{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test of F12 matrix elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let png_image = print_endline ;;\n",
    "\n",
    "(* --------- *)\n",
    "\n",
    "#cd \"/home/scemama/QCaml\";;\n",
    "#use \"topfind\";;\n",
    "#require \"jupyter.notebook\";;\n",
    "\n",
    "let png_image name = \n",
    "    Jupyter_notebook.display_file ~base64:true \"image/png\" (\"Notebooks/images/\"^name)\n",
    ";;\n",
    "\n",
    "#require \"lacaml.top\";;\n",
    "#require \"alcotest\";;\n",
    "#require \"str\";;\n",
    "#require \"bigarray\";;\n",
    "#require \"zarith\";;\n",
    "#require \"getopt\";;\n",
    "#directory \"_build\";;\n",
    "#directory \"_build/Basis\";;\n",
    "#directory \"_build/CI\";;\n",
    "#directory \"_build/MOBasis\";;\n",
    "#directory \"_build/Nuclei\";;\n",
    "#directory \"_build/Parallel\";;\n",
    "#directory \"_build/Perturbation\";;\n",
    "#directory \"_build/SCF\";;\n",
    "#directory \"_build/Utils\";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#load \"Constants.cmo\";;\n",
    "#load_rec \"Util.cma\";;\n",
    "#load_rec \"Matrix.cmo\";;\n",
    "#load_rec \"Simulation.cmo\";;\n",
    "#load_rec \"Spindeterminant.cmo\";;\n",
    "#load_rec \"Determinant.cmo\";;\n",
    "#load_rec \"HartreeFock.cmo\";;\n",
    "#load_rec \"MOBasis.cmo\";;\n",
    "#load_rec \"F12CI.cmo\";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Printers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install_printer AngularMomentum.pp_string ;;\n",
    "#install_printer Basis.pp ;;\n",
    "#install_printer Charge.pp ;;\n",
    "#install_printer Coordinate.pp ;;\n",
    "#install_printer Vector.pp;;\n",
    "#install_printer Matrix.pp;;\n",
    "#install_printer Util.pp_float_2darray;;\n",
    "#install_printer Util.pp_float_array;;\n",
    "#install_printer Util.pp_matrix;;\n",
    "#install_printer HartreeFock.pp ;;\n",
    "#install_printer Fock.pp ;;\n",
    "#install_printer MOClass.pp ;;\n",
    "let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n",
    "#install_printer pp_mo;;\n",
    "(*\n",
    "#install_printer DeterminantSpace.pp;;\n",
    "*)\n",
    "#install_printer SpindeterminantSpace.pp;;\n",
    "#install_printer Bitstring.pp;;\n",
    "\n",
    "(* --------- *)\n",
    "\n",
    "open Lacaml.D\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let basis_filename  = \"/home/scemama/qp2/data/basis/6-31g\" \n",
    "let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n",
    "let nuclei = Nuclei.of_zmt_string \"c\" \n",
    "let frozen_core = false\n",
    "let multiplicity = 1\n",
    "let state = 1\n",
    "\n",
    "let basis =  Basis.of_nuclei_and_basis_filenames ~nuclei [basis_filename] \n",
    "let aux_basis =  Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n",
    "let f12 = F12factor.gaussian_geminal 1.0 \n",
    "let charge = 0 \n",
    "\n",
    "\n",
    "let simulation =\n",
    "    Simulation.make \n",
    "        ~f12 ~charge ~multiplicity ~nuclei\n",
    "        ~cartesian:true\n",
    "        basis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let n_elec_alfa, n_elec_beta, n_elec = \n",
    "  let e =  Simulation.electrons simulation in\n",
    "  Electrons.(n_alfa e, n_beta e, n_elec e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hartree-Fock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let hf =  HartreeFock.make ~guess:`Hcore ~max_scf:1 simulation  ;;\n",
    "\n",
    "let mo_basis = MOBasis.of_hartree_fock hf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FCI-F12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let f12 = Util.of_some @@ Simulation.f12 simulation \n",
    "\n",
    "let mo_num = MOBasis.size mo_basis \n",
    "\n",
    "let pp_spindet = Spindeterminant.pp mo_num\n",
    "\n",
    "let pp_det = Determinant.pp mo_num\n",
    "\n",
    ";;\n",
    "\n",
    "#install_printer pp_spindet ;;\n",
    "#install_printer pp_det ;;\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let simulation_aux = \n",
    "    let charge        = Charge.to_int @@ Simulation.charge simulation \n",
    "    and multiplicity  = Electrons.multiplicity @@ Simulation.electrons simulation\n",
    "    and nuclei        = Simulation.nuclei simulation\n",
    "    in\n",
    "    let general_basis = \n",
    "      Basis.general_basis @@ Simulation.basis simulation\n",
    "    in\n",
    "    GeneralBasis.combine [\n",
    "      general_basis ; GeneralBasis.read aux_basis_filename\n",
    "    ]\n",
    "    |> Basis.of_nuclei_and_general_basis nuclei\n",
    "    |> Simulation.make ~f12 ~charge ~multiplicity ~nuclei \n",
    "\n",
    "\n",
    "let aux_basis = \n",
    "  MOBasis.of_mo_basis simulation_aux mo_basis\n",
    "\n",
    "let aux_num = \n",
    "  MOBasis.size aux_basis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let () = ignore @@ MOBasis.f12_ints   aux_basis\n",
    "let () = ignore @@ MOBasis.two_e_ints aux_basis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integral-based functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "\\langle I | \\hat{H} | J \\rangle = \\begin{cases}\n",
    "\\sum_i h_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n",
    "h_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n",
    "\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\langle I | \\hat{F} | J \\rangle = \\begin{cases}\n",
    "\\sum_i f_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n",
    "f_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n",
    "\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n",
    "\\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let cancel_singles = false \n",
    "\n",
    "let mos_cabs = \n",
    "  Util.list_range (mo_num+1) aux_num\n",
    "  \n",
    "let mos_abs = \n",
    "  Util.list_range 1 aux_num\n",
    "  \n",
    "let mos_in = \n",
    "  Util.list_range 1 mo_num\n",
    "\n",
    "let mos_a k =\n",
    "  Determinant.alfa k\n",
    "  |> Spindeterminant.to_list\n",
    "  \n",
    "let mos_b k =\n",
    "  Determinant.beta k\n",
    "  |> Spindeterminant.to_list\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### H integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let h_one =\n",
    "  let h = \n",
    "    MOBasis.one_e_ints aux_basis\n",
    "  in fun i j _ -> h.{i,j}\n",
    "  \n",
    "let h_two = \n",
    "  let two_e_ints = MOBasis.two_e_ints aux_basis in\n",
    "  let h2 i j k l (s:Spin.t) (s':Spin.t) =\n",
    "    if s' <> s then\n",
    "        ERI.get_phys two_e_ints i j k l\n",
    "    else\n",
    "        (ERI.get_phys two_e_ints i j k l) -.                                                 \n",
    "        (ERI.get_phys two_e_ints i j l k)\n",
    "  in\n",
    "  h2\n",
    "\n",
