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synced 2024-06-01 19:05:18 +02:00
661 lines
19 KiB
OCaml
661 lines
19 KiB
OCaml
open Lacaml.D
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module Ds = DeterminantSpace
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module Sd = Spindeterminant
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type t =
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{
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e_shift : float ; (* Diagonal energy shift for increasing numerical precision *)
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det_space : Ds.t ;
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m_H : Matrix.t lazy_t ;
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m_S2 : Matrix.t lazy_t ;
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eigensystem : (Mat.t * Vec.t) lazy_t;
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n_states : int;
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}
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let det_space t = t.det_space
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let n_states t = t.n_states
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let m_H t = Lazy.force t.m_H
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let m_S2 t = Lazy.force t.m_S2
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let eigensystem t = Lazy.force t.eigensystem
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let eigenvectors t =
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let (x,_) = eigensystem t in x
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let eigenvalues t =
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let (_,x) = eigensystem t in x
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let h_integrals mo_basis =
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let one_e_ints = MOBasis.one_e_ints mo_basis
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and two_e_ints = MOBasis.two_e_ints mo_basis
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in
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( (fun i j _ -> one_e_ints.{i,j}),
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(fun i j k l s s' ->
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if s' = Spin.other s then
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ERI.get_phys two_e_ints i j k l
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else
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(ERI.get_phys two_e_ints i j k l) -.
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(ERI.get_phys two_e_ints i j l k)
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) )
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let h_ij mo_basis ki kj =
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let integrals =
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List.map (fun f -> f mo_basis)
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[ h_integrals ]
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in
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CIMatrixElement.make integrals ki kj
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|> List.hd
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let create_matrix_arbitrary f det_space =
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lazy (
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let ndet = Ds.size det_space in
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let data =
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match Ds.determinants det_space with
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| Ds.Arbitrary a -> a
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| _ -> assert false
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in
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let det_alfa = data.Ds.det_alfa
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and det_beta = data.Ds.det_beta
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and det = data.Ds.det
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and index_start = data.Ds.index_start
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in
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(** Array of (list of singles, list of doubles) in the beta spin *)
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let degree_bb =
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Array.map (fun det_i ->
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let deg = Spindeterminant.degree det_i in
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let doubles =
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Array.mapi (fun i det_j ->
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let d = deg det_j in
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if d < 3 then
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Some (i,d,det_j)
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else
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None
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) det_beta
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|> Array.to_list
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|> Util.list_some
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in
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let singles =
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List.filter (fun (i,d,det_j) -> d < 2) doubles
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|> List.map (fun (i,_,det_j) -> (i,det_j))
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in
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let doubles =
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List.map (fun (i,_,det_j) -> (i,det_j)) doubles
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in
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(singles, doubles)
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) det_beta
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in
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let task (i,i_dets) =
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let shift = index_start.(i) in
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let result =
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Array.init (index_start.(i+1) - shift)
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(fun _ -> [])
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in
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(** Update function when ki and kj are connected *)
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let update i j ki kj =
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let x = f ki kj in
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if abs_float x > Constants.epsilon then
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result.(i - shift) <- (j, x) :: result.(i - shift) ;
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in
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let i_alfa = det_alfa.(i) in
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let deg_a = Spindeterminant.degree i_alfa in
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Array.iteri (fun j j_dets ->
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let j_alfa = det_alfa.(j) in
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let degree_a = deg_a j_alfa in
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begin
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match degree_a with
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| 2 ->
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Array.iteri (fun i' i_b ->
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try
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Array.iteri (fun j' j_b ->
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if j_b >= i_b then
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( if j_b = i_b then
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( let i_beta = det_beta.(i_b) in
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let ki = Determinant.of_spindeterminants i_alfa i_beta in
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let kj = Determinant.of_spindeterminants j_alfa i_beta in
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update (index_start.(i) + i')
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(index_start.(j) + j' + 1) ki kj);
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raise Exit)
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) j_dets
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with Exit -> ()
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) i_dets
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| 1 ->
