LCPQ/QCaml
10
1
Fork 0
mirror of https://gitlab.com/scemama/QCaml.git synced 2024-07-11 22:03:37 +02:00
Code Releases Activity

Working on contraction

Browse Source
This commit is contained in:
Anthony Scemama 2018-02-09 19:41:22 +01:00
parent 5420d41503
commit 365735d111
8 changed files with 366 additions and 296 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

132
Basis/ContractedShellPair.ml
View File

@ -6,7 +6,17 @@ exception Null_contribution
(** Array of shell pairs obtained from combining two contracted shells. The (** Array of shell pairs obtained from combining two contracted shells. The
two integers correspond to the indices of the combined shells. two integers correspond to the indices of the combined shells.
*) *)
type t = ShellPair.t array type t =
{
shell_a : Contracted_shell.t;
shell_b : Contracted_shell.t;
shell_pairs : ShellPair.t array;
coef : float array;
expo_inv : float array;
center_ab : Coordinate.t; (* A-B *)
norm_sq : float; (* |A-B|^2 *)
norm_coef_scale : float array; (* norm_coef.(i) / norm_coef.(0) *)
}
(** Creates an contracted shell pair : an array of pairs of primitive shells. (** Creates an contracted shell pair : an array of pairs of primitive shells.
@ -38,62 +48,72 @@ let create ?cutoff p_a p_b =
|> Array.to_list |> Array.to_list
|> Array.concat |> Array.concat
in in
Array.init (Contracted_shell.size p_a) (fun i -> let shell_pairs =
let p_a_expo_center = Coordinate.( Array.init (Contracted_shell.size p_a) (fun i ->
Contracted_shell.expo p_a i |. Contracted_shell.center p_a ) let p_a_expo_center = Coordinate.(
in Contracted_shell.expo p_a i |. Contracted_shell.center p_a )
let norm_coef_a = in
Contracted_shell.norm_coef p_a i let norm_coef_a =
in Contracted_shell.norm_coef p_a i
in
Array.init (Contracted_shell.size p_b) (fun j -> Array.init (Contracted_shell.size p_b) (fun j ->
try try
let norm_coef_b = let norm_coef_b =
Contracted_shell.norm_coef p_b j Contracted_shell.norm_coef p_b j
in in
let norm_coef = let norm_coef =
norm_coef_a *. norm_coef_b norm_coef_a *. norm_coef_b
in in
if (norm_coef < cutoff) then if (norm_coef < cutoff) then
raise Null_contribution; raise Null_contribution;
let p_b_expo_center = Coordinate.( let p_b_expo_center = Coordinate.(
Contracted_shell.expo p_b j |. Contracted_shell.center p_b ) Contracted_shell.expo p_b j |. Contracted_shell.center p_b )
in in
let expo = Contracted_shell.(expo p_a i +. expo p_b j) in let expo = Contracted_shell.(expo p_a i +. expo p_b j) in
let expo_inv = 1. /. expo in let expo_inv = 1. /. expo in
let center = Coordinate.( let center = Coordinate.(
expo_inv |. (p_a_expo_center |+ p_b_expo_center ) ) expo_inv |. (p_a_expo_center |+ p_b_expo_center ) )
in in
let argexpo = let argexpo =
Contracted_shell.(expo p_a i *. expo p_b j) *. norm_sq *. expo_inv Contracted_shell.(expo p_a i *. expo p_b j) *. norm_sq *. expo_inv
in in
if (argexpo > log_cutoff) then if (argexpo > log_cutoff) then
raise Null_contribution; raise Null_contribution;
let g = let g =
(pi *. expo_inv)**(1.5) *. exp(-. argexpo) (pi *. expo_inv)**(1.5) *. exp(-. argexpo)
in in
let coef = let coef =
norm_coef *. Contracted_shell.(coef p_a i *. coef p_b j) *. g norm_coef *. Contracted_shell.(coef p_a i *. coef p_b j) *. g
in in
if (abs_float coef < cutoff) then if (abs_float coef < cutoff) then
raise Null_contribution; raise Null_contribution;
let center_a = let center_a =
Coordinate.(center |- Contracted_shell.center p_a) Coordinate.(center |- Contracted_shell.center p_a)
in in
let monocentric = let monocentric =
Contracted_shell.center p_a = Contracted_shell.center p_b Contracted_shell.center p_a = Contracted_shell.center p_b
in in
Some ShellPair.{ i ; j ; shell_a=p_a ; shell_b=p_b ; norm_coef ; coef ; expo ; expo_inv ; center ; center_a ; center_ab ; norm_sq ; norm_coef_scale ; monocentric } Some ShellPair.{ i ; j ; shell_a=p_a ; shell_b=p_b ; norm_coef ; coef ; expo ; expo_inv ; center ; center_a ; center_ab ; norm_sq ; monocentric }
with with
| Null_contribution -> None | Null_contribution -> None
) )
) )
|> Array.to_list |> Array.to_list
|> Array.concat |> Array.concat
|> Array.to_list |> Array.to_list
|> List.filter (function Some _ -> true | None -> false) |> List.filter (function Some _ -> true | None -> false)
|> List.map (function Some x -> x | None -> assert false) |> List.map (function Some x -> x | None -> assert false)
|> Array.of_list |> Array.of_list
in
let coef = Array.map (fun x -> (fun y -> y.ShellPair.coef) x) shell_pairs
and expo_inv = Array.map (fun x -> (fun y -> y.ShellPair.expo_inv) x) shell_pairs
in
{
shell_a = p_a ; shell_b = p_b ; coef ; expo_inv ;
shell_pairs ; center_ab=shell_pairs.(0).center_ab;
norm_coef_scale ; norm_sq=shell_pairs.(0).norm_sq
}
(** Returns an integer characteristic of a contracted shell pair *) (** Returns an integer characteristic of a contracted shell pair *)

