{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test of F12 matrix elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val png_image : string -> unit = <fun>\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "- : unit = ()\n",
      "Findlib has been successfully loaded. Additional directives:\n",
      "  #require \"package\";;      to load a package\n",
      "  #list;;                   to list the available packages\n",
      "  #camlp4o;;                to load camlp4 (standard syntax)\n",
      "  #camlp4r;;                to load camlp4 (revised syntax)\n",
      "  #predicates \"p,q,...\";;   to set these predicates\n",
      "  Topfind.reset();;         to force that packages will be reloaded\n",
      "  #thread;;                 to enable threads\n",
      "\n",
      "- : unit = ()\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/scemama/qp2/external/opam/4.07.1/lib/bytes: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/base64: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/base64/base64.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlcommon.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/result: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/result/result.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime/ppx_deriving_runtime.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime/ppx_deriving_yojson_runtime.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/unix.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/uuidm: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/uuidm/uuidm.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/easy-format: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/easy-format/easy_format.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/biniou: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/biniou/biniou.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/yojson: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/yojson/yojson.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/jupyter.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook/jupyter_notebook.cma: loaded\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val png_image : string -> Jupyter_notebook.display_id = <fun>\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlbytecomp.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamltoplevel.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/bigarray.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/lacaml.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/top: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/top/lacaml_top.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/astring: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/astring/astring.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner/cmdliner.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/seq: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims/stdlib_shims.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_cli.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_tty.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/alcotest: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/alcotest/alcotest.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/str.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/zarith: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/zarith/zarith.cma: loaded\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/getopt: added to search path\n",
      "/home/scemama/qp2/external/opam/4.07.1/lib/getopt/getopt.cma: loaded\n"
     ]
    }
   ],
   "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": 2,
   "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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val pp_mo : Format.formatter -> MOBasis.t -> unit = <fun>\n"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val basis_filename : string = \"/home/scemama/qp2/data/basis/6-31g\"\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val nuclei : Nuclei.t = [|(Element.N,   0.0000   0.0000   0.0000)|]\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val frozen_core : bool = true\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val multiplicity : int = 2\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val state : int = 1\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val basis : Basis.t =\n",
       "  \n",
       "                          Atomic Basis set\n",
       "                          ----------------\n",
       "\n",
       "-----------------------------------------------------------------------\n",
       " #   Angular   Coordinates (Bohr)       Exponents       Coefficients\n",
       "    Momentum  X        Y        Z\n",
       "-----------------------------------------------------------------------\n",
       "  1-3  S   0.0000   0.0000   0.0000   4.17351100e+03    1.83480000e-03\n",
       "                                      6.27457900e+02    1.39950000e-02\n",
       "                                      1.42902100e+02    6.85870000e-02\n",
       "                                      4.02343300e+01    2.32241000e-01\n",
       "                                      1.28202100e+01    4.69070000e-01\n",
       "                                      4.39043700e+00    3.60455000e-01\n",
       "                                    \n",
       "                                      1.16263580e+01   -1.14961000e-01\n",
       "                                      2.71628000e+00   -1.69118000e-01\n",
       "                                      7.72218000e-01    1.14585200e+00\n",
       "                                    \n",
       "                                      2.12031300e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "  3-8  P   0.0000   0.0000   0.0000   1.16263580e+01    6.75800000e-02\n",
       "                                      2.71628000e+00    3.23907000e-01\n",
       "                                      7.72218000e-01    7.40895000e-01\n",
       "                                    \n",
       "                                      2.12031300e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis : Basis.t =\n",
       "  \n",
       "                          Atomic Basis set\n",
       "                          ----------------\n",
       "\n",
       "-----------------------------------------------------------------------\n",
       " #   Angular   Coordinates (Bohr)       Exponents       Coefficients\n",
       "    Momentum  X        Y        Z\n",
       "-----------------------------------------------------------------------\n",
       "  1-6  S   0.0000   0.0000   0.0000   4.17351100e+03    1.83480000e-03\n",
       "                                      6.27457900e+02    1.39950000e-02\n",
       "                                      1.42902100e+02    6.85870000e-02\n",
       "                                      4.02343300e+01    2.32241000e-01\n",
       "                                      1.28202100e+01    4.69070000e-01\n",
       "                                      4.39043700e+00    3.60455000e-01\n",
       "                                    \n",
       "                                      1.16263580e+01   -1.14961000e-01\n",
       "                                      2.71628000e+00   -1.69118000e-01\n",
       "                                      7.72218000e-01    1.14585200e+00\n",
       "                                    \n",
       "                                      2.12031300e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      9.04600000e+03    7.00000000e-04\n",
       "                                      1.35700000e+03    5.38900000e-03\n",
       "                                      3.09300000e+02    2.74060000e-02\n",
