2018-01-25 01:28:10 +01:00
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open Util
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2018-02-09 19:41:22 +01:00
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open Lacaml.D
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open Bigarray
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2018-01-25 01:28:10 +01:00
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2018-02-02 01:25:10 +01:00
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let cutoff = Constants.cutoff
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2018-01-25 01:28:10 +01:00
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let cutoff2 = cutoff *. cutoff
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exception NullQuartet
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2018-01-31 15:05:01 +01:00
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exception Found
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2018-02-10 01:07:34 +01:00
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let at_least_one_valid arr =
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try
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Array.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false
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with Found -> true
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2018-02-09 19:41:22 +01:00
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2018-01-25 01:28:10 +01:00
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(** Horizontal and Vertical Recurrence Relations (HVRR) *)
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2018-01-31 15:05:01 +01:00
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let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
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2018-01-25 01:28:10 +01:00
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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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2018-01-25 13:59:31 +01:00
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(center_ab, center_cd, center_pq)
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2018-02-10 03:37:00 +01:00
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map_1d map_2d np nq
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2018-01-25 01:28:10 +01:00
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=
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2018-02-10 22:19:13 +01:00
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let empty = Array.make nq 0. in
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let tmp_1 = Array.make nq 0. in
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2018-01-29 22:48:09 +01:00
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2018-02-09 20:32:39 +01:00
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2018-01-25 01:28:10 +01:00
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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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2018-02-09 20:32:39 +01:00
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let rec vrr0_v m angMom_a = function
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2018-02-10 03:37:00 +01:00
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| 0 -> Some zero_m_array.(m)
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2018-01-25 01:28:10 +01:00
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| totAngMom_a ->
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2018-02-02 11:59:30 +01:00
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let key = Zkey.of_int_tuple (Zkey.Three angMom_a)
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2018-01-25 01:28:10 +01:00
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in
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2018-02-09 20:32:39 +01:00
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try Zmap.find map_1d.(m) key with
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2018-02-02 11:59:30 +01:00
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| Not_found ->
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2018-02-03 19:01:30 +01:00
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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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2018-02-09 20:32:39 +01:00
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if amxyz < 0 then
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None
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else
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2018-02-10 22:19:13 +01:00
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begin
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let cab = Coordinate.coord center_ab xyz in
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let v1_top, p1_top =
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if abs_float cab < cutoff then
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None,
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vrr0_v (m+1) am (totAngMom_a-1)
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else
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vrr0_v m am (totAngMom_a-1),
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vrr0_v (m+1) am (totAngMom_a-1)
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in
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let v1_top2, p1_top2 =
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if amxyz < 1 then (None,None) else
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vrr0_v m amm (totAngMom_a-2),
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vrr0_v (m+1) amm (totAngMom_a-2)
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in
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2018-02-09 20:32:39 +01:00
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2018-02-10 22:19:13 +01:00
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let result = Array.make_matrix np nq 0. in
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for l=0 to np-1
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do
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let p0 =
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match p1_top with
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| Some p1_top -> p1_top.(l)
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| _ -> assert false
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in
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let f0 =
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-. expo_b.(l) *. expo_inv_p.(l) *. cab
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in
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let v0 =
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match v1_top with
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| Some v1_top -> v1_top.(l)
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| None -> empty
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in
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for k=0 to nq-1
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do
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tmp_1.(k) <- v0.(k) *. f0
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done;
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let v0 = tmp_1 in
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if amxyz < 1 then
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begin
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for k=0 to nq-1
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do
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result.(l).(k) <- v0.(k) +. expo_inv_p.(l) *. center_pq.(xyz).(l).(k) *. p0.(k)
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done
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end
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else
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begin
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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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let v1 =