13
Basis/ERI.ml
View File

@ -134,6 +134,10 @@ let of_basis basis =
shell_p = shell_pairs.(i).(j) shell_p = shell_pairs.(i).(j)
in in
let sp =
shell_p.ContractedShellPair.shell_pairs
in
for k=0 to i do for k=0 to i do
for l=0 to k do for l=0 to k do
let schwartz_q, schwartz_q_max = schwartz.(k).(l) in let schwartz_q, schwartz_q_max = schwartz.(k).(l) in
@ -143,20 +147,23 @@ let of_basis basis =
let let
shell_q = shell_pairs.(k).(l) shell_q = shell_pairs.(k).(l)
in in
let sq =
shell_q.ContractedShellPair.shell_pairs
in
let swap = let swap =
Array.length shell_q < Array.length shell_p Array.length sp > Array.length sq
in in
(* Compute all the integrals of the class *) (* Compute all the integrals of the class *)
let cls = let cls =
if swap then if swap then
if Array.length shell_p < 2 then if Array.length sp < 2 then
contracted_class_shell_pairs ~schwartz_p:schwartz_q ~schwartz_q:schwartz_p shell_q shell_p contracted_class_shell_pairs ~schwartz_p:schwartz_q ~schwartz_q:schwartz_p shell_q shell_p
else else
contracted_class_shell_pairs_vec ~schwartz_p:schwartz_q ~schwartz_q:schwartz_p shell_q shell_p contracted_class_shell_pairs_vec ~schwartz_p:schwartz_q ~schwartz_q:schwartz_p shell_q shell_p
else else
if Array.length shell_q < 2 then if Array.length sq < 2 then
contracted_class_shell_pairs ~schwartz_p ~schwartz_q shell_p shell_q contracted_class_shell_pairs ~schwartz_p ~schwartz_q shell_p shell_q
else else
contracted_class_shell_pairs_vec ~schwartz_p ~schwartz_q shell_p shell_q contracted_class_shell_pairs_vec ~schwartz_p ~schwartz_q shell_p shell_q

28
Basis/KinInt.ml
View File

@ -24,33 +24,35 @@ let contracted_class shell_a shell_b : float Zmap.t =
(* 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) let sp = shell_p.ContractedShellPair.shell_pairs in
let center_ab =
shell_p.ContractedShellPair.center_ab
in
let norm_coef_scale =
shell_p.ContractedShellPair.norm_coef_scale
in
for ab=0 to (Array.length sp - 1)
do do
let coef_prod = let coef_prod =
shell_p.(ab).ShellPair.coef shell_p.ContractedShellPair.coef.(ab)
in in
(** Screening on thr product of coefficients *) (** Screening on thr product of coefficients *)
if (abs_float coef_prod) > 1.e-4*.cutoff then if (abs_float coef_prod) > 1.e-4*.cutoff then
begin begin
let center_ab =
shell_p.(ab).ShellPair.center_ab
in
let center_pa = let center_pa =
shell_p.(ab).ShellPair.center_a sp.(ab).ShellPair.center_a
in in
let expo_inv = let expo_inv =
shell_p.(ab).ShellPair.expo_inv shell_p.ContractedShellPair.expo_inv.(ab)
in
let norm_coef_scale =
shell_p.(ab).ShellPair.norm_coef_scale
in in
let i, j = let i, j =
shell_p.(ab).ShellPair.i, shell_p.(ab).ShellPair.j sp.(ab).ShellPair.i, sp.(ab).ShellPair.j
in in
let expo_a = let expo_a =
Contracted_shell.expo shell_p.(ab).ShellPair.shell_a i Contracted_shell.expo sp.(ab).ShellPair.shell_a i
and expo_b = and expo_b =
Contracted_shell.expo shell_p.(ab).ShellPair.shell_b j Contracted_shell.expo sp.(ab).ShellPair.shell_b j
in in
Array.iteri (fun i key -> Array.iteri (fun i key ->

