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Working on contraction

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Anthony Scemama 2018-02-09 20:32:39 +01:00
parent 365735d111
commit 032f1a0913
1 changed files with 226 additions and 123 deletions
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347
Basis/TwoElectronRRVectorized.ml
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@ -8,14 +8,6 @@ let cutoff2 = cutoff *. cutoff
exception NullQuartet exception NullQuartet
exception Found exception Found
let at_least_one_valid arr =
try
Vec.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false
with Found -> true
(*TODO : REMOVE *)
let sum integral =
Array.fold_left (+.) 0. integral
(** Horizontal and Vertical Recurrence Relations (HVRR) *) (** Horizontal and Vertical Recurrence Relations (HVRR) *)
let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d) let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
@ -34,6 +26,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
Array.make nq 0. Array.make nq 0.
in in
let totAngMom_a = Angular_momentum.to_int totAngMom_a let totAngMom_a = Angular_momentum.to_int totAngMom_a
and totAngMom_b = Angular_momentum.to_int totAngMom_b and totAngMom_b = Angular_momentum.to_int totAngMom_b
and totAngMom_c = Angular_momentum.to_int totAngMom_c and totAngMom_c = Angular_momentum.to_int totAngMom_c
@ -41,7 +34,8 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
in in
(** Vertical recurrence relations *) (** Vertical recurrence relations *)
let rec vrr0_v l m angMom_a = function let rec vrr0_v m angMom_a = function
(*
| 1 -> | 1 ->
let xyz = let xyz =
match angMom_a with match angMom_a with
@ -49,16 +43,36 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
| (_,1,_) -> 1 | (_,1,_) -> 1
| _ -> 2 | _ -> 2
in in
let f = expo_b.{l} *. (Coordinate.coord center_ab xyz) in let a = Mat.mul center_pq.(xyz) zero_m_array.(m+1) in
Array.init nq (fun k -> coef_prod.{k+1,l} *. expo_inv_p.{l} *. let b = copy expo_b in
(center_pq.{xyz+1,k+1,l} *. zero_m_array.(m+1).{k+1,l} scal (Coordinate.coord center_ab xyz) b;
-. f *. zero_m_array.(m).{k+1,l} ) ) let c = Mat.map (fun x -> x) zero_m_array.(m) in
| 0 -> Array.init nq (fun k -> zero_m_array.(m).{k+1,l} *. coef_prod.{k+1,l}) Mat.scal_cols c b;
let d = Mat.sub a c in
Mat.scal_cols d expo_inv_p;
Some (Mat.mul coef_prod d)
*)
| 1 ->
let xyz =
match angMom_a with
| (1,_,_) -> 0
| (_,1,_) -> 1
| _ -> 2
in
Some (
Array.init np (fun ab -> let l=ab+1 in
Array.init nq (fun k ->
let f = expo_b.{l} *. (Coordinate.coord center_ab xyz) in
coef_prod.{k+1,l} *. expo_inv_p.{l} *.
