mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-06-19 19:52:06 +02:00
491 lines
16 KiB
OCaml
491 lines
16 KiB
OCaml
open Util
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open Lacaml.D
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open Bigarray
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let cutoff = Constants.cutoff
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let cutoff2 = cutoff *. cutoff
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exception NullQuartet
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exception Found
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let at_least_one_valid arr =
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try
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Vec.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false
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with Found -> true
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(*TODO : REMOVE *)
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let sum integral =
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Array.fold_left (+.) 0. integral
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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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(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
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(maxm, 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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coef_prod map_1d map_2d
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=
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let nq = Mat.dim1 coef_prod in
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let np = Mat.dim2 coef_prod in
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let empty =
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Array.make nq 0.
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in
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let totAngMom_a = Angular_momentum.to_int totAngMom_a
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and totAngMom_b = Angular_momentum.to_int totAngMom_b
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and totAngMom_c = Angular_momentum.to_int totAngMom_c
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and totAngMom_d = Angular_momentum.to_int totAngMom_d
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in
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(** Vertical recurrence relations *)
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let rec vrr0_v l m angMom_a = function
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| 1 ->
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let xyz =
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match angMom_a with
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| (1,_,_) -> 0
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| (_,1,_) -> 1
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| _ -> 2
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in
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let f = expo_b.{l} *. (Coordinate.coord center_ab xyz) in
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Array.init nq (fun k -> coef_prod.{k+1,l} *. expo_inv_p.{l} *.
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(center_pq.{xyz+1,k+1,l} *. zero_m_array.(m+1).{k+1,l}
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-. f *. zero_m_array.(m).{k+1,l} ) )
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| 0 -> Array.init nq (fun k -> zero_m_array.(m).{k+1,l} *. coef_prod.{k+1,l})
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| totAngMom_a ->
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let key = Zkey.of_int_tuple (Zkey.Three angMom_a)
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in
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try Zmap.find map_1d.(m).(l-1) key with
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| Not_found ->
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let result =
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let am, amm, amxyz, xyz =
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match angMom_a with
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| (x,0,0) -> (x-1,0,0),(x-2,0,0), x-1, 0
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| (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1
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| (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2
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in
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if amxyz < 0 then empty else
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let v1 =
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let f =
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-. expo_b.{l} *. expo_inv_p.{l} *. (Coordinate.coord center_ab xyz)
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in
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if (abs_float f < cutoff) then empty else
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Array.map (fun v1k -> f *. v1k) (vrr0_v l m am (totAngMom_a-1) )
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in
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let p1 =
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Array.mapi (fun k v2k -> v1.(k) +. expo_inv_p.{l} *. center_pq.{xyz+1,k+1,l} *. v2k) (vrr0_v l (m+1) am (totAngMom_a-1))
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in
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if amxyz < 1 then p1 else
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let f = (float_of_int amxyz) *. expo_inv_p.{l} *. 0.5
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in
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if (abs_float f < cutoff) then empty else
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let v1 = vrr0_v l m amm (totAngMom_a-2)
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in
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let v2 =
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if (abs_float (f *. expo_inv_p.{l})) < cutoff then empty else
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vrr0_v l (m+1) amm (totAngMom_a-2)
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in
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Array.init nq (fun k -> p1.(k) +.
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f *. (v1.(k) +. v2.(k) *. expo_inv_p.{l} ) )
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in Zmap.add map_1d.(m).(l-1) key result;
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result
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and vrr_v l m angMom_a angMom_c totAngMom_a totAngMom_c =
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match (totAngMom_a, totAngMom_c) with
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| (i,0) -> if (i>0) then
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vrr0_v l m angMom_a totAngMom_a
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else
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Array.init nq (fun k -> zero_m_array.(m).{k+1,l} *. coef_prod.{k+1,l})
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| (_,_) ->
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let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c))
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in
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try Zmap.find map_2d.(m).(l-1) key with
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| Not_found ->
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let result =
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begin
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let am, cm, cmm, axyz, cxyz, xyz =
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let (aax, aay, aaz) = angMom_a
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and (acx, acy, acz) = angMom_c in
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if (acz > 0) then
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(aax, aay, aaz-1),
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(acx, acy, acz-1),
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(acx, acy, acz-2),
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aaz, acz, 2
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else if (acy > 0) then
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(aax, aay-1,aaz),
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(acx, acy-1,acz),
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(acx, acy-2,acz),
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aay,acy, 1
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else
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(aax-1,aay,aaz),
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(acx-1,acy,acz),
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(acx-2,acy,acz),
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aax,acx, 0
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in
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(*
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if cxyz < 1 then empty else
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*)
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let f1 =
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let f = (Coordinate.coord center_cd xyz) in
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Array.init nq (fun k ->
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expo_d.{k+1} *. expo_inv_q.{k+1} *. f)
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|> Vec.of_array
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in
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let f2 =
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Array.init nq (fun k ->
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expo_inv_q.{k+1} *. center_pq.{xyz+1,k+1,l} )
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|> Vec.of_array
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in
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let v1 =
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if (at_least_one_valid f1) then
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vrr_v l m angMom_a cm totAngMom_a (totAngMom_c-1)
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else empty
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and v2 =
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if (at_least_one_valid f2) then
