open Util

let cutoff = Constants.cutoff 
let cutoff2 = cutoff *. cutoff

exception NullQuartet
exception Found

let at_least_one_valid arr =
  try
    Array.fold_left (fun _ x -> if (abs_float x > cutoff) then raise Found else false ) false arr
  with Found -> true

(** Horizontal and Vertical Recurrence Relations (HVRR) *)
let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
    (totAngMom_a, totAngMom_b, totAngMom_c, totAngMom_d)
    (maxm, zero_m_array)
    (expo_b, expo_d)
    (expo_inv_p, expo_inv_q)
    (center_ab, center_cd, center_pq)
    coef_prod map_1d map_2d
  =

  let ncoef = (Array.length coef_prod) in
  let empty =
    Array.make ncoef 0. 
  in

  let totAngMom_a = Angular_momentum.to_int totAngMom_a
  and totAngMom_b = Angular_momentum.to_int totAngMom_b
  and totAngMom_c = Angular_momentum.to_int totAngMom_c
  and totAngMom_d = Angular_momentum.to_int totAngMom_d
  in

  (** Vertical recurrence relations *)
  let rec vrr0_v m angMom_a = function
    | 1 ->
      let xyz =
        match angMom_a with 
        | (1,_,_) -> 0 
        | (_,1,_) -> 1 
        | _       -> 2 
      in
      let f = expo_b *. (Coordinate.coord center_ab xyz) in
      Array.init ncoef (fun k -> coef_prod.(k) *.  expo_inv_p *.
                                 ( (Coordinate.coord center_pq.(k) xyz) *. zero_m_array.(m+1).(k)
                                   -. f *. zero_m_array.(m).(k) ) ) 
    | 0 -> Array.map2 ( *. ) zero_m_array.(m) coef_prod
    | totAngMom_a ->
      let key = Zkey.of_int_tuple (Zkey.Three angMom_a)
      in

      try Zmap.find map_1d.(m) 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, 0
            | (x,y,0) -> (x,y-1,0),(x,y-2,0), y-1, 1
            | (x,y,z) -> (x,y,z-1),(x,y,z-2), z-1, 2
          in
          if amxyz < 0 then empty else
            let v1 = 
              let f = 
                -. expo_b *. expo_inv_p *. (Coordinate.coord center_ab xyz)
              in
              if (abs_float f < cutoff) then empty else
                Array.map (fun v1k -> f *. v1k) (vrr0_v m am (totAngMom_a-1) )
            in
            let p1 = 

              Array.mapi (fun k v2k -> v1.(k) +. expo_inv_p *. (Coordinate.coord center_pq.(k) xyz) *. v2k) (vrr0_v (m+1) am (totAngMom_a-1))
            in
            if amxyz < 1 then p1 else
              let f = (float_of_int amxyz) *. expo_inv_p *. 0.5
              in
              if (abs_float f < cutoff) then empty else
                let v1 = vrr0_v m amm (totAngMom_a-2)  
                in
                let v2 = 
                  if (abs_float (f *. expo_inv_p)) < cutoff then empty else
                    vrr0_v (m+1) amm (totAngMom_a-2) 
                in
                Array.init ncoef (fun k -> p1.(k) +.
                                           f *. (v1.(k) +. v2.(k) *. expo_inv_p ) ) 
        in Zmap.add map_1d.(m) key result;
        result

  and vrr_v m angMom_a angMom_c totAngMom_a totAngMom_c =

    match (totAngMom_a, totAngMom_c) with
    | (i,0) -> if (i>0) then
        vrr0_v m angMom_a totAngMom_a
      else
        Array.map2 ( *. ) zero_m_array.(m) coef_prod
    | (_,_) ->

