellPair.coef)
(Vec.of_array @@ filter_p shell_p.ContractedShellPair.coef)
result;
result
in
let zm_array = Mat.init_cols np nq (fun i j ->
try
if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then
raise NullQuartet;
let expo_pq_inv =
expo_inv_p.{i} +. expo_inv_q.{j}
in
let center_pq =
Coordinate.(sp.(i-1).ShellPair.center |- sq.(j-1).ShellPair.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
in
let zero_m_array =
zero_m ~maxm:0 ~expo_pq_inv ~norm_pq_sq
in
zero_m_array.(0)
with NullQuartet -> 0.
) in
Mat.gemm_trace zm_array coef
with (Invalid_argument _) -> 0.
end
| _ ->
let coef =
let cp = filter_p shell_p.ContractedShellPair.coef
and cq = filter_q shell_q.ContractedShellPair.coef
in
Array.init np (fun l -> Array.init nq (fun k -> cq.(k) *. cp.(l)) )
in
let expo_inv_p =
Array.map (fun shell_ab -> shell_ab.ShellPair.expo_inv) sp
and expo_inv_q =
Array.map (fun shell_cd -> shell_cd.ShellPair.expo_inv) sq
in
let expo_b =
Array.map (fun shell_ab -> Contracted_shell.expo shell_b shell_ab.ShellPair.j) sp
and expo_d =
Array.map (fun shell_cd -> Contracted_shell.expo shell_d shell_cd.ShellPair.j) sq
in
let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
let center_pq =
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 =
Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
in
match xyz with
| 0 -> Coordinate.x cpq;
| 1 -> Coordinate.y cpq;
| 2 -> Coordinate.z cpq;
| _ -> assert false
)
)
)
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 =
center_pq.(0).(ab).(cd) *. center_pq.(0).(ab).(cd) +.
center_pq.(1).(ab).(cd) *. center_pq.(1).(ab).(cd) +.
center_pq.(2).(ab).(cd) *. center_pq.(2).(ab).(cd)
in
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
) sq
in
(* Transpose result *)
for m=0 to maxm do
for cd=0 to nq-1 do
result.(m).(ab).(cd) <- zero_m_array_tmp.(cd).(m) *. coef.(ab).(cd)
done
done
) sp;
result
in
let norm =
let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
Array.map (fun v1 ->
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
) norm_coef_scale_p
|> Array.to_list
|> Array.concat
in
let map_1d = Array.init (maxm+1) (fun _ -> Zmap.create (4*maxm))
and map_2d = Array.init (maxm+1) (fun _ -> Zmap.create (Array.length class_indices))
in
(* Compute the integral class from the primitive shell quartet *)
Array.iteri (fun i key ->
let a = Zkey.to_int_array Zkey.Kind_12 key in
let (angMomA,angMomB,angMomC,angMomD) =
( [| a.(0) ; a.(1) ; a.(2) |],
[| a.(3) ; a.(4) ; a.(5) |],
[| a.(6) ; a.(7) ; a.(8) |],
[| a.(9) ; a.(10) ; a.(11) |] )
in
let integral =
hvrr_two_e_vector (angMomA, angMomB, angMomC, angMomD)
(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
(maxm, zero_m_array)
(expo_b, expo_d)
(expo_inv_p, expo_inv_q)
(shell_p.ContractedShellPair.center_ab,
shell_q.ContractedShellPair.center_ab, center_pq)
map_1d map_2d np nq
in
contracted_class.(i) <- contracted_class.(i) +. integral *. norm.(i)
) class_indices
end;
let result =
Zmap.create (Array.length contracted_class)
in
Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
result
(** Computes all the two-electron integrals of the contracted shell quartet *)
let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
let shell_p = ContractedShellPair.create ~cutoff shell_a shell_b
and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d
in
contracted_class_shell_pairs ~zero_m shell_p shell_q