mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-06-19 19:52:06 +02:00
459 lines
16 KiB
OCaml
459 lines
16 KiB
OCaml
open Util
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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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Array.fold_left (fun _ x -> if (abs_float x > cutoff) then raise Found else false ) false arr
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with Found -> true
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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 ncoef = (Array.length coef_prod) in
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let empty =
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Array.make ncoef 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 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 *. (Coordinate.coord center_ab xyz) in
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Array.init ncoef (fun k -> coef_prod.(k) *. expo_inv_p *.
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( (Coordinate.coord center_pq.(k) xyz) *. zero_m_array.(m+1).(k)
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-. f *. zero_m_array.(m).(k) ) )
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| 0 -> Array.map2 ( *. ) zero_m_array.(m) coef_prod
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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) 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) -> (* 28_336 *) (x-1,0,0),(x-2,0,0), x-1, 0
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| (x,y,0) -> (* 52_221 *) (x,y-1,0),(x,y-2,0), y-1, 1
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| (x,y,z) -> (* 87_215 *) (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 *. expo_inv_p *. (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 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 *. (Coordinate.coord center_pq.(k) xyz) *. v2k) (vrr0_v (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 *. 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 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)) < cutoff then empty else
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vrr0_v (m+1) amm (totAngMom_a-2)
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in
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Array.init ncoef (fun k -> p1.(k) +.
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f *. (v1.(k) +. v2.(k) *. expo_inv_p ) )
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in Zmap.add map_1d.(m) key result;
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result
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and vrr_v 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 m angMom_a totAngMom_a
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else
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Array.map2 ( *. ) zero_m_array.(m) coef_prod
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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) 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 angMom_ax, angMom_ay, angMom_az = angMom_a
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and angMom_cx, angMom_cy, angMom_cz = angMom_c in
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match angMom_c with
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| (_,0,0) -> (* 321_984 *)
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(angMom_ax-1, angMom_ay, angMom_az),
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(angMom_cx-1, angMom_cy, angMom_cz),
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(angMom_cx-2, angMom_cy, angMom_cz),
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angMom_ax,angMom_cx, 0
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| (_,_,0) -> (* 612_002 *)
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(angMom_ax, angMom_ay-1, angMom_az),
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(angMom_cx, angMom_cy-1, angMom_cz),
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(angMom_cx, angMom_cy-2, angMom_cz),
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angMom_ay,angMom_cy, 1
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| _ -> (* 1_067_324 *)
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(angMom_ax, angMom_ay, angMom_az-1),
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(angMom_cx, angMom_cy, angMom_cz-1),
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(angMom_cx, angMom_cy, angMom_cz-2),
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angMom_az,angMom_cz, 2
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in
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if cxyz < 1 then empty else
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let f1 =
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Array.init ncoef (fun k ->
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expo_d.(k) *. expo_inv_q.(k) *.
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(Coordinate.coord center_cd.(k) xyz) )
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in
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let f2 =
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Array.init ncoef (fun k ->
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expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz) )
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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 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 (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 ncoef (fun k -> -. v1.(k) *. f1.(k) -. v2.(k) *. f2.(k))
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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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Array.map (fun e -> fcm *. e) expo_inv_q
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in
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let f2 =
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Array.map2 ( *. ) 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 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 (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 ncoef (fun k -> p1.(k) +. f1.(k) *. v1.(k) +. f2.(k) *. 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 *. 0.5
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in
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let f1 =
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Array.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 (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
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in
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Array.init ncoef (fun k -> p2.(k) -. f1.(k) *. v.(k))
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else p2
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end
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in Zmap.add map_2d.(m) key result;
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result
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(** Horizontal recurrence relations *)
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and hrr0_v 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) -> Array.map2 ( *. ) zero_m_array.(0) coef_prod
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| (_,0) -> vrr0_v 0 angMom_a totAngMom_a
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| (_,_) -> vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c
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end
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| 1 ->
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let angMom_ax, angMom_ay, angMom_az = angMom_a in
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(* 5_045_008 *)
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let ap, xyz =
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match angMom_b with
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| (1,_,_) -> (angMom_ax+1,angMom_ay,angMom_az), 0
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| (_,1,_) -> (angMom_ax,angMom_ay+1,angMom_az), 1
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| (_,_,_) -> (angMom_ax,angMom_ay,angMom_az+1), 2
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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 0 ap angMom_c (totAngMom_a+1) totAngMom_c
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in
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if (abs_float f < cutoff) then v1 else
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let v2 =
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vrr_v 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
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| _ ->
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let angMom_ax, angMom_ay, angMom_az = angMom_a
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and angMom_bx, angMom_by, angMom_bz = angMom_b in
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(* 3_403_478 *)
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let bxyz, xyz =
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match angMom_b with
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| (1,_,_) -> angMom_bx, 0
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| (_,1,_) -> angMom_by, 1
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| (_,_,_) -> angMom_bz, 2
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in
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if (bxyz < 1) then empty else
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let ap, bm =
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match xyz with
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| 0 -> (angMom_ax+1,angMom_ay,angMom_az),(angMom_bx-1,angMom_by,angMom_bz)
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| 1 -> (angMom_ax,angMom_ay+1,angMom_az),(angMom_bx,angMom_by-1,angMom_bz)