    "    \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### F12 integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let f_two = \n",
    "  let two_e_ints = MOBasis.f12_ints aux_basis in\n",
    "  let f2 i j k l (s:Spin.t) (s':Spin.t) =\n",
    "    if s' <> s then\n",
    "        0.5 *. F12.get_phys two_e_ints i j k l\n",
    "    else\n",
    "        0.5 *. (\n",
    "         (F12.get_phys two_e_ints i j k l) -.                                                 \n",
    "         (F12.get_phys two_e_ints i j l k) )\n",
    "  in\n",
    "  let f3 i j k l (s:Spin.t) (s':Spin.t) = \n",
    "      if (i=k && j<>l) || (j=l && i<>k) then\n",
    "        0.\n",
    "      else\n",
    "        f2 i j k l s s'\n",
    "  in\n",
    "  if cancel_singles then f3 else f2\n",
    "\n",
    "let f_one = fun _ _ _ -> 0.\n",
    "\n",
    "(*\n",
    "let f_two = h_two\n",
    "\n",
    "let f_one = h_one\n",
    "*)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determinant-based functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let f12_integrals mo_basis =\n",
    "  ( f_one, f_two, None )\n",
    "\n",
    "let h_ij mo_basis ki kj =\n",
    "  let integrals =\n",
    "    List.map (fun f -> f mo_basis)\n",
    "      [ CI.h_integrals ]\n",
    "  in\n",
    "  CIMatrixElement.make integrals ki kj \n",
    "  |> List.hd\n",
    "\n",
    "\n",
    "let f_ij mo_basis ki kj =\n",
    "  let integrals =\n",
    "    List.map (fun f -> f mo_basis)\n",
    "      [ f12_integrals ]\n",
    "  in\n",
    "  CIMatrixElement.make integrals ki kj \n",
    "  |> List.hd                                                                                  \n",
    "\n",
    "\n",
    "let hf_ij mo_basis ki kj =\n",
    "  let integrals =\n",
    "    List.map (fun f -> f mo_basis)\n",
    "      [ CI.h_integrals ; f12_integrals ]\n",
    "  in\n",
    "  CIMatrixElement.make integrals ki kj\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determinant space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let is_a_double det_space =\n",
    "    let mo_class = DeterminantSpace.mo_class det_space in\n",
    "    let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
    "    let m l =\n",
    "      List.fold_left (fun accu i ->\n",
    "          let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
    "        ) (Bitstring.zero mo_num) l\n",
    "    in\n",
    "    let aux_mask   = m (MOClass.auxiliary_mos mo_class) in\n",
    "    fun k ->                                                                                  \n",
    "      let alfa =\n",
    "        Determinant.alfa k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let beta =\n",
    "        Determinant.beta k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let a = Bitstring.logand aux_mask alfa\n",
    "      and b = Bitstring.logand aux_mask beta\n",
    "      in\n",
    "      match Bitstring.popcount a + Bitstring.popcount b with\n",
    "      | 2 | 1 -> true\n",
    "      | 0 | _ -> false\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let in_space = \n",
    "    DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num\n",
    "    \n",
    "let aux_space = \n",
    "    DeterminantSpace.fci_of_mo_basis aux_basis ~frozen_core \n",
    "\n",
    "let det_space_in () =\n",
    "    DeterminantSpace.determinant_stream in_space\n",
    "\n",
    "let det_space_out () =\n",
    "    let s = \n",
    "        DeterminantSpace.determinant_stream aux_space\n",
    "    in\n",
    "    Stream.from (fun _ ->\n",
    "        try\n",
    "          let is_a_double = is_a_double in_space in\n",
    "          let rec result () =\n",
    "            let ki = Stream.next s in\n",
    "            if is_a_double ki then\n",
    "              Some (ki,ki)\n",
    "            else\n",
    "              result ()\n",
    "          in\n",
    "          result ()\n",
    "        with Stream.Failure -> None\n",
    "      )\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let ci = CI.make ~n_states:state in_space\n",
    "\n",
    "let ci_coef, ci_energy = Lazy.force ci.eigensystem \n",
    "\n",
    "let _ = print_newline () \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "let p12 det_space =\n",
    "    let mo_class = DeterminantSpace.mo_class det_space in\n",
    "    let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n",
    "    let m l =\n",
    "      List.fold_left (fun accu i ->\n",
    "          let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
    "        ) (Bitstring.zero mo_num) l\n",
    "    in\n",
    "    let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
    "    let not_aux_mask =\n",
    "      Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask)\n",
    "    in\n",
    "    fun k ->\n",
    "      let alfa =\n",
    "        Determinant.alfa k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let beta =\n",
    "        Determinant.beta k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let a = Bitstring.logand aux_mask alfa\n",
    "      and b = Bitstring.logand aux_mask beta\n",
    "      in\n",
    "      match Bitstring.popcount a, Bitstring.popcount b with\n",
    "      | 2, 0  \n",
    "      | 0, 2 -> Some (Determinant.negate_phase k)\n",
    "      | 1, 1 -> Some (Determinant.of_spindeterminants\n",
    "                  (Spindeterminant.of_bitstring  @@\n",
    "                    Bitstring.(logor b (logand not_aux_mask alfa)) )\n",
    "                  (Spindeterminant.of_bitstring  @@\n",
    "                    Bitstring.(logor a (logand not_aux_mask beta))\n",
    "                  ) )\n",
    "      | 1, 0 \n",
    "      | 0, 1 -> Some k\n",
    "      | _ -> None\n",
    "                    \n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "let randomize = false\n",
    "\n",
    "let out_list =\n",
    "    Util.stream_to_list (det_space_out ())\n",
    "    \n",
    "let in_list =\n",
    "    Util.stream_to_list (det_space_in ())\n",
    "    \n",
    "let det_a = Array.of_list out_list\n",
    "            |> Array.map (fun (i,_) -> i)\n",
    "\n",
    "let det_I =\n",
    "  if randomize then\n",
    "    let n = 123456789 in\n",
    "    in_list\n",
    "    |> List.map (fun k -> (Random.int n, k))\n",
    "    |> List.sort compare\n",
    "    |> List.map  (fun (_,k) -> k)\n",
    "    |> Array.of_list\n",
    "  else\n",
    "    Array.of_list in_list\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/markdown"
   },
   "source": [
    "let m_H_aux, m_F_aux = \n",
    "        \n",
    "    let rec col_vecs_list accu_H accu_F = function\n",
    "    | [] -> \n",
    "        List.rev accu_H, \n",
    "        List.rev accu_F \n",
    "    | (ki, ki') :: rest when ki = ki' ->\n",
    "        begin\n",
    "            let h, f = \n",