(center_pq.(xyz).{k+1,l} *. zero_m_array.(m+1).{k+1,l}
-. f *. zero_m_array.(m).{k+1,l} ) ))
)
| 0 -> Some (Mat.mul zero_m_array.(m) coef_prod |> Mat.transpose_copy |> Mat.to_array)
| totAngMom_a -> | totAngMom_a ->
let key = Zkey.of_int_tuple (Zkey.Three angMom_a) let key = Zkey.of_int_tuple (Zkey.Three angMom_a)
in in
try Zmap.find map_1d.(m).(l-1) key with try Zmap.find map_1d.(m) key with
| Not_found -> | Not_found ->
let result = let result =
let am, amm, amxyz, xyz = let am, amm, amxyz, xyz =
@ -67,46 +81,84 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
| (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1 | (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1
| (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2 | (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2
in in
if amxyz < 0 then empty else if amxyz < 0 then
let v1 = None
let f = else
-. expo_b.{l} *. expo_inv_p.{l} *. (Coordinate.coord center_ab xyz) let v1_top, p1_top =
in if abs_float (Coordinate.coord center_ab xyz) < cutoff then
if (abs_float f < cutoff) then empty else None,
Array.map (fun v1k -> f *. v1k) (vrr0_v l m am (totAngMom_a-1) ) vrr0_v (m+1) am (totAngMom_a-1)
else
vrr0_v m am (totAngMom_a-1),
vrr0_v (m+1) am (totAngMom_a-1)
in
let v1_top2, p1_top2 =
if amxyz < 1 then (None,None) else
vrr0_v m amm (totAngMom_a-2),
vrr0_v (m+1) amm (totAngMom_a-2)
in in
let p1 =
Array.mapi (fun k v2k -> v1.(k) +. expo_inv_p.{l} *. center_pq.{xyz+1,k+1,l} *. v2k) (vrr0_v l (m+1) am (totAngMom_a-1)) Some (
in Array.init np (fun ab -> let l = ab+1 in
if amxyz < 1 then p1 else let v1 =
let f = (float_of_int amxyz) *. expo_inv_p.{l} *. 0.5 let f =
in -. expo_b.{l} *. expo_inv_p.{l} *. (Coordinate.coord center_ab xyz)
if (abs_float f < cutoff) then empty else in
let v1 = vrr0_v l m amm (totAngMom_a-2) match v1_top with
in | Some v1_top ->
let v2 = v1_top.(l-1)
if (abs_float (f *. expo_inv_p.{l})) < cutoff then empty else |> Array.map (fun x -> f *. x)
vrr0_v l (m+1) amm (totAngMom_a-2) | None -> empty
in in
Array.init nq (fun k -> p1.(k) +. let p1 =
f *. (v1.(k) +. v2.(k) *. expo_inv_p.{l} ) ) match p1_top with
in Zmap.add map_1d.(m).(l-1) key result; | Some p1_top ->
p1_top.(l-1)
| _ -> assert false
in
let p1 =
Array.init nq (fun k ->
v1.(k) +. expo_inv_p.{l} *. center_pq.(xyz).{k+1,l} *. p1.(k))
in
if amxyz < 1 then p1 else
let f = (float_of_int amxyz) *. expo_inv_p.{l} *. 0.5
in
let v1 =
match v1_top2 with
| Some v1_top2 -> v1_top2.(l-1)
| None -> assert false
in
let v2 =
match p1_top2 with
| Some p1_top2 -> p1_top2.(l-1)
| None -> assert false
in
Array.init nq (fun k ->
p1.(k) +. f *. (v1.(k) +. v2.(k) *. expo_inv_p.{l} ) )
)
)
in Zmap.add map_1d.(m) key result;
result result
and vrr_v l m angMom_a angMom_c totAngMom_a totAngMom_c =
and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =
match (totAngMom_a, totAngMom_c) with match (totAngMom_a, totAngMom_c) with
| (i,0) -> if (i>0) then | (i,0) ->
vrr0_v l m angMom_a totAngMom_a if (i>0) then
begin
match vrr0_v m angMom_a totAngMom_a with
| Some x -> Some (Mat.of_array x |> Mat.transpose_copy)
| None -> None
end
else else
Array.init nq (fun k -> zero_m_array.(m).{k+1,l} *. coef_prod.{k+1,l}) Some (Mat.mul zero_m_array.(m) coef_prod )
| (_,_) -> | (_,_) ->
let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c)) let key = Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c))