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match v1_top2 with
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| Some v1_top2 -> v1_top2.(l)
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| None -> assert false
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in
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let v2 =
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match p1_top2 with
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| Some p1_top2 -> p1_top2.(l)
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| None -> assert false
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in
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for k=0 to nq-1
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do
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result.(l).(k) <-
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v0.(k)
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+. expo_inv_p.(l) *. center_pq.(xyz).(l).(k) *. p0.(k)
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+. f *. (v1.(k) +. v2.(k) *. expo_inv_p.(l) )
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done
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end
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done;
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Some result
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end
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in
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Zmap.add map_1d.(m) key result;
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result
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2018-01-25 01:28:10 +01:00
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2018-02-09 20:32:39 +01:00
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and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =
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2018-01-25 01:28:10 +01:00
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match (totAngMom_a, totAngMom_c) with
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2018-02-10 03:37:00 +01:00
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| (i,0) -> vrr0_v m angMom_a totAngMom_a
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2018-01-25 01:28:10 +01:00
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| (_,_) ->
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2018-02-02 11:59:30 +01:00
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let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c))
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2018-01-25 01:28:10 +01:00
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in
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2018-02-09 20:32:39 +01:00
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try Zmap.find map_2d.(m) key with
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2018-02-03 19:01:30 +01:00
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| Not_found ->
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let result =
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2018-02-10 03:37:00 +01:00
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begin
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2018-02-03 19:01:30 +01:00
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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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2018-02-10 22:19:13 +01:00
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(*
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let result = Array.make_matrix np nq 0. in
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*)
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2018-02-03 19:01:30 +01:00
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let f1 =
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2018-02-09 12:57:42 +01:00
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let f = (Coordinate.coord center_cd xyz) in
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2018-02-10 01:07:34 +01:00
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Array.init nq (fun k -> expo_d.(k) *. expo_inv_q.(k) *. f)
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2018-02-09 20:32:39 +01:00
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in
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let v1 =
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2018-02-10 01:07:34 +01:00
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if (at_least_one_valid f1) then
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2018-02-09 20:32:39 +01:00
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vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1)
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else None
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2018-02-03 19:01:30 +01:00
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in
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let f2 =
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2018-02-10 01:07:34 +01:00
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Array.init np (fun l ->
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Array.init nq (fun k ->
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expo_inv_q.(k) *. center_pq.(xyz).(l).(k) ) )
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2018-02-03 19:01:30 +01:00
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in
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2018-02-09 20:32:39 +01:00
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let v2 =
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2018-02-10 01:07:34 +01:00
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if (at_least_one_valid (Array.to_list f2 |> Array.concat)) then
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2018-02-09 20:32:39 +01:00
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vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
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2018-02-10 01:07:34 +01:00
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else
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None
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2018-02-03 19:01:30 +01:00
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in
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2018-02-09 20:32:39 +01:00
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2018-02-03 19:01:30 +01:00
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let p1 =
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2018-02-09 20:32:39 +01:00
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match v1, v2 with
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| Some v1, Some v2 ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k ->
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-. v1.(l).(k) *. f1.(k) -. v2.(l).(k) *. f2.(l).(k)) ) )
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2018-02-09 20:32:39 +01:00
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| None, Some v2 ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k -> -. v2.(l).(k) *. f2.(l).(k)) ) )
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2018-02-09 20:32:39 +01:00
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| Some v1, None ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k -> -. v1.(l).(k) *. f1.(k) ) ) )
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2018-02-09 20:32:39 +01:00
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| None, None -> None
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2018-02-03 19:01:30 +01:00
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in
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2018-02-09 20:32:39 +01:00
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2018-02-03 19:01:30 +01:00
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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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2018-02-10 01:07:34 +01:00
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Array.init nq (fun k -> fcm *. expo_inv_q.(k))