21
Basis/OneElectronRR.ml
View File

@ -123,8 +123,8 @@ let hvrr_one_e
(** Computes all the one-electron integrals of the contracted shell pair *) (** Computes all the one-electron integrals of the contracted shell pair *)
let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t = let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
let shell_a = shell_p.(0).ShellPair.shell_a let shell_a = shell_p.ContractedShellPair.shell_a
and shell_b = shell_p.(0).ShellPair.shell_b and shell_b = shell_p.ContractedShellPair.shell_b
in in
let maxm = let maxm =
let open Angular_momentum in let open Angular_momentum in
@ -144,13 +144,14 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
(* 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) let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale
in
for ab=0 to (Array.length shell_p.ContractedShellPair.shell_pairs - 1)
do do
let b = shell_p.(ab).ShellPair.j in let b = shell_p.ContractedShellPair.shell_pairs.(ab).ShellPair.j in
try try
begin begin
let coef_prod = shell_p.(ab).ShellPair.coef in let coef_prod = shell_p.ContractedShellPair.coef.(ab) in
let norm_coef_scale_p = shell_p.(ab).ShellPair.norm_coef_scale in
(** Screening on the product of coefficients *) (** Screening on the product of coefficients *)
if (abs_float coef_prod) < 1.e-4*.cutoff then if (abs_float coef_prod) < 1.e-4*.cutoff then
@ -158,14 +159,14 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
let expo_pq_inv = let expo_pq_inv =
shell_p.(ab).ShellPair.expo_inv shell_p.ContractedShellPair.expo_inv.(ab)
in in
let center_ab = let center_ab =
shell_p.(ab).ShellPair.center_ab shell_p.ContractedShellPair.center_ab
in in
let center_p = let center_p =
shell_p.(ab).ShellPair.center shell_p.ContractedShellPair.shell_pairs.(ab).ShellPair.center
in in
let center_pa = let center_pa =
Coordinate.(center_p |- Contracted_shell.center shell_a) Coordinate.(center_p |- Contracted_shell.center shell_a)
@ -208,7 +209,7 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t =
(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b) (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b)
(maxm, zero_m_array) (maxm, zero_m_array)
(Contracted_shell.expo shell_b b) (Contracted_shell.expo shell_b b)
(shell_p.(ab).ShellPair.expo_inv) (shell_p.ContractedShellPair.expo_inv.(ab))
(center_ab, center_pa, center_pc) (center_ab, center_pa, center_pc)
map map
in in

26
Basis/Overlap.ml
View File

@ -22,27 +22,31 @@ let contracted_class shell_a shell_b : float Zmap.t =
Array.make (Array.length class_indices) 0. Array.make (Array.length class_indices) 0.
in in
let sp =
shell_p.ContractedShellPair.shell_pairs
in
let center_ab =
shell_p.ContractedShellPair.center_ab
in
let norm_coef_scale =
shell_p.ContractedShellPair.norm_coef_scale
in
(* 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) for ab=0 to (Array.length sp - 1)
do do
let coef_prod = let coef_prod =
shell_p.(ab).ShellPair.coef shell_p.ContractedShellPair.coef.(ab)
in in
(** Screening on thr product of coefficients *) (** Screening on thr product of coefficients *)
if (abs_float coef_prod) > 1.e-4*.cutoff then if (abs_float coef_prod) > 1.e-4*.cutoff then
begin begin
let center_ab = let expo_inv =
shell_p.(ab).ShellPair.center_ab shell_p.ContractedShellPair.expo_inv.(ab)
in in
let center_pa = let center_pa =
shell_p.(ab).ShellPair.center_a sp.(ab).ShellPair.center_a
in
let expo_inv =
shell_p.(ab).ShellPair.expo_inv
in
let norm_coef_scale =
shell_p.(ab).ShellPair.norm_coef_scale
in in
Array.iteri (fun i key -> Array.iteri (fun i key ->

1
Basis/ShellPair.ml
View File

@ -11,7 +11,6 @@ type t = {
norm_coef: float; (* norm_coef_a * norm_coef_b *) norm_coef: float; (* norm_coef_a * norm_coef_b *)
coef : float; (* norm_coef * coef_a * coef_b * g, with coef : float; (* norm_coef * coef_a * coef_b * g, with
g = (pi/(alpha+beta))^(3/2) exp (-|A-B|^2 * alpha*beta/(alpha+beta)) *) g = (pi/(alpha+beta))^(3/2) exp (-|A-B|^2 * alpha*beta/(alpha+beta)) *)
norm_coef_scale : float array; (* norm_coef.(i) / norm_coef.(0) *)
i : int; i : int;
j : int; j : int;
shell_a : Contracted_shell.t; shell_a : Contracted_shell.t;

