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Working on AO shells
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44
Basis/Contracted_shell.ml
Normal file
44
Basis/Contracted_shell.ml
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@ -0,0 +1,44 @@
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open Util
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type t = {
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expo : float array;
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coef : float array;
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center : Coordinate.t;
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totAngMom : Angular_momentum.t;
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size : int;
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norm_coef : (int array -> float) array;
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}
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(** Normalization coefficient of contracted function i, which depends on the
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exponent and the angular momentum. Two conventions can be chosen : a single
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normalisation factor for all functions of the class, or a coefficient which
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depends on the powers of x,y and z.
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*)
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let compute_norm_coef s =
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let atot =
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Angular_momentum.to_int s.totAngMom
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in
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Array.mapi (fun i alpha ->
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let c =
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((alpha +. alpha) *. pi_inv)**(1.5) *. (pow (4. *. alpha) atot)
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in
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let result a =
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let dfa = Array.map (fun j ->
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fact (j+j) /. ( float_of_int (1 lsl j) *. fact j)
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) a
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in sqrt (c /. (dfa.(0) *.dfa.(1) *. dfa.(2)))
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in
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result
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) s.expo
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let create ~expo ~coef ~center ~totAngMom =
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assert (Array.length expo = Array.length coef);
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assert (Array.length expo > 0);
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let tmp =
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{ expo ; coef ; center ; totAngMom ; size=Array.length expo ; norm_coef = [||]}
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in
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{ tmp with norm_coef = compute_norm_coef tmp }
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103
Basis/Shell_pair.ml
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103
Basis/Shell_pair.ml
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@ -0,0 +1,103 @@
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open Util
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type t = {
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expo : float;
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expo_inv : float;
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center_ab: float array;
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center : float array;
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norm_sq : float;
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norm : float;
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coef : float;
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norm_fun : int array -> int array -> float;
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i : int;
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j : int;
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}
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exception Null_contribution
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let create_array ?(cutoff=0.) p_a p_b =
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let log_cutoff =
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if (cutoff = 0.) then infinity
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else -. (log cutoff)
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in
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let x_a = Coordinate.x p_a.Contracted_shell.center
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and y_a = Coordinate.y p_a.Contracted_shell.center
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and z_a = Coordinate.z p_a.Contracted_shell.center
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and x_b = Coordinate.x p_b.Contracted_shell.center
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and y_b = Coordinate.y p_b.Contracted_shell.center
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and z_b = Coordinate.z p_b.Contracted_shell.center
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in
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(*
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match p_a.Contracted_shell.center, p_b.Contracted_shell.center with
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| [|x_a; y_a; z_a|], [|x_b; y_b; z_b|] ->
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*)
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let center_ab =
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Coordinate.(p_a.Contracted_shell.center |- p_b.Contracted_shell.center)
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in
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let norm_sq =
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Coordinate.dot center_ab center_ab
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in
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Array.init p_a.Contracted_shell.size (fun i ->
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let p_a_expo_center =
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[| p_a.Contracted_shell.expo.(i) *. x_a ; p_a.Contracted_shell.expo.(i) *. y_a ; p_a.Contracted_shell.expo.(i) *. z_a |]
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in
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Array.init p_b.Contracted_shell.size (fun j ->
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try
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let f1 =
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p_a.Contracted_shell.norm_coef.(i)
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in
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let f2 =
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p_b.Contracted_shell.norm_coef.(j)
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in
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let norm_fun a b =
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f1 a *. f2 b
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in
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let norm =
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norm_fun
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[| Angular_momentum.to_int p_a.Contracted_shell.totAngMom ; 0 ; 0 |]
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[| Angular_momentum.to_int p_b.Contracted_shell.totAngMom ; 0 ; 0 |]
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in
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if (norm < cutoff) then
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raise Null_contribution;
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let p_b_expo_center =
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[| p_b.Contracted_shell.expo.(j) *. x_b ; p_b.Contracted_shell.expo.(j) *. y_b ; p_b.Contracted_shell.expo.(j) *. z_b |]
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in
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let expo = p_a.Contracted_shell.expo.(i) +. p_b.Contracted_shell.expo.(j) in
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let expo_inv = 1. /. expo in
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let center =
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[| (p_a_expo_center.(0) +. p_b_expo_center.(0)) *. expo_inv;
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(p_a_expo_center.(1) +. p_b_expo_center.(1)) *. expo_inv;
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(p_a_expo_center.(2) +. p_b_expo_center.(2)) *. expo_inv |]
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in
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let argexpo =
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p_a.Contracted_shell.expo.(i) *. p_b.Contracted_shell.expo.(j)
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*. norm_sq *. expo_inv
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in
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if (argexpo > log_cutoff) then