    "              List.map (fun kj ->\n",
    "              match hf_ij aux_basis kj ki with\n",
    "              | [ a ; b ] -> a, b\n",
    "              | _ -> assert false ) in_list\n",
    "              |> List.split\n",
    "            in\n",
    "            let h  = Vec.of_list h in\n",
    "            let f  = Vec.of_list f in\n",
    "            scal 0.5 f;  (* Specific to He singlet *)\n",
    "            col_vecs_list (h::accu_H) (f::accu_F) rest\n",
    "        end\n",
    "    | (ki, ki') :: rest ->\n",
    "        begin\n",
    "        assert false;\n",
    "        end\n",
    "    in\n",
    "    let h, f = \n",
    "      col_vecs_list [] [] out_list\n",
    "    in\n",
    "    Mat.of_col_vecs_list h,\n",
    "    Mat.of_col_vecs_list f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function to generate all intermediate external determinants $|\\alpha \\rangle$ between $|I\\rangle$ and $|J\\rangle$, with a positive phase factor.\n",
    "\n",
    "* `exc` is the degree of excitation between $|I\\rangle$ and $|J\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let generate_alphas ki kj exc =\n",
    "  (* Check input excitation degree *)\n",
    "  let d = Determinant.degree ki kj in\n",
    "  if d <> exc then\n",
    "    Printf.sprintf \"Invalid excitation degree. Expected %d and found %d.\" exc d\n",
    "    |> failwith;\n",
    "    \n",
    "  (* Generate single excitations *)\n",
    "  let all_singles ki =\n",
    "      let mos_a, mos_b = Determinant.to_lists ki in\n",
    "      [ List.map (fun hole -> \n",
    "          List.map (fun particle ->\n",
    "               if hole = particle then None else\n",
    "                  Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n",
    "              ) mos_abs\n",
    "          ) mos_a\n",
    "      ;\n",
    "        List.map (fun hole -> \n",
    "          List.map (fun particle ->\n",
    "               if hole = particle then None else\n",
    "                 Some (Determinant.single_excitation Spin.Beta hole particle ki)\n",
    "              ) mos_abs\n",
    "          ) mos_b \n",
    "      ]\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> Util.list_some\n",
    "      |> List.filter (fun x -> Determinant.is_none x = false)\n",
    "      |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
    "  in\n",
    "  \n",
    "  (* Generate double excitations *)\n",
    "  let all_doubles ki =\n",
    "      let mos_a, mos_b = Determinant.to_lists ki in\n",
    "      [ List.map (fun hole ->  (* Alpha-Alpha *)\n",
    "          List.map (fun particle ->\n",
    "            List.map (fun hole' -> \n",
    "              List.map (fun particle' ->\n",
    "                if hole = particle || hole' = particle' then None else\n",
    "                if hole' > hole && particle' < particle then\n",
    "                  Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
    "                else None\n",
    "                      ) mos_abs\n",
    "                  ) mos_a \n",
    "              ) mos_abs\n",
    "          ) mos_a\n",
    "        ; \n",
    "        List.map (fun hole ->  (* Beta-Beta *)\n",
    "          List.map (fun particle ->\n",
    "            List.map (fun hole' -> \n",
    "              List.map (fun particle' ->\n",
    "                if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then\n",
    "                  Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n",
    "                else None\n",
    "                      ) mos_abs\n",
    "                  ) mos_b \n",
    "              ) mos_abs\n",
    "          ) mos_b\n",
    "        ;\n",
    "        List.map (fun hole ->  (* Alpha-Beta *)\n",
    "          List.map (fun particle ->\n",
    "            List.map (fun hole' -> \n",
    "              List.map (fun particle' ->\n",
    "                  if hole = particle || hole' = particle' then None else\n",
    "                  Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n",
    "                      ) mos_abs\n",
    "                  ) mos_b \n",
    "              ) mos_abs\n",
    "          ) mos_a\n",
    "      ]\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> Util.list_some\n",
    "      |> List.filter (fun x -> Determinant.is_none x = false)\n",
    "      |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
    "  in\n",
    "\n",
    "  (* Generate left and right excitations *)\n",
    "  let al = List.concat [ all_singles ki ; all_doubles ki ] in\n",
    "  let ar = List.concat [ all_singles kj ; all_doubles kj ] in\n",
    "  \n",
    "  let mo_class = DeterminantSpace.mo_class in_space in\n",
    "  let m l =\n",
    "    List.fold_left (fun accu i ->\n",
    "        let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
    "      ) (Bitstring.zero mo_num) l\n",
    "  in\n",
    "  let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
    "  let good_cabs k = \n",
    "      let alfa =\n",
    "        Determinant.alfa k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let beta =\n",
    "        Determinant.beta k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let a = Bitstring.logand aux_mask alfa\n",
    "      and b = Bitstring.logand aux_mask beta\n",
    "      in\n",
    "      match Bitstring.popcount a + Bitstring.popcount b with\n",
    "      | 1 | 2 -> true\n",
    "      | _ -> false\n",
    "  in\n",
    "  \n",
    "  (* Merge lists in a set of unique determinants *)\n",
    "  List.concat [ al; ar ]\n",
    "  |> List.sort_uniq compare\n",
    "  \n",
    "  (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n",
    "  |> List.filter good_cabs \n",
    "  \n",
    "  \n",
    "let compute_HaaF ki alphas kj =\n",
    "   List.fold_left (fun accu alpha -> accu\n",
    "      +. h_ij aux_basis ki alpha\n",
    "      *. f_ij aux_basis alpha kj\n",
    "    ) 0. alphas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let check n integral_value exc =\n",
    "  let cpudet, cpuint = ref 0., ref 0. in\n",
    "  let det_list =\n",
    "      match n with\n",
    "        | 0 -> det_I\n",
    "        | n -> Array.sub det_I 0 n\n",
    "  in\n",
    "  let result =\n",
    "        Printf.printf \"Checking ... \\n%!\";\n",
    "        let percent = ref 0 in\n",
    "        let task (i,ki) =\n",
    "            (let p = (10 * (i+1))/(Array.length det_list) in\n",
    "            if p <> !percent then\n",
    "                ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) ));\n",
    "            Array.mapi (fun j kj -> \n",
    "                if i > j || Determinant.degree ki kj <> exc then\n",
    "                    (0,0,0.,0.)\n",
    "                else\n",
    "                  begin\n",