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vrr_v l (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
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else empty
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in
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let p1 =
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Array.init nq (fun k -> -. v1.(k) *. f1.{k+1} -. v2.(k) *. f2.{k+1})
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in
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let p2 =
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if cxyz < 2 then p1 else
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let fcm =
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(float_of_int (cxyz-1)) *. 0.5
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in
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let f1 =
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Vec.map (fun e -> fcm *. e) expo_inv_q
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in
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let f2 =
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Vec.mul f1 expo_inv_q
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in
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let v1 =
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if (at_least_one_valid f1) then
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vrr_v l m angMom_a cmm totAngMom_a (totAngMom_c-2)
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else empty
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in
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let v2 =
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if (at_least_one_valid f2) then
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vrr_v l (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
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else empty
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in
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Array.init nq (fun k -> p1.(k) +. f1.{k+1} *. v1.(k) +. f2.{k+1} *. v2.(k))
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in
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if (axyz < 1) || (cxyz < 1) then p2 else
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let fa =
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(float_of_int axyz) *. expo_inv_p.{l} *. 0.5
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in
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let f1 =
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Vec.map (fun e -> fa *. e ) expo_inv_q
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in
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if (at_least_one_valid f1) then
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let v =
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vrr_v l (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
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in
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Array.init nq (fun k -> p2.(k) -. f1.{k+1} *. v.(k))
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else p2
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end
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in Zmap.add map_2d.(m).(l-1) key result;
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result
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(** Horizontal recurrence relations *)
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and hrr0_v l angMom_a angMom_b angMom_c
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totAngMom_a totAngMom_b totAngMom_c =
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match totAngMom_b with
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| 0 ->
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begin
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match (totAngMom_a, totAngMom_c) with
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| (0,0) ->
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Array.init nq (fun k -> zero_m_array.(0).{k+1,l} *. coef_prod.{k+1,l})
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|> sum
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| (_,0) -> vrr0_v l 0 angMom_a totAngMom_a |> sum
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| (_,_) -> vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c |> sum
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end
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| 1 ->
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let (aax, aay, aaz) = angMom_a in
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let ap, xyz =
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match angMom_b with
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| (_,_,1) -> (aax,aay,aaz+1), 2
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| (_,1,_) -> (aax,aay+1,aaz), 1
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| (_,_,_) -> (aax+1,aay,aaz), 0
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in
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let f = Coordinate.coord center_ab xyz in
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let v1 =
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vrr_v l 0 ap angMom_c (totAngMom_a+1) totAngMom_c
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in
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if (abs_float f < cutoff) then sum v1 else
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let v2 =
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vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c
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in
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Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2 |> sum
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| _ ->
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let (aax, aay, aaz) = angMom_a
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and (abx, aby, abz) = angMom_b in
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let bxyz, xyz =
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match angMom_b with
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| (0,0,_) -> abz, 2
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| (0,_,_) -> aby, 1
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| _ -> abx, 0
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in
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if (bxyz < 1) then 0. else
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let ap, bm =
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match xyz with
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| 0 -> (aax+1,aay,aaz),(abx-1,aby,abz)
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| 1 -> (aax,aay+1,aaz),(abx,aby-1,abz)
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| _ -> (aax,aay,aaz+1),(abx,aby,abz-1)
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in
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let h1 =
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hrr0_v l ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
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in
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let f = (Coordinate.coord center_ab xyz) in
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if (abs_float f < cutoff) then h1 else
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let h2 =
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hrr0_v l angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
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in
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h1 +. h2 *. f
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and hrr_v l angMom_a angMom_b angMom_c angMom_d
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
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match (totAngMom_b, totAngMom_d) with
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| (_,0) -> if (totAngMom_b = 0) then
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vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c
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|> sum
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else
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hrr0_v l angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (_,_) ->
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let (acx, acy, acz) = angMom_c
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and (adx, ady, adz) = angMom_d in
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let cp, dm, xyz =
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match angMom_d with
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| (_,0,0) -> (acx+1, acy, acz), (adx-1, ady, adz), 0
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| (_,_,0) -> (acx, acy+1, acz), (adx, ady-1, adz), 1
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| _ -> (acx, acy, acz+1), (adx, ady, adz-1), 2
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in
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let h1 =
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hrr_v l angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
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and h2 =
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hrr_v l angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
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in
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let f = (Coordinate.coord center_cd xyz) in
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h1 +. f *. h2
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in
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Array.init np (fun ab ->
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hrr_v (ab+1)
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(angMom_a.(0),angMom_a.(1),angMom_a.(2))
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(angMom_b.(0),angMom_b.(1),angMom_b.(2))
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(angMom_c.(0),angMom_c.(1),angMom_c.(2))
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(angMom_d.(0),angMom_d.(1),angMom_d.(2))
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totAngMom_a totAngMom_b totAngMom_c totAngMom_d
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) |> sum
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let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
