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synced 2024-11-07 06:33:39 +01:00
1160 lines
38 KiB
OCaml
1160 lines
38 KiB
OCaml
open Lacaml.D
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open Util
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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 mo_class t = DeterminantSpace.mo_class t.det_space
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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' <> 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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), None )
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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 h_ij_non_zero mo_basis deg_a deg_b 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.non_zero integrals deg_a deg_b 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 deg_a deg_b ki kj =
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let x = f deg_a deg_b 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) 2 0 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 [@tailcall]) 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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1 (Determinant.degree_beta ki kj) ki kj;
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(aux [@tailcall]) r_singles (j'+1);)
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| 1 -> if (j' < Array.length j_dets) then (aux [@tailcall]) 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 [@tailcall]) 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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0 (Determinant.degree_beta ki kj) ki kj;
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(aux [@tailcall]) r_doubles (j'+1);)
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| 1 -> if (j' < Array.length j_dets) then (aux [@tailcall]) 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 ?(nmax=2) 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, list of triples) in the beta spin *)
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let degree_bb =
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match nmax with
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| 2 -> begin
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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 triples = [] 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, triples)
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) b
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end
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| 3 -> begin
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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 triples =
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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 < 4 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 doubles =
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List.filter (fun (i,d,det_j) -> d < 3) triples
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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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in
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let triples =
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List.map (fun (i,_,det_j) -> (i,det_j)) triples
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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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let singles =
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List.map (fun (i,_,det_j) -> (i,det_j)) singles
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in
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(singles, doubles, triples)
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) b
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end
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| _ -> assert false
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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 =
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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 deg_a deg_b ki kj =
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let x = f deg_a deg_b 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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fun (i,i_alfa) ->
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begin match nmax with
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| 2 -> begin
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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) 2 0 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, _doubles, _triples = 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) 1 (Determinant.degree_beta ki kj) 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, _triples = 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) 0 (Determinant.degree_beta ki kj) 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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end
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| 3 -> begin
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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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| 3 ->
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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) 3 0 ki kj;
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incr i';
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) b;
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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 singles, _doubles, _triples = 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) 2 (Determinant.degree_beta ki kj) ki kj
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) singles;
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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, doubles, _triples = 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) 1 (Determinant.degree_beta ki kj) ki kj
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) doubles;
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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, triples = 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) 0 (Determinant.degree_beta ki kj) ki kj
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) triples;
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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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end
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| _ -> assert false
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end;
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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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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+Array.length r) ndet;
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) ;
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Matrix.sparse_of_vector_array result
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)
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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_computed ?(nmax=2) 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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let h2 i_alfa j_alfa =
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let deg_a = Spindeterminant.degree a.(i_alfa) a.(j_alfa) in
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match deg_a with
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| 2 ->
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let ai, aj = a.(i_alfa), a.(j_alfa) in
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(fun i_beta j_beta ->
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if i_beta <> j_beta then 0. else
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let deg_b = 0 in
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let ki = Determinant.of_spindeterminants ai b.(i_beta) in
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let kj = Determinant.of_spindeterminants aj b.(j_beta) in
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f deg_a deg_b ki kj
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)
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| 1 ->
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let ai, aj = a.(i_alfa), a.(j_alfa) in
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(fun i_beta j_beta ->
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let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
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match deg_b with
|
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| 0 | 1 ->
|
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let ki = Determinant.of_spindeterminants ai b.(i_beta) in
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let kj = Determinant.of_spindeterminants aj b.(j_beta) in
|
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f deg_a deg_b ki kj
|
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| _ -> 0.
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)
|
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| 0 ->
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let ai, aj = a.(i_alfa), a.(j_alfa) in
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(fun i_beta j_beta ->
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let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
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match deg_b with
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| 0 | 1 | 2 ->
|
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let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
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let ki = Determinant.of_spindeterminants ai b.(i_beta) in
|
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let kj = Determinant.of_spindeterminants aj b.(j_beta) in
|
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f deg_a deg_b ki kj
|
|
| _ -> 0.
|
|
)
|
|
| _ -> (fun _ _ -> 0.)