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2018-02-03 19:01:30 +01:00
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in
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let f2 =
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2018-02-10 01:07:34 +01:00
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Array.mapi (fun k x -> x *. expo_inv_q.(k)) f1
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2018-02-03 19:01:30 +01:00
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in
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let v1 =
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2018-02-10 01:07:34 +01:00
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if (at_least_one_valid f1) then
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2018-02-09 20:32:39 +01:00
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vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2)
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else None
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2018-02-03 19:01:30 +01:00
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in
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let v2 =
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2018-02-10 01:07:34 +01:00
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if (at_least_one_valid f2) then
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2018-02-09 20:32:39 +01:00
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vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
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else None
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2018-02-03 19:01:30 +01:00
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in
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2018-02-09 20:32:39 +01:00
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match p1, v1, v2 with
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| Some p1, Some v1, Some v2 ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k ->
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p1.(l).(k) +. f1.(k) *. v1.(l).(k) +. f2.(k) *. v2.(l).(k)) ) )
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2018-02-09 20:32:39 +01:00
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| Some p1, Some v1, None ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k -> p1.(l).(k) +. f1.(k) *. v1.(l).(k) ) ) )
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2018-02-09 20:32:39 +01:00
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| Some p1, None, Some v2 ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k -> p1.(l).(k) +. f2.(k) *. v2.(l).(k)) ) )
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2018-02-09 20:32:39 +01:00
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| None , Some v1, Some v2 ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k ->
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f1.(k) *. v1.(l).(k) +. f2.(k) *. v2.(l).(k)) ) )
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2018-02-09 20:32:39 +01:00
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| Some p1, None, None -> Some p1
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| None , Some v1, None ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k -> f1.(k) *. v1.(l).(k) ) ) )
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2018-02-09 20:32:39 +01:00
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| None, None, Some v2 ->
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2018-02-10 01:07:34 +01:00
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Some (Array.init np (fun l ->
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Array.init nq (fun k -> f2.(k) *. v2.(l).(k)) ) )
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2018-02-09 20:32:39 +01:00
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| None, None, None -> None
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2018-02-03 19:01:30 +01:00
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in
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if (axyz < 1) || (cxyz < 1) then p2 else
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2018-02-09 20:32:39 +01:00
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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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2018-02-03 19:01:30 +01:00
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in
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2018-02-09 20:32:39 +01:00
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begin
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match (p2, v) with
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| Some p2, Some v -> Some (
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2018-02-10 01:07:34 +01:00
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Array.init np (fun l ->
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2018-02-09 20:32:39 +01:00
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let fa =
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2018-02-10 01:07:34 +01:00
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(float_of_int axyz) *. expo_inv_p.(l) *. 0.5
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2018-02-09 20:32:39 +01:00
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in
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2018-02-10 01:07:34 +01:00
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Array.init nq (fun k -> p2.(l).(k) -. expo_inv_q.(k) *. fa *. v.(l).(k))
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) )
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2018-02-09 20:32:39 +01:00
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| Some p2, None -> Some p2
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| None, Some v -> Some (
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2018-02-10 01:07:34 +01:00
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Array.init np (fun l ->
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2018-02-09 20:32:39 +01:00
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let fa =
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2018-02-10 01:07:34 +01:00
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(float_of_int axyz) *. expo_inv_p.(l) *. 0.5
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2018-02-09 20:32:39 +01:00
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in
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2018-02-10 01:07:34 +01:00
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Array.init nq (fun k -> -. fa *. expo_inv_q.(k) *. v.(l).(k))
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) )
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2018-02-09 20:32:39 +01:00
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| None, None -> None
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end
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2018-02-03 19:01:30 +01:00
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end
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2018-02-09 20:32:39 +01:00
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in Zmap.add map_2d.(m) key result;
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2018-02-03 19:01:30 +01:00
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result
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2018-01-25 01:28:10 +01:00
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(** Horizontal recurrence relations *)
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2018-02-09 20:32:39 +01:00
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and hrr0_v angMom_a angMom_b angMom_c
|
2018-01-25 01:28:10 +01:00
|
|
|
totAngMom_a totAngMom_b totAngMom_c =
|
|
|
|
|
|
|
|
match totAngMom_b with
|
2018-01-29 22:48:09 +01:00
|
|
|
| 0 ->
|
|
|
|
begin
|
|
|
|
match (totAngMom_a, totAngMom_c) with
|
2018-02-10 03:37:00 +01:00
|
|
|
| (0,0) -> Array.fold_left (fun accu c ->
|
|
|
|
accu +. Array.fold_left (+.) 0. c) 0. zero_m_array.(0)
|
|
|
|
| (_,_) ->
|
2018-02-10 01:07:34 +01:00
|
|
|
begin
|
2018-02-10 03:37:00 +01:00
|
|
|
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.