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let shell_a = shell_p.ContractedShellPair.shell_a
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and shell_b = shell_p.ContractedShellPair.shell_b
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and shell_c = shell_q.ContractedShellPair.shell_a
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and shell_d = shell_q.ContractedShellPair.shell_b
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and sp = shell_p.ContractedShellPair.shell_pairs
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and sq = shell_q.ContractedShellPair.shell_pairs
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in
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let maxm =
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let open Angular_momentum in
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(to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b)
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+ (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
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in
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(* Pre-computation of integral class indices *)
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let class_indices =
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Angular_momentum.zkey_array
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(Angular_momentum.Quartet
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Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d))
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in
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let contracted_class =
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Array.make (Array.length class_indices) 0.;
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in
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(* Compute all integrals in the shell for each pair of significant shell pairs *)
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let expo_inv_p =
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Array.map (fun shell_ab -> shell_ab.ShellPair.expo_inv) sp
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|> Vec.of_array
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and expo_inv_q =
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Array.map (fun shell_cd -> shell_cd.ShellPair.expo_inv) sq
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|> Vec.of_array
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in
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let np, nq =
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Vec.dim expo_inv_p, Vec.dim expo_inv_q
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in
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let coef =
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let result = Mat.make0 nq np in
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Lacaml.D.ger
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(Vec.of_array shell_q.ContractedShellPair.coef)
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(Vec.of_array shell_p.ContractedShellPair.coef)
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result;
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result
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in
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begin
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match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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totAngMom shell_c, totAngMom shell_d) with
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| Angular_momentum.(S,S,S,S) ->
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contracted_class.(0) <-
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let zm_array = Mat.init_rows np nq (fun i j ->
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(** Screening on the product of coefficients *)
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try
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if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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expo_inv_p.{i} +. expo_inv_q.{j}
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in
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let center_pq =
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Coordinate.(sp.(i-1).ShellPair.center |- sq.(j-1).ShellPair.center)
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in
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let norm_pq_sq =
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Coordinate.dot center_pq center_pq
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in
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let zero_m_array =
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zero_m ~maxm:0 ~expo_pq_inv ~norm_pq_sq
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in
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zero_m_array.(0)
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with NullQuartet -> 0.
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) in
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Mat.gemm_trace zm_array coef
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| _ ->
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let expo_b =
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Array.map (fun shell_ab -> Contracted_shell.expo shell_b shell_ab.ShellPair.j) sp
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|> Vec.of_array
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and expo_d =
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Array.map (fun shell_cd -> Contracted_shell.expo shell_d shell_cd.ShellPair.j) sq
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|> Vec.of_array
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in
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let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
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let center_pq =
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let result =
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Array3.create Float64 fortran_layout 3 nq np
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in
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Array.iteri (fun ab shell_ab ->
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Array.iteri (fun cd shell_cd ->
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let cpq =
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Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
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in
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result.{1,cd+1,ab+1} <- Coordinate.x cpq;
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result.{2,cd+1,ab+1} <- Coordinate.y cpq;
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result.{3,cd+1,ab+1} <- Coordinate.z cpq;
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) sq
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) sp;
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result
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in
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let zero_m_array =
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let result =
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Array.init (maxm+1) (fun _ -> Mat.make0 nq np)
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in
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Array.iteri (fun ab shell_ab ->
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let zero_m_array_tmp =
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Array.mapi (fun cd shell_cd ->
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let expo_pq_inv =
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expo_inv_p.{ab+1} +. expo_inv_q.{cd+1}
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in
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let norm_pq_sq =
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center_pq.{1,cd+1,ab+1} *. center_pq.{1,cd+1,ab+1} +.
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center_pq.{2,cd+1,ab+1} *. center_pq.{2,cd+1,ab+1} +.
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center_pq.{3,cd+1,ab+1} *. center_pq.{3,cd+1,ab+1}
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in
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zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
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) sq
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(*
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|> Array.to_list
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|> List.filter (fun (zero_m_array, d,
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center_pq,coef_prod) -> abs_float coef_prod >= 1.e-4 *. cutoff)
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|> Array.of_list
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*)
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in
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(* Transpose result *)
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for m=0 to maxm do
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for cd=1 to nq do
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result.(m).{cd,ab+1} <- zero_m_array_tmp.(cd-1).(m)
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done
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done
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) sp;
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result
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in
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let norm =
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let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
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Array.map (fun v1 ->
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Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
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) norm_coef_scale_p
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|> Array.to_list
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|> Array.concat
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|
in
|
|
|
|
let map_1d = Array.init maxm (fun _ -> Array.init np (fun _ -> Zmap.create (4*maxm)))
|
|
and map_2d = Array.init maxm (fun _ -> Array.init np (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)
|
|
coef map_1d map_2d
|
|
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
|
|
|