|
|
in
|
|
|
|
let h3 i_alfa j_alfa =
|
|
let deg_a = Spindeterminant.degree a.(i_alfa) a.(j_alfa) in
|
|
match deg_a with
|
|
| 3 ->
|
|
let ai, aj = a.(i_alfa), a.(j_alfa) in
|
|
(fun i_beta j_beta ->
|
|
if i_beta <> j_beta then 0. else
|
|
let deg_b = 0 in
|
|
let ki = Determinant.of_spindeterminants ai b.(i_beta) in
|
|
let kj = Determinant.of_spindeterminants aj b.(j_beta) in
|
|
f deg_a deg_b ki kj
|
|
)
|
|
| 2 ->
|
|
let ai, aj = a.(i_alfa), a.(j_alfa) in
|
|
(fun i_beta j_beta ->
|
|
let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
|
match deg_b with
|
|
| 0 | 1 ->
|
|
let ki = Determinant.of_spindeterminants ai b.(i_beta) in
|
|
let kj = Determinant.of_spindeterminants aj b.(j_beta) in
|
|
f deg_a deg_b ki kj
|
|
| _ -> 0.
|
|
)
|
|
| 1 ->
|
|
let ai, aj = a.(i_alfa), a.(j_alfa) in
|
|
(fun i_beta j_beta ->
|
|
let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
|
match deg_b with
|
|
| 0 | 1 | 2 ->
|
|
let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
|
let ki = Determinant.of_spindeterminants ai b.(i_beta) in
|
|
let kj = Determinant.of_spindeterminants aj b.(j_beta) in
|
|
f deg_a deg_b ki kj
|
|
| _ -> 0.
|
|
)
|
|
| 0 ->
|
|
let ai, aj = a.(i_alfa), a.(j_alfa) in
|
|
(fun i_beta j_beta ->
|
|
let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
|
match deg_b with
|
|
| 0 | 1 | 2 | 3 ->
|
|
let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in
|
|
let ki = Determinant.of_spindeterminants ai b.(i_beta) in
|
|
let kj = Determinant.of_spindeterminants aj b.(j_beta) in
|
|
f deg_a deg_b ki kj
|
|
| _ -> 0.
|
|
)
|
|
| _ -> (fun _ _ -> 0.)
|
|
in
|
|
|
|
let i_prev = ref (-10)
|
|
and result = ref (fun _ -> 0.)
|
|
in
|
|
let h123 = ref (fun _ -> 0.) in
|
|
|
|
let h = if nmax = 2 then h2 else h3 in
|
|
|
|
let g i =
|
|
(*
|
|
i : index of the i-th determinant. 1 <= i <= ndet
|
|
i_prev : index of the i-th determinant in the previous function call.
|
|
1 <= i_prev <= ndet
|
|
i_a : index of the i_a-th alpha determinant. 0 <= i_a < n_alfa
|
|
i_b : index of the i_b-th beta determinant. 0 <= i_b < n_beta
|
|
j0 : index - 1 of the first determinant with the same alfa component
|
|
0 <= j0 < n_beta*(n_alfa-1)
|
|
j1 : index - 1 of the next determinant with the 1st beta determinant
|
|
n_beta <= j1 <= ndet
|
|
j_a : index of the j_a-th alpha determinant. 0 <= j_a < n_alfa
|
|
j_b : index of the j_b-th beta determinant. 0 <= j_b < n_beta
|
|
*)
|
|
if i <> !i_prev then
|
|
begin
|
|
i_prev := i;
|
|
let i_a = (i-1)/n_beta in
|
|
let h1 = h i_a in
|
|
let i_b = i - i_a*n_beta - 1 in
|
|
let j0 = ref (2*ndet) in
|
|
let j1 = ref (2*ndet) in
|
|
let j_a = ref 0 in
|
|
result := fun j ->
|
|
if (!j0 < j) && (j <= !j1) then
|
|
()
|
|
else
|
|
begin
|
|
if (!j1 < j) && (j <= !j1 + n_beta) then
|
|
begin
|
|
incr j_a;
|
|
j0 := !j1;
|
|
end
|
|
else
|
|
begin
|
|
j_a := (j-1)/n_beta;