    "                    let alphas = generate_alphas ki kj exc in\n",
    "                    let det_value =\n",
    "                      let t0 = Unix.gettimeofday () in\n",
    "                      let result = compute_HaaF ki alphas kj in\n",
    "                      cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n",
    "                      result\n",
    "                    in\n",
    "                    let int_value = \n",
    "                      let t0 = Unix.gettimeofday () in\n",
    "                      let result = integral_value ki kj in\n",
    "                      cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n",
    "                      result\n",
    "                    in\n",
    "(*   Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value;  *)\n",
    "                    (i,j,det_value,int_value)\n",
    "                  end\n",
    "            ) det_list\n",
    "        in\n",
    "        det_list\n",
    "        |> Array.mapi (fun i ki -> (i,ki))\n",
    "        |> Array.to_list\n",
    "        |> Stream.of_list\n",
    "        |> Farm.run ~f:task\n",
    "        |> Util.stream_to_list\n",
    "        |> Array.concat\n",
    "  in\n",
    "  let i,j,d,v = \n",
    "      let rec aux k imax jmax emax dmax vmax = \n",
    "        if k = -1 then\n",
    "          imax, jmax, dmax, vmax\n",
    "        else\n",
    "          let i, j, d, v = result.(k) in\n",
    "          let e = abs_float (d -. v) in\n",
    "          if e >= emax then\n",
    "            aux (k-1) i j e d v\n",
    "          else\n",
    "            aux (k-1) imax jmax emax dmax vmax\n",
    "      in\n",
    "      aux (Array.length result - 1) 0 0 0. 0. 0.\n",
    "  in\n",
    "  let error = abs_float (d -. v) in\n",
    "  if error < epsilon_float then\n",
    "  (*\n",
    "      Printf.printf \"OK: %e\\n%!\" error\n",
    "      *)\n",
    "      Printf.printf \"OK: (%d, %d) | %e %e | %e  |  cpu : %f  %f\\n%!\" i j d v error !cpudet !cpuint\n",
    "  else\n",
    "      Printf.printf \"Failed: (%d, %d) | %e %e | %e  |  cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n",
    "\n",
    "    \n",
    "let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let array_3_init d1 d2 d3 f =\n",
    "  let result = \n",
    "      Bigarray.(Array3.create Float64 fortran_layout) d1 d2 d3\n",
    "  in\n",
    "  for k=1 to d3 do\n",
    "      for j=1 to d2 do\n",
    "          for i=1 to d1 do\n",
    "             result.{i,j,k} <- f i j k\n",
    "          done\n",
    "      done\n",
    "  done;\n",
    "  result\n",
    "\n",
    "\n",
    "let array_4_init d1 d2 d3 d4 f =\n",
    "  let result = \n",
    "      Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |]\n",
    "  in\n",
    "  for l=1 to d4 do\n",
    "    for k=1 to d3 do\n",
    "      for j=1 to d2 do\n",
    "        for i=1 to d1 do\n",
    "           result.{i,j,k,l} <- f i j k l\n",
    "        done\n",
    "      done\n",
    "    done\n",
    "  done;\n",
    "  result\n",
    "\n",
    "\n",
    "let array_5_init d1 d2 d3 d4 d5 f =\n",
    "  let result = \n",
    "      Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |]\n",
    "  in\n",
    "  for m=1 to d5 do\n",
    "    for l=1 to d4 do\n",
    "      for k=1 to d3 do\n",
    "        for j=1 to d2 do\n",
    "          for i=1 to d1 do\n",
    "             result.{i,j,k,l,m} <- f i j k l m\n",
    "          done\n",
    "        done\n",
    "      done\n",
    "    done\n",
    "  done;\n",
    "  result\n",
    "\n",
    "(* ----- *)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "******"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let m_0111_1H_1F = \n",
    "  Vec.init mo_num (fun i -> \n",
    "        sum mos_cabs (fun a ->\n",
    "            h_one i a Spin.Alfa *. f_one a i Spin.Alfa ))\n",
    "\n",
    "let m_0111_1H_2Fa, m_0111_2Ha_2Fa =\n",
    "\n",
    "    let m_0122_Haa = \n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "          sum mos_cabs (fun a ->\n",
    "            h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa\n",
    "            ) )\n",
    "    in      \n",
    "    \n",
    "    let m_0111_1H_2Fa = \n",
    "      Mat.init_cols mo_num mo_num (fun i j ->\n",
    "          sum mos_cabs (fun a ->\n",
    "            h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa +.\n",
    "            h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa\n",
    "          ) +.\n",
    "          if i < j then 0. else\n",
    "              begin\n",
    "                  sum mos_cabs (fun a ->\n",
    "                      sum mos_cabs (fun b -> if b >= a then 0. else\n",
    "                        h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa\n",
    "                      )\n",
    "                  ) +.\n",
    "                  sum mos_in (fun k -> m_0122_Haa.{i,j,k}) \n",
    "              end\n",
    "      )\n",
    "    in\n",
    "    \n",
    "    let m_0111_2Ha_2Fa =\n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "          f_two a k i k Spin.Alfa Spin.Alfa \n",
    "        ) -. if i < j then 0. else m_0122_Haa.{i,j,k}\n",
    "      )\n",
    "    in m_0111_1H_2Fa, m_0111_2Ha_2Fa\n",
    "\n",
    "\n",
    "    \n",
    "let m_0111_1H_2Fb, m_0111_2Hb_2Fb =\n",
    "    let m_0122_Hab = \n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "          sum mos_cabs (fun a ->\n",
    "             h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta\n",
    "          ) )\n",
    "    in\n",
    "    \n",
    "    let m_0111_1H_2Fb = \n",
    "      Mat.init_cols mo_num mo_num (fun i j ->\n",
    "          sum mos_cabs (fun a ->\n",
    "            h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta +. \n",
    "            h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa +.\n",
    "            h_one j a Spin.Alfa *. f_two a i j i Spin.Alfa Spin.Beta +. \n",
    "            h_two j i a i Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa\n",
    "          ) +.\n",
    "        sum mos_in (fun k -> m_0122_Hab.{i,j,k} +. m_0122_Hab.{j,i,k} ) +.\n",
    "        sum mos_cabs (fun a ->\n",
    "            sum mos_cabs (fun b ->\n",
    "            h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta\n",
    "            )\n",
    "          )\n",
    "        )\n",
    "    in    \n",
    "    \n",
    "    let m_0111_2Hb_2Fb =\n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two k i a i Spin.Alfa Spin.Beta *.\n",
    "          f_two a j k j Spin.Alfa Spin.Beta +.\n",
    "          h_two i k a k Spin.Alfa Spin.Beta *.\n",
    "          f_two a j i j Spin.Alfa Spin.Alfa \n",
    "        ) -. m_0122_Hab.{k,i,j}\n",
    "      )\n",
    "    in\n",
    "    m_0111_1H_2Fb, m_0111_2Hb_2Fb\n",
    "    \n",
    "\n",
