open Lacaml.D
open Simulation
open Constants
open Util


type t =
  {
    fock     : Mat.t ;
    core     : Mat.t ;
    coulomb  : Mat.t ;
    exchange : Mat.t ;
  }


let fock t = t.fock
let core t = t.core
let coulomb t = t.coulomb
let exchange t = t.exchange


module Ao = AOBasis

let make_rhf ~density ?(threshold=Constants.epsilon) ao_basis =
  let m_P  = density
  and m_T  = Ao.kin_ints ao_basis |> KinInt.matrix 
  and m_V  = Ao.eN_ints  ao_basis |> NucInt.matrix
  and m_G  = Ao.ee_ints  ao_basis 
  in
  let nBas = Mat.dim1 m_T
  in

  let m_Hc = Mat.add m_T m_V 
  and m_J = Array.make_matrix nBas nBas 0.
  and m_K = Array.make_matrix nBas nBas 0.
  in

  for sigma = 1 to nBas do
    let m_Ksigma = m_K.(sigma-1) in
    for nu = 1 to nBas do
      let m_Jnu = m_J.(nu-1) in
      for lambda = 1 to nBas do
        let pJ = m_P.{lambda,sigma}
        and pK = 0.5 *. m_P.{lambda,nu}
        in
        match (abs_float pJ > threshold , abs_float pK > threshold, nu < sigma) with
        | (false, false, _) -> ()
        | (true , true , true) ->
          begin
            for mu = 1 to nu do
              let integral = 
                ERI.get_phys m_G mu lambda nu sigma
              in
              if (integral <> 0.) then begin
                m_Jnu.(mu-1) <- m_Jnu.(mu-1) +.  pJ *. integral;
                m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral
              end
            done;
            for mu = nu+1 to sigma do
              m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *.
                                                    ERI.get_phys m_G mu lambda nu sigma
            done
          end
        | (true , true , false) ->
          begin
            for mu = 1 to sigma do
              let integral = 
                ERI.get_phys m_G mu lambda nu sigma
              in
              if (integral <> 0.) then begin
                m_Jnu.(mu-1) <- m_Jnu.(mu-1) +.  pJ *. integral;
                m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral
              end
            done;
            for mu = sigma+1 to nu do
              m_Jnu.(mu-1) <-
                m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma
            done
          end
        | (false, true , _) ->
          for mu = 1 to sigma do
            m_Ksigma.(mu-1) <-
              m_Ksigma.(mu-1) +. pK *. ERI.get_phys m_G mu lambda nu sigma
          done
        | (true , false, _) ->
          for mu = 1 to nu do
            m_Jnu.(mu-1) <-
              m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma
          done
      done
    done;
    for mu = 1 to sigma-1 do
      m_K.(mu-1).(sigma-1) <- m_Ksigma.(mu-1);
    done
  done;
  for nu = 1 to nBas do
    let m_Jnu = m_J.(nu-1) in
    for mu = 1 to nu-1 do
      m_J.(mu-1).(nu-1) <- m_Jnu.(mu-1)
    done
  done;

  let m_J =  Mat.of_array m_J
  and m_K =  Mat.of_array m_K
  in
  { fock = Mat.add m_Hc (Mat.sub m_J m_K) ;
    core = m_Hc ; coulomb = m_J ; exchange = m_K }



let make_uhf ~density_same ~density_other ?(threshold=Constants.epsilon) ao_basis =
  let m_P_a  = density_same
  and m_P_b  = density_other
  and m_T  = Ao.kin_ints ao_basis |> KinInt.matrix 
  and m_V  = Ao.eN_ints  ao_basis |> NucInt.matrix
  and m_G  = Ao.ee_ints  ao_basis 
  in
  let nBas = Mat.dim1 m_T
  in

  let m_Hc = Mat.add m_T m_V 
  and m_J = Array.make_matrix nBas nBas 0.
  and m_K = Array.make_matrix nBas nBas 0.
  in