|
|
j0 := !j_a * n_beta;
|
|
end;
|
|
j1 := !j0 + n_beta;
|
|
h123 := h1 !j_a i_b;
|
|
end;
|
|
let j_b = j - !j0 - 1 in
|
|
!h123 j_b
|
|
end;
|
|
!result
|
|
in
|
|
|
|
Matrix.of_fun ndet ndet g
|
|
)
|
|
|
|
|
|
|
|
let make ?(n_states=1) ?(algo=`Direct) det_space =
|
|
|
|
let mo_basis = Ds.mo_basis det_space in
|
|
|
|
let e_shift =
|
|
let d0 =
|
|
Ds.determinant_stream det_space
|
|
|> Stream.next
|
|
in
|
|
h_ij_non_zero mo_basis 0 0 d0 d0
|
|
in
|
|
|
|
let m_H =
|
|
|
|
(* While in a sequential region, initiate the parallel
|
|
4-idx transformation to avoid nested parallel jobs
|
|
*)
|
|
ignore @@ MOBasis.two_e_ints mo_basis;
|
|
|
|
let f =
|
|
match Ds.determinants det_space with
|
|
| Ds.Arbitrary _ -> create_matrix_arbitrary
|
|
| Ds.Spin _ ->
|
|
if algo = `Direct then
|
|
create_matrix_spin_computed ~nmax:2
|
|
else
|
|
create_matrix_spin ~nmax:2
|
|
in
|
|
f (fun deg_a deg_b ki kj ->
|
|
if deg_a + deg_b > 0 then
|
|
h_ij_non_zero mo_basis deg_a deg_b ki kj
|
|
else
|
|
h_ij_non_zero mo_basis 0 0 ki ki -. e_shift
|
|
) det_space
|
|
in
|
|
|
|
let m_S2 =
|
|
let f =
|
|
match Ds.determinants det_space with
|
|
| Ds.Arbitrary _ -> create_matrix_arbitrary
|
|
| Ds.Spin _ -> create_matrix_spin ~nmax:2
|
|
in
|
|
f (fun _deg_a _deg_b ki kj -> CIMatrixElement.make_s2 ki kj) det_space
|
|
(*TODO*)
|
|
in
|
|
|
|
let eigensystem = lazy (
|
|
|
|
let eigensystem_incore () =
|
|
let m_H =
|
|
Lazy.force m_H
|
|
in
|
|
let diagonal =
|
|
Parallel.broadcast (lazy (
|
|
Vec.init (Matrix.dim1 m_H) (fun i -> Matrix.get m_H i i)
|
|
))
|
|
in
|
|
let matrix_prod psi =
|
|
let result =
|
|
Matrix.mm ~transa:`T m_H psi
|
|
in
|
|
Parallel.broadcast (lazy result)
|
|
in
|
|
let eigenvectors, eigenvalues =
|
|
let result =
|
|
Davidson.make ~threshold:1.e-6 ~n_states diagonal matrix_prod
|
|
in
|
|
Parallel.broadcast (lazy result)
|
|
in
|
|
let eigenvalues = Vec.map (fun x -> x +. e_shift) eigenvalues in
|
|
(Conventions.rephase @@ Util.remove_epsilons eigenvectors), eigenvalues
|
|
in
|
|
|
|
let eigensystem_direct () =
|
|
let m_H =
|
|
Lazy.force m_H
|
|
in
|
|
let diagonal =
|
|
Parallel.broadcast (lazy (
|
|
Vec.init (Matrix.dim1 m_H) (fun i -> Matrix.get m_H i i)
|
|
))
|
|
in
|
|
let matrix_prod psi =
|
|
let result =
|
|
Matrix.parallel_mm ~transa:`T ~transb:`N psi m_H
|
|
|> Matrix.transpose
|
|
in
|
|
Parallel.broadcast (lazy result)
|
|
in
|
|
let eigenvectors, eigenvalues =
|
|
let result =
|
|
Davidson.make ~threshold:1.e-6 ~n_states diagonal matrix_prod
|
|
in
|
|
Parallel.broadcast (lazy result)
|
|
in
|
|
let eigenvalues = Vec.map (fun x -> x +. e_shift) eigenvalues in
|
|
(Conventions.rephase @@ Util.remove_epsilons eigenvectors), eigenvalues
|
|
in
|
|
|
|
match algo with
|
|
| `Direct -> eigensystem_direct ()
|
|
| `InCore -> eigensystem_incore ()
|
|
)
|
|
in
|
|