    "let m_0111_2Ha_2Fb =\n",
    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "      f_two a k i k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "let integral_value ki kj = \n",
    "\n",
    "   let mos_i, mos_i' = mos_a ki, mos_b ki in\n",
    "   let same = (mos_i = mos_i') in\n",
    "   \n",
    "   (* Alpha *)\n",
    "   let a = \n",
    "       sum mos_i  (fun i -> m_0111_1H_1F.{i}) \n",
    "   in\n",
    "   \n",
    "   let b = \n",
    "       if same then a else\n",
    "       sum mos_i' (fun i -> m_0111_1H_1F.{i})\n",
    "   in\n",
    "   \n",
    "   let aa = \n",
    "       sum mos_i (fun j ->\n",
    "         sum mos_i (fun i -> m_0111_1H_2Fa.{i,j} ))\n",
    "   in\n",
    "   \n",
    "   let bb = \n",
    "     if same then aa else\n",
    "     sum mos_i' (fun j ->\n",
    "       sum mos_i' (fun i -> m_0111_1H_2Fa.{i,j} ))\n",
    "   in\n",
    "   \n",
    "   let ab = \n",
    "     sum mos_i' (fun j ->\n",
    "       sum mos_i (fun i -> m_0111_1H_2Fb.{i,j}  )) \n",
    "   in\n",
    "   \n",
    "   let aaa = \n",
    "       sum mos_i (fun k ->\n",
    "         sum mos_i (fun j ->\n",
    "           sum mos_i (fun i -> m_0111_2Ha_2Fa.{i,j,k} ))) \n",
    "   in\n",
    "   \n",
    "   let bbb = \n",
    "     if same then aaa else\n",
    "       sum mos_i' (fun k ->\n",
    "         sum mos_i' (fun j ->\n",
    "           sum mos_i' (fun i -> m_0111_2Ha_2Fa.{i,j,k} )))\n",
    "   in\n",
    "   \n",
    "   let baa = \n",
    "       sum mos_i' (fun k ->\n",
    "         sum mos_i (fun j ->\n",
    "           sum mos_i (fun i ->\n",
    "             m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{i,j,k}\n",
    "       )))\n",
    "   in\n",
    "   \n",
    "   let bba = \n",
    "       sum mos_i  (fun k ->\n",
    "         sum mos_i' (fun j ->\n",
    "           sum mos_i' (fun i ->\n",
    "             m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{j,i,k} \n",
    "       ))) \n",
    "   in\n",
    "\n",
    "   a +. b +. aa +. bb +. ab +. aaa +. baa +. bba +. bbb\n",
    "   \n",
    "     \n",
    "let _ =\n",
    "  check 0 integral_value 0 \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let m_1111_1H_1F = \n",
    "  Mat.init_cols mo_num mo_num (fun i k -> \n",
    "        sum mos_cabs (fun a -> h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "let m_1111_2Ha_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    if l=i then\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two j l a l Spin.Alfa Spin.Alfa *.\n",
    "          f_two a i j k Spin.Alfa Spin.Alfa \n",
    "        )\n",
    "    else\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "          f_two a l k l Spin.Alfa Spin.Alfa +.\n",
    "          h_two j l a l Spin.Alfa Spin.Alfa *.\n",
    "          f_two a i j k Spin.Alfa Spin.Alfa )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "let m_1111_2Hb_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    if l=i then\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two j l a l Spin.Alfa Spin.Beta *.\n",
    "          f_two a i j k Spin.Alfa Spin.Beta \n",
    "        )\n",
    "    else\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two i j a j Spin.Alfa Spin.Beta *.\n",
    "          f_two a l k l Spin.Alfa Spin.Alfa +.\n",
    "          h_two j l a l Spin.Alfa Spin.Beta *.\n",
    "          f_two a i j k Spin.Alfa Spin.Beta \n",
    "        )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1111_2Ha_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "      f_two a l k l Spin.Alfa Spin.Beta +.\n",
    "      h_two j l a l Spin.Alfa Spin.Beta *.\n",
    "      f_two a i j k Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "let m_1111_2Hb_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a j Spin.Alfa Spin.Beta *.\n",
    "      f_two a l k l Spin.Alfa Spin.Beta +.\n",
    "      h_two j l a l Spin.Alfa Spin.Alfa *.\n",
    "      f_two a i j k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "\n",
    "let m_1121_2Ha_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
    "      f_two l a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1121_2Hb_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two l a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1121_2Ha_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
    "      f_two l a l j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1121_2Hb_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two l a l j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1122_va =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j i a l Spin.Alfa Spin.Alfa *.\n",
    "      f_two l a k j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "  \n",
    "let m_1111_1H_2Fa = \n",
    "  array_3_init mo_num mo_num mo_num (fun j i k ->\n",
    "      sum mos_in (fun l -> m_1122_va.{l,j,i,k}) +.\n",
    "      sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa +.\n",
    "        h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n",
    "        h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa +.\n",
    "        h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa +.\n",
    "        sum mos_cabs (fun b -> if b > a then 0. else\n",
    "          h_two i j a b Spin.Alfa Spin.Alfa *.\n",
    "          f_two a b k j Spin.Alfa Spin.Alfa )\n",
    "      )\n",
    "    )\n",
    "\n",
    "\n",
    "let m_1122_v2 =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j l a Spin.Alfa Spin.Beta *.\n",
    "      f_two l a k j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1122_v3 =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a l Spin.Alfa Spin.Beta *.\n",
    "      f_two a l k j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "  \n",
    "let m_1111_1H_2Fb = \n",
    "  array_3_init mo_num mo_num mo_num (fun j i k ->\n",
    "      sum mos_in (fun l -> m_1122_v2.{l,j,i,k} +. m_1122_v3.{l,j,i,k}) +.\n",
    "      sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta +.\n",
    "        h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n",
    "        h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta +.\n",
    "        h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta +.\n",
    "        sum mos_cabs (fun b ->\n",
    "          h_two i j a b Spin.Alfa Spin.Beta *.\n",
    "          f_two a b k j Spin.Alfa Spin.Beta \n",
    "        )\n",
    "      )\n",
    "    )\n",
    "  \n",
    "let m_1122_oa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "  if l > j then\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j l a k Spin.Alfa Spin.Alfa *.\n",
    "      f_two i a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  else 0.\n",
    "  )\n",
    "\n",