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raise Null_contribution;
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let g =
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(pi *. expo_inv)**(1.5) *. exp(-. argexpo)
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in
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let norm_inv = 1./.norm in
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let norm_fun a b =
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norm_inv *. norm_fun a b
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in
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let coef =
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norm *. p_a.Contracted_shell.coef.(i) *. p_b.Contracted_shell.coef.(j) *. g
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in
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if (abs_float coef < cutoff) then
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raise Null_contribution;
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Some { i ; j ; norm_fun ; norm ; coef ; expo ; expo_inv ; center ; center_ab=(Coordinate.to_float_array center_ab) ; norm_sq }
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with
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| Null_contribution -> None
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)
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)
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|> Array.to_list
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|> Array.concat
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|> Array.to_list
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|> List.filter (function Some _ -> true | None -> false)
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|> List.map (function Some x -> x | None -> assert false)
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|> Array.of_list
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@ -52,3 +52,68 @@ let of_int = function
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type kind =
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| Kind_2 of (t*t)
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| Kind_4 of (t*t*t*t)
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(** Returns an array of Zkeys corresponding to all possible angular momenta *)
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let zkey_array a =
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let keys_1d l =
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let create_z (x,y,_) =
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(x,y,l-(x+y))
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in
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let rec create_y accu xyz =
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let (x,y,z) = xyz in
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match y with
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| 0 -> (create_z xyz)::accu
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| i -> let ynew = y-1 in
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create_y ( (create_z xyz)::accu) (x,ynew,z)
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in
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let rec create_x accu xyz =
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let (x,y,z) = xyz in
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match x with
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| 0 -> (create_y [] xyz)@accu
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| i -> let xnew = x-1 in
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let ynew = l-xnew in
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create_x ((create_y [] xyz)@accu) (xnew, ynew, z)
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in
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create_x [] (l,0,0)
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|> List.rev
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in
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begin
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match a with
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| Kind_2 (l1, l2) ->
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let a = Array.init 6 (fun _ -> 0) in
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List.map (fun (cx,cy,cz) ->
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a.(0) <- cx ; a.(1) <- cy ; a.(2) <- cz ;
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List.map (fun (dx,dy,dz) ->
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a.(3) <- dx ; a.(4) <- dy ; a.(5) <- dz ;
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Zkey.(of_int_array Kind_6 a)
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) (keys_1d @@ to_int l1)
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) (keys_1d @@ to_int l2)
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| Kind_4 (l1, l2, l3, l4) ->
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let a = Array.init 12 (fun _ -> 0) in
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List.map (fun (ax,ay,az) ->
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a.(0) <- ax ; a.(1) <- ay ; a.(2) <- az ;
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List.map (fun (bx,by,bz) ->
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a.(3) <- bx ; a.(4) <- by ; a.(5) <- bz ;
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List.map (fun (cx,cy,cz) ->
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a.(6) <- cx ; a.(7) <- cy ; a.(8) <- cz ;
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List.map (fun (dx,dy,dz) ->
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a.(9) <- dx ; a.(10) <- dy ; a.(11) <- dz ;
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Zkey.(of_int_array Kind_12 a)
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) (keys_1d @@ to_int l4)
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) (keys_1d @@ to_int l3)
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|> List.concat
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) (keys_1d @@ to_int l2)
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|> List.concat
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) (keys_1d @@ to_int l1)
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end
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|> List.concat
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|> Array.of_list
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55
Utils/Coordinate.ml
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55
Utils/Coordinate.ml
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@ -0,0 +1,55 @@
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type t = float array
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let zero =
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[| 0. ; 0. ; 0. |]
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let of_float_triplet (x,y,z) =
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[|x;y;z|]
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let of_3_floats x y z =
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[|x;y;z|]
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let to_string x =
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(string_of_float x.(0))^" "^(string_of_float x.(1))^" "^(string_of_float x.(2))
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let x a = a.(0)
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let y a = a.(1)
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let z a = a.(2)
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let coord a = function
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| 0 -> a.(0)
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| 1 -> a.(1)
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| 2 -> a.(2)
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| _ -> raise (Invalid_argument "Coordinate")
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let to_float_array a = a
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(** Linear algebra *)
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let (|-) a b =
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match a,b with
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| [|x;y;z|], [|x';y';z'|] -> [| x-.x'; y-.y'; z-.z' |]
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| _ -> assert false
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let (|+) a b =
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match a,b with
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| [|x;y;z|], [|x';y';z'|] -> [| x+.x'; y+.y'; z+.z' |]
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| _ -> assert false
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let (|.) s a =
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match a with
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| [|x;y;z|] -> [| s*.x; s*.y; s*.z |]
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| _ -> assert false
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let dot a b =
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match a,b with
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| [|x;y;z|], [|x';y';z'|] -> x*.x' +. y*.y' +. z*.z'
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| _ -> assert false