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Array.iteri (fun i' i_b ->
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let i_beta = det_beta.(i_b) in
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let ki = Determinant.of_spindeterminants i_alfa i_beta in
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let singles, _ = degree_bb.(i_b) in
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let rec aux singles j' =
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match singles with
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| [] -> ()
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| (js, j_beta)::r_singles ->
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begin
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match compare js j_dets.(j') with
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| -1 -> aux r_singles j'
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| 0 ->
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let kj =
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Determinant.of_spindeterminants j_alfa j_beta
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in (update
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(index_start.(i) + i') (index_start.(j) + j' + 1)
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ki kj;
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aux r_singles (j'+1);)
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| 1 -> if (j' < Array.length j_dets) then aux singles (j'+1)
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| _ -> assert false
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end
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in aux singles 0
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) i_dets
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| 0 ->
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Array.iteri (fun i' i_b ->
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let i_beta = det_beta.(i_b) in
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let ki = Determinant.of_spindeterminants i_alfa i_beta in
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let _, doubles = degree_bb.(i_b) in
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let rec aux doubles j' =
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match doubles with
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| [] -> ()
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| (js, j_beta)::r_doubles ->
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begin
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match compare js j_dets.(j') with
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| -1 -> aux r_doubles j'
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| 0 ->
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let kj =
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Determinant.of_spindeterminants j_alfa j_beta
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in (update
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(index_start.(i) + i') (index_start.(j) + j' + 1)
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ki kj;
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aux r_doubles (j'+1);)
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| 1 -> if (j' < Array.length j_dets) then aux doubles (j'+1)
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| _ -> assert false
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end
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in aux doubles 0
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) i_dets
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| _ -> ();
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end
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) det;
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let r =
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Array.map (fun l ->
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List.rev l
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|> Vector.sparse_of_assoc_list ndet
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) result
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in (i,r)
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in
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let result =
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if Parallel.master then
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Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet [])
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else
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Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet [])
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in
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let n_det_alfa =
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Array.length det_alfa
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in
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Array.mapi (fun i i_dets -> i, i_dets) det
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|> Array.to_list
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|> Stream.of_list
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|> Farm.run ~ordered:false ~f:task
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|> Stream.iter (fun (k, r) ->
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let shift = index_start.(k) in
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let det_k = det.(k) in
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Array.iteri (fun j r_j -> result.(shift+det_k.(j)) <- r_j) r;
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Printf.eprintf "%8d / %8d\r%!" (k+1) n_det_alfa;
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) ;
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Matrix.sparse_of_vector_array result
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)
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(* Create a matrix using the fact that the determinant space is made of
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the outer product of spindeterminants. *)
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let create_matrix_spin f det_space =
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lazy (
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let ndet = Ds.size det_space in
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let a, b =
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match Ds.determinants det_space with
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| Ds.Spin (a,b) -> (a,b)
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| _ -> assert false
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in
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let n_beta = Array.length b in
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(** Array of (list of singles, list of doubles) in the beta spin *)
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let degree_bb =
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Array.map (fun det_i ->
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let deg = Spindeterminant.degree det_i in
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let doubles =
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Array.mapi (fun i det_j ->
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let d = deg det_j in
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if d < 3 then
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Some (i,d,det_j)
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else
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None
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) b
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|> Array.to_list
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|> Util.list_some
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in
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let singles =
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List.filter (fun (i,d,det_j) -> d < 2) doubles
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|> List.map (fun (i,_,det_j) -> (i,det_j))
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in
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let doubles =
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List.map (fun (i,_,det_j) -> (i,det_j)) doubles
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in
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(singles, doubles)
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) b
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in
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let a = Array.to_list a