    "let m_1122_o =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two l j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two i a l j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "  \n",
    "\n",
    "\n",
    "(*----*)\n",
    "\n",
    "let integral_value ki kj = \n",
    "    let i, k, s, phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
    "            hole, particle, spin, phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "    \n",
    "    let mos_novirt, mos_novirt' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      let beta  = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let mos_ij, mos_ij' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      let beta  = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let mos_i, mos_i' =\n",
    "      match s with\n",
    "      | Spin.Alfa -> mos_a ki, mos_b ki\n",
    "      | Spin.Beta -> mos_b ki, mos_a ki\n",
    "    in\n",
    "   \n",
    "    let mos_j, mos_j' =\n",
    "      match s with\n",
    "      | Spin.Alfa -> mos_a kj, mos_b kj\n",
    "      | Spin.Beta -> mos_b kj, mos_a kj\n",
    "    in\n",
    "   \n",
    "    let result = \n",
    "     m_1111_1H_1F.{i,k} +. \n",
    "     sum mos_ij (fun j -> \n",
    "          m_1111_1H_2Fa.{j,i,k} \n",
    "       +. sum mos_i  (fun l -> m_1111_2Ha_2Fa.{l,j,i,k})\n",
    "       +. sum mos_i' (fun l -> m_1111_2Ha_2Fb.{l,j,i,k})\n",
    "       +. sum mos_j  (fun l -> m_1121_2Ha_2Fa.{l,j,i,k})\n",
    "       +. sum mos_j' (fun l -> m_1121_2Ha_2Fb.{l,j,i,k})\n",
    "       -. sum mos_novirt (fun l -> m_1122_va.{l,j,i,k})\n",
    "       -. sum mos_ij (fun l -> m_1122_oa.{l,j,i,k} )\n",
    "       ) +.\n",
    "     sum mos_ij' (fun j ->\n",
    "          m_1111_1H_2Fb.{j,i,k} \n",
    "       +. sum mos_i  (fun l -> m_1111_2Hb_2Fa.{l,j,i,k})\n",
    "       +. sum mos_i' (fun l -> m_1111_2Hb_2Fb.{l,j,i,k})\n",
    "       +. sum mos_j  (fun l -> m_1121_2Hb_2Fb.{l,j,i,k})\n",
    "       +. sum mos_j' (fun l -> m_1121_2Hb_2Fa.{l,j,i,k})\n",
    "       -. sum mos_novirt  (fun l ->  m_1122_v2.{l,j,i,k}) \n",
    "       -. sum mos_novirt' (fun l ->  m_1122_v3.{l,j,i,k})\n",
    "       -. sum mos_ij    (fun l ->  m_1122_o.{l,j,i,k})\n",
    "       ) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "(*\n",
    "let ki = det_I.(77)\n",
    "let kj = det_I.(83)\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "let _ = \n",
    "    let alphas =  generate_alphas ki kj 1 1\n",
    "    in compute_HaaF ki alphas kj\n",
    "*)\n",
    "\n",
    "let _ = check 100 integral_value 1 \n",
    "\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Timing : 40.020974 0.019294"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_2112_1H_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_1H_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2121_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2121_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2121_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Ha_2Fa_ij :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_ij :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_ij2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Ha_2Fa_ij2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Ha_2Fa_nv :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_nv :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_nv2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking ... \n",
      " -  10 %\n",
      " -  20 %\n",
      " -  30 %\n",
      " -  40 %\n",
      " -  50 %\n",
      " -  60 %\n",
      " -  70 %\n",
      " -  80 %\n",
      " -  90 %\n",
      " - 100 %\n",
      "OK: (2, 45) | 2.332967e-02 2.332967e-02 | 2.428613e-17  |  cpu : 109.679883  0.039116\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val ki : Determinant.t =\n",
       "  phase:+1\n",
       "  a:+1 +--++-----------------------------------------------------------\n",
       "  b:+1 +++-------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val kj : Determinant.t =\n",
       "  phase:+1\n",
       "  a:+1 +-+-+-----------------------------------------------------------\n",
       "  b:+1 ++-+------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : float = 0.000896378780435275082\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : float = 0.000896378780435274107\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let m_2112_1H_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n",
    "        h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa +. \n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n",
    "        h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa +.\n",
    "        sum mos_in  (fun m -> -. h_two i j a m Spin.Alfa Spin.Alfa *.\n",
    "                                 f_two m a k l Spin.Alfa Spin.Alfa) +.\n",
    "        sum mos_cabs (fun b -> if b >= a then 0. else\n",
    "            h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b k l Spin.Alfa Spin.Alfa \n",
    "        )\n",
    "      )\n",
    "    )\n",
    "\n",
    "let m_2112_1H_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n",
    "        h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta +.\n",
    "        h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n",
    "        h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa +.\n",
    "        sum mos_in (fun m ->\n",
    "          h_two i j a m Spin.Alfa Spin.Beta *.  f_two a m k l Spin.Alfa Spin.Beta +.\n",
    "          h_two i j m a Spin.Alfa Spin.Beta *.  f_two m a k l Spin.Alfa Spin.Beta ) +.\n",
    "        sum mos_cabs (fun b -> \n",
    "            h_two i j a b Spin.Alfa Spin.Beta *. f_two a b k l Spin.Alfa Spin.Beta \n",
    "        )\n",
    "      )\n",
    "    )\n",
    "\n",
    "let m_2112_2Ha_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +. \n",
    "        h_two j n a n Spin.Alfa Spin.Alfa *. f_two a i l k Spin.Alfa Spin.Alfa \n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Hb_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Beta *. f_two a j k l Spin.Alfa Spin.Alfa +.\n",
    "        h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Alfa \n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Ha_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n",
    "        h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Beta )\n",
    "    )\n",
    "    \n",
    "    \n",
    "let m_2121_2Ha_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Alfa +.\n",
    "        h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Alfa \n",
    "      )\n",
    "    )\n",
    "    \n",
    "\n",
    "let m_2121_2Hb_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Beta *. f_two a n k n Spin.Alfa Spin.Alfa +.\n",
    "        h_two j i a k Spin.Alfa Spin.Beta *. f_two a n l n Spin.Alfa Spin.Beta \n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2121_2Ha_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Beta +.\n",
