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Accelerated HRR and VRR

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This commit is contained in:
Anthony Scemama 2018-01-24 16:29:48 +01:00
parent e9c0a8d0db
commit 5cc48e59d7
2 changed files with 191 additions and 164 deletions
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344
Basis/TwoElectronRR.ml
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@ -21,12 +21,13 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
in in
(** Vertical recurrence relations *) (** Vertical recurrence relations *)
let rec vrr m angMom_a angMom_c totAngMom_a totAngMom_c = let rec vrr0 m angMom_a = function
| 0 -> zero_m_array.(m)
match (totAngMom_a, totAngMom_c) with | 1 -> let i = if angMom_a.(0) = 1 then 0 else if angMom_a.(1) = 1 then 1 else 2
| (0,0) -> zero_m_array.(m) in expo_inv_p *.( (Coordinate.coord center_pq i) *. zero_m_array.(m+1)
| (_,0) -> -. expo_b *. (Coordinate.coord center_ab i) *. zero_m_array.(m) )
| totAngMom_a ->
let key = Zkey.of_int_tuple (Zkey.Three let key = Zkey.of_int_tuple (Zkey.Three
(angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) ) (angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1) )
in in
@ -37,7 +38,6 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] let am = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] and amm = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and xyz = and xyz =
match angMom_a with
| [|0;0;_|] -> 2 | [|0;0;_|] -> 2
| [|0;_;_|] -> 1 | [|0;_;_|] -> 1
| _ -> 0 | _ -> 0
@ -46,19 +46,25 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
amm.(xyz) <- amm.(xyz) - 2; amm.(xyz) <- amm.(xyz) - 2;
if am.(xyz) < 0 then 0. else if am.(xyz) < 0 then 0. else
chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)) chop (-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz))
(fun () -> vrr m am angMom_c (totAngMom_a-1) totAngMom_c ) (fun () -> vrr0 m am (totAngMom_a-1) )
+. chop (expo_inv_p *. (Coordinate.coord center_pq xyz)) +. chop (expo_inv_p *. (Coordinate.coord center_pq xyz))
(fun () -> vrr (m+1) am angMom_c (totAngMom_a-1) totAngMom_c ) (fun () -> vrr0 (m+1) am (totAngMom_a-1) )
+. (if amm.(xyz) < 0 then 0. else +. (if amm.(xyz) < 0 then 0. else
chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5) chop ((float_of_int am.(xyz)) *. expo_inv_p *. 0.5)
(fun () -> vrr m amm angMom_c (totAngMom_a-2) totAngMom_c (fun () -> vrr0 m amm (totAngMom_a-2)
+. chop expo_inv_p (fun () -> +. chop expo_inv_p (fun () ->
vrr (m+1) amm angMom_c (totAngMom_a-2) totAngMom_c) ) ) ) vrr0 (m+1) amm (totAngMom_a-2) ) ) )
)
in in
if not found then if not found then
Zmap.add map.(m) key result; Zmap.add map.(m) key result;
result result
and vrr m angMom_a angMom_c totAngMom_a totAngMom_c =
match (totAngMom_a, totAngMom_c) with
| (0,0) -> zero_m_array.(m)
| (_,0) -> vrr0 m angMom_a totAngMom_a
| (_,_) -> | (_,_) ->
let key = Zkey.of_int_tuple (Zkey.Six let key = Zkey.of_int_tuple (Zkey.Six
@ -104,65 +110,57 @@ let hvrr_two_e m (angMom_a, angMom_b, angMom_c, angMom_d)
(** Horizontal recurrence relations *) (** Horizontal recurrence relations *)
and hrr0 m angMom_a angMom_b angMom_c
totAngMom_a totAngMom_b totAngMom_c =
match totAngMom_b with
| 0 -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c
| 1 -> let xyz = if angMom_b.(0) = 1 then 0 else if angMom_b.(1) = 1 then 1 else 2 in
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |] in
ap.(xyz) <- ap.(xyz) + 1;
vrr m ap angMom_c (totAngMom_a+1) totAngMom_c
+. chop (Coordinate.coord center_ab xyz) (fun () ->
vrr m angMom_a angMom_c totAngMom_a totAngMom_c)
| _ ->
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
and xyz =
match angMom_b with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
ap.(xyz) <- ap.(xyz) + 1;
bm.(xyz) <- bm.(xyz) - 1;
if (bm.(xyz) < 0) then 0. else
hrr0 m ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
+. chop (Coordinate.coord center_ab xyz) (fun () ->
hrr0 m angMom_a bm angMom_c totAngMom_a (totAngMom_b-1)
totAngMom_c )
and hrr m angMom_a angMom_b angMom_c angMom_d and hrr m angMom_a angMom_b angMom_c angMom_d
totAngMom_a totAngMom_b totAngMom_c totAngMom_d = totAngMom_a totAngMom_b totAngMom_c totAngMom_d =
