QCaml/Basis/TwoElectronRR.ml

open Util
open Constants
open Coordinate

let debug=false

let cutoff2 = cutoff *. cutoff

exception NullQuartet

(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let rec hvrr_two_e (angMom_a, angMom_b, angMom_c, angMom_d)
    (totAngMom_a_in, totAngMom_b_in, totAngMom_c_in, totAngMom_d_in)
    (maxm, zero_m_array)
    (expo_b, expo_d)
    (expo_inv_p, expo_inv_q)
    (center_ab, center_cd, center_pq)
    map_1d map_2d map_1d' map_2d'
  =

  let maxsze = maxm+1 in
  let totAngMom_a = Angular_momentum.to_int totAngMom_a_in
  and totAngMom_b = Angular_momentum.to_int totAngMom_b_in
  and totAngMom_c = Angular_momentum.to_int totAngMom_c_in
  and totAngMom_d = Angular_momentum.to_int totAngMom_d_in
  in

  (* Swap electrons 1 and 2 so that the max angular momentum is on 1 *)
  if (totAngMom_a+totAngMom_b < totAngMom_c+totAngMom_d) then
    hvrr_two_e (angMom_c, angMom_d, angMom_a, angMom_b)
      (totAngMom_c_in, totAngMom_d_in, totAngMom_a_in, totAngMom_b_in)
      (maxm, zero_m_array)
      (expo_d, expo_b)
      (expo_inv_q, expo_inv_p)
      (center_cd, center_ab, (Coordinate.neg center_pq) )
      map_1d' map_2d' map_1d map_2d
  else
    let maxm = totAngMom_a + totAngMom_b + totAngMom_c + totAngMom_d in
    let empty = Array.make (maxm+1) 0. 
    in
    if debug then begin
      Printf.printf "\n---- %d %d %d %d ----\n"  totAngMom_a totAngMom_b totAngMom_c totAngMom_d;
      let (x,y,z) = angMom_a in Printf.printf "%d %d %d\n" x y z;
      let (x,y,z) = angMom_b in Printf.printf "%d %d %d\n" x y z;
      let (x,y,z) = angMom_c in Printf.printf "%d %d %d\n" x y z;
      let (x,y,z) = angMom_d in Printf.printf "%d %d %d\n" x y z;
      Printf.printf "%f %f %f %f\n%f %f %f\n%f %f %f\n%f %f %f\n"  expo_b expo_d
        expo_inv_p expo_inv_q
        (get X center_ab) (get Y center_ab) (get Z center_ab)
        (get X center_cd) (get Y center_cd) (get Z center_cd)
        (get X center_pq) (get Y center_pq) (get Z center_pq)
    end;

    (** Vertical recurrence relations *)
    let rec vrr0 angMom_a totAngMom_a = 
      if debug then
        begin
          let (x,y,z) = angMom_a in
          Printf.printf "vrr0: %d : %d %d %d\n" totAngMom_a x y z
        end;

      match totAngMom_a with 
      | 0 -> zero_m_array
      | _ ->
        let key = Zkey.of_int_tuple (Zkey.Three angMom_a) in

        try Zmap.find map_1d key with
        | Not_found ->
          let result = 
            let am, amm, amxyz, xyz  =
              match angMom_a with
              | (x,0,0) -> (x-1,0,0),(x-2,0,0), x-1, X
              | (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, Y
              | (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, Z
            in
            if amxyz < 0 then empty else
              let f1 = expo_inv_p *. (Coordinate.get xyz center_pq) 
              and f2 = expo_b *. expo_inv_p *.  (Coordinate.get xyz center_ab)
              in
              let result = Array.create_float maxsze in
              if amxyz < 1 then
                begin
                  let v1 = 
                    vrr0 am (totAngMom_a-1) 
                  in
                  for m=0 to maxm-1 do
                      result.(m) <- f1 *. v1.(m+1)  -. f2 *. v1.(m) 
                  done;
                  result.(maxm) <- -. f2 *. v1.(maxm) 
                end
              else
                begin
                  let v3 = 
                    vrr0 amm (totAngMom_a-2) 
                  in
                  let v1 = 
                    vrr0 am (totAngMom_a-1) 
                  in
                  let f3 = (float_of_int amxyz) *. expo_inv_p *. 0.5 in
                  for m=0 to maxm-1 do
                    result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m) 
                      +. f3 *. (v3.(m) +. expo_inv_p *. v3.(m+1))
                  done;
                  result.(maxm) <- f3 *. v3.(maxm) 
                end;
              result
          in Zmap.add map_1d key result;
          result