36
Basis/TwoElectronRR.ml
View File

@ -310,10 +310,12 @@ let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t = let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
let shell_a = shell_p.(0).ShellPair.shell_a let shell_a = shell_p.ContractedShellPair.shell_a
and shell_b = shell_p.(0).ShellPair.shell_b and shell_b = shell_p.ContractedShellPair.shell_b
and shell_c = shell_q.(0).ShellPair.shell_a and shell_c = shell_q.ContractedShellPair.shell_a
and shell_d = shell_q.(0).ShellPair.shell_b and shell_d = shell_q.ContractedShellPair.shell_b
and sp = shell_p.ContractedShellPair.shell_pairs
and sq = shell_q.ContractedShellPair.shell_pairs
in in
let maxm = let maxm =
let open Angular_momentum in let open Angular_momentum in
@ -335,13 +337,14 @@ 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) do let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
let cab = shell_p.(ab).ShellPair.coef in let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
let b = shell_p.(ab).ShellPair.j in for ab=0 to (Array.length sp - 1) do
let norm_coef_scale_p = shell_p.(ab).ShellPair.norm_coef_scale in let cab = shell_p.ContractedShellPair.coef.(ab) in
for cd=0 to (Array.length shell_q - 1) do let b = sp.(ab).ShellPair.j in
for cd=0 to (Array.length shell_q.ContractedShellPair.shell_pairs - 1) do
let coef_prod = let coef_prod =
cab *. shell_q.(cd).ShellPair.coef cab *. shell_q.ContractedShellPair.coef.(cd)
in in
(** Screening on the product of coefficients *) (** Screening on the product of coefficients *)
try try
@ -349,10 +352,11 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
raise NullQuartet; raise NullQuartet;
let expo_pq_inv = let expo_pq_inv =
shell_p.(ab).ShellPair.expo_inv +. shell_q.(cd).ShellPair.expo_inv shell_p.ContractedShellPair.expo_inv.(ab) +.
shell_q.ContractedShellPair.expo_inv.(cd)
in in
let center_pq = let center_pq =
Coordinate.(shell_p.(ab).ShellPair.center |- shell_q.(cd).ShellPair.center) Coordinate.(sp.(ab).ShellPair.center |- sq.(cd).ShellPair.center)
in in
let norm_pq_sq = let norm_pq_sq =
Coordinate.dot center_pq center_pq Coordinate.dot center_pq center_pq
@ -370,12 +374,11 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
in in
contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
| _ -> | _ ->
let d = shell_q.(cd).ShellPair.j in let d = shell_q.ContractedShellPair.shell_pairs.(cd).ShellPair.j in
let map_1d = Zmap.create (4*maxm) in let map_1d = Zmap.create (4*maxm) in
let map_2d = Zmap.create (Array.length class_indices) in let map_2d = Zmap.create (Array.length class_indices) in
let map_1d' = Zmap.create (4*maxm) in let map_1d' = Zmap.create (4*maxm) in
let map_2d' = Zmap.create (Array.length class_indices) in let map_2d' = Zmap.create (Array.length class_indices) in
let norm_coef_scale_q = shell_q.(cd).ShellPair.norm_coef_scale in
let norm_coef_scale = let norm_coef_scale =
Array.map (fun v1 -> Array.map (fun v1 ->
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
@ -446,8 +449,9 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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).ShellPair.expo_inv, shell_q.(cd).ShellPair.expo_inv) (shell_p.ContractedShellPair.expo_inv.(ab),
(shell_p.(ab).ShellPair.center_ab, shell_q.(cd).ShellPair.center_ab, center_pq) shell_q.ContractedShellPair.expo_inv.(cd) )
(sp.(ab).ShellPair.center_ab, sq.(cd).ShellPair.center_ab, center_pq)
map_1d map_2d map_1d' map_2d' map_1d map_2d map_1d' map_2d'
in in
contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral

405
Basis/TwoElectronRRVectorized.ml
View File

@ -1,4 +1,6 @@
open Util open Util
open Lacaml.D
open Bigarray
let cutoff = Constants.cutoff let cutoff = Constants.cutoff
let cutoff2 = cutoff *. cutoff let cutoff2 = cutoff *. cutoff
@ -8,9 +10,13 @@ exception Found
let at_least_one_valid arr = let at_least_one_valid arr =
try try
Array.fold_left (fun _ x -> if (abs_float x > cutoff) then raise Found else false ) false arr Vec.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false
with Found -> true 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)
(totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d) (totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
@ -18,12 +24,14 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
(expo_b, expo_d) (expo_b, expo_d)
(expo_inv_p, expo_inv_q) (expo_inv_p, expo_inv_q)
(center_ab, center_cd, center_pq) (center_ab, center_cd, center_pq)
coef_prod map_1d map_2d coef_prod map_1d map_2d
= =
let ncoef = (Array.length coef_prod) in let nq = Mat.dim1 coef_prod in
let np = Mat.dim2 coef_prod in
let empty = let empty =
Array.make ncoef 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
@ -33,7 +41,7 @@ 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 m angMom_a = function let rec vrr0_v l m angMom_a = function
| 1 -> | 1 ->
let xyz = let xyz =
match angMom_a with match angMom_a with
@ -41,16 +49,16 @@ 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 *. (Coordinate.coord center_ab xyz) in let f = expo_b.{l} *. (Coordinate.coord center_ab xyz) in
Array.init ncoef (fun k -> coef_prod.(k) *. expo_inv_p *. Array.init nq (fun k -> coef_prod.{k+1,l} *. expo_inv_p.{l} *.
( (Coordinate.coord center_pq.(k) xyz) *. zero_m_array.(m+1).(k) (center_pq.{xyz+1,k+1,l} *. zero_m_array.(m+1).{k+1,l}
-. f *. zero_m_array.(m).(k) ) ) -. f *. zero_m_array.(m).{k+1,l} ) )
| 0 -> Array.map2 ( *. ) zero_m_array.(m) coef_prod | 0 -> Array.init nq (fun k -> zero_m_array.(m).{k+1,l} *. coef_prod.{k+1,l})
| 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) key with try Zmap.find map_1d.(m).(l-1) key with
| Not_found -> | Not_found ->
let result = let result =
let am, amm, amxyz, xyz = let am, amm, amxyz, xyz =
@ -62,43 +70,43 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
if amxyz < 0 then empty else if amxyz < 0 then empty else
let v1 = let v1 =
let f = let f =
-. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz) -. expo_b.{l} *. expo_inv_p.{l} *. (Coordinate.coord center_ab xyz)
in in
if (abs_float f < cutoff) then empty else if (abs_float f < cutoff) then empty else
Array.map (fun v1k -> f *. v1k) (vrr0_v m am (totAngMom_a-1) ) Array.map (fun v1k -> f *. v1k) (vrr0_v l m am (totAngMom_a-1) )
in in
let p1 = let p1 =
Array.mapi (fun k v2k -> v1.(k) +. expo_inv_p *. (Coordinate.coord center_pq.(k) xyz) *. v2k) (vrr0_v (m+1) am (totAngMom_a-1)) 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))
in in
if amxyz < 1 then p1 else if amxyz < 1 then p1 else
let f = (float_of_int amxyz) *. expo_inv_p *. 0.5 let f = (float_of_int amxyz) *. expo_inv_p.{l} *. 0.5
in in
if (abs_float f < cutoff) then empty else if (abs_float f < cutoff) then empty else
let v1 = vrr0_v m amm (totAngMom_a-2) let v1 = vrr0_v l m amm (totAngMom_a-2)
in in
let v2 = let v2 =
if (abs_float (f *. expo_inv_p)) < cutoff then empty else if (abs_float (f *. expo_inv_p.{l})) < cutoff then empty else
vrr0_v (m+1) amm (totAngMom_a-2) vrr0_v l (m+1) amm (totAngMom_a-2)
in in
Array.init ncoef (fun k -> p1.(k) +. Array.init nq (fun k -> p1.(k) +.
f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) f *. (v1.(k) +. v2.(k) *. expo_inv_p.{l} ) )
in Zmap.add map_1d.(m) key result; in Zmap.add map_1d.(m).(l-1) key result;
result result
and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c = and vrr_v l 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) -> if (i>0) then
vrr0_v m angMom_a totAngMom_a vrr0_v l m angMom_a totAngMom_a
else else
Array.map2 ( *. ) zero_m_array.(m) coef_prod Array.init nq (fun k -> zero_m_array.(m).{k+1,l} *. coef_prod.{k+1,l})
| (_,_) -> | (_,_) ->
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) key with try Zmap.find map_2d.(m).(l-1) key with
| Not_found -> | Not_found ->
let result = let result =
begin begin
@ -126,24 +134,26 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
*) *)
let f1 = let f1 =