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and b = Array.to_list b
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in
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let task (i,i_alfa) =
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let result =
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Array.init n_beta (fun _ -> [])
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in
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(** Update function when ki and kj are connected *)
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let update i j ki kj =
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let x = f ki kj in
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if abs_float x > Constants.epsilon then
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result.(i) <- (j, x) :: result.(i) ;
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in
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let j = ref 1 in
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let deg_a = Spindeterminant.degree i_alfa in
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List.iter (fun j_alfa ->
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let degree_a = deg_a j_alfa in
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begin
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match degree_a with
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| 2 ->
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let i' = ref 0 in
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List.iteri (fun ib i_beta ->
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let ki = Determinant.of_spindeterminants i_alfa i_beta in
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let kj = Determinant.of_spindeterminants j_alfa i_beta in
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update !i' (ib + !j) ki kj;
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incr i';
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) b;
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| 1 ->
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let i' = ref 0 in
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List.iteri (fun ib i_beta ->
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let ki = Determinant.of_spindeterminants i_alfa i_beta in
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let singles, _ = degree_bb.(ib) in
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List.iter (fun (j', j_beta) ->
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let kj = Determinant.of_spindeterminants j_alfa j_beta in
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update !i' (j' + !j) ki kj
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) singles;
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incr i';
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) b;
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| 0 ->
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let i' = ref 0 in
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List.iteri (fun ib i_beta ->
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let ki = Determinant.of_spindeterminants i_alfa i_beta in
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let _singles, doubles = degree_bb.(ib) in
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List.iter (fun (j', j_beta) ->
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let kj = Determinant.of_spindeterminants j_alfa j_beta in
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update !i' (j' + !j) ki kj
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) doubles;
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incr i';
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) b;
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| _ -> ();
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end;
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j := !j + n_beta
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) a;
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let r =
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Array.map (fun l ->
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List.rev l
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|> Vector.sparse_of_assoc_list ndet
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) result
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in (i,r)
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in
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let result =
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if Parallel.master then
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Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet [])
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else
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Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet [])
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in
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List.mapi (fun i i_alfa -> i*n_beta, i_alfa) a
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|> Stream.of_list
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|> Farm.run ~ordered:false ~f:task
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|> Stream.iter (fun (k, r) ->
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Array.iteri (fun j r_j -> result.(k+j) <- r_j) r;
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Printf.eprintf "%8d / %8d\r%!" (k+1) ndet;
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) ;
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Matrix.sparse_of_vector_array result
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)
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let make ?(n_states=1) det_space =
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let mo_basis = Ds.mo_basis det_space in
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let e_shift =
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let d0 =
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Ds.determinant_stream det_space
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|> Stream.next
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in
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h_ij mo_basis d0 d0
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in
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let m_H =
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(* While in a sequential region, initiate the parallel
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4-idx transformation to avoid nested parallel jobs
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*)
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ignore @@ MOBasis.two_e_ints mo_basis;
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let f =
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match Ds.determinants det_space with
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| Ds.Arbitrary _ -> create_matrix_arbitrary
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| Ds.Spin _ -> create_matrix_spin
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in
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f (fun ki kj ->
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if ki <> kj then
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h_ij mo_basis ki kj
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else
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h_ij mo_basis ki kj -. e_shift
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) det_space
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in
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let m_S2 =
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let f =
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match Ds.determinants det_space with
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| Ds.Arbitrary _ -> create_matrix_arbitrary
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| Ds.Spin _ -> create_matrix_spin
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in
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f (fun ki kj -> CIMatrixElement.make_s2 ki kj) det_space
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in
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let eigensystem = lazy (
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let m_H =
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Lazy.force m_H
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in
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let diagonal =
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Vec.init (Matrix.dim1 m_H) (fun i -> Matrix.get m_H i i)
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in
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let matrix_prod psi =