      let key =  Zkey.of_int_tuple (Zkey.Six (angMom_a, angMom_c))
      in

      try Zmap.find map_2d.(m) key with
      | Not_found -> 
        let result = 
          begin
            let am, cm, cmm, axyz, cxyz, xyz =
              let (aax, aay, aaz) = angMom_a 
              and (acx, acy, acz) = angMom_c in
              if (acz > 0) then
                (aax, aay, aaz-1),
                (acx, acy, acz-1),
                (acx, acy, acz-2),
                aaz, acz, 2
              else if (acy > 0) then
                (aax, aay-1,aaz),
                (acx, acy-1,acz),
                (acx, acy-2,acz),
                aay,acy, 1
              else
                (aax-1,aay,aaz),
                (acx-1,acy,acz),
                (acx-2,acy,acz),
                aax,acx, 0
            in
                (*
		if cxyz < 1 then empty else
                *)
            let f1 =
              let f = (Coordinate.coord center_cd xyz) in
              Array.init ncoef (fun k -> 
                  expo_d.(k) *. expo_inv_q.(k) *. f)
            in
            let f2 =
              Array.init ncoef (fun k -> 
                  expo_inv_q.(k) *. (Coordinate.coord center_pq.(k) xyz) )
            in
            let v1 = 
              if (at_least_one_valid f1) then
                vrr_v m angMom_a cm totAngMom_a (totAngMom_c-1) 
              else empty
            and v2 =
              if (at_least_one_valid f2) then
                vrr_v (m+1) angMom_a cm totAngMom_a (totAngMom_c-1)
              else empty
            in
            let p1 = 
              Array.init ncoef (fun k -> -. v1.(k) *. f1.(k) -. v2.(k) *. f2.(k)) 
            in
            let p2 = 
              if cxyz < 2 then p1 else
                let fcm = 
                  (float_of_int (cxyz-1)) *. 0.5
                in
                let f1 =
                  Array.map (fun e -> fcm *. e) expo_inv_q
                in
                let f2 =
                  Array.map2 ( *. ) f1 expo_inv_q 
                in
                let v1 = 
                  if (at_least_one_valid f1) then
                    vrr_v m angMom_a cmm totAngMom_a (totAngMom_c-2)
                  else empty
                in
                let v2 = 
                  if (at_least_one_valid f2) then
                    vrr_v (m+1) angMom_a cmm totAngMom_a (totAngMom_c-2) 
                  else empty
                in
                Array.init ncoef (fun k -> p1.(k) +.  f1.(k) *. v1.(k) +. f2.(k) *. v2.(k)) 
            in
            if (axyz < 1) || (cxyz < 1) then p2 else
              let fa =
                (float_of_int axyz) *. expo_inv_p *. 0.5
              in
              let f1 =
                Array.map (fun e -> fa *. e ) expo_inv_q
              in
              if (at_least_one_valid f1) then
                let v = 
                  vrr_v (m+1) am cm (totAngMom_a-1) (totAngMom_c-1) 
                in
                Array.init ncoef (fun k -> p2.(k) -. f1.(k) *. v.(k)) 
              else p2
          end
        in Zmap.add map_2d.(m) key result;
        result




  (** Horizontal recurrence relations *)
  and hrr0_v angMom_a angMom_b angMom_c 
      totAngMom_a totAngMom_b totAngMom_c =

    match totAngMom_b with
    | 0 ->
      begin
        match (totAngMom_a, totAngMom_c) with
        | (0,0) -> Array.map2 ( *. )  zero_m_array.(0) coef_prod
        | (_,0) -> vrr0_v 0 angMom_a totAngMom_a
        | (_,_) -> vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c
      end
    | 1 ->
      let (aax, aay, aaz) = angMom_a in
      let ap, xyz =
        match angMom_b with
        | (_,_,1) -> (aax,aay,aaz+1), 2
        | (_,1,_) -> (aax,aay+1,aaz), 1
        | (_,_,_) -> (aax+1,aay,aaz), 0
      in
      let f = Coordinate.coord center_ab xyz in
      let v1 = 
        vrr_v 0 ap angMom_c (totAngMom_a+1) totAngMom_c
      in
      if (abs_float f < cutoff) then v1 else
        let v2 = 
          vrr_v 0 angMom_a angMom_c totAngMom_a totAngMom_c
        in
        Array.map2 (fun v1 v2 -> v1 +. v2 *. f) v1 v2
    | _ ->
      let (aax, aay, aaz) = angMom_a
      and (abx, aby, abz) = angMom_b in
      let bxyz, xyz =
        match angMom_b with
        | (0,0,_) -> abz, 2
        | (0,_,_) -> aby, 1
        | _       -> abx, 0
      in
      if (bxyz < 1) then empty else
        let ap, bm =
          match xyz with
          | 0 -> (aax+1,aay,aaz),(abx-1,aby,abz)
          | 1 -> (aax,aay+1,aaz),(abx,aby-1,abz)
          | _ -> (aax,aay,aaz+1),(abx,aby,abz-1)
        in

