QCaml/CI/F12CI.ml

let debug s =
  Printf.printf "%s\n%!" s;

open Lacaml.D

type t = 
  {
    gamma     : float;
    mo_basis  : MOBasis.t ;
    aux_basis : MOBasis.t ;
    det_space : DeterminantSpace.t ;
    ci        : CI.t ;
    eigensystem : (Mat.t * Vec.t) lazy_t;
  }

let ci t        =  t.ci
let mo_basis t  =  t.mo_basis
let det_space t =  t.det_space
let mo_class t  =  DeterminantSpace.mo_class @@ det_space t
let eigensystem t =  Lazy.force t.eigensystem


let f12_integrals mo_basis =
  let two_e_ints  = MOBasis.f12_ints mo_basis in
  ( (fun i j _ -> 0.),
    (fun i j k l s s' ->
       if s' = Spin.other s then
         F12.get_phys two_e_ints i j k l
       else
         (F12.get_phys two_e_ints i j k l) -.
         (F12.get_phys two_e_ints i j l k)
    ) )




let h_ij mo_basis ki kj =
  let integrals =
    List.map (fun f -> f mo_basis)
      [ CI.h_integrals ]
  in
  CIMatrixElement.make integrals ki kj 
  |> List.hd


let f_ij mo_basis ki kj =
  let integrals =
    List.map (fun f -> f mo_basis)
      [ f12_integrals ]
  in
  CIMatrixElement.make integrals ki kj 
  |> List.hd


let is_internal det_space =
    let m l =
      List.fold_left (fun accu i ->
          let j = i-1 in Z.(logor accu (shift_left one j))
        ) Z.zero l
    in
    let mo_class   = DeterminantSpace.mo_class det_space in
    let aux_mask   = m (MOClass.auxiliary_mos   mo_class) in
    fun a ->
      let alfa =
        Determinant.alfa a
        |> Spindeterminant.bitstring
      in
      if Z.logand aux_mask alfa <> Z.zero then
        false
      else
        let beta =
          Determinant.beta a
          |> Spindeterminant.bitstring
        in
        Z.logand aux_mask beta = Z.zero 


let dressing_vector aux_basis f12_amplitudes ci =

debug "Computing dressing vector";

(*
  let i_o1_alfa = h_ij aux_basis in
  let alfa_o2_i = f_ij aux_basis in

  let w_alfa _ _ = 1. in

  let mo_class = CI.mo_class ci in

  let list_holes = List.concat
    [ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ]
  and list_particles2 = MOClass.auxiliary_mos mo_class
  and list_particles1 = List.concat
    [ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ; MOClass.auxiliary_mos mo_class ]
  in
(*
Util.debug_matrix "f12 amplitudes" f12_amplitudes;
*)
  (* Single state here *)
  let result = 
    CI.second_order_sum  ci  list_holes  list_particles1  list_holes  list_particles2
        (is_internal ci.det_space) i_o1_alfa  alfa_o2_i  w_alfa  f12_amplitudes ~unique:false
    |> Vec.of_list
  in
  Matrix.sparse_of_vector_array [| Vector.sparse_of_vec result |]

*)

  let out_dets =
    DeterminantSpace.fci_of_mo_basis ~frozen_core:false aux_basis
    |> DeterminantSpace.determinants_array
    |> Array.to_list
    |> List.filter (fun i -> not (is_internal ci.CI.det_space i))
    |> Array.of_list
  in

  let in_dets =
    DeterminantSpace.determinants_array ci.CI.det_space 
  in

  let m_H_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_F_aux = 
    Array.map (fun ki ->
      Array.map (fun kj ->
        f_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 m_HF f12_amplitudes
  |> Matrix.sparse_of_mat





let make ~simulation ?(threshold=1.e-12) ?(frozen_core=true) ~mo_basis ~aux_basis_filename () =