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Matrix.mm ~transa:`T m_H psi
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in
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let eigenvectors, eigenvalues =
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Davidson.make ~threshold:1.e-12 ~n_states diagonal matrix_prod
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in
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let eigenvalues = Vec.map (fun x -> x +. e_shift) eigenvalues in
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eigenvectors, eigenvalues
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)
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in
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{ det_space ; e_shift ; m_H ; m_S2 ; eigensystem ; n_states }
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let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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i_o1_alfa alfa_o2_i w_alfa =
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let mo_basis = Ds.mo_basis det_space in
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let mo_class = DeterminantSpace.mo_class det_space in
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let mo_indices =
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let cls = MOClass.mo_class_array mo_class in
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Util.list_range 1 (MOBasis.size mo_basis)
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|> List.filter (fun i -> match cls.(i) with
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| MOClass.Deleted _
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| MOClass.Core _ -> false
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| _ -> true
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)
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in
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let psi0 =
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let psi0, _ = Lazy.force eigensystem in
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let stream =
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Ds.determinant_stream det_space
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in
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Array.init (Ds.size det_space) (fun i ->
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Stream.next stream, psi0.{i+1,1})
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in
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(*
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let is_internal =
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let m l =
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List.fold_left (fun accu i ->
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let j = i-1 in Z.(logor accu (shift_left one j))
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) Z.zero l
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in
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let active_mask = m (MOClass.active_mos mo_class) in
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let occ_mask = m (MOClass.core_mos mo_class) in
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let inactive_mask = m (MOClass.inactive_mos mo_class) in
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let occ_mask = Z.logor occ_mask inactive_mask in
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let neg_active_mask = Z.lognot active_mask in
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fun a ->
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let alfa =
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Determinant.alfa a
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|> Spindeterminant.bitstring
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in
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if Z.logand neg_active_mask alfa <> occ_mask then
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false
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else
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let beta =
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Determinant.beta a
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|> Spindeterminant.bitstring
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in
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Z.logand neg_active_mask beta = occ_mask
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in
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*)
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let symmetric = i_o1_alfa == alfa_o2_i in
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let is_internal alfa =
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let rec aux = function
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| -1 -> false
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| j -> Determinant.degree (fst psi0.(j)) alfa = 0
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|| aux (j-1)
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in
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aux (Array.length psi0 - 1)
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in
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let det_contribution i =
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let already_generated alfa =
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if is_internal alfa then
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true
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else
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let rec aux = function
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| -1 -> false
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| j -> Determinant.degree (fst psi0.(j)) alfa <= 2
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|| aux (j-1)
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in
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aux (i-1)
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in
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let psi_filtered_idx =
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let rec aux accu = function
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| j when j < i -> List.rev accu
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| j -> if Determinant.degree (fst psi0.(i)) (fst psi0.(j)) < 4 then
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aux (j::accu) (j-1)
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else
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aux accu (j-1)
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in aux [] (Array.length psi0 - 1)
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in
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let psi_filtered =
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List.map (fun i -> psi0.(i)) psi_filtered_idx
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in
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let psi_h_alfa alfa =
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List.fold_left (fun accu (det, coef) ->
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accu +. coef *. (i_o1_alfa det alfa)) 0. psi_filtered
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in
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let alfa_h_psi =
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if symmetric then
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psi_h_alfa
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else
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fun alfa ->
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List.fold_left (fun accu (det, coef) ->
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accu +. coef *. (alfa_o2_i alfa det)) 0. psi_filtered
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in
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let psi_h_alfa_alfa_h_psi alfa =
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if symmetric then
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let x = psi_h_alfa alfa in x *. x
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else
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(psi_h_alfa alfa) *. (alfa_h_psi alfa)
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in
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let det_i = fst psi0.(i) in
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let w_alfa = w_alfa det_i in
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let same_spin =
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List.fold_left (fun accu spin ->
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accu +.