in in
try Zmap.find map_2d.(m).(l-1) key with try Zmap.find map_2d.(m) key with
| Not_found -> | Not_found ->
let result = let result =
begin begin
@ -129,32 +181,39 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
(acx-2,acy,acz), (acx-2,acy,acz),
aax,acx, 0 aax,acx, 0
in in
(*
if cxyz < 1 then empty else
*)
let f1 = let f1 =
let f = (Coordinate.coord center_cd xyz) in let f = (Coordinate.coord center_cd xyz) in
Array.init nq (fun k -> Vec.init nq (fun k ->
expo_d.{k+1} *. expo_inv_q.{k+1} *. f) expo_d.{k} *. expo_inv_q.{k} *. f)
|> Vec.of_array
in
let f2 =
Array.init nq (fun k ->
expo_inv_q.{k+1} *. center_pq.{xyz+1,k+1,l} )
|> Vec.of_array
in in
let v1 = let v1 =
if (at_least_one_valid f1) then if (abs_float @@ amax f1 > cutoff) then
vrr_v l m angMom_a cm totAngMom_a (totAngMom_c-1) vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1)
else empty else None
and v2 =
if (at_least_one_valid f2) then
vrr_v l (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
else empty
in in
let f2 =
Mat.init_cols nq np (fun k l ->
expo_inv_q.{k} *. center_pq.(xyz).{k,l} )
in
let v2 =
if (Mat.as_vec f2 |> amax |> abs_float) < cutoff then
None
else
vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
in
let p1 = let p1 =
Array.init nq (fun k -> -. v1.(k) *. f1.{k+1} -. v2.(k) *. f2.{k+1}) match v1, v2 with
| Some v1, Some v2 ->
Some (Mat.init_cols nq np (fun k l ->
-. v1.{k,l} *. f1.{k} -. v2.{k,l} *. f2.{k,l}) )
| None, Some v2 ->
Some (Mat.init_cols nq np (fun k l -> -. v2.{k,l} *. f2.{k,l}) )
| Some v1, None ->
Some (Mat.init_cols nq np (fun k l -> -. v1.{k,l} *. f1.{k} ) )
| None, None -> None
in in
let p2 = let p2 =
if cxyz < 2 then p1 else if cxyz < 2 then p1 else
let fcm = let fcm =
@ -167,50 +226,88 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
Vec.mul f1 expo_inv_q Vec.mul f1 expo_inv_q
in in
let v1 = let v1 =
if (at_least_one_valid f1) then if (abs_float @@ amax f1 > cutoff) then
vrr_v l m angMom_a cmm totAngMom_a (totAngMom_c-2) vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2)
else empty else None
in in
let v2 = let v2 =
if (at_least_one_valid f2) then if (abs_float @@ amax f2 > cutoff) then
vrr_v l (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
else empty else None
in in
Array.init nq (fun k -> p1.(k) +. f1.{k+1} *. v1.(k) +. f2.{k+1} *. v2.(k)) match p1, v1, v2 with
| Some p1, Some v1, Some v2 ->
Some (Mat.init_cols nq np (fun k l -> p1.{k,l} +. f1.{k} *. v1.{k,l} +. f2.{k} *. v2.{k,l}) )
| Some p1, Some v1, None ->
Some (Mat.init_cols nq np (fun k l -> p1.{k,l} +. f1.{k} *. v1.{k,l} ))
| Some p1, None, Some v2 ->
Some (Mat.init_cols nq np (fun k l -> p1.{k,l} +. f2.{k} *. v2.{k,l}) )
| None , Some v1, Some v2 ->
Some (Mat.init_cols nq np (fun k l -> f1.{k} *. v1.{k,l} +. f2.{k} *. v2.{k,l}) )
| Some p1, None, None -> Some p1
| None , Some v1, None ->
Some (Mat.init_cols nq np (fun k l -> f1.{k} *. v1.{k,l}))
| None, None, Some v2 ->
Some (Mat.init_cols nq np (fun k l -> f2.{k} *. v2.{k,l}) )
| None, None, None -> None
in in
if (axyz < 1) || (cxyz < 1) then p2 else if (axyz < 1) || (cxyz < 1) then p2 else
let fa = let v =
(float_of_int axyz) *. expo_inv_p.{l} *. 0.5 vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
in in
let f1 = begin
Vec.map (fun e -> fa *. e ) expo_inv_q match (p2, v) with
in | Some p2, Some v -> Some (