        let h1 = 
          hrr0_v ap bm angMom_c (totAngMom_a+1) (totAngMom_b-1) totAngMom_c 
        in
        let f = (Coordinate.coord center_ab xyz) in
        if (abs_float f < cutoff) then h1 else
          let h2 = 
            hrr0_v angMom_a bm angMom_c totAngMom_a (totAngMom_b-1) totAngMom_c 
          in Array.map2 (fun h1 h2 -> h1 +. h2 *. f) h1 h2

  and hrr_v 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_v 0 angMom_a angMom_c totAngMom_a totAngMom_c
      else
        hrr0_v angMom_a angMom_b angMom_c totAngMom_a totAngMom_b totAngMom_c
    | (_,_) ->
      let (acx, acy, acz) = angMom_c
      and (adx, ady, adz) = angMom_d in
      let cp, dm, xyz =
        match angMom_d with
        | (_,0,0) -> (acx+1, acy, acz), (adx-1, ady, adz), 0
        | (_,_,0) -> (acx, acy+1, acz), (adx, ady-1, adz), 1
        | _       -> (acx, acy, acz+1), (adx, ady, adz-1), 2
      in
      let h1 = 
        hrr_v angMom_a angMom_b cp dm totAngMom_a totAngMom_b (totAngMom_c+1) (totAngMom_d-1)
      and h2 =
        hrr_v angMom_a angMom_b angMom_c dm totAngMom_a totAngMom_b totAngMom_c (totAngMom_d-1)
      in
      let f = (Coordinate.coord center_cd xyz) in
      Array.init ncoef (fun k -> h1.(k) +. h2.(k) *. f) 
  in
  hrr_v
    (angMom_a.(0),angMom_a.(1),angMom_a.(2))
    (angMom_b.(0),angMom_b.(1),angMom_b.(2))
    (angMom_c.(0),angMom_c.(1),angMom_c.(2))
    (angMom_d.(0),angMom_d.(1),angMom_d.(2))
    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.(0).ShellPair.shell_a
  and shell_b = shell_p.(0).ShellPair.shell_b
  and shell_c = shell_q.(0).ShellPair.shell_a
  and shell_d = shell_q.(0).ShellPair.shell_b
  in
  let maxm = 
    let open Angular_momentum in
    (to_int @@ Contracted_shell.totAngMom shell_a) + (to_int @@ Contracted_shell.totAngMom shell_b) 
    + (to_int @@ Contracted_shell.totAngMom shell_c) + (to_int @@ Contracted_shell.totAngMom shell_d)
  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

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

  begin
    match Contracted_shell.(totAngMom shell_a, totAngMom shell_b,
                            totAngMom shell_c, totAngMom shell_d) with
    | Angular_momentum.(S,S,S,S) ->
      contracted_class.(0) <-
        Array.fold_left
          (fun accu shell_ab -> accu +.
                                Array.fold_left (fun accu shell_cd ->
                                    let coef_prod =
                                      shell_ab.ShellPair.coef *. shell_cd.ShellPair.coef
                                    in
                                    (** Screening on the product of coefficients *)
                                    try
                                      if (abs_float coef_prod) < 1.e-3*.cutoff then
                                        raise NullQuartet;

                                      let expo_pq_inv =
                                        shell_ab.ShellPair.expo_inv +. shell_cd.ShellPair.expo_inv
                                      in
                                      let center_pq =
                                        Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
                                      in
                                      let norm_pq_sq =
                                        Coordinate.dot center_pq center_pq
                                      in

                                      let zero_m_array = 
                                        zero_m ~maxm:0 ~expo_pq_inv ~norm_pq_sq
                                      in