let f = (Coordinate.coord center_cd xyz) in let f = (Coordinate.coord center_cd xyz) in
Array.init ncoef (fun k -> Array.init nq (fun k ->
expo_d.(k) *. expo_inv_q.(k) *. f) expo_d.{k+1} *. expo_inv_q.{k+1} *. f)
|> Vec.of_array
in in
let f2 = let f2 =
Array.init ncoef (fun k -> Array.init nq (fun k ->
expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz) ) 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 (at_least_one_valid f1) then
vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1) vrr_v l m angMom_a cm totAngMom_a (totAngMom_c-1)
else empty else empty
and v2 = and v2 =
if (at_least_one_valid f2) then if (at_least_one_valid f2) then
vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1) vrr_v l (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
else empty else empty
in in
let p1 = let p1 =
Array.init ncoef (fun k -> -. v1.(k) *. f1.(k) -. v2.(k) *. f2.(k)) Array.init nq (fun k -> -. v1.(k) *. f1.{k+1} -. v2.(k) *. f2.{k+1})
in in
let p2 = let p2 =
if cxyz < 2 then p1 else if cxyz < 2 then p1 else
@ -151,54 +161,56 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
(float_of_int (cxyz-1)) *. 0.5 (float_of_int (cxyz-1)) *. 0.5
in in
let f1 = let f1 =
Array.map (fun e -> fcm *. e) expo_inv_q Vec.map (fun e -> fcm *. e) expo_inv_q
in in
let f2 = let f2 =
Array.map2 ( *. ) f1 expo_inv_q Vec.mul f1 expo_inv_q
in in
let v1 = let v1 =
if (at_least_one_valid f1) then if (at_least_one_valid f1) then
vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2) vrr_v l m angMom_a cmm totAngMom_a (totAngMom_c-2)
else empty else empty
in in
let v2 = let v2 =
if (at_least_one_valid f2) then if (at_least_one_valid f2) then
vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) vrr_v l (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2)
else empty else empty
in in
Array.init ncoef (fun k -> p1.(k) +. f1.(k) *. v1.(k) +. f2.(k) *. v2.(k)) Array.init nq (fun k -> p1.(k) +. f1.{k+1} *. v1.(k) +. f2.{k+1} *. v2.(k))
in in
if (axyz < 1) || (cxyz < 1) then p2 else if (axyz < 1) || (cxyz < 1) then p2 else
let fa = let fa =
(float_of_int axyz) *. expo_inv_p *. 0.5 (float_of_int axyz) *. expo_inv_p.{l} *. 0.5
in in
let f1 = let f1 =
Array.map (fun e -> fa *. e ) expo_inv_q Vec.map (fun e -> fa *. e ) expo_inv_q
in in
if (at_least_one_valid f1) then if (at_least_one_valid f1) then
let v = let v =
vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) vrr_v l (m+1) am cm (totAngMom_a-1) (totAngMom_c-1)
in in
Array.init ncoef (fun k -> p2.(k) -. f1.(k) *. v.(k)) Array.init nq (fun k -> p2.(k) -. f1.{k+1} *. v.(k))
else p2 else p2
end end
in Zmap.add map_2d.(m) key result; in Zmap.add map_2d.(m).(l-1) key result;
result result
(** Horizontal recurrence relations *) (** Horizontal recurrence relations *)
and hrr0_v angMom_a angMom_b angMom_c and hrr0_v l 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) -> Array.map2 ( *. ) zero_m_array.(0) coef_prod | (0,0) ->
| (_,0) -> vrr0_v 0 angMom_a totAngMom_a Array.init nq (fun k -> zero_m_array.(0).{k+1,l} *. coef_prod.{k+1,l})
| (_,_) -> vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c |> sum
| (_,0) -> vrr0_v l 0 angMom_a totAngMom_a |> sum
| (_,_) -> vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c |> sum
end end
| 1 -> | 1 ->
let (aax, aay, aaz) = angMom_a in let (aax, aay, aaz) = angMom_a in
@ -210,13 +222,13 @@ 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 0 ap angMom_c (totAngMom_a+1) totAngMom_c vrr_v l 0 ap angMom_c (totAngMom_a+1) totAngMom_c
in in
if (abs_float f < cutoff) then v1 else if (abs_float f < cutoff) then sum v1 else
let v2 = let v2 =
vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c
in in
Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2 Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2 |> sum
| _ -> | _ ->
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
@ -226,7 +238,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
| (0,_,_) -> aby, 1 | (0,_,_) -> aby, 1
| _ -> abx, 0 | _ -> abx, 0
in in
if (bxyz < 1) then empty else if (bxyz < 1) then 0. else
let ap, bm = let ap, bm =
match xyz with match xyz with
| 0 -> (aax+1,aay,aaz),(abx-1,aby,abz) | 0 -> (aax+1,aay,aaz),(abx-1,aby,abz)
@ -235,22 +247,24 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
in in
let h1 = let h1 =
hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c hrr0_v l 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 angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c hrr0_v l angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c
in Array.map2 (fun h1 h2 -> h1 +. h2 *. f) h1 h2 in
h1 +. h2 *. f
and hrr_v angMom_a angMom_b angMom_c angMom_d and hrr_v l 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 0 angMom_a angMom_c totAngMom_a totAngMom_c vrr_v l 0 angMom_a angMom_c totAngMom_a totAngMom_c
|> sum
else else
hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c hrr0_v l 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
@ -261,19 +275,21 @@ 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 angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1) hrr_v l angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
and h2 = and h2 =
hrr_v angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1) hrr_v l 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
Array.init ncoef (fun k -> h1.(k) +. h2.(k) *. f) h1 +. f *. h2
in in
hrr_v Array.init np (fun ab ->
(angMom_a.(0),angMom_a.(1),angMom_a.(2)) hrr_v (ab+1)
(angMom_b.(0),angMom_b.(1),angMom_b.(2)) (angMom_a.(0),angMom_a.(1),angMom_a.(2))
(angMom_c.(0),angMom_c.(1),angMom_c.(2)) (angMom_b.(0),angMom_b.(1),angMom_b.(2))
(angMom_d.(0),angMom_d.(1),angMom_d.(2)) (angMom_c.(0),angMom_c.(1),angMom_c.(2))
totAngMom_a totAngMom_b totAngMom_c totAngMom_d (angMom_d.(0),angMom_d.(1),angMom_d.(2))
totAngMom_a totAngMom_b totAngMom_c totAngMom_d
) |> sum
@ -283,10 +299,12 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t = let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
let shell_a = shell_p.(0).ShellPair.shell_a let shell_a = shell_p.ContractedShellPair.shell_a
and shell_b = shell_p.(0).ShellPair.shell_b and shell_b = shell_p.ContractedShellPair.shell_b
and shell_c = shell_q.(0).ShellPair.shell_a and shell_c = shell_q.ContractedShellPair.shell_a
and shell_d = shell_q.(0).ShellPair.shell_b and shell_d = shell_q.ContractedShellPair.shell_b
and sp = shell_p.ContractedShellPair.shell_pairs
and sq = shell_q.ContractedShellPair.shell_pairs
in in
let maxm = let maxm =
let open Angular_momentum in let open Angular_momentum in
@ -308,134 +326,149 @@ 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 *)
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
begin begin
match Contracted_shell.(totAngMom shell_a, totAngMom shell_b, match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
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) <-
Array.fold_left let zm_array = Mat.init_rows np nq (fun i j ->
(fun accu shell_ab -> accu +. (** Screening on the product of coefficients *)
Array.fold_left (fun accu shell_cd -> try
let coef_prod = if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then
shell_ab.ShellPair.coef *. shell_cd.ShellPair.coef raise NullQuartet;
in
(** Screening on the product of coefficients *)
try
if (abs_float coef_prod) < 1.e-3*.cutoff then
raise NullQuartet;
let expo_pq_inv = let expo_pq_inv =
shell_ab.ShellPair.expo_inv +. shell_cd.ShellPair.expo_inv expo_inv_p.{i} +. expo_inv_q.{j}
in in
let center_pq = let center_pq =
Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center) Coordinate.(sp.(i-1).ShellPair.center |- sq.(j-1).ShellPair.center)
in in
let norm_pq_sq = let norm_pq_sq =
Coordinate.dot center_pq center_pq Coordinate.dot center_pq center_pq
in in
let zero_m_array =
zero_m ~maxm:0 ~expo_pq_inv ~norm_pq_sq
in
accu +. coef_prod *. zero_m_array.(0)
with NullQuartet -> accu
) 0. shell_q
) 0. shell_p
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
| _ -> | _ ->
Array.iter (fun shell_ab -> let expo_b =
let norm_coef_scale_p = shell_ab.ShellPair.norm_coef_scale in Array.map (fun shell_ab -> Contracted_shell.expo shell_b shell_ab.ShellPair.j) sp
let b = shell_ab.ShellPair.j in |> Vec.of_array
let common = and expo_d =
Array.map (fun shell_cd -> Array.map (fun shell_cd -> Contracted_shell.expo shell_d shell_cd.ShellPair.j) sq
let coef_prod = |> Vec.of_array
shell_ab.ShellPair.coef *. shell_cd.ShellPair.coef in
in let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
let expo_pq_inv =
shell_ab.ShellPair.expo_inv +. shell_cd.ShellPair.expo_inv
in let center_pq =
let center_pq = let result =
Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center) Array3.create Float64 fortran_layout 3 nq np
in in