if (at_least_one_valid f1) then Array.init np (fun ab -> let l = ab+1 in
let v = let fa =
vrr_v l (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) (float_of_int axyz) *. expo_inv_p.{l} *. 0.5
in in
Array.init nq (fun k -> p2.(k) -. f1.{k+1} *. v.(k)) let f1 =
else p2 Vec.map (fun e -> fa *. e ) expo_inv_q
in
Vec.init nq (fun k -> p2.{k,l} -. f1.{k} *. v.{k,l})
)
|> Mat.of_col_vecs )
| Some p2, None -> Some p2
| None, Some v -> Some (
Array.init np (fun ab -> let l = ab+1 in
let fa =
(float_of_int axyz) *. expo_inv_p.{l} *. 0.5
in
let f1 =
Vec.map (fun e -> fa *. e ) expo_inv_q
in
Vec.init nq (fun k -> -. f1.{k} *. v.{k,l})
)
|> Mat.of_col_vecs )
| None, None -> None
end
end end
in Zmap.add map_2d.(m).(l-1) key result; in Zmap.add map_2d.(m) key result;
result result
(** Horizontal recurrence relations *) (** Horizontal recurrence relations *)
and hrr0_v l angMom_a angMom_b angMom_c and hrr0_v angMom_a angMom_b angMom_c
totAngMom_a totAngMom_b totAngMom_c = totAngMom_a totAngMom_b totAngMom_c =
match totAngMom_b with match totAngMom_b with
| 0 -> | 0 ->
begin begin
match (totAngMom_a, totAngMom_c) with match (totAngMom_a, totAngMom_c) with
| (0,0) -> | (0,0) -> Mat.gemm_trace zero_m_array.(0) coef_prod
Array.init nq (fun k -> zero_m_array.(0).{k+1,l} *. coef_prod.{k+1,l}) | (_,0) ->
|> sum begin
| (_,0) -> vrr0_v l 0 angMom_a totAngMom_a |> sum match vrr0_v 0 angMom_a totAngMom_a with
| (_,_) -> vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c |> sum | Some matrix -> Mat.sum (Mat.of_array matrix)
| None -> 0.
end
| (_,_) ->
match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
| Some matrix -> Mat.sum matrix
| None -> 0.
end end
| 1 -> | 1 ->
let (aax, aay, aaz) = angMom_a in let (aax, aay, aaz) = angMom_a in
@ -222,13 +319,17 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
in in
let f = Coordinate.coord center_ab xyz in let f = Coordinate.coord center_ab xyz in
let v1 = let v1 =
vrr_v l 0 ap angMom_c (totAngMom_a+1) totAngMom_c match vrr_v 0 ap angMom_c (totAngMom_a+1) totAngMom_c with
| Some matrix -> Mat.sum matrix
| None -> 0.
in in
if (abs_float f < cutoff) then sum v1 else if (abs_float f < cutoff) then v1 else
let v2 = let v2 =
vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
| Some matrix -> Mat.sum matrix
| None -> 0.
in in
Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2 |> sum v1 +. v2 *. f
| _ -> | _ ->
let (aax, aay, aaz) = angMom_a let (aax, aay, aaz) = angMom_a
and (abx, aby, abz) = angMom_b in and (abx, aby, abz) = angMom_b in
@ -247,24 +348,27 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
in in
let h1 = let h1 =
hrr0_v l ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c
in in
let f = (Coordinate.coord center_ab xyz) in let f = (Coordinate.coord center_ab xyz) in
if (abs_float f < cutoff) then h1 else if (abs_float f < cutoff) then h1 else
let h2 = let h2 =
hrr0_v l angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c hrr0_v angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
in in
h1 +. h2 *. f h1 +. h2 *. f
and hrr_v l angMom_a angMom_b angMom_c angMom_d and hrr_v 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) -> if (totAngMom_b = 0) then | (_,0) -> if (totAngMom_b = 0) then
vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c begin
|> sum match vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c with
| Some matrix -> Mat.sum matrix
| None -> 0.