    "        h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Beta \n",
    "      )\n",
    "    )\n",
    "    \n",
    "\n",
    "let m_2122_2Ha_2Fa_ij =\n",
    "  let s = Spin.Alfa in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "           h_two i n a k s s  *.  f_two j a n l s s \n",
    "        +. h_two i n a l s s  *.  f_two j a k n s s \n",
    "        -. h_two j n a k s s  *.  f_two i a n l s s   \n",
    "        -. h_two j n a l s s  *.  f_two i a k n s s\n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2122_2Hb_2Fb_ij =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "          h_two n i a k s  s  *.  f_two a j n l s  s'\n",
    "       +. h_two n j a l s  s' *.  f_two i a k n s  s \n",
    "       -. h_two n j k a s  s' *.  f_two i a n l s  s'\n",
    "    )\n",
    "  )\n",
    "    \n",
    "let m_2122_2Hb_2Fb_ij2 =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      -. h_two i n a l s  s' *.  f_two a j k n s  s' +.\n",
    "      (if n < j then\n",
    "                  h_two i n k a s  s' *.  f_two j a l n s' s'\n",
    "               +. h_two n j a l s' s' *.  f_two i a k n s  s'\n",
    "       else \n",
    "               -. h_two i n k a s  s' *.  f_two j a n l s' s' \n",
    "               -. h_two j n a l s' s' *.  f_two i a k n s  s'\n",
    "      )\n",
    "    )\n",
    "  )\n",
    "    \n",
    "let m_2122_2Ha_2Fa_ij2 =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "         h_two i n k a s s' *.  f_two j a l n s s'\n",
    "      +. h_two j n l a s s' *.  f_two i a k n s s'\n",
    "      -. h_two i n l a s s' *.  f_two j a k n s s'\n",
    "      -. h_two j n k a s s' *.  f_two i a l n s s'\n",
    "      )\n",
    "    ) \n",
    "    \n",
    "let m_2122_2Ha_2Fa_nv =\n",
    "  let s = Spin.Alfa in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a -> h_two i j a n s  s  *.  f_two n a k l s  s ) ) \n",
    "    \n",
    "    \n",
    "    \n",
    "let m_2122_2Hb_2Fb_nv =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a -> -. h_two i j a n s s'  *.  f_two a n k l s s' ) ) \n",
    "    \n",
    "let m_2122_2Hb_2Fb_nv2 =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a -> -. h_two i j n a s s'  *.  f_two n a k l s s' ) ) \n",
    "    \n",
    "    \n",
    "    \n",
    "let integral_value ki kj = \n",
    "    let i, j, k, l, s, s', phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
    "            hole, hole', particle, particle', spin, spin', phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "    let mos_i, mos_i' =\n",
    "       match s with\n",
    "       | Spin.Alfa -> mos_a ki, mos_b ki\n",
    "       | Spin.Beta -> mos_b ki, mos_a ki\n",
    "    in\n",
    "    \n",
    "    let mos_j, mos_j' =\n",
    "       match s with\n",
    "       | Spin.Alfa -> mos_a kj, mos_b kj\n",
    "       | Spin.Beta -> mos_b kj, mos_a kj\n",
    "    in\n",
    "    \n",
    "    let mos_ij, mos_ij' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      let beta  =  \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let mos_novirt, mos_novirt' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      let beta  = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let result = \n",
    "       if s = s' then\n",
    "         m_2112_1H_2Fa.{i,j,k,l} +. \n",
    "         sum mos_i      (fun n -> m_2112_2Ha_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_i'     (fun n -> m_2112_2Hb_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_j      (fun n -> m_2121_2Ha_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_j'     (fun n -> m_2121_2Ha_2Fb.{n,i,j,k,l} ) +.\n",
    "         sum mos_ij     (fun n -> m_2122_2Ha_2Fa_ij.{n,i,j,k,l} ) +. \n",
    "         sum mos_ij'    (fun n -> m_2122_2Ha_2Fa_ij2.{n,i,j,k,l} ) +. \n",
    "         sum mos_novirt (fun n -> m_2122_2Ha_2Fa_nv.{n,i,j,k,l} ) \n",
    "       else\n",
    "         m_2112_1H_2Fb.{i,j,k,l} +. \n",
    "         sum mos_i      (fun n -> m_2112_2Ha_2Fb.{n,i,j,k,l} ) +.\n",
    "         sum mos_i'     (fun n -> m_2112_2Ha_2Fb.{n,j,i,l,k} ) +.\n",
    "         sum mos_j      (fun n -> m_2121_2Hb_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_j'     (fun n -> m_2121_2Hb_2Fa.{n,j,i,l,k} ) +.\n",
    "         sum mos_novirt'(fun n -> m_2122_2Hb_2Fb_nv.{n,i,j,k,l} ) +.\n",
    "         sum mos_novirt (fun n -> m_2122_2Hb_2Fb_nv2.{n,i,j,k,l} )+.\n",
    "         sum mos_ij     (fun n -> m_2122_2Hb_2Fb_ij.{n,i,j,k,l} ) +. \n",
    "         sum mos_ij'    (fun n -> m_2122_2Hb_2Fb_ij2.{n,i,j,k,l} ) \n",
    "     in\n",
    "\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "let _ = check 100  integral_value 2 \n",
    "\n",
    "let ki = det_I.(7)\n",
    "let kj = det_I.(89)\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "let _ = \n",
    "    let alphas =  generate_alphas ki kj 2 \n",
    "    in compute_HaaF ki alphas kj\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking ... \n",
      " -  10 %\n",
      " -  20 %\n",
      " -  30 %\n",
      " -  40 %\n",
      " -  50 %\n",
      " -  60 %\n",
      " -  70 %\n",
      " -  80 %\n",
      " -  90 %\n",
      " - 100 %\n",
      "OK: (13, 52) | 6.122906e-04 6.122906e-04 | 3.252607e-19  |  cpu : 77.238524  0.119682\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let integral_value ki kj = \n",
    "    let i, j, m, k, l, n, s1, s2, s3, phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Triple (phase,\n",
    "              { hole=h1 ; particle=p1 ; spin=s1 },\n",
    "              { hole=h2 ; particle=p2 ; spin=s2 },\n",
    "              { hole=h3 ; particle=p3 ; spin=s3 }) )  -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "\n",
    "    let result = \n",
    "       let open Spin in \n",
    "       match s1, s2, s3 with\n",
    "       | Alfa, Alfa, Alfa\n",
    "       | Beta, Beta, Beta -> \n",
    "           sum mos_cabs (fun a -> \n",
    "                h_two i j a k s1 s2 *.  f_two m a l n s3 s3 \n",
    "             +. h_two i j a n s1 s2 *.  f_two m a k l s3 s2 \n",
    "             +. h_two i m a l s1 s3 *.  f_two j a k n s2 s3 \n",
    "             +. h_two j m a k s2 s3 *.  f_two i a l n s1 s3 \n",
    "             +. h_two j m a n s2 s3 *.  f_two i a k l s1 s2 \n",
    "             -. h_two i j a l s1 s2 *.  f_two m a k n s3 s3 \n",
    "             -. h_two i m a k s1 s3 *.  f_two j a l n s2 s3 \n",
    "             -. h_two i m a n s1 s3 *.  f_two j a k l s2 s2 \n",
    "             -. h_two j m a l s2 s3 *.  f_two i a k n s1 s3 )\n",
    "       | Alfa, Alfa, Beta\n",
    "       | Beta, Beta, Alfa -> \n",
    "           sum mos_cabs (fun a -> \n",
    "                h_two i j a l s1 s2 *.  f_two a m k n s1 s3\n",
    "             +. h_two i m k a s1 s3 *.  f_two j a l n s2 s3\n",