    and vrr angMom_a angMom_c totAngMom_a totAngMom_c =

      if debug then
        begin
          let angMom_ax, angMom_ay, angMom_az = angMom_a in
          let angMom_cx, angMom_cy, angMom_cz = angMom_c in
          Printf.printf "vrr : %d %d : %d %d %d  %d %d %d\n" totAngMom_a totAngMom_c
            angMom_ax angMom_ay angMom_az angMom_cx angMom_cy angMom_cz
        end;

      match (totAngMom_a, totAngMom_c) with
      | (i,0) -> if (i>0) then
          vrr0 angMom_a totAngMom_a
    (*
    OneElectronRR.hvrr_one_e (angMom_a, angMom_b) (totAngMom_a_in, totAngMom_b_in)
      (maxm, zero_m_array) (expo_b) (expo_inv_p) (center_ab, center_pq, center_ab)
                map_1d
    *)
        else zero_m_array 
      | (_,_) ->
        let key =  Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c) ) in

        try Zmap.find map_2d key with
        | Not_found -> 
          let result = 
            let am, cm, cmm, axyz, cmxyz, xyz =
              let angMom_ax, angMom_ay, angMom_az = angMom_a 
              and angMom_cx, angMom_cy, angMom_cz = angMom_c in
              match angMom_c with
              | (_,0,0) -> 
                (angMom_ax-1, angMom_ay, angMom_az),
                (angMom_cx-1, angMom_cy, angMom_cz),
                (angMom_cx-2, angMom_cy, angMom_cz),
                angMom_ax,angMom_cx-1, X
              | (_,_,0) -> 
                (angMom_ax, angMom_ay-1, angMom_az),
                (angMom_cx, angMom_cy-1, angMom_cz),
                (angMom_cx, angMom_cy-2, angMom_cz),
                angMom_ay,angMom_cy-1, Y
              | _       -> 
                (angMom_ax, angMom_ay, angMom_az-1),
                (angMom_cx, angMom_cy, angMom_cz-1),
                (angMom_cx, angMom_cy, angMom_cz-2),
                angMom_az,angMom_cz-1, Z
            in
            if cmxyz < 0 then empty
            else
              let f1 =
                -. expo_d *. expo_inv_q *. (Coordinate.get xyz center_cd) 
              and f2 = 
                expo_inv_q *. (Coordinate.get xyz center_pq)
              in
              let result = Array.make maxsze 0. in
              if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then
                begin
                  let v1 = 
                    vrr angMom_a cm totAngMom_a (totAngMom_c-1)
                  in
                  for m=0 to maxm-1 do
                    result.(m) <- f1 *. v1.(m) -.  f2 *. v1.(m+1) ;
                  done;
                  result.(maxm) <- f1 *. v1.(maxm) ;
                end;
              if cmxyz > 0 then 
                begin
                  let f3 =
                    (float_of_int cmxyz) *. expo_inv_q *. 0.5 
                  in
                  if (abs_float f3 > cutoff) ||
                      (abs_float (f3 *. expo_inv_q) > cutoff) then 
                    begin
                      let v3 = 
                        vrr angMom_a cmm totAngMom_a (totAngMom_c-2)
                      in
                      for m=0 to maxm-1 do
                        result.(m) <- result.(m) +.
                            f3 *. (v3.(m) +. expo_inv_q *. v3.(m+1))
                      done;
                      result.(maxm) <- result.(maxm) +. f3 *. v3.(maxm)
                    end
                end;
              if (axyz > 0) && (cmxyz >= 0) then 
                begin
                  let f5 = 
                    (float_of_int axyz) *. expo_inv_p *. expo_inv_q *. 0.5 
                  in
                  if (abs_float f5 > cutoff) then 
                    let v5 =
                      vrr am cm (totAngMom_a-1) (totAngMom_c-1)
                    in
                    for m=0 to maxm-1 do
                      result.(m) <- result.(m) -.  f5 *. v5.(m+1)
                    done
                end;
              result
          in Zmap.add map_2d key result;
          result





    (** Horizontal recurrence relations *)
    and hrr0 angMom_a angMom_b angMom_c 
        totAngMom_a totAngMom_b totAngMom_c =

      (*
      if debug then
        begin
          let angMom_ax, angMom_ay, angMom_az = angMom_a 
          and angMom_bx, angMom_by, angMom_bz = angMom_b 
          and angMom_cx, angMom_cy, angMom_cz = angMom_c in
          Printf.printf "hrr0: %d %d %d : %d %d %d  %d %d %d  %d %d %d\n" 
            totAngMom_a totAngMom_b totAngMom_c 
            angMom_ax angMom_ay angMom_az
            angMom_bx angMom_by angMom_bz
            angMom_cx angMom_cy angMom_cz
        end;
        *)