let norm_pq_sq = Array.iteri (fun ab shell_ab ->
Coordinate.dot center_pq center_pq Array.iteri (fun cd shell_cd ->
in let cpq =
Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
in
result.{1,cd+1,ab+1} <- Coordinate.x cpq;
result.{2,cd+1,ab+1} <- Coordinate.y cpq;
result.{3,cd+1,ab+1} <- Coordinate.z cpq;
) sq
) sp;
result
in
let zero_m_array =
let result =
Array.init (maxm+1) (fun _ -> Mat.make0 nq np)
in
Array.iteri (fun ab shell_ab ->
let zero_m_array_tmp =
Array.mapi (fun cd shell_cd ->
let expo_pq_inv =
expo_inv_p.{ab+1} +. expo_inv_q.{cd+1}
in
let norm_pq_sq =
center_pq.{1,cd+1,ab+1} *. center_pq.{1,cd+1,ab+1} +.
center_pq.{2,cd+1,ab+1} *. center_pq.{2,cd+1,ab+1} +.
center_pq.{3,cd+1,ab+1} *. center_pq.{3,cd+1,ab+1}
in
let zero_m_array =
zero_m ~maxm ~expo_pq_inv ~norm_pq_sq zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
in ) sq
(*
let d = shell_cd.ShellPair.j in |> Array.to_list
|> List.filter (fun (zero_m_array, d,
(zero_m_array, shell_cd.ShellPair.expo_inv, center_pq,coef_prod) -> abs_float coef_prod >= 1.e-4 *. cutoff)
Contracted_shell.expo shell_d d, |> Array.of_list
center_pq,coef_prod) *)
) shell_q
|> Array.to_list
|> List.filter (fun (zero_m_array, expo_inv, d,
center_pq,coef_prod) -> abs_float coef_prod >= 1.e-4 *. cutoff)
|> Array.of_list
in
let zero_m_array = Array.map (fun (zero_m_array, expo_inv, d,
center_pq,coef_prod) -> zero_m_array) common
and expo_inv = Array.map (fun (zero_m_array, expo_inv, d,
center_pq,coef_prod) -> expo_inv ) common
and d = Array.map (fun (zero_m_array, expo_inv, d,
center_pq,coef_prod) -> d) common
and center_pq = Array.map (fun (zero_m_array, expo_inv, d,
center_pq,coef_prod) -> center_pq) common
and coef_prod = Array.map (fun (zero_m_array, expo_inv, d,
center_pq,coef_prod) -> coef_prod) common
in
(* Transpose zero_m_array
*)
let zero_m_array =
let result = Array.init (maxm+1) (fun _ ->
Array.make (Array.length coef_prod) 0.)
in in
for m=0 to maxm do (* Transpose result *)
for k=0 to (Array.length coef_prod-1) do for m=0 to maxm do
result.(m).(k) <- zero_m_array.(k).(m) for cd=1 to nq do
done; result.(m).{cd,ab+1} <- zero_m_array_tmp.(cd-1).(m)
done; done
result done
in ) sp;
result
in
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
let map_1d = Array.init maxm (fun _ -> Array.init np (fun _ -> Zmap.create (4*maxm)))
and map_2d = Array.init maxm (fun _ -> Array.init np (fun _ -> Zmap.create (Array.length class_indices)))
in
(* Compute the integral class from the primitive shell quartet *) (* Compute the integral class from the primitive shell quartet *)
let map_1d = Array.init maxm (fun _ -> Zmap.create (4*maxm)) in Array.iteri (fun i key ->
let map_2d = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in let a = Zkey.to_int_array Zkey.Kind_12 key in
let norm = let (angMomA,angMomB,angMomC,angMomD) =
let norm_coef_scale_q = shell_q.(0).ShellPair.norm_coef_scale in ( [| a.(0) ; a.(1) ; a.(2) |],
Array.map (fun v1 -> [| a.(3) ; a.(4) ; a.(5) |],
Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q [| a.(6) ; a.(7) ; a.(8) |],
) norm_coef_scale_p [| a.(9) ; a.(10) ; a.(11) |] )
|> Array.to_list in
|> Array.concat let integral =
in hvrr_two_e_vector (angMomA, angMomB, angMomC, angMomD)
Array.iteri (fun i key -> (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
let a = Zkey.to_int_array Zkey.Kind_12 key in Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
let (angMomA,angMomB,angMomC,angMomD) = (maxm, zero_m_array)
( [| a.(0) ; a.(1) ; a.(2) |], (expo_b, expo_d)
[| a.(3) ; a.(4) ; a.(5) |], (expo_inv_p, expo_inv_q)
[| a.(6) ; a.(7) ; a.(8) |], (shell_p.ContractedShellPair.center_ab,
[| a.(9) ; a.(10) ; a.(11) |] ) shell_q.ContractedShellPair.center_ab, center_pq)
in coef map_1d map_2d
let integral = in
hvrr_two_e_vector (angMomA, angMomB, angMomC, angMomD) contracted_class.(i) <- contracted_class.(i) +. integral *. norm.(i)
(Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b, ) class_indices
Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
(maxm, zero_m_array)
(Contracted_shell.expo shell_b b, d)
(shell_ab.ShellPair.expo_inv, expo_inv)
(shell_p.(0).ShellPair.center_ab,
shell_q.(0).ShellPair.center_ab, center_pq)
coef_prod map_1d map_2d
in
let x = Array.fold_left (+.) 0. integral in
contracted_class.(i) <- contracted_class.(i) +. x *. norm.(i)
) class_indices
) shell_p
end; end;