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306 lines
7.2 KiB
OCaml
306 lines
7.2 KiB
OCaml
let debug s =
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Printf.printf "%s\n%!" s;
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open Lacaml.D
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type t =
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{
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gamma : float;
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mo_basis : MOBasis.t ;
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aux_basis : MOBasis.t ;
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det_space : DeterminantSpace.t ;
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ci : CI.t ;
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eigensystem : (Mat.t * Vec.t) lazy_t;
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}
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let ci t = t.ci
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let mo_basis t = t.mo_basis
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let det_space t = t.det_space
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let mo_class t = DeterminantSpace.mo_class @@ det_space t
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let eigensystem t = Lazy.force t.eigensystem
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let f12_integrals mo_basis =
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let two_e_ints = MOBasis.f12_ints mo_basis in
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( (fun i j _ -> 0.),
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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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F12.get_phys two_e_ints i j k l
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else
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(F12.get_phys two_e_ints i j k l) -.
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(F12.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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[ CI.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 f_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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[ f12_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 is_internal det_space =
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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 mo_class = DeterminantSpace.mo_class det_space in
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let aux_mask = m (MOClass.auxiliary_mos mo_class) 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 aux_mask alfa <> Z.zero 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 aux_mask beta = Z.zero
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let dressing_vector aux_basis f12_amplitudes ci =
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debug "Computing dressing vector";
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(*
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let i_o1_alfa = h_ij aux_basis in
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let alfa_o2_i = f_ij aux_basis in
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let w_alfa _ _ = 1. in
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let mo_class = CI.mo_class ci in
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let list_holes = List.concat
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[ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
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and list_particles2 = MOClass.auxiliary_mos mo_class
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and list_particles1 = List.concat
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[ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ; MOClass.auxiliary_mos mo_class ]
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in
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(*
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Util.debug_matrix "f12 amplitudes" f12_amplitudes;
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*)
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(* Single state here *)
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let result =
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CI.second_order_sum ci list_holes list_particles1 list_holes list_particles2
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(is_internal ci.det_space) i_o1_alfa alfa_o2_i w_alfa f12_amplitudes ~unique:false
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|> Vec.of_list
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in
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Matrix.sparse_of_vector_array [| Vector.sparse_of_vec result |]
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*)
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let out_dets =
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DeterminantSpace.fci_of_mo_basis ~frozen_core:false aux_basis
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|> DeterminantSpace.determinants_array
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|> Array.to_list
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|> List.filter (fun i -> not (is_internal ci.CI.det_space i))
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|> Array.of_list
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in
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let in_dets =
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DeterminantSpace.determinants_array ci.CI.det_space
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in
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let m_H_aux =
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Array.map (fun ki ->
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Array.map (fun kj ->
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h_ij aux_basis ki kj
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) out_dets
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) in_dets
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|> Mat.of_array
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in
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let m_F_aux =
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Array.map (fun ki ->
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Array.map (fun kj ->
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f_ij aux_basis ki kj
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) out_dets
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) in_dets
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|> Mat.of_array
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in
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let m_HF =
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gemm m_H_aux m_F_aux ~transb:`T
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in
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gemm m_HF f12_amplitudes
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|> Matrix.sparse_of_mat
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let make ~simulation ?(threshold=1.e-12) ?(frozen_core=true) ~mo_basis ~aux_basis_filename () =
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let gamma = 1.0 in
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let mo_num = MOBasis.size mo_basis in
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(* Add auxiliary basis set *)
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let s =
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let charge = Charge.to_int @@ Simulation.charge simulation
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and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation
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and nuclei = Simulation.nuclei simulation
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in
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let general_basis =
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Basis.general_basis @@ Simulation.basis simulation
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in
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GeneralBasis.combine [
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general_basis ; GeneralBasis.read aux_basis_filename
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]
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|> Basis.of_nuclei_and_general_basis nuclei
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|> Simulation.make ~charge ~multiplicity ~nuclei
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in
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let aux_basis =