      match totAngMom_b with
      | 0 -> (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
      | 1 ->
        let angMom_ax, angMom_ay, angMom_az = angMom_a in
        let ap, xyz =
          match angMom_b with
          | (1,_,_) -> (angMom_ax+1,angMom_ay,angMom_az), X
          | (_,1,_) -> (angMom_ax,angMom_ay+1,angMom_az), Y 
          | _       -> (angMom_ax,angMom_ay,angMom_az+1), Z
        in
        let v1 = 
          vrr ap angMom_c (totAngMom_a+1) totAngMom_c
        in
        let f2 =
          (Coordinate.get xyz center_ab)
        in
        if (abs_float f2 < cutoff) then v1.(0) else
          let v2 = 
            vrr angMom_a angMom_c totAngMom_a totAngMom_c
          in
          v1.(0) +. f2 *. v2.(0)
      | _ ->
        let angMom_ax, angMom_ay, angMom_az = angMom_a 
        and angMom_bx, angMom_by, angMom_bz = angMom_b in
        let bxyz, xyz =
          match angMom_b with
          | (_,0,0) -> angMom_bx, X
          | (_,_,0) -> angMom_by, Y
          | (_,_,_) -> angMom_bz, Z
        in
        if (bxyz < 1) then 0. else
          let ap, bm =
            match xyz with
            | X -> (angMom_ax+1,angMom_ay,angMom_az),(angMom_bx-1,angMom_by,angMom_bz)
            | Y -> (angMom_ax,angMom_ay+1,angMom_az),(angMom_bx,angMom_by-1,angMom_bz)
            | Z -> (angMom_ax,angMom_ay,angMom_az+1),(angMom_bx,angMom_by,angMom_bz-1)
          in
          let h1 = 
            hrr0 ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c 
          in
          let f2 =
            (Coordinate.get xyz center_ab)
          in
          if (abs_float f2 < cutoff) then h1 else
            let h2 = 
              hrr0 angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c 
            in
            h1 +. f2 *. h2


    and hrr angMom_a angMom_b angMom_c angMom_d
        totAngMom_a totAngMom_b totAngMom_c totAngMom_d =

      match (totAngMom_b, totAngMom_d) with
      | (_,0) -> if (totAngMom_b = 0) then 
          (vrr angMom_a angMom_c totAngMom_a totAngMom_c).(0)
        else
          hrr0 angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
      | (_,_) ->
        let (angMom_cx, angMom_cy, angMom_cz) = angMom_c 
        and (angMom_dx, angMom_dy, angMom_dz) = angMom_d in
        let cp, dm, xyz =
          match angMom_d with
          | (_,0,0) -> (angMom_cx+1, angMom_cy, angMom_cz), (angMom_dx-1, angMom_dy, angMom_dz), X
          | (_,_,0) -> (angMom_cx, angMom_cy+1, angMom_cz), (angMom_dx, angMom_dy-1, angMom_dz), Y
          | _       -> (angMom_cx, angMom_cy, angMom_cz+1), (angMom_dx, angMom_dy, angMom_dz-1), Z
        in
        let h1 = 
          hrr angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1) 
        in
        let f2 = Coordinate.get xyz center_cd in
        if (abs_float f2 < cutoff) then h1 else
          let h2 = 
            hrr angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1) 
          in
          h1 +. f2 *. h2

    in
    hrr angMom_a angMom_b angMom_c angMom_d
      totAngMom_a totAngMom_b totAngMom_c totAngMom_d




let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =

  let shell_a = shell_p.ContractedShellPair.shell_a
  and shell_b = shell_p.ContractedShellPair.shell_b
  and shell_c = shell_q.ContractedShellPair.shell_a
  and shell_d = shell_q.ContractedShellPair.shell_b
  and sp = shell_p.ContractedShellPair.shell_pairs
  and sq = shell_q.ContractedShellPair.shell_pairs
  in
  let maxm = 
    shell_p.ContractedShellPair.totAngMomInt +
    shell_q.ContractedShellPair.totAngMomInt 
  in

  (* Pre-computation of integral class indices *)
  let class_indices = 
    Angular_momentum.zkey_array
      (Angular_momentum.Quartet
         Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
                           totAngMom shell_c, totAngMom shell_d))
  in

  let contracted_class = 
    Array.make (Array.length class_indices) 0.;
  in

  let monocentric =
      shell_p.ContractedShellPair.monocentric &&
      shell_q.ContractedShellPair.monocentric &&
      Contracted_shell.center shell_p.ContractedShellPair.shell_a = 
      Contracted_shell.center shell_q.ContractedShellPair.shell_a
  in