    "             +. h_two j m a n s2 s3 *.  f_two i a k l s1 s2 \n",
    "             +. h_two j m l a s2 s3 *.  f_two i a k n s1 s3\n",
    "             -. h_two i j a k s1 s2 *.  f_two a m l n s1 s3\n",
    "             -. h_two i m a n s1 s3 *.  f_two j a k l s2 s2 \n",
    "             -. h_two i m l a s1 s3 *.  f_two j a k n s2 s3\n",
    "             -. h_two j m k a s2 s3 *.  f_two i a l n s1 s3\n",
    "           ) \n",
    "       | Alfa, Beta, Beta\n",
    "       | Beta, Alfa, Alfa -> \n",
    "           sum mos_cabs (fun a -> \n",
    "                h_two i j a l s1 s2 *.  f_two a m k n s1 s3 \n",
    "             +. h_two i m a n s1 s3 *.  f_two a j k l s1 s2 \n",
    "             +. h_two i m k a s1 s3 *.  f_two j a l n s2 s3 \n",
    "             +. h_two j m a n s2 s3 *.  f_two i a k l s1 s2 \n",
    "             -. h_two i j a n s1 s2 *.  f_two a m k l s1 s2 \n",
    "             -. h_two i j k a s1 s2 *.  f_two m a l n s2 s3 \n",
    "             -. h_two i m a l s1 s3 *.  f_two a j k n s1 s3 \n",
    "             -. h_two j m a l s2 s3 *.  f_two i a k n s1 s3 \n",
    "           ) \n",
    "       | Beta, Alfa, Beta\n",
    "       | Alfa, Beta, Alfa ->  assert false (*TODO *)\n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 3 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let ki = det_I.(129)\n",
    "let kj = det_I.(349)\n",
    "\n",
    "let alpha_to_string alpha = \n",
    "   \n",
    "      let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
    " \n",
    "      let i, j, m, k, l, n,  s, s', s'',  phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Triple (phase,\n",
    "              { hole ; particle ; spin },\n",
    "              {hole=hole' ; particle=particle' ; spin=spin' }, \n",
    "              {hole=hole''; particle=particle''; spin=spin''}  )) ->\n",
    "            hole, hole', hole'', particle, particle', particle'', spin, spin', spin'', phase\n",
    "          | _ -> assert false\n",
    "      in\n",
    "      let spin = function\n",
    "        | Spin.Alfa -> 0\n",
    "        | _ -> 1\n",
    "      in\n",
    "        exc0.(i).(spin s  ) <- \"i\" \n",
    "      ; exc0.(j).(spin s' ) <- \"j\" \n",
    "      ; exc0.(k).(spin s  ) <- \"k\" \n",
    "      ; exc0.(l).(spin s' ) <- \"l\" \n",
    "      ; exc0.(m).(spin s'') <- \"m\" \n",
    "      ; exc0.(n).(spin s'') <- \"n\" \n",
    "      ;\n",
    "      let s0, s0', s0'' = s, s', s'' in\n",
    "    \n",
    "      let i, j, k, l, s, s', p1 =\n",
    "          match Excitation.of_det ki alpha with\n",
    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
    "            hole, hole', particle, particle', spin, spin', phase\n",
    "          | _ -> assert false\n",
    "      in\n",
    "      \n",
    "      if exc0.(i).(spin s ) =  \"-\" then exc0.(i).(spin s ) <- \"p\";\n",
    "      if exc0.(j).(spin s') =  \"-\" then exc0.(j).(spin s') <- \"p\";\n",
    "      if exc0.(k).(spin s ) =  \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"q\";\n",
    "      if exc0.(l).(spin s') =  \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"q\";\n",
    "      \n",
    "      let string_h = \n",
    "          Printf.sprintf \"h_two %s %s %s %s %s %s *.  \" \n",
    "            exc0.(i).(spin s )\n",
    "            exc0.(j).(spin s')\n",
    "            exc0.(k).(spin s )\n",
    "            exc0.(l).(spin s')\n",
    "            (if s  = s0  then \"s \" else if s = s0'  then \"s'\"  else \"s''\")\n",
    "            (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\"  )\n",
    "      in \n",
    "      \n",
    "      let i, j, k, l, s, s', p2 =\n",
    "          match Excitation.of_det alpha kj with\n",
    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
    "            hole, hole', particle, particle', spin, spin', phase\n",
    "          | _ -> assert false\n",
    "      in\n",
    "      \n",
    "      let string_f = \n",
    "          Printf.sprintf \"f_two %s %s %s %s %s %s\" \n",
    "            exc0.(i).(spin s )\n",
    "            exc0.(j).(spin s')\n",
    "            exc0.(k).(spin s )\n",
    "            exc0.(l).(spin s')\n",
    "            (if s  = s0  then \"s \" else if s = s0'  then \"s'\"  else \"s''\")\n",
    "            (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\"  )\n",
    "      in\n",
    "        (*\n",
    "        Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n",
    "        Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n",
    "        *)\n",
    "\n",
    "    \n",
    "        let sign = \n",
    "            if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n",
    "        in\n",
    "        sign ^ string_h ^ string_f\n",
    "    \n",
    "\n",
    "let alpha_debug alpha = \n",
    "   \n",
    "      let i, j, k, l, s, s', p1 =\n",
    "          match Excitation.of_det ki alpha with\n",
    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
    "            hole, hole', particle, particle', spin, spin', phase\n",
    "          | _ -> assert false\n",
    "      in\n",
    "      Printf.printf \"%d %d %d %d \" i j k l;\n",
    "      \n",
    "      let i, j, k, l, s, s', p2 =\n",
    "          match Excitation.of_det alpha kj with\n",
    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
    "            hole, hole', particle, particle', spin, spin', phase\n",
    "          | _ -> assert false\n",
    "      in\n",
    "      (*\n",
    "        Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n",
    "        Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n",
    "        *)\n",
    "      Printf.printf \"%d %d %d %d \\n%!\" i j k l\n",
    "\n",
    "      \n",
    "let strings = \n",
    "    Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
    "    generate_alphas ki kj 3 1 2 2\n",
    "    |> Array.of_list\n",
    "    |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n",
    "    |> Array.to_list\n",
    "    |> List.sort_uniq compare\n",
    "    |> Array.of_list\n",
    "\n",
    "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n",
    "\n",
    "let _ =\n",
    "  let v =\n",
    "    let alphas =\n",
    "      generate_alphas ki kj 3 1 2 2\n",
    "      (*\n",
    "      |> List.filter (fun alpha ->\n",
    "        let x =  alpha_to_string alpha in\n",
    "           x = strings.(6)\n",
    "        )\n",
    "        *)\n",
    "    in\n",
    "    (*\n",
    "    List.iter alpha_debug alphas ;\n",
    "    Printf.printf \"\\n%!\";\n",
    "    *)\n",
    "    compute_HaaF ki alphas kj \n",
    "  in\n",
    "  let x = (integral_value ki kj) in\n",
    "  Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n"
   ]
  }
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