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let norm u =
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sqrt @@ dot u u
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16
Utils/Coordinate.mli
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16
Utils/Coordinate.mli
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@ -0,0 +1,16 @@
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type t
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val zero : t
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val of_float_triplet : float * float * float -> t
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val of_3_floats : float -> float -> float -> t
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val to_string : t -> string
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val x : t -> float
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val y : t -> float
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val z : t -> float
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val coord : t -> int -> float
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val to_float_array : t -> float array
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val (|-) : t -> t -> t
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val (|+) : t -> t -> t
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val (|.) : float -> t -> t
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val dot : t -> t -> float
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val norm : t -> float
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96
Utils/Zkey.ml
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96
Utils/Zkey.ml
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@ -0,0 +1,96 @@
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(** Key for hastables that contain tuples of integers encoded in a Zarith integer *)
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include Z
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type kind =
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| Kind_2
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| Kind_3
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| Kind_4
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| Kind_6
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| Kind_12
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(** Build a Zkey from an array or 2, 3, 4, 6, or 12 integers *)
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let of_int_array ~kind a =
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let (<|) x a =
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Z.logor (Z.shift_left x 64) a
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in
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let (<<) x a =
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Int64.logor (Int64.shift_left x 10) (Int64.of_int a)
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in
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let (<+) x a =
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Int64.logor (Int64.shift_left x 16) (Int64.of_int a)
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in
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match kind with
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| Kind_2 -> (Int64.of_int a.(0)) <+ a.(1) |> Z.of_int64
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| Kind_3 -> (Int64.of_int a.(0)) << a.(1) << a.(2) |> Z.of_int64
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| Kind_4 -> (Int64.of_int a.(0)) <+ a.(1) <+ a.(2) <+ a.(3) |> Z.of_int64
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| Kind_6 -> (Int64.of_int a.(0)) << a.(1) << a.(2) << a.(3) << a.(4) << a.(5)
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|> Z.of_int64
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| Kind_12 ->
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let a =
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(Int64.of_int a.(0)) << a.(1) << a.(2) << a.(3) << a.(4) << a.(5)
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|> Z.of_int64
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and b =
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(Int64.of_int a.(6)) << a.(7) << a.(8) << a.(9) << a.(10) << a.(11)
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|> Z.of_int64
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in a <| b
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(** Transform the Zkey into an int array *)
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let to_int_array ~kind a =
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match kind with
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| Kind_2 -> [| Z.to_int @@ Z.extract a 16 16 ;
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Z.to_int @@ Z.extract a 0 16 |]
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| Kind_3 -> [| Z.to_int @@ Z.extract a 20 10 ;
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Z.to_int @@ Z.extract a 10 10 ;
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Z.to_int @@ Z.extract a 0 10 |]
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| Kind_4 -> [| Z.to_int @@ Z.extract a 48 16 ;
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Z.to_int @@ Z.extract a 32 16 ;
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Z.to_int @@ Z.extract a 16 16 ;
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Z.to_int @@ Z.extract a 0 16 |]
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| Kind_6 -> [| Z.to_int @@ Z.extract a 50 10 ;
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Z.to_int @@ Z.extract a 40 10 ;
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Z.to_int @@ Z.extract a 30 10 ;
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Z.to_int @@ Z.extract a 20 10 ;
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Z.to_int @@ Z.extract a 10 10 ;
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Z.to_int @@ Z.extract a 0 10 |]
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| Kind_12 -> [| Z.to_int @@ Z.extract a 114 10 ;
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Z.to_int @@ Z.extract a 104 10 ;
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Z.to_int @@ Z.extract a 94 10 ;
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Z.to_int @@ Z.extract a 84 10 ;
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Z.to_int @@ Z.extract a 74 10 ;
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Z.to_int @@ Z.extract a 64 10 ;
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Z.to_int @@ Z.extract a 50 10 ;
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Z.to_int @@ Z.extract a 40 10 ;
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Z.to_int @@ Z.extract a 30 10 ;
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Z.to_int @@ Z.extract a 20 10 ;
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Z.to_int @@ Z.extract a 10 10 ;
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Z.to_int @@ Z.extract a 0 10 |]
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let to_string ~kind a =
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"< " ^ ( Z.to_string a ) ^ " | " ^ (
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to_int_array kind a
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|> Array.map string_of_int
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|> Array.to_list
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|> String.concat ", "
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) ^ " >"
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(*
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let debug () =
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let k2 = of_int_array Kind_2 [| 1 ; 2 |]
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and k3 = of_int_array Kind_3 [| 1 ; 2 ; 3 |]
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and k4 = of_int_array Kind_4 [| 1 ; 2 ; 3; 4 |]
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and k6 = of_int_array Kind_6 [| 1 ; 2 ; 3; 4 ; 5; 6|]
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and k12 = of_int_array Kind_12 [| 1 ; 2 ; 3; 4 ; 5; 6 ; 7 ; 8 ; 9 ; 10 ; 11; 12|]
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in
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print_endline @@ to_string Kind_2 k2 ;
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print_endline @@ to_string Kind_3 k3 ;
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print_endline @@ to_string Kind_4 k4 ;
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print_endline @@ to_string Kind_6 k6 ;
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print_endline @@ to_string Kind_12 k12
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let () = debug ()
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*)
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4
Utils/Zmap.ml
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4
Utils/Zmap.ml
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@ -0,0 +1,4 @@
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(** Hash table where the keys are of type Zkey.t (tuples of integers) *)
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module Zmap = Hashtbl.Make(Zkey)
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include Zmap
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