  (* Compute all integrals in the shell for each pair of significant shell pairs *)

  let norm_coef_scale_p = shell_p.ContractedShellPair.norm_coef_scale in
  let norm_coef_scale_q = shell_q.ContractedShellPair.norm_coef_scale in
  for ab=0 to (Array.length sp - 1) do
    let cab = shell_p.ContractedShellPair.coef.(ab)  in
    let b = sp.(ab).ShellPair.j in
    for cd=0 to (Array.length shell_q.ContractedShellPair.shell_pairs - 1) do
      let coef_prod =
        cab *. shell_q.ContractedShellPair.coef.(cd)
      in
      (** Screening on the product of coefficients *)
      try
        if (abs_float coef_prod) < 1.e-3*.cutoff then
          raise NullQuartet;

        let center_pq = 
          sp.(ab).ShellPair.center |- sq.(cd).ShellPair.center
        in
        let norm_pq_sq =
          Coordinate.dot center_pq center_pq
        in

        let expo_pq_inv =
          shell_p.ContractedShellPair.expo_inv.(ab) +.
          shell_q.ContractedShellPair.expo_inv.(cd) 
        in

        let zero_m_array = 
          zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
        in
        begin
          match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
                                  totAngMom shell_c, totAngMom shell_d) with
          | Angular_momentum.(S,S,S,S) ->
            let integral =
              zero_m_array.(0)
            in
            contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral
          | _ -> 
            let d = shell_q.ContractedShellPair.shell_pairs.(cd).ShellPair.j in
            let map_1d = Zmap.create (4*maxm) in
            let map_2d = Zmap.create (Array.length class_indices) in
            let map_1d' = Zmap.create (4*maxm) in
            let map_2d' = Zmap.create (Array.length class_indices) in
            let norm_coef_scale =
              Array.to_list norm_coef_scale_p
              |> List.map (fun v1 ->
                  Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q) 
              |> Array.concat
            in

            (* Compute the integral class from the primitive shell quartet *)
            class_indices
            |> Array.iteri (fun i key ->
                let (angMomA,angMomB,angMomC,angMomD) =
                  match Zkey.to_int_tuple ~kind:Zkey.Kind_12 key with
                  | Zkey.Twelve x -> x
                  | _             -> assert false
                in
                try
                  if monocentric then
                    begin
                      let ax,ay,az = angMomA
                      and bx,by,bz = angMomB
                      and cx,cy,cz = angMomC
                      and dx,dy,dz = angMomD
                      in
                      if (  ((1 land ax+bx+cx+dx)=1) ||
                            ((1 land ay+by+cy+dy)=1) ||
                            ((1 land az+bz+cz+dz)=1) 
                          ) then
                        raise NullQuartet
                    end;
                  (*
                  (* Schwartz screening *)
                  if (maxm > 2) then
                  (
                    let schwartz_p = 
                      let key = Zkey.of_int_tuple (Zkey.Twelve
                      (angMomA, angMomB, angMomA, angMomB) )
                      in
                      match schwartz_p with
                      | None -> 1.
                      | Some schwartz_p -> Zmap.find schwartz_p key
                    in
                    if schwartz_p < cutoff then raise NullQuartet;
                    let schwartz_q = 
                      let key = Zkey.of_int_tuple (Zkey.Twelve
                      (angMomC, angMomD, angMomC, angMomD) ) 
                      in
                      match schwartz_q with
                      | None -> 1.
                      | Some schwartz_q -> Zmap.find schwartz_q key
                    in
                    if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet;
                    );
                  *)


                  let norm =  norm_coef_scale.(i) in
                  let coef_prod = coef_prod *. norm in
                  let integral = 
                    hvrr_two_e (angMomA, angMomB, angMomC, angMomD)
                      (Contracted_shell.totAngMom shell_a, Contracted_shell.totAngMom shell_b,
                       Contracted_shell.totAngMom shell_c, Contracted_shell.totAngMom shell_d)
                      (maxm, zero_m_array)
                      (Contracted_shell.expo shell_b b, Contracted_shell.expo shell_d d)
                      (shell_p.ContractedShellPair.expo_inv.(ab), 
                       shell_q.ContractedShellPair.expo_inv.(cd) )
                      (sp.(ab).ShellPair.center_ab, sq.(cd).ShellPair.center_ab, center_pq)
                      map_1d map_2d map_1d' map_2d'
                  in
                  contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral
                with NullQuartet -> ()
              )
        end
      with NullQuartet -> ()
    done
  done;

  let result = 
    Zmap.create (Array.length contracted_class)
  in
  Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices;
  result



(** Computes all the two-electron integrals of the contracted shell quartet *)
let contracted_class ~zero_m shell_a shell_b shell_c shell_d : float Zmap.t =

  let shell_p = ContractedShellPair.create ~cutoff shell_a shell_b
  and shell_q = ContractedShellPair.create ~cutoff shell_c shell_d
  in
  contracted_class_shell_pairs ~zero_m shell_p shell_q