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242 lines
8.1 KiB
OCaml
242 lines
8.1 KiB
OCaml
open Common
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open Linear_algebra
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open Gaussian
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open Constants
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type t = (Basis.t, Basis.t) Matrix.t array
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(*
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[| "x"; "y"; "z"; "x2"; "y2"; "z2" |]
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*)
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module Am = Angular_momentum
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module Bs = Basis
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module Co = Coordinate
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module Cs = Contracted_shell
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module Csp = Contracted_shell_pair
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module Po = Powers
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module Psp = Primitive_shell_pair
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let matrix t = function
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| "x" -> t.(0)
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| "y" -> t.(1)
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| "z" -> t.(2)
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| "x2" -> t.(3)
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| "y2" -> t.(4)
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| "z2" -> t.(5)
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| "xy" -> t.(6)
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| "xz" -> t.(8)
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| "yz" -> t.(7)
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| "x3" -> t.(9)
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| "y3" -> t.(10)
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| "z3" -> t.(11)
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| "x4" -> t.(12)
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| "y4" -> t.(13)
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| "z4" -> t.(14)
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| _ -> Util.not_implemented ()
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let cutoff = integrals_cutoff
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let to_powers x =
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let open Zkey in
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match to_powers x with
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| Six x -> x
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| _ -> assert false
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(** Computes all the integrals of the contracted shell pair *)
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let contracted_class shell_a shell_b : float Zmap.t array =
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match Csp.make shell_a shell_b with
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| None -> Array.init 15 (fun _ -> Zmap.create 0)
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| Some shell_p ->
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begin
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(* Pre-computation of integral class indices *)
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let class_indices = Csp.zkey_array shell_p in
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let contracted_class =
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Array.init 15 (fun _ -> Array.make (Array.length class_indices) 0.)
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in
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let a_minus_b =
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Csp.a_minus_b shell_p
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in
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let norm_coef_scales =
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Csp.norm_scales shell_p
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in
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(* Compute all integrals in the shell for each pair of significant shell pairs *)
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let xyz_of_int k =
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match k with
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| 0 -> Co.X
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| 1 -> Co.Y
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| _ -> Co.Z
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in
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List.iter (fun (coef_prod, psp) ->
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(* Screening on the product of coefficients *)
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if (abs_float coef_prod) > 1.e-6*.cutoff then
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begin
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let expo_inv = Psp.exponent_inv psp
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and center_pa = Psp.center_minus_a psp
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and xa = Co.(get X) @@ Cs.center shell_a
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and ya = Co.(get Y) @@ Cs.center shell_a
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and za = Co.(get Z) @@ Cs.center shell_a
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in
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Array.iteri (fun i key ->
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let (angMomA, angMomB) = to_powers key in
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(* 1D Overlap <i|j> *)
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let f k =
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let xyz = xyz_of_int k in
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Overlap_primitives.hvrr (Po.get xyz angMomA, Po.get xyz angMomB)
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expo_inv
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(Co.get xyz a_minus_b, Co.get xyz center_pa)
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in
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(* 1D <i|x-Xa|j> *)
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let g k =
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let xyz = xyz_of_int k in
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Overlap_primitives.hvrr (Po.get xyz angMomA + 1, Po.get xyz angMomB)
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expo_inv
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(Co.get xyz a_minus_b, Co.get xyz center_pa)
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in
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(* 1D <i|(x-Xa)^2|j> *)
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let h k =
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let xyz = xyz_of_int k in
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Overlap_primitives.hvrr (Po.get xyz angMomA + 2, Po.get xyz angMomB)
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expo_inv
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(Co.get xyz a_minus_b, Co.get xyz center_pa)
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in
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(* 1D <i|(x-Xa)^3|j> *)
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let j k =
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let xyz = xyz_of_int k in
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Overlap_primitives.hvrr (Po.get xyz angMomA + 3, Po.get xyz angMomB)
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expo_inv
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(Co.get xyz a_minus_b, Co.get xyz center_pa)
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in
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(* 1D <i|(x-Xa)^4|j> *)
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let l k =
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let xyz = xyz_of_int k in
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Overlap_primitives.hvrr (Po.get xyz angMomA + 4, Po.get xyz angMomB)
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expo_inv
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(Co.get xyz a_minus_b, Co.get xyz center_pa)
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in
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let norm = norm_coef_scales.(i) in