{ det_space ; e_shift ; m_H ; m_S2 ; eigensystem ; n_states }
|
|
|
|
|
|
|
|
|
|
let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
|
|
list_holes list_particles ?(unique=true) is_internal
|
|
i_o1_alfa alfa_o2_i w_alfa psi0 =
|
|
|
|
let list_holes = Array.of_list list_holes in
|
|
let list_particles = Array.of_list list_particles in
|
|
|
|
let psi0 =
|
|
let stream =
|
|
Ds.determinant_stream det_space
|
|
in
|
|
Array.init (Ds.size det_space) (fun i ->
|
|
(Stream.next stream), (Mat.copy_row psi0 (i+1)) )
|
|
in
|
|
|
|
|
|
|
|
let symmetric = i_o1_alfa == alfa_o2_i in
|
|
|
|
|
|
let det_contribution i =
|
|
|
|
let already_generated =
|
|
if unique then
|
|
(fun alfa ->
|
|
if is_internal alfa then
|
|
true
|
|
else
|
|
let rec aux = function
|
|
| -1 -> false
|
|
| j -> Determinant.degree (fst psi0.(j)) alfa <= 2
|
|
|| aux (j-1)
|
|
in
|
|
aux (i-1)
|
|
)
|
|
else
|
|
is_internal
|
|
in
|
|
|
|
let psi_filtered_idx =
|
|
let rec aux accu = function
|
|
| j when j < i -> List.rev accu
|
|
| j ->
|
|
if Determinant.degree (fst psi0.(i)) (fst psi0.(j)) < 4
|
|
then
|
|
aux (j::accu) (j-1)
|
|
else
|
|
aux accu (j-1)
|
|
in aux [] (Array.length psi0 - 1)
|
|
in
|
|
|
|
let psi_filtered =
|
|
List.map (fun i -> psi0.(i)) psi_filtered_idx
|
|
in
|
|
|
|
let psi_h_alfa alfa =
|
|
List.fold_left (fun accu (det, coef) ->
|
|
(* Single state here *)
|
|
accu +. coef.{1} *. (i_o1_alfa det alfa)) 0. psi_filtered
|
|
in
|
|
|
|
let alfa_h_psi alfa =
|
|
List.fold_left (fun accu (det, coef) ->
|
|
(* Single state here *)
|
|
accu +. coef.{1} *. (alfa_o2_i alfa det)) 0. psi_filtered
|
|
in
|
|
|
|
let psi_h_alfa_alfa_h_psi alfa =
|
|
if symmetric then
|
|
let x = psi_h_alfa alfa in x *. x
|
|
else
|
|
(psi_h_alfa alfa) *. (alfa_h_psi alfa)
|
|
in
|
|
|
|
let det_i = fst psi0.(i) in
|
|
let w_alfa = w_alfa det_i in
|
|
|
|
let same_spin =
|
|
List.fold_left (fun accu spin ->
|
|
accu +.
|
|
Array.fold_left (fun accu particle ->
|
|
accu +.
|
|
Array.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 =
|
|
Array.fold_left (fun accu particle' ->
|
|
if particle' >= particle || particle' = hole then
|
|
accu
|
|
else
|
|
accu +.
|
|
Array.fold_left (fun accu hole' ->
|
|
if hole' = particle' || hole' = particle || hole' <= hole then
|
|
accu
|
|
else
|
|
let alfa =
|
|
Determinant.single_excitation
|
|
spin hole' particle' alfa
|
|
in
|
|
if Determinant.is_none alfa ||
|
|
already_generated alfa then
|
|
accu
|
|
else
|
|
accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
|
|
) 0. list_holes
|
|
) 0. list_particles
|
|
in
|
|
accu +. single +. double
|
|
) 0. list_holes
|
|
) 0. list_particles
|
|
) 0. [ Spin.Alfa ; Spin.Beta ]
|
|
in
|
|
|
|
let opposite_spin =
|
|
Array.fold_left (fun accu particle ->
|
|
accu +.
|
|
Array.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_ab =
|
|
Array.fold_left (fun accu particle' ->
|
|
accu +.