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| _ -> (angMom_ax,angMom_ay,angMom_az+1),(angMom_bx,angMom_by,angMom_bz-1)
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in
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let h1 =
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hrr0_v 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 angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
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in Array.map2 (fun h1 h2 -> h1 +. h2 *. f) h1 h2
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and hrr_v 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 0 angMom_a angMom_c totAngMom_a totAngMom_c
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else
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hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (_,_) ->
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let (angMom_cx, angMom_cy, angMom_cz) = angMom_c
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and (angMom_dx, angMom_dy, angMom_dz) = 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) -> (* 1_524_451 *) (angMom_cx+1, angMom_cy, angMom_cz), (angMom_dx-1, angMom_dy, angMom_dz), 0
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| (_,_,0) -> (* 1_302_937 *) (angMom_cx, angMom_cy+1, angMom_cz), (angMom_dx, angMom_dy-1, angMom_dz), 1
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| _ -> (* 1_302_937 *) (angMom_cx, angMom_cy, angMom_cz+1), (angMom_dx, angMom_dy, angMom_dz-1), 2
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in
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let h1 =
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hrr_v 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 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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Array.mapi (fun k center_cd -> h1.(k) +. h2.(k) *. (Coordinate.coord center_cd xyz)) center_cd
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in
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hrr_v
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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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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.(0).Shell_pair.shell_a
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and shell_b = shell_p.(0).Shell_pair.shell_b
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and shell_c = shell_q.(0).Shell_pair.shell_a
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and shell_d = shell_q.(0).Shell_pair.shell_b
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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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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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Array.fold_left
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(fun accu shell_ab -> accu +.
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Array.fold_left (fun accu shell_cd ->
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let coef_prod =
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shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef
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in
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(** Screening on the product of coefficients *)
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try
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if (abs_float coef_prod) < 1.e-3*.cutoff then
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raise NullQuartet;
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let expo_pq_inv =
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shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_ab.Shell_pair.center |- shell_cd.Shell_pair.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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accu +. coef_prod *. zero_m_array.(0)
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with NullQuartet -> accu
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) 0. shell_q
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) 0. shell_p
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| _ ->
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Array.iter (fun shell_ab ->
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let norm_coef_scale_p = shell_ab.Shell_pair.norm_coef_scale in
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let b = shell_ab.Shell_pair.j in
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let common =
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Array.map (fun shell_cd ->
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let coef_prod =
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shell_ab.Shell_pair.coef *. shell_cd.Shell_pair.coef
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in
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let expo_pq_inv =
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shell_ab.Shell_pair.expo_inv +. shell_cd.Shell_pair.expo_inv
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in
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let center_pq =
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Coordinate.(shell_ab.Shell_pair.center |- shell_cd.Shell_pair.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 ~expo_pq_inv ~norm_pq_sq
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in
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let d = shell_cd.Shell_pair.j in
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(zero_m_array, shell_cd.Shell_pair.expo_inv,
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Contracted_shell.expo shell_d d, shell_cd.Shell_pair.center_ab,
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center_pq,coef_prod)
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) shell_q
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|> Array.to_list
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|> List.filter (fun (zero_m_array, expo_inv, d, center_cd,
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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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in
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let zero_m_array = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod) -> zero_m_array) common
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and expo_inv = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod) -> expo_inv ) common
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and d = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod) -> d) common
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and center_cd = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod) -> center_cd) common
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and center_pq = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod) -> center_pq) common
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and coef_prod = Array.map (fun (zero_m_array, expo_inv, d, center_cd,
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center_pq,coef_prod) -> coef_prod) common
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in
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(* Transpose zero_m_array
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*)
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let zero_m_array =
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let result = Array.init (maxm+1) (fun _ ->
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Array.make (Array.length coef_prod) 0.)
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in
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for m=0 to maxm do
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for k=0 to (Array.length coef_prod-1) do
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result.(m).(k) <- zero_m_array.(k).(m)
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done;
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done;
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result
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in
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(* Compute the integral class from the primitive shell quartet *)
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let map_1d = Array.init maxm (fun _ -> Zmap.create (4*maxm)) in
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let map_2d = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
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let norm =
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let norm_coef_scale_q = shell_q.(0).Shell_pair.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
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Array.iteri (fun i key ->
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let a = Zkey.to_int_array Zkey.Kind_12 key in
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let (angMomA,angMomB,angMomC,angMomD) =
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( [| a.(0) ; a.(1) ; a.(2) |],
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[| 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)
|
|
(Contracted_shell.expo shell_b b, d)
|
|
(shell_ab.Shell_pair.expo_inv, expo_inv)
|
|
(shell_ab.Shell_pair.center_ab, center_cd, center_pq)
|
|
coef_prod map_1d map_2d
|
|
in
|
|
let x = Array.fold_left (+.) 0. integral in
|
|
contracted_class.(i) <- contracted_class.(i) +. x *. norm.(i)
|
|
) class_indices
|
|
) shell_p
|
|
|
|
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 = Shell_pair.create_array ~cutoff shell_a shell_b
|
|
and shell_q = Shell_pair.create_array ~cutoff shell_c shell_d
|
|
in
|
|
contracted_class_shell_pairs ~zero_m shell_p shell_q
|
|
|