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MOBasis.of_mo_basis s mo_basis
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in
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let det_space =
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DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num
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in
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let ci = CI.make det_space in
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let ci_coef, ci_energy =
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let x = Lazy.force ci.eigensystem in
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Parallel.broadcast (lazy x)
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in
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let f12_amplitudes =
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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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debug "Four-idx transform of f12 intergals";
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ignore @@ MOBasis.f12_ints aux_basis;
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let f = fun ki kj ->
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if ki <> kj then
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gamma *. (f_ij aux_basis ki kj)
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else
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1. +. gamma *. (f_ij aux_basis ki kj)
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in
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debug "Computing F matrix";
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let m_F =
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CI.create_matrix_spin f det_space
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|> Lazy.force
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in
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fun ci_coef ->
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(*
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Util.debug_matrix "F" (Matrix.to_mat m_F);
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debug "Solving linear system";
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*)
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Matrix.ax_eq_b m_F (Matrix.dense_of_mat ci_coef)
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|> Matrix.to_mat
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in
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let e_shift =
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let det =
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DeterminantSpace.determinant_stream det_space
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|> Stream.next
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in
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h_ij aux_basis det det
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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 ci.CI.m_H
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in
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(*
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Util.debug_matrix "H" (Matrix.to_mat m_H);
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*)
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let rec iteration ?(state=1) psi =
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(*
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debug "Iteration";
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Util.debug_matrix "T" (f12_amplitudes psi);
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*)
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let delta =
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dressing_vector aux_basis (f12_amplitudes psi) ci
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in
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(*
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Util.debug_matrix "psi" psi;
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*)
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Format.printf "Amplitude (1,1) : %f@." (f12_amplitudes psi).{1,1};
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Format.printf "Dressing vector(1,1) : %f@." (Matrix.get delta 1 1);
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let f = 1.0 /. psi.{1,1} in
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let delta_00 =
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Util.list_range 2 (Mat.dim1 psi)
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|> List.fold_left (fun accu i -> accu +.
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(Matrix.get delta i 1) *. psi.{i,1} *. f) 0.
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in
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let delta = Matrix.to_mat delta in
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delta.{1,1} <- delta.{1,1} -. delta_00;
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(*------
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TODO SINGLE STATE HERE
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*)
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let n_states = ci.CI.n_states in
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let diagonal =
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Vec.init (Matrix.dim1 m_H) (fun i ->
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if i = 1 then
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Matrix.get m_H i i +. delta.{1,1} *. f
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else
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Matrix.get m_H i i
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)
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in
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let matrix_prod c =
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let w =
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Matrix.mm ~transa:`T m_H c
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|> Matrix.to_mat
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in
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let c11 = Matrix.get c 1 1 in
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Util.list_range 1 (Mat.dim1 w)
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|> List.iter (fun i ->
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let dci =
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delta.{i,1} *. f ;
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in
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w.{i,1} <- w.{i,1} +. dci *. c11;
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if (i <> 1) then
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w.{1,1} <- w.{1,1} +. dci *. (Matrix.get c i 1);
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);
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Matrix.dense_of_mat w
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in
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let eigenvectors, eigenvalues =
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Davidson.make ~threshold:1.e-6 ~guess:psi ~n_states diagonal matrix_prod
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in
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let conv =
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1.0 -. abs_float ( dot
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(Mat.to_col_vecs psi).(0)
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(Mat.to_col_vecs eigenvectors).(0) )
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in
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Printf.printf "Convergence : %e %f\n" conv (eigenvalues.{1} +. e_shift);
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if conv > threshold then
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iteration eigenvectors
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else
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let eigenvalues =
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Vec.map (fun x -> x +. e_shift) eigenvalues
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in
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eigenvectors, eigenvalues
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in
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iteration ci_coef
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)
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in
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{ mo_basis ; aux_basis ; det_space ; ci ; eigensystem ; gamma }
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