|
|
Array.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. list_holes
|
|
) 0. list_particles
|
|
in
|
|
|
|
accu +. double_ab
|
|
) 0. list_holes
|
|
) 0. list_particles
|
|
in
|
|
same_spin +. opposite_spin
|
|
in
|
|
|
|
Util.stream_range 0 (Array.length psi0 - 1)
|
|
|> Farm.run ~ordered:true ~f:det_contribution
|
|
|> Util.stream_to_list
|
|
|
|
|
|
|
|
let second_order_sum2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
|
|
list_holes list_particles i_o1_alfa e0 psi0 =
|
|
|
|
let psi0 =
|
|
let stream =
|
|
Ds.determinant_stream det_space
|
|
in
|
|
Array.init (Ds.size det_space) (fun i ->
|
|
(Stream.next stream), (Mat.copy_row psi0 (i+1)) )
|
|
in
|
|
|
|
let determinants =
|
|
|
|
Ds.determinants_array det_space
|
|
|> Array.to_list
|
|
|> List.map (fun det_i ->
|
|
[ Spin.Alfa ; Spin.Beta ]
|
|
|> List.map (fun spin ->
|
|
List.map (fun particle ->
|
|
List.map (fun hole ->
|
|
[ [ Determinant.single_excitation spin hole particle det_i ] ;
|
|
List.map (fun particle' ->
|
|
List.map (fun hole' ->
|
|
Determinant.double_excitation
|
|
spin hole particle
|
|
spin hole' particle' det_i
|
|
) list_holes
|
|
) list_particles
|
|
|> List.concat
|
|
;
|
|
List.map (fun particle' ->
|
|
List.map (fun hole' ->
|
|
Determinant.double_excitation
|
|
spin hole particle
|
|
(Spin.other spin) hole' particle' det_i
|
|
) list_holes
|
|
) list_particles
|
|
|> List.concat
|
|
]
|
|
|> List.concat
|
|
) list_holes
|
|
) list_particles
|
|
|> List.concat
|
|
)
|
|
|> List.concat
|
|
)
|
|
|> List.concat
|
|
|> List.concat
|
|
|> List.filter (fun alfa -> not (Determinant.is_none alfa))
|
|
|> List.sort_uniq compare
|
|
in
|
|
|
|
List.fold_left (fun accu alfa ->
|
|
let alfa_o2 = i_o1_alfa alfa in
|
|
let a_h_psi =
|
|
Array.fold_left (fun accu (det,ci) -> ci.{1} *. (alfa_o2 det)) 0. psi0
|
|
in
|
|
accu +. (a_h_psi *. a_h_psi) /. (e0 -. (alfa_o2 alfa))
|
|
) 0. determinants
|
|
|
|
|
|
|
|
|
|
let is_internal det_space =
|
|
let mo_class = DeterminantSpace.mo_class det_space in
|
|
let numbits = Array.length @@ MOClass.mo_class_array mo_class in
|
|
let m l =
|
|
List.fold_left (fun accu i ->
|
|
let j = i-1 in
|
|
Bitstring.logor accu (Bitstring.shift_left_one numbits j)
|
|
) (Bitstring.zero numbits) l
|
|
in
|
|
let active_mask = m (MOClass.active_mos mo_class) in
|
|
let occ_mask = m (MOClass.core_mos mo_class) in
|
|
let inactive_mask = m (MOClass.inactive_mos mo_class) in
|
|
let occ_mask = Bitstring.logor occ_mask inactive_mask in
|
|
let neg_active_mask = Bitstring.lognot active_mask in
|
|
fun a ->
|
|
let alfa =
|
|
Determinant.alfa a
|
|
|> Spindeterminant.bitstring
|
|
in
|
|
if Bitstring.logand neg_active_mask alfa <> occ_mask then
|
|
false
|
|
else
|
|
let beta =
|
|
Determinant.beta a
|
|
|> Spindeterminant.bitstring
|
|
in
|
|
Bitstring.logand neg_active_mask beta = occ_mask
|
|
|
|
|
|
let _pt2_en ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
let psi0, e0 = Parallel.broadcast ci.eigensystem in
|
|
|
|
let i_o1_alfa = h_ij mo_basis in
|
|
|
|
let w_alfa det_i =
|
|
let one_e, two_e, _ = h_integrals mo_basis in
|
|
let fock_diag_alfa, fock_diag_beta =
|
|
Ds.fock_diag ci.det_space det_i
|
|
in
|
|
let h_aa alfa =
|
|
match Excitation.of_det det_i alfa with
|
|
| Excitation.Double (_,
|
|
{hole = h ; particle = p ; spin = s },
|
|
{hole = h'; particle = p'; spin = s'}) ->
|
|
let fock_diag1 =
|
|
if s = Spin.Alfa then
|
|
fock_diag_alfa
|
|
else
|
|
fock_diag_beta
|
|
in
|
|
let fock_diag2 =
|
|
if s' = Spin.Alfa then
|
|
fock_diag_alfa
|
|
else
|
|
fock_diag_beta
|
|
in
|
|
fock_diag1.(0) -. fock_diag1.(h)
|
|
+. (fock_diag1.(p ) -. two_e h p h p s s)
|
|
-. (fock_diag2.(h') -. two_e h h' h h' s s' +. two_e p h' p h' s s')
|
|
+. (fock_diag2.(p') -. two_e h p' h p' s s'
|
|
+. two_e p p' p p' s s' -. two_e h' p' h' p' s' s')
|
|
| Excitation.Single (_,
|
|
{hole = h ; particle = p ; spin = s }) ->
|
|
let fock_diag =
|
|
if s = Spin.Alfa then
|
|
fock_diag_alfa
|
|
else
|
|
fock_diag_beta
|
|
in
|
|
fock_diag.(0) -. fock_diag.(h)
|
|
+. (fock_diag.(p) -. two_e h p h p s s)
|
|
|> ignore;
|
|
h_ij mo_basis alfa alfa
|
|
| _ -> e0.{1} -. 1.0
|
|
in
|
|
let e0 = e0.{1} in
|
|
fun alfa ->
|
|
1. /. (e0 -. h_aa alfa)
|
|
in
|
|
|
|
let mo_class = mo_class ci in
|
|
let list_holes = List.concat
|
|
[ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
|
|
and list_particles = List.concat
|
|
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
|
in
|
|
|
|
second_order_sum ci list_holes list_particles
|
|
(is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0
|
|
|> List.fold_left (+.) 0.