end
else else
hrr0_v l angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
| (_,_) -> | (_,_) ->
let (acx, acy, acz) = angMom_c let (acx, acy, acz) = angMom_c
and (adx, ady, adz) = angMom_d in and (adx, ady, adz) = angMom_d in
@ -275,21 +379,19 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
| _ -> (acx, acy, acz+1), (adx, ady, adz-1), 2 | _ -> (acx, acy, acz+1), (adx, ady, adz-1), 2
in in
let h1 = let h1 =
hrr_v l angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1) hrr_v angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
and h2 = and h2 =
hrr_v l angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1) hrr_v angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
in in
let f = (Coordinate.coord center_cd xyz) in let f = (Coordinate.coord center_cd xyz) in
h1 +. f *. h2 h1 +. f *. h2
in in
Array.init np (fun ab -> hrr_v
hrr_v (ab+1)
(angMom_a.(0),angMom_a.(1),angMom_a.(2)) (angMom_a.(0),angMom_a.(1),angMom_a.(2))
(angMom_b.(0),angMom_b.(1),angMom_b.(2)) (angMom_b.(0),angMom_b.(1),angMom_b.(2))
(angMom_c.(0),angMom_c.(1),angMom_c.(2)) (angMom_c.(0),angMom_c.(1),angMom_c.(2))
(angMom_d.(0),angMom_d.(1),angMom_d.(2)) (angMom_d.(0),angMom_d.(1),angMom_d.(2))
totAngMom_a totAngMom_b totAngMom_c totAngMom_d totAngMom_a totAngMom_b totAngMom_c totAngMom_d
) |> sum
@ -350,7 +452,7 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
totAngMom shell_c, totAngMom shell_d) with totAngMom shell_c, totAngMom shell_d) with
| Angular_momentum.(S,S,S,S) -> | Angular_momentum.(S,S,S,S) ->
contracted_class.(0) <- contracted_class.(0) <-
let zm_array = Mat.init_rows np nq (fun i j -> let zm_array = Mat.init_cols np nq (fun i j ->
(** Screening on the product of coefficients *) (** Screening on the product of coefficients *)
try try
if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then
@ -385,20 +487,21 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
let center_pq = let center_pq =
let result = Array.init 3 (fun xyz ->
Array3.create Float64 fortran_layout 3 nq np Mat.init_cols nq np (fun cd ab ->
in let shell_ab = sp.(ab-1)
Array.iteri (fun ab shell_ab -> and shell_cd = sq.(cd-1)
Array.iteri (fun cd shell_cd -> in
let cpq = let cpq =
Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center) Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
in in
result.{1,cd+1,ab+1} <- Coordinate.x cpq; match xyz with
result.{2,cd+1,ab+1} <- Coordinate.y cpq; | 0 -> Coordinate.x cpq;
result.{3,cd+1,ab+1} <- Coordinate.z cpq; | 1 -> Coordinate.y cpq;
) sq | 2 -> Coordinate.z cpq;
) sp; | _ -> assert false
result )
)
in in
let zero_m_array = let zero_m_array =
let result = let result =
@ -411,9 +514,9 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
expo_inv_p.{ab+1} +. expo_inv_q.{cd+1} expo_inv_p.{ab+1} +. expo_inv_q.{cd+1}
in in
let norm_pq_sq = let norm_pq_sq =
center_pq.{1,cd+1,ab+1} *. center_pq.{1,cd+1,ab+1} +. center_pq.(0).{cd+1,ab+1} *. center_pq.(0).{cd+1,ab+1} +.
center_pq.{2,cd+1,ab+1} *. center_pq.{2,cd+1,ab+1} +. center_pq.(1).{cd+1,ab+1} *. center_pq.(1).{cd+1,ab+1} +.
center_pq.{3,cd+1,ab+1} *. center_pq.{3,cd+1,ab+1} center_pq.(2).{cd+1,ab+1} *. center_pq.(2).{cd+1,ab+1}
in in
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
@ -444,8 +547,8 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
|> Array.concat |> Array.concat
in in
let map_1d = Array.init maxm (fun _ -> Array.init np (fun _ -> Zmap.create (4*maxm))) let map_1d = Array.init maxm (fun _ -> Zmap.create (4*maxm))
and map_2d = Array.init maxm (fun _ -> Array.init np (fun _ -> Zmap.create (Array.length class_indices))) and map_2d = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices))
in in
(* Compute the integral class from the primitive shell quartet *) (* Compute the integral class from the primitive shell quartet *)
Array.iteri (fun i key -> Array.iteri (fun i key ->