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let f0, f1, f2, g0, g1, g2, h0, h1, h2, j0, j1, j2 , l0, l1, l2 =
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f 0, f 1, f 2, g 0, g 1, g 2, h 0, h 1, h 2, j 0, j 1, j 2, l 0, l 1, l 2
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in
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let x = g0 +. f0 *. xa in
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let y = g1 +. f1 *. ya in
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let z = g2 +. f2 *. za in
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let x2 = h0 +. xa *. (2. *. x -. xa *. f0) in
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let y2 = h1 +. ya *. (2. *. y -. ya *. f1) in
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let z2 = h2 +. za *. (2. *. z -. za *. f2) in
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let x3 = j0 +. xa *. f0 *. (3. *. x2 -. 3. *. x *. xa +. xa *. xa) in
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let y3 = j1 +. ya *. f1 *. (3. *. y2 -. 3. *. y *. ya +. ya *. ya) in
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let z3 = j2 +. za *. f2 *. (3. *. z2 -. 3. *. z *. za +. za *. za) in
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let x4 = l0 +. xa *. f0 *. ( 4. *. x3 -. 6. *. x2 *. xa +. 4. *. x *. xa *. xa -. xa *. xa *. xa) in
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let y4 = l1 +. ya *. f1 *. ( 4. *. y3 -. 6. *. y2 *. ya +. 4. *. y *. ya *. ya -. ya *. ya *. ya) in
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let z4 = l2 +. za *. f2 *. ( 4. *. z3 -. 6. *. z2 *. za +. 4. *. z *. za *. za -. za *. za *. za) in
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let c = contracted_class in
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let d = coef_prod *. norm in
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c.(0).(i) <- c.(0).(i) +. d *. x *. f1 *. f2;
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c.(1).(i) <- c.(1).(i) +. d *. f0 *. y *. f2;
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c.(2).(i) <- c.(2).(i) +. d *. f0 *. f1 *. z;
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c.(3).(i) <- c.(3).(i) +. d *. x2 *. f1 *. f2;
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c.(4).(i) <- c.(4).(i) +. d *. f0 *. y2 *. f2;
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c.(5).(i) <- c.(5).(i) +. d *. f0 *. f1 *. z2;
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c.(6).(i) <- c.(6).(i) +. d *. x *. y *. f2;
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c.(7).(i) <- c.(7).(i) +. d *. f0 *. y *. z;
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c.(8).(i) <- c.(8).(i) +. d *. x *. f1 *. z;
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c.(9).(i) <- c.(9).(i) +. d *. x3 *. f1 *. f2;
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c.(10).(i) <- c.(10).(i) +. d *. f0 *. y3 *. f2;
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c.(11).(i) <- c.(11).(i) +. d *. f0 *. f1 *. z3;
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c.(12).(i) <- c.(12).(i) +. d *. x4 *. f1 *. f2;
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c.(13).(i) <- c.(13).(i) +. d *. f0 *. y4 *. f2;
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c.(14).(i) <- c.(14).(i) +. d *. f0 *. f1 *. z4;
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) class_indices
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end
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) (Csp.coefs_and_shell_pairs shell_p);
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let result =
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Array.map (fun c -> Zmap.create (Array.length c) ) contracted_class
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in
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for j=0 to Array.length result -1 do
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let rj = result.(j) in
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let cj = contracted_class.(j) in
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Array.iteri (fun i key -> Zmap.add rj key cj.(i)) class_indices
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done;
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result
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end
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(** Create multipole matrices *)
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let of_basis basis =
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let to_powers x =
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let open Zkey in
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match to_powers x with
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| Three x -> x
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| _ -> assert false
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in
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let n = Bs.size basis
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and shell = Bs.contracted_shells basis
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in
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let result = Array.init 15 (fun _ -> Matrix.create n n |> Matrix.to_bigarray_inplace) in
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for j=0 to (Array.length shell) - 1 do
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for i=0 to j do
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(* Compute all the integrals of the class *)
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let cls =
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contracted_class shell.(i) shell.(j)
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in
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for k=0 to 14 do
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Array.iteri (fun j_c powers_j ->
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let j_c = Cs.index shell.(j) + j_c + 1 in
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let xj = to_powers powers_j in
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Array.iteri (fun i_c powers_i ->
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let i_c = Cs.index shell.(i) + i_c + 1 in
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let xi = to_powers powers_i in
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let key =
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Zkey.of_powers_six xi xj
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in
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let value =
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try Zmap.find cls.(k) key
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with Not_found -> 0.
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in
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result.(k).{i_c,j_c} <- value;
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result.(k).{j_c,i_c} <- value;
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) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i))))
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) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j))))
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done;
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done;
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done;
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let result =
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Array.map Matrix.of_bigarray_inplace result
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in
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Array.iter Matrix.detri_inplace result;
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result
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let to_file ~filename eni_array =
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let n = Matrix.dim1 eni_array in
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let eni_array = Matrix.to_bigarray_inplace eni_array in
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let oc = open_out filename in
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for j=1 to n do
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for i=1 to j do
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let value = eni_array.{i,j} in
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if (value <> 0.) then
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Printf.fprintf oc " %5d %5d %20.15f\n" i j value;
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done;
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done;
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close_out oc
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