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Optimized vectorized routines
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@ -3,9 +3,15 @@ open Util
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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 m (angMom_a, angMom_b, angMom_c, angMom_d)
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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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@ -30,6 +36,7 @@ let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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| 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2
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in
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let f = expo_b *. (Coordinate.coord center_ab i) in
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if (abs_float f < cutoff) then empty else
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Array.mapi (fun k c -> c *. expo_inv_p *.
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( (Coordinate.coord center_pq.(k) i) *. zero_m_array.(k).(m+1)
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-. f *. zero_m_array.(k).(m) ) ) coef_prod
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@ -70,7 +77,10 @@ let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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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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and v2 = vrr0_v (m+1) 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.mapi (fun k _ -> p1.(k) +.
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f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) coef_prod
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@ -111,43 +121,62 @@ let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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if cm.(xyz) < 0 then
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empty
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else
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let f1 =
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Array.mapi (fun k _ ->
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expo_d.(k) *. expo_inv_q.(k) *. (Coordinate.coord center_cd.(k) xyz) ) expo_inv_q
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in
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let f2 =
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Array.mapi (fun k _ ->
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expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz) ) expo_inv_q
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in
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let v1 =
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vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1)
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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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vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
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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.mapi (fun k _ ->
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-. v1.(k) *. expo_d.(k) *. expo_inv_q.(k) *. (Coordinate.coord center_cd.(k) xyz)
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-. v2.(k) *. (expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz))
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) coef_prod
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Array.mapi (fun k _ -> -. v1.(k) *. f1.(k) -. v2.(k) *. f2.(k)) coef_prod
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in
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let p2 =
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if cmm.(xyz) < 0 then p1 else
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let v1 =
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vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2)
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and v2 =
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vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
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and fcm =
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let fcm =
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(float_of_int cm.(xyz)) *. 0.5
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in
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Array.mapi (fun k _ -> p1.(k) +. fcm *. expo_inv_q.(k)
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*. (v1.(k) +. expo_inv_q.(k) *. v2.(k))
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) coef_prod
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let f1 =
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Array.mapi (fun k _ -> fcm *. expo_inv_q.(k) ) coef_prod
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and f2 =
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Array.mapi (fun k _ -> f1.(k) *. expo_inv_q.(k) ) coef_prod
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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.mapi (fun k _ -> p1.(k) +. f1.(k) *. v1.(k) +. f2.(k) *. v2.(k)) coef_prod
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in
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if (am.(xyz) < 0) || (cm.(xyz) < 0) then p2 else
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let fa =
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(float_of_int angMom_a.(xyz)) *. expo_inv_p *. 0.5
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in
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(*
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if (abs_float fa < cutoff) then empty else
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*)
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let f1 =
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Array.mapi (fun k _ -> fa *. expo_inv_q.(k) ) coef_prod
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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.mapi (fun k _ ->
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p2.(k) -. fa *. expo_inv_q.(k) *. v.(k)
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) coef_prod
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Array.mapi (fun k _ -> p2.(k) -. f1.(k) *. v.(k)) coef_prod
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else p2
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)
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in
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if not found then
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@ -158,27 +187,27 @@ let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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(** Horizontal recurrence relations *)
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and hrr0_v m angMom_a angMom_b angMom_c
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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.mapi (fun k c -> c *. zero_m_array.(k).(m)) coef_prod
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| (_,0) -> vrr0_v m angMom_a totAngMom_a
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| (_,_) -> vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
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| (0,0) -> Array.mapi (fun k c -> c *. zero_m_array.(k).(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 -> let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in
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let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in
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ap.(xyz) <- ap.(xyz) + 1;
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let f = Coordinate.coord center_ab xyz in
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let v1 =
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vrr_v m ap angMom_c (totAngMom_a+1) totAngMom_c
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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 m angMom_a angMom_c totAngMom_a totAngMom_c
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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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@ -194,20 +223,20 @@ let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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bm.(xyz) <- bm.(xyz) - 1;
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if (bm.(xyz) < 0) then empty else
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let h1 =
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hrr0_v m ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
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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 m angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
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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 m angMom_a angMom_b angMom_c angMom_d
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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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| (0,0) -> vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,0) -> hrr0_v m angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (0,0) -> vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c
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| (_,0) -> hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
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| (_,_) ->
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let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
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and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
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@ -220,13 +249,13 @@ let hvrr_two_e_vector m (angMom_a, angMom_b, angMom_c, angMom_d)
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cp.(xyz) <- cp.(xyz) + 1;
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dm.(xyz) <- dm.(xyz) - 1;
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let h1 =
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hrr_v m angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
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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 m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
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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 m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
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hrr_v angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
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totAngMom_c totAngMom_d
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@ -361,7 +390,7 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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) shell_q
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in
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let integral =
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hvrr_two_e_vector 0 (angMomA, angMomB, angMomC, angMomD)
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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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