match (totAngMom_b, totAngMom_d) with match (totAngMom_b, totAngMom_d) with
| (0,0) -> vrr m angMom_a angMom_c totAngMom_a totAngMom_c | (0,0) ->
vrr m angMom_a angMom_c totAngMom_a totAngMom_c
| (_,0) -> hrr0 m angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
| (_,_) -> | (_,_) ->
let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
let key = Zkey.of_int_tuple (Zkey.Twelve and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
(( angMom_a.(0)+1, angMom_a.(1)+1, angMom_a.(2)+1), and xyz =
( angMom_b.(0)+1, angMom_b.(1)+1, angMom_b.(2)+1), match angMom_d with
( angMom_c.(0)+1, angMom_c.(1)+1, angMom_c.(2)+1), | [|0;0;_|] -> 2
( angMom_d.(0)+1, angMom_d.(1)+1, angMom_d.(2)+1)) ) | [|0;_;_|] -> 1
| _ -> 0
in in
cp.(xyz) <- cp.(xyz) + 1;
let (found, result) = dm.(xyz) <- dm.(xyz) - 1;
try (true, Zmap.find map.(m) key) with hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
| Not_found -> (false, (totAngMom_c+1) (totAngMom_d-1)
begin +. chop (Coordinate.coord center_cd xyz) (fun () ->
match totAngMom_d with hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
| 0 -> totAngMom_c (totAngMom_d-1) )
let ap = [| angMom_a.(0) ; angMom_a.(1) ; angMom_a.(2) |]
and bm = [| angMom_b.(0) ; angMom_b.(1) ; angMom_b.(2) |]
and xyz =
match angMom_b with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
ap.(xyz) <- ap.(xyz) + 1;
bm.(xyz) <- bm.(xyz) - 1;
if (bm.(xyz) < 0) then 0. else
hrr m ap bm angMom_c angMom_d
(totAngMom_a+1) (totAngMom_b-1) totAngMom_c totAngMom_d
+. chop (Coordinate.coord center_ab xyz) (fun () ->
hrr m angMom_a bm angMom_c angMom_d totAngMom_a (totAngMom_b-1)
totAngMom_c totAngMom_d )
| _ ->
let cp = [| angMom_c.(0) ; angMom_c.(1) ; angMom_c.(2) |]
and dm = [| angMom_d.(0) ; angMom_d.(1) ; angMom_d.(2) |]
and xyz =
match angMom_d with
| [|0;0;_|] -> 2
| [|0;_;_|] -> 1
| _ -> 0
in
cp.(xyz) <- cp.(xyz) + 1;
dm.(xyz) <- dm.(xyz) - 1;
hrr m angMom_a angMom_b cp dm totAngMom_a totAngMom_b
(totAngMom_c+1) (totAngMom_d-1)
+. chop (Coordinate.coord center_cd xyz) (fun () ->
hrr m angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b
totAngMom_c (totAngMom_d-1) )
end)
in
if not found then
Zmap.add map.(m) key result;
result
in in
hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b hrr m angMom_a angMom_b angMom_c angMom_d totAngMom_a totAngMom_b
totAngMom_c totAngMom_d totAngMom_c totAngMom_d
@ -197,109 +195,139 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
(* Compute all integrals in the shell for each pair of significant shell pairs *) (* Compute all integrals in the shell for each pair of significant shell pairs *)
for ab=0 to (Array.length shell_p - 1) begin
do match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
let b = shell_p.(ab).Shell_pair.j in totAngMom shell_c, totAngMom shell_d) with
| Angular_momentum.(S,S,S,S) ->
for cd=0 to (Array.length shell_q - 1) begin
do for ab=0 to (Array.length shell_p - 1) do
try for cd=0 to (Array.length shell_q - 1) do
let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
in
(** Screening on the product of coefficients *)
if (abs_float coef_prod) < 1.e-4*.cutoff then
raise NullQuartet;
let expo_pq_inv =
shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
in
let center_pq =
Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
in
let zero_m_array =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
totAngMom shell_c, totAngMom shell_d) with
| Angular_momentum.(S,S,S,S) -> Array.iteri (fun i key ->
let coef_prod = let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
in in
let integral = (** Screening on the product of coefficients *)
zero_m_array.(0) try
in if (abs_float coef_prod) < 1.e-4*.cutoff then
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral raise NullQuartet;
) class_indices
| _ -> let expo_pq_inv =
let d = shell_q.(cd).Shell_pair.j in shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
(* Compute the integral class from the primitive shell quartet *)
Array.iteri (fun i key ->
let a = Zkey.to_int_array Zkey.Kind_12 key in
let (angMomA,angMomB,angMomC,angMomD) =
( [| a.(0) ; a.(1) ; a.(2) |],
[| a.(3) ; a.(4) ; a.(5) |],
[| a.(6) ; a.(7) ; a.(8) |],
[| a.(9) ; a.(10) ; a.(11) |] )
in in
try let center_pq =
(* Schwartz screening *) Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