|
2018-02-10 01:07:34 +01:00
|
|
|
end
|
2018-01-29 22:48:09 +01:00
|
|
|
end
|
2018-02-02 11:59:30 +01:00
|
|
|
| 1 ->
|
2018-02-03 16:41:29 +01:00
|
|
|
let (aax, aay, aaz) = angMom_a in
|
2018-02-02 11:59:30 +01:00
|
|
|
let ap, xyz =
|
2018-02-03 19:01:30 +01:00
|
|
|
match angMom_b with
|
|
|
|
| (_,_,1) -> (aax,aay,aaz+1), 2
|
|
|
|
| (_,1,_) -> (aax,aay+1,aaz), 1
|
|
|
|
| (_,_,_) -> (aax+1,aay,aaz), 0
|
2018-02-02 11:59:30 +01:00
|
|
|
in
|
2018-01-30 00:06:04 +01:00
|
|
|
let f = Coordinate.coord center_ab xyz in
|
2018-01-29 13:39:59 +01:00
|
|
|
let v1 =
|
2018-02-09 20:32:39 +01:00
|
|
|
match vrr_v 0 ap angMom_c (totAngMom_a+1) totAngMom_c with
|
2018-02-10 01:07:34 +01:00
|
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
2018-02-09 20:32:39 +01:00
|
|
|
| None -> 0.
|
2018-01-29 22:48:09 +01:00
|
|
|
in
|
2018-02-09 20:32:39 +01:00
|
|
|
if (abs_float f < cutoff) then v1 else
|
|
|
|
let v2 =
|
|
|
|
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
|
2018-02-10 01:07:34 +01:00
|
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
2018-02-09 20:32:39 +01:00
|
|
|
| None -> 0.
|
2018-01-30 00:06:04 +01:00
|
|
|
in
|
2018-02-09 20:32:39 +01:00
|
|
|
v1 +. v2 *. f
|
2018-01-25 01:28:10 +01:00
|
|
|
| _ ->
|
2018-02-03 16:41:29 +01:00
|
|
|
let (aax, aay, aaz) = angMom_a
|
|
|
|
and (abx, aby, abz) = angMom_b in
|
2018-02-02 11:59:30 +01:00
|
|
|
let bxyz, xyz =
|
2018-02-03 19:01:30 +01:00
|
|
|
match angMom_b with
|
|
|
|
| (0,0,_) -> abz, 2
|
|
|
|
| (0,_,_) -> aby, 1
|
|
|
|
| _ -> abx, 0
|
2018-01-25 01:28:10 +01:00
|
|
|
in
|
2018-02-09 19:41:22 +01:00
|
|
|
if (bxyz < 1) then 0. else
|
2018-02-03 19:01:30 +01:00
|
|
|
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
|
2018-02-02 11:59:30 +01:00
|
|
|
|
2018-01-29 13:39:59 +01:00
|
|
|
let h1 =
|
2018-02-09 20:32:39 +01:00
|
|
|
hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
|
2018-01-30 00:06:04 +01:00
|
|
|
in
|
|
|
|
let f = (Coordinate.coord center_ab xyz) in
|
|
|
|
if (abs_float f < cutoff) then h1 else
|
2018-02-03 19:01:30 +01:00
|
|
|
let h2 =
|
2018-02-09 20:32:39 +01:00
|
|
|
hrr0_v angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
|
2018-02-09 19:41:22 +01:00
|
|
|
in
|
|
|
|
h1 +. h2 *. f
|
2018-01-25 01:28:10 +01:00
|
|
|
|
2018-02-09 20:32:39 +01:00
|
|
|
and hrr_v angMom_a angMom_b angMom_c angMom_d
|
2018-01-25 01:28:10 +01:00
|
|
|
totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
|
|
|
|
|
|
|
|
match (totAngMom_b, totAngMom_d) with
|
2018-02-02 11:59:30 +01:00
|
|
|
| (_,0) -> if (totAngMom_b = 0) then
|
2018-02-09 20:32:39 +01:00
|
|
|
begin
|
|
|
|
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
|
2018-02-10 01:07:34 +01:00
|
|
|
| Some matrix -> Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix
|
2018-02-09 20:32:39 +01:00
|
|
|
| None -> 0.