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List.fold_left (fun accu particle ->
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|
accu +.
|
|
List.fold_left (fun accu hole ->
|
|
if hole = particle then accu else
|
|
let alfa =
|
|
Determinant.single_excitation spin hole particle det_i
|
|
in
|
|
if Determinant.is_none alfa then accu else
|
|
|
|
let single =
|
|
if already_generated alfa then 0. else
|
|
w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
|
|
in
|
|
|
|
let double =
|
|
List.fold_left (fun accu particle' ->
|
|
if particle' > particle || particle' = hole then
|
|
accu
|
|
else
|
|
accu +.
|
|
List.fold_left (fun accu hole' ->
|
|
if hole' = particle' || hole' = particle || hole' < hole then
|
|
accu
|
|
else
|
|
let alfa =
|
|
Determinant.double_excitation
|
|
spin hole particle
|
|
spin hole' particle' det_i
|
|
in
|
|
if Determinant.is_none alfa ||
|
|
already_generated alfa then
|
|
accu
|
|
else
|
|
accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
|
|
) 0. mo_indices
|
|
) 0. mo_indices
|
|
in
|
|
accu +. single +. double
|
|
) 0. mo_indices
|
|
) 0. mo_indices
|
|
) 0. [ Spin.Alfa ; Spin.Beta ]
|
|
in
|
|
|
|
let opposite_spin =
|
|
List.fold_left (fun accu particle ->
|
|
accu +.
|
|
List.fold_left (fun accu hole ->
|
|
if hole = particle then accu else
|
|
let alfa =
|
|
Determinant.single_excitation Spin.Alfa hole particle det_i
|
|
in
|
|
if Determinant.is_none alfa then accu else
|
|
|
|
let double =
|
|
List.fold_left (fun accu particle' ->
|
|
accu +.
|
|
List.fold_left (fun accu hole' ->
|
|
if hole' = particle' then accu else
|
|
let alfa =
|
|
Determinant.double_excitation
|
|
Spin.Alfa hole particle
|
|
Spin.Beta hole' particle' det_i
|
|
in
|
|
if Determinant.is_none alfa ||
|
|
already_generated alfa then
|
|
accu
|
|
else
|
|
accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
|
|
) 0. mo_indices
|
|
) 0. mo_indices
|
|
in
|
|
accu +. double
|
|
) 0. mo_indices
|
|
) 0. mo_indices
|
|
in
|
|
same_spin +. opposite_spin
|
|
in
|
|
|
|
Array.mapi (fun i (_,c_i) -> det_contribution i) psi0
|
|
|> Array.fold_left (+.) 0.
|
|
|
|
|
|
|
|
let pt2_en ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
let _psi0, e0 = Lazy.force ci.eigensystem in
|
|
|
|
let i_o1_alfa = h_ij mo_basis in
|
|
|
|
let w_alfa _ =
|
|
let e0 = e0.{1} in
|
|
let h_aa alfa = h_ij mo_basis alfa alfa in
|
|
fun alfa ->
|
|
1. /. (e0 -. h_aa alfa)
|
|
in
|
|
|
|
second_order_sum ci i_o1_alfa i_o1_alfa w_alfa
|
|
|
|
|
|
|
|
let pt2_mp ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
|
|
let i_o1_alfa = h_ij mo_basis in
|
|
|
|
let eps = MOBasis.mo_energies mo_basis in
|
|
let w_alfa det_i alfa=
|
|
match Excitation.of_det det_i alfa with
|
|
| Excitation.Single (_, { hole ; particle ; spin })->
|
|
1./.(eps.{hole} -. eps.{particle})
|
|
| Excitation.Double (_, { hole=h ; particle=p ; spin=s },
|
|
{ hole=h'; particle=p'; spin=s'})->
|
|
1./.(eps.{h} +. eps.{h'} -. eps.{p} -. eps.{p'})
|
|
| _ -> assert false
|
|
in
|
|
|
|
second_order_sum ci i_o1_alfa i_o1_alfa w_alfa
|
|
|
|
|
|
let variance ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
|
|
let i_o1_alfa = h_ij mo_basis in
|
|
|
|
let w_alfa _ _ = 1. in
|
|
|
|
second_order_sum ci i_o1_alfa i_o1_alfa w_alfa
|
|
|
|
|