  let gamma = 1.0 in

  let mo_num = MOBasis.size mo_basis in

  (* Add auxiliary basis set *)
  let s =
    let charge        = Charge.to_int @@ Simulation.charge simulation 
    and multiplicity  = Electrons.multiplicity @@ Simulation.electrons simulation
    and nuclei        = Simulation.nuclei simulation
    in
    let general_basis = 
      Basis.general_basis @@ Simulation.basis simulation
    in
    GeneralBasis.combine [
      general_basis ; GeneralBasis.read aux_basis_filename
    ]
    |> Basis.of_nuclei_and_general_basis nuclei
    |> Simulation.make ~charge ~multiplicity ~nuclei 
  in

  let aux_basis = 
    MOBasis.of_mo_basis s mo_basis
  in

  let det_space = 
    DeterminantSpace.fci_f12_of_mo_basis  aux_basis  ~frozen_core  mo_num
  in

  let ci = CI.make det_space in

  let ci_coef, ci_energy =
    let x = Lazy.force ci.eigensystem in
    Parallel.broadcast (lazy x)
  in


  let f12_amplitudes = 
    (* While in a sequential region, initiate the parallel
       4-idx transformation to avoid nested parallel jobs
    *)
debug "Four-idx transform of f12 intergals";
    ignore @@ MOBasis.f12_ints aux_basis;

    let f = fun ki kj ->
      if ki <> kj then
        gamma *. (f_ij aux_basis ki kj)
      else
        1. +. gamma *. (f_ij aux_basis ki kj)
    in
    let m_F = 
      CI.create_matrix_spin f det_space
      |> Lazy.force
    in
    fun ci_coef -> 
(*
Util.debug_matrix "F" (Matrix.to_mat m_F);
debug "Solving linear system";
*)
    Matrix.ax_eq_b m_F (Matrix.dense_of_mat ci_coef)
    |> Matrix.to_mat
  in

  let e_shift = 
    let det =
      DeterminantSpace.determinant_stream det_space 
      |> Stream.next
    in
    h_ij aux_basis det det
  in

  let eigensystem = lazy (
    let m_H =
      Lazy.force ci.CI.m_H
    in
(*
Util.debug_matrix "H" (Matrix.to_mat m_H);
*)

    let rec iteration ?(state=1) psi = 
debug "Iteration";
      let delta = 
         dressing_vector aux_basis (f12_amplitudes psi) ci
      in

      let f = 1.0 /. psi.{1,1} in
      let delta_00 =
        Util.list_range 2 (Mat.dim1 psi)
        |> List.fold_left (fun accu i -> accu +.
            (Matrix.get delta i 1) *. psi.{i,1} *. f) 0. 
      in
      let delta = Matrix.to_mat delta in
      delta.{1,1} <- delta.{1,1} -. delta_00;

(*------
TODO SINGLE STATE HERE
*)
      let n_states = ci.CI.n_states in
      let diagonal =
        Vec.init (Matrix.dim1 m_H) (fun i ->
          if i = 1 then
            Matrix.get m_H i i +. delta.{1,1} *. f 
          else
            Matrix.get m_H i i
          )
      in

      let matrix_prod c = 
        let w = 
          Matrix.mm ~transa:`T m_H c
          |> Matrix.to_mat
        in
        let c11 = Matrix.get c 1 1 in
        Util.list_range 1 (Mat.dim1 w)
        |> List.iter (fun i ->
          let dci = 
            delta.{i,1} *. f ;
          in
          w.{i,1} <- w.{i,1} +. dci *.  c11;
          if (i <> 1) then
            w.{1,1} <- w.{1,1} +. dci *. (Matrix.get c i 1);
          );
        Matrix.dense_of_mat w
      in

      let eigenvectors, eigenvalues = 
          Davidson.make ~threshold:1.e-6 ~guess:psi ~n_states diagonal matrix_prod
      in

      let conv =
        1.0 -. abs_float ( dot
          (Mat.to_col_vecs psi).(0)
          (Mat.to_col_vecs eigenvectors).(0) )
      in
      Printf.printf "Convergence : %e  %f\n" conv (eigenvalues.{1} +. e_shift);

      if conv > threshold then
        iteration eigenvectors
      else
        let eigenvalues =
          Vec.map (fun x -> x +. e_shift) eigenvalues
        in
        eigenvectors, eigenvalues
    in
    iteration ci_coef

  )
  in
  { mo_basis ; aux_basis ; det_space ; ci ; eigensystem ; gamma }