|
|
|
|
end
|
2018-02-03 19:01:30 +01:00
|
|
|
else
|
2018-02-09 20:32:39 +01:00
|
|
|
hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
|
2018-01-25 01:28:10 +01:00
|
|
|
| (_,_) ->
|
2018-02-03 16:41:29 +01:00
|
|
|
let (acx, acy, acz) = angMom_c
|
|
|
|
and (adx, ady, adz) = angMom_d in
|
2018-02-02 11:59:30 +01:00
|
|
|
let cp, dm, xyz =
|
|
|
|
match angMom_d with
|
2018-02-03 16:41:29 +01:00
|
|
|
| (_,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
|
2018-01-25 01:28:10 +01:00
|
|
|
in
|
2018-01-29 22:48:09 +01:00
|
|
|
let h1 =
|
2018-02-09 20:32:39 +01:00
|
|
|
hrr_v angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
|
2018-01-25 13:59:31 +01:00
|
|
|
in
|
2018-02-09 12:57:42 +01:00
|
|
|
let f = (Coordinate.coord center_cd xyz) in
|
2018-02-10 03:37:00 +01:00
|
|
|
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
|
2018-01-25 01:28:10 +01:00
|
|
|
in
|
2018-02-10 03:37:00 +01:00
|
|
|
hrr_v
|
2018-02-09 19:41:22 +01:00
|
|
|
(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
|
2018-01-25 01:28:10 +01:00
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2018-01-29 22:48:09 +01:00
|
|
|
|
|
|
|
|
|
|
|
|
2018-01-25 01:28:10 +01:00
|
|
|
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
|
|
|
|
|
2018-02-09 19:41:22 +01:00
|
|
|
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
|
2018-01-25 01:28:10 +01:00
|
|
|
in
|
|
|
|
let maxm =
|
2018-02-10 03:37:00 +01:00
|
|
|
shell_p.ContractedShellPair.totAngMomInt +
|
|
|
|
shell_q.ContractedShellPair.totAngMomInt
|
2018-01-25 01:28:10 +01:00
|
|
|
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
|
|
|
|
|
|
|
|
(* 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) ->
|
2018-02-09 19:41:22 +01:00
|
|
|
contracted_class.(0) <-
|
2018-02-10 01:07:34 +01:00
|
|
|
let expo_inv_p =
|
|
|
|
Array.map (fun shell_ab -> shell_ab.ShellPair.expo_inv) sp
|
|
|
|
|> Vec.of_array
|
|
|
|
and expo_inv_q =
|
|
|
|
Array.map (fun shell_cd -> shell_cd.ShellPair.expo_inv) sq
|
|
|
|
|> Vec.of_array
|
|
|
|
in
|
|
|
|
let np, nq =
|
|
|
|
Vec.dim expo_inv_p, Vec.dim expo_inv_q
|
|
|
|
in
|
|
|
|
|
|
|
|
let coef =
|
|
|
|
let result = Mat.make0 nq np in
|
|
|
|
Lacaml.D.ger
|
|
|
|
(Vec.of_array shell_q.ContractedShellPair.coef)
|
|
|
|
(Vec.of_array shell_p.ContractedShellPair.coef)
|
|
|
|
result;
|
|
|
|
result
|
|
|
|
in
|
2018-02-09 20:32:39 +01:00
|
|
|
let zm_array = Mat.init_cols np nq (fun i j ->
|
2018-02-09 19:41:22 +01:00
|
|
|
(** Screening on the product of coefficients *)
|
|
|
|
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
|
2018-01-25 01:28:10 +01:00
|
|
|
| _ ->
|
2018-02-10 01:07:34 +01:00
|
|
|
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 np, nq =
|
|
|
|
Array.length expo_inv_p, Array.length expo_inv_q
|
|
|
|
in
|
2018-02-09 19:41:22 +01:00
|
|
|
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
|
2018-01-29 15:29:38 +01:00
|
|
|
|
2018-02-10 01:07:34 +01:00
|
|
|
let coef =
|
|
|
|
Array.init np (fun l ->
|
|
|
|
Array.init nq (fun k ->
|
|
|
|
shell_q.ContractedShellPair.coef.(k) *.