|
|
|
|
|
|
let pt2_en ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
let psi0, e0 = Parallel.broadcast ci.eigensystem in
|
|
|
|
let i_o1_alfa = h_ij mo_basis in
|
|
|
|
let mo_class = mo_class ci in
|
|
let list_holes = List.concat
|
|
[ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
|
|
and list_particles = List.concat
|
|
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
|
in
|
|
second_order_sum2 ci list_holes list_particles i_o1_alfa e0.{1} psi0
|
|
|
|
|
|
|
|
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
|
|
|
|
let mo_class = mo_class ci in
|
|
let list_holes = List.concat
|
|
[ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
|
|
and list_particles = List.concat
|
|
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
|
in
|
|
|
|
let psi0, _ = Parallel.broadcast ci.eigensystem in
|
|
second_order_sum ci list_holes list_particles
|
|
(is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0
|
|
|> List.fold_left (+.) 0.
|
|
|
|
|
|
let variance ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
let psi0, _ = Parallel.broadcast ci.eigensystem in
|
|
|
|
let i_o1_alfa = h_ij mo_basis in
|
|
|
|
let w_alfa _ _ = 1. in
|
|
|
|
let mo_class = mo_class ci in
|
|
let list_holes = List.concat
|
|
[ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
|
|
and list_particles = List.concat
|
|
[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ]
|
|
in
|
|
|
|
second_order_sum ci list_holes list_particles
|
|
(is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0
|
|
|> List.fold_left (+.) 0.
|
|
|
|
|
|
|
|
|
|
let pt2_en_reference ci =
|
|
|
|
let mo_basis = Ds.mo_basis ci.det_space in
|
|
let psi0, e0 = Parallel.broadcast ci.eigensystem in
|
|
|
|
let aux_basis = mo_basis in
|
|
let ds =
|
|
DeterminantSpace.fci_of_mo_basis ~frozen_core:false aux_basis
|
|
in
|
|
let out_dets =
|
|
ds
|
|
|> DeterminantSpace.determinants_array
|
|
|> Array.to_list
|
|
|> List.filter (fun i -> not (is_internal ci.det_space i))
|
|
|> Array.of_list
|
|
in
|
|
|
|
let in_dets =
|
|
DeterminantSpace.determinants_array ci.det_space
|
|
in
|
|
|
|
let m_H_aux =
|
|
let h_aa =
|
|
Array.map (fun ki -> h_ij aux_basis ki ki) out_dets
|
|
in
|
|
Array.map (fun ki ->
|
|
Array.mapi (fun j kj ->
|
|
(h_ij aux_basis ki kj) /. (e0.{1} -. h_aa.(j))
|
|
) out_dets
|
|
) in_dets
|
|
|> Mat.of_array
|
|
in
|
|
|
|
let m_F_aux =
|
|
Array.map (fun ki ->
|
|
Array.map (fun kj ->
|
|
h_ij aux_basis ki kj
|
|
) out_dets
|
|
) in_dets
|
|
|> Mat.of_array
|
|
in
|
|
|
|
let m_HF =
|
|
gemm m_H_aux m_F_aux ~transb:`T
|
|
in
|
|
(gemm ~transa:`T psi0 @@ gemm m_HF psi0).{1,1}
|
|
|
|
|
|
|
|
|