                                      accu +. coef_prod *. zero_m_array.(0)
                                    with NullQuartet -> accu
                                  ) 0. shell_q
          ) 0. shell_p

    | _ -> 
      Array.iter (fun shell_ab ->
          let norm_coef_scale_p = shell_ab.ShellPair.norm_coef_scale in
          let b = shell_ab.ShellPair.j in
          let common =
            Array.map (fun shell_cd ->
                let coef_prod =
                  shell_ab.ShellPair.coef *. shell_cd.ShellPair.coef
                in
                let expo_pq_inv =
                  shell_ab.ShellPair.expo_inv +. shell_cd.ShellPair.expo_inv
                in
                let center_pq =
                  Coordinate.(shell_ab.ShellPair.center |- shell_cd.ShellPair.center)
                in
                let norm_pq_sq =
                  Coordinate.dot center_pq center_pq
                in

                let zero_m_array = 
                  zero_m ~maxm ~expo_pq_inv ~norm_pq_sq
                in

                let d = shell_cd.ShellPair.j in

                (zero_m_array, shell_cd.ShellPair.expo_inv,
                 Contracted_shell.expo shell_d d, 
                 center_pq,coef_prod)
              ) shell_q
            |> Array.to_list
            |> List.filter (fun (zero_m_array, expo_inv, d, 
                                 center_pq,coef_prod) -> abs_float coef_prod >= 1.e-4 *. cutoff)
            |> Array.of_list
          in
          let zero_m_array = Array.map (fun (zero_m_array, expo_inv, d, 
                                             center_pq,coef_prod) -> zero_m_array) common
          and expo_inv = Array.map (fun (zero_m_array, expo_inv, d, 
                                         center_pq,coef_prod) -> expo_inv ) common
          and d = Array.map (fun (zero_m_array, expo_inv, d, 
                                  center_pq,coef_prod) -> d) common
          and center_pq = Array.map (fun (zero_m_array, expo_inv, d, 
                                          center_pq,coef_prod) -> center_pq) common
          and coef_prod = Array.map (fun (zero_m_array, expo_inv, d, 
                                          center_pq,coef_prod) -> coef_prod) common
          in
          (* Transpose zero_m_array 
          *)
          let zero_m_array =
            let result = Array.init (maxm+1) (fun _ ->
                Array.make (Array.length coef_prod) 0.)
            in
            for m=0 to maxm do
              for k=0 to (Array.length coef_prod-1) do
                result.(m).(k) <- zero_m_array.(k).(m)
              done;
            done;
            result
          in

          (* Compute the integral class from the primitive shell quartet *)
          let map_1d = Array.init maxm (fun _ -> Zmap.create (4*maxm)) in
          let map_2d = Array.init maxm (fun _ -> Zmap.create (Array.length class_indices)) in
          let norm = 
            let norm_coef_scale_q = shell_q.(0).ShellPair.norm_coef_scale in
            Array.map (fun v1 ->
                Array.map (fun v2 -> v1 *. v2) norm_coef_scale_q
              ) norm_coef_scale_p
            |> Array.to_list
            |> Array.concat
          in
          Array.iteri (fun i key ->
              let a = Zkey.to_int_array Zkey.Kind_12 key in
              let (angMomA,angMomB,angMomC,angMomD) =
                ( [| a.(0) ;  a.(1) ;  a.(2) |], 
                  [| a.(3) ;  a.(4) ;  a.(5) |], 
                  [| a.(6) ;  a.(7) ;  a.(8) |], 
                  [| a.(9) ; a.(10) ; a.(11) |] )
              in
              let integral = 
                hvrr_two_e_vector (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, d)
                  (shell_ab.ShellPair.expo_inv, expo_inv)
                  (shell_p.(0).ShellPair.center_ab,
                   shell_q.(0).ShellPair.center_ab, center_pq)
                  coef_prod map_1d map_2d
              in
              let x = Array.fold_left (+.) 0. integral in
              contracted_class.(i) <- contracted_class.(i) +. x *. norm.(i)
            ) class_indices
        ) shell_p

  end;

  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