(* in
let schwartz_p = let norm_pq_sq =
let key = Coordinate.dot center_pq center_pq
Zkey.of_int_array Zkey.Kind_12 in
[| a.(0) ; a.(1) ; a.(2) ;
a.(3) ; a.(4) ; a.(5) ; let zero_m_array =
a.(0) ; a.(1) ; a.(2) ; zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
a.(3) ; a.(4) ; a.(5) |] in
let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
in
let integral =
zero_m_array.(0)
in
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
with NullQuartet -> ()
done
done;
end
| _ ->
begin
for ab=0 to (Array.length shell_p - 1) do
let b = shell_p.(ab).Shell_pair.j in
for cd=0 to (Array.length shell_q - 1) do
try
let coef_prod =
shell_p.(ab).Shell_pair.coef *. shell_q.(cd).Shell_pair.coef
in
(** Screening on the product of coefficients *)
if (abs_float coef_prod) < 1.e-4*.cutoff then
raise NullQuartet;
let expo_pq_inv =
shell_p.(ab).Shell_pair.expo_inv +. shell_q.(cd).Shell_pair.expo_inv
in
let center_pq =
Coordinate.(shell_p.(ab).Shell_pair.center |- shell_q.(cd).Shell_pair.center)
in
let norm_pq_sq =
Coordinate.dot center_pq center_pq
in
let zero_m_array =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in
let d = shell_q.(cd).Shell_pair.j in
let map = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
(* Compute the integral class from the primitive shell quartet *)
Array.iteri (fun i key ->
let a = Zkey.to_int_array Zkey.Kind_12 key in
let (angMomA,angMomB,angMomC,angMomD) =
( [| a.(0) ; a.(1) ; a.(2) |],
[| a.(3) ; a.(4) ; a.(5) |],
[| a.(6) ; a.(7) ; a.(8) |],
[| a.(9) ; a.(10) ; a.(11) |] )
in in
match schwartz_p with try
| None -> 1. (* Schwartz screening *)
| Some schwartz_p -> Zmap.find schwartz_p key (*
in let schwartz_p =
if schwartz_p < cutoff then raise NullQuartet; let key =
let schwartz_q = Zkey.of_int_array Zkey.Kind_12
let key = [| a.(0) ; a.(1) ; a.(2) ;
Zkey.of_int_array Zkey.Kind_12 a.(3) ; a.(4) ; a.(5) ;
[| a.(6) ; a.(7) ; a.(8) ; a.(0) ; a.(1) ; a.(2) ;
a.(9) ; a.(10) ; a.(11) ; a.(3) ; a.(4) ; a.(5) |]
a.(6) ; a.(7) ; a.(8) ; in
a.(9) ; a.(10) ; a.(11) |] match schwartz_p with
| None -> 1.
| Some schwartz_p -> Zmap.find schwartz_p key
in in
match schwartz_q with if schwartz_p < cutoff then raise NullQuartet;
| None -> 1. let schwartz_q =
| Some schwartz_q -> Zmap.find schwartz_q key let key =
in Zkey.of_int_array Zkey.Kind_12
if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet; [| a.(6) ; a.(7) ; a.(8) ;
*) a.(9) ; a.(10) ; a.(11) ;
a.(6) ; a.(7) ; a.(8) ;
a.(9) ; a.(10) ; a.(11) |]
in
match schwartz_q with
| None -> 1.
| Some schwartz_q -> Zmap.find schwartz_q key
in
if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet;
*)
let norm = let norm =
shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD shell_p.(ab).Shell_pair.norm_fun angMomA angMomB *. shell_q.(cd).Shell_pair.norm_fun angMomC angMomD
in in
let integral = chop norm (fun () -> let integral = chop norm (fun () ->
hvrr_two_e 0 (angMomA, angMomB, angMomC, angMomD) hvrr_two_e 0 (angMomA, angMomB, angMomC, angMomD)
(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b, (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d) Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
(maxm, zero_m_array) (maxm, zero_m_array)
(Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d) (Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d)
(shell_p.(ab).Shell_pair.expo_inv, shell_q.(cd).Shell_pair.expo_inv) (shell_p.(ab).Shell_pair.expo_inv, shell_q.(cd).Shell_pair.expo_inv)
(shell_p.(ab).Shell_pair.center_ab, shell_q.(cd).Shell_pair.center_ab, center_pq) (shell_p.(ab).Shell_pair.center_ab, shell_q.(cd).Shell_pair.center_ab, center_pq)
map ) map )
in in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
with NullQuartet -> () with NullQuartet -> ()
) class_indices ) class_indices
with NullQuartet -> () with NullQuartet -> ()
done done
done; done;
end
end;
let result = let result =
Zmap.create (Array.length contracted_class) Zmap.create (Array.length contracted_class)
in in

1
Utils/Zkey.ml
View File

@ -1,6 +1,5 @@
(** Key for hastables that contain tuples of integers encoded in a Zarith integer *) (** Key for hastables that contain tuples of integers encoded in a Zarith integer *)
type kind_array = type kind_array =
| Kind_3 | Kind_3
| Kind_6 | Kind_6