|
|
|
|
shell_p.ContractedShellPair.coef.(l)
|
|
|
|
) )
|
|
|
|
in
|
2018-01-29 15:29:38 +01:00
|
|
|
|
2018-02-09 19:41:22 +01:00
|
|
|
let center_pq =
|
2018-02-09 20:32:39 +01:00
|
|
|
Array.init 3 (fun xyz ->
|
2018-02-10 01:07:34 +01:00
|
|
|
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
|
|
|
|
)
|
2018-02-09 20:32:39 +01:00
|
|
|
)
|
2018-02-10 01:07:34 +01:00
|
|
|
)
|
2018-02-09 19:41:22 +01:00
|
|
|
in
|
|
|
|
let zero_m_array =
|
|
|
|
let result =
|
2018-02-10 01:07:34 +01:00
|
|
|
Array.init (maxm+1) (fun _ ->
|
|
|
|
Array.init np (fun _ -> Array.make nq 0. ) )
|
2018-02-09 19:41:22 +01:00
|
|
|
in
|
2018-02-10 22:19:13 +01:00
|
|
|
let empty = Array.make (maxm+1) 0. in
|
2018-02-09 19:41:22 +01:00
|
|
|
Array.iteri (fun ab shell_ab ->
|
|
|
|
let zero_m_array_tmp =
|
|
|
|
Array.mapi (fun cd shell_cd ->
|
2018-02-10 22:19:13 +01:00
|
|
|
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
|
2018-02-09 19:41:22 +01:00
|
|
|
) sq
|
|
|
|
(*
|
|
|
|
|> Array.to_list
|
|
|
|
|> List.filter (fun (zero_m_array, d,
|
|
|
|
center_pq,coef_prod) -> abs_float coef_prod >= 1.e-4 *. cutoff)
|
|
|
|
|> Array.of_list
|
|
|
|
*)
|
2018-02-02 18:51:17 +01:00
|
|
|
in
|
2018-02-09 19:41:22 +01:00
|
|
|
(* Transpose result *)
|
|
|
|
for m=0 to maxm do
|
2018-02-10 01:07:34 +01:00
|
|
|
for cd=0 to nq-1 do
|
2018-02-10 03:37:00 +01:00
|
|
|
result.(m).(ab).(cd) <- zero_m_array_tmp.(cd).(m) *. coef.(ab).(cd)
|
2018-02-09 19:41:22 +01:00
|
|
|
done
|
|
|
|
done
|
|
|
|
) sp;
|
|
|
|
result
|
|
|
|
in
|
2018-02-02 18:51:17 +01:00
|
|
|
|
2018-02-09 19:41:22 +01:00
|
|
|
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
|
|
|
|
|
2018-02-10 03:37:00 +01:00
|
|
|
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))
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2018-02-09 19:41:22 +01:00
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in
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2018-02-03 19:01:30 +01:00
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(* Compute the integral class from the primitive shell quartet *)
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2018-02-09 19:41:22 +01:00
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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) |],
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[| a.(6) ; a.(7) ; a.(8) |],
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[| a.(9) ; a.(10) ; a.(11) |] )
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in
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let integral =
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hvrr_two_e_vector (angMomA, angMomB, angMomC, angMomD)
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(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
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Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_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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(shell_p.ContractedShellPair.center_ab,
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shell_q.ContractedShellPair.center_ab, center_pq)
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2018-02-10 03:37:00 +01:00
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map_1d map_2d np nq
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2018-02-09 19:41:22 +01:00
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in
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contracted_class.(i) <- contracted_class.(i) +. integral *. norm.(i)
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) class_indices
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2018-01-25 13:59:31 +01:00
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2018-01-25 01:28:10 +01:00
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end;
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let result =
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Zmap.create (Array.length contracted_class)
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in
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Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
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result
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(** Computes all the two-electron integrals of the contracted shell quartet *)
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let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =
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2018-02-07 17:07:05 +01:00
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let shell_p = ContractedShellPair.create ~cutoff shell_a shell_b
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and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d
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2018-01-25 01:28:10 +01:00
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in
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contracted_class_shell_pairs ~zero_m shell_p shell_q
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