  for sigma = 1 to nBas do
    let m_Ksigma = m_K.(sigma-1) in
    for nu = 1 to nBas do
      let m_Jnu = m_J.(nu-1) in
      for lambda = 1 to nBas do
        let pJ = m_P_a.{lambda,sigma} +. m_P_b.{lambda,sigma}
        and pK = m_P_a.{lambda,nu}
        in
        match (abs_float pJ > threshold , abs_float pK > threshold, nu < sigma) with
        | (false, false, _) -> ()
        | (true , true , true) ->
          begin
            for mu = 1 to nu do
              let integral = 
                ERI.get_phys m_G mu lambda nu sigma
              in
              if (integral <> 0.) then begin
                m_Jnu.(mu-1) <- m_Jnu.(mu-1) +.  pJ *. integral;
                m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral
              end
            done;
            for mu = nu+1 to sigma do
              m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *.
                                                    ERI.get_phys m_G mu lambda nu sigma
            done
          end
        | (true , true , false) ->
          begin
            for mu = 1 to sigma do
              let integral = 
                ERI.get_phys m_G mu lambda nu sigma
              in
              if (integral <> 0.) then begin
                m_Jnu.(mu-1) <- m_Jnu.(mu-1) +.  pJ *. integral;
                m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral
              end
            done;
            for mu = sigma+1 to nu do
              m_Jnu.(mu-1) <-
                m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma
            done
          end
        | (false, true , _) ->
          for mu = 1 to sigma do
            m_Ksigma.(mu-1) <-
              m_Ksigma.(mu-1) +. pK *. ERI.get_phys m_G mu lambda nu sigma
          done
        | (true , false, _) ->
          for mu = 1 to nu do
            m_Jnu.(mu-1) <-
              m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma
          done
      done
    done;
    for mu = 1 to sigma-1 do
      m_K.(mu-1).(sigma-1) <- m_Ksigma.(mu-1);
    done
  done;
  for nu = 1 to nBas do
    let m_Jnu = m_J.(nu-1) in
    for mu = 1 to nu-1 do
      m_J.(mu-1).(nu-1) <- m_Jnu.(mu-1)
    done
  done;

  let m_J =  Mat.of_array m_J
  and m_K =  Mat.of_array m_K
  in
  { fock = Mat.add m_Hc (Mat.sub m_J m_K) ;
    core = m_Hc ; coulomb = m_J ; exchange = m_K }







let op ~f f1 f2 =
  assert (f1.core = f2.core);
  let m_Hc = f1.core
  and m_J = f f1.coulomb f2.coulomb
  and m_K = f f1.exchange f2.exchange
  in
  {
    fock     = Mat.add m_Hc (Mat.sub m_J m_K);
    core     = m_Hc;
    coulomb  = m_J;
    exchange = m_K;
  }


let add = op ~f:(fun a b -> Mat.add a b)

let sub = op ~f:(fun a b -> Mat.sub a b)

let scale alpha f1 = 
  let m_Hc = f1.core
  and m_J = lacpy f1.coulomb 
  and m_K = lacpy f1.exchange 
  in
  Mat.scal alpha m_J;
  Mat.scal alpha m_K;
  {
    fock     = Mat.add m_Hc (Mat.sub m_J m_K);
    core     = m_Hc;
    coulomb  = m_J;
    exchange = m_K;
  }



let pp ppf a =
  Format.fprintf ppf "@[<2>";
  Format.fprintf ppf "@[ Fock matrix:@[<2>@[%a@]@.]@]" pp_matrix a.fock;
  Format.fprintf ppf "@[ Core Hamiltonian:@[<2>@[%a@]@.]@]" pp_matrix a.core;
  Format.fprintf ppf "@[ Coulomb matrix:@[<2>@[%a@]@.]@]" pp_matrix a.coulomb;
  Format.fprintf ppf "@[ Exchange matrix:@[<2>@[%a@]@.]@]" pp_matrix a.exchange;
  Format.fprintf ppf "@]"