       "                                      8.77300000e+01    1.03207000e-01\n",
       "                                      2.85600000e+01    2.78723000e-01\n",
       "                                      1.02100000e+01    4.48540000e-01\n",
       "                                      3.83800000e+00    2.78238000e-01\n",
       "                                      7.46600000e-01    1.54400000e-02\n",
       "                                    \n",
       "                                      9.04600000e+03   -1.53000000e-04\n",
       "                                      1.35700000e+03   -1.20800000e-03\n",
       "                                      3.09300000e+02   -5.99200000e-03\n",
       "                                      8.77300000e+01   -2.45440000e-02\n",
       "                                      2.85600000e+01   -6.74590000e-02\n",
       "                                      1.02100000e+01   -1.58078000e-01\n",
       "                                      3.83800000e+00   -1.21831000e-01\n",
       "                                      7.46600000e-01    5.49003000e-01\n",
       "                                    \n",
       "                                      2.24800000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "  3-14 P   0.0000   0.0000   0.0000   1.16263580e+01    6.75800000e-02\n",
       "                                      2.71628000e+00    3.23907000e-01\n",
       "                                      7.72218000e-01    7.40895000e-01\n",
       "                                    \n",
       "                                      2.12031300e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      1.35500000e+01    3.99190000e-02\n",
       "                                      2.91700000e+00    2.17169000e-01\n",
       "                                      7.97300000e-01    5.10319000e-01\n",
       "                                    \n",
       "                                      2.18500000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       " 19-24 D   0.0000   0.0000   0.0000   8.17000000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f12 : F12factor.t =\n",
       "  {F12factor.expo_s = 1.;\n",
       "   gaussian =\n",
       "    {GaussianOperator.coef_g =\n",
       "      [  -0.314400  -0.303700  -0.168100  -0.098110  -0.060240  -0.037260 ];\n",
       "     expo_sg =\n",
       "      [   0.220900   1.004000   3.622000  12.160000  45.870000 254.400000 ];\n",
       "     expo_sg_inv =\n",
       "      [   4.526935   0.996016   0.276091   0.082237   0.021801   0.003931 ]}}\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val charge : int = 0\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val simulation : Simulation.t = <abstr>\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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 \"n\" \n",
    "let frozen_core = true \n",
    "let multiplicity = 2\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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val n_elec_alfa : int = 4\n",
       "val n_elec_beta : int = 3\n",
       "val n_elec : int = 7\n"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15 significant shell pairs computed in 0.005208 seconds\n",
      "1\n",
      "2\n",
      "5\n",
      "6\n",
      "Computed ERIs in 0.026325 seconds\n",
      "MOs =\n",
      "\n",
      "\n",
      "          -- 1 --      -- 2 --     -- 3 --     -- 4 --   -- 5 --\n",
      "            1    0.995805    -0.228629          -0           0        -0\n",
      "            2   0.0207488     0.523688 2.54045E-16 1.78891E-15        -0\n",
      "            3           0 -3.45043E-16    0.516899 5.11587E-15  0.306901\n",
      "                      ...          ...         ...         ...       ...\n",
      "            7           0           -0    0.381023  3.3482E-15  0.401251\n",
      "            8           0 -6.37589E-16   -0.238604    0.273454  0.404641\n",
      "            9           0     -6.8E-16    0.182264    0.357982 -0.309095\n",
      "      \n",
      "\n",
      "            -- 6 --      -- 7 --      -- 8 --      -- 9 --\n",
      "            1            -0            0    0.0896964  4.08276E-15\n",
      "            2   1.33506E-15 -3.60646E-15     -1.51213 -6.87142E-14\n",
      "            3     -0.759946     0.656011 -2.25085E-15 -1.25628E-14\n",
      "                        ...          ...          ...          ...\n",
      "            7      0.836375    -0.602939  2.17188E-15  1.39379E-14\n",
      "            8     -0.523755    -0.608033 -2.87741E-14     0.655571\n",
      "            9      0.400083     0.464461 -3.95033E-14     0.858218\n",
      "      \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val hf : HartreeFock.t = \n",
       "======================================================================\n",
       "             Restricted Open-shell Hartree-Fock                      \n",
       "======================================================================\n",
       "\n",
       "    ------------------------------------------------------------\n",
       "        #     HF energy       Convergence  HOMO-LUMO\n",
       "    ------------------------------------------------------------\n",
       "        1    -52.57862719      9.9817e-01     0.0835\n",
       "        2    -54.20380931      2.2021e-01     0.2639\n",
       "        3    -54.23392256      5.7771e-02     0.2682\n",
       "        4    -54.24023663      2.1083e-02     0.2680\n",
       "        5    -54.24159726      8.9827e-03     0.2673\n",
       "        6    -54.24188853      4.2281e-03     0.2669\n",
       "        7    -54.24195106      1.9862e-03     0.2667\n",
       "        8    -54.24196836      1.6000e-05     0.2665\n",
       "        9    -54.24196836      1.6302e-06     0.2665\n",
       "       10    -54.24196843      3.8429e-08     0.2665\n",
       "    ------------------------------------------------------------\n",
       "\n",
       "\n",
       "    ============================================================\n",
       "               One-electron energy  -73.7477460896\n",
       "                           Kinetic   54.1465371332\n",
       "                         Potential -127.8942832228\n",
       "      --------------------------------------------------------  \n",
       "               Two-electron energy   19.5057776578\n",
       "                           Coulomb   26.0005985081\n",
       "                          Exchange   -6.4948208503\n",
       "      --------------------------------------------------------  \n",
       "                           HF HOMO   -5.3102635644\n",
       "                           HF LUMO    1.9421331121\n",
       "                      HF LUMO-LUMO    7.2523966765\n",
       "      --------------------------------------------------------  \n",
       "               Electronic   energy  -54.2419684318\n",
       "               Nuclear   repulsion    0.0000000000\n",
       "               Hartree-Fock energy  -54.2419684318\n",
       "    ============================================================\n",
       "    \n",
       "\n"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mo_basis : MOBasis.t =\n",
       "  Eigenvalues:   -15.681404    -0.961606    -0.451178    -0.195149     0.040479 \n",
       "            -- 1 --      -- 2 --     -- 3 --     -- 4 --   -- 5 --\n",
       "      1    0.995805    -0.228629          -0           0        -0\n",
       "      2   0.0207488     0.523688 2.54045E-16 1.78891E-15        -0\n",
       "      3           0 -3.45043E-16    0.516899 5.11587E-15  0.306901\n",
       "                ...          ...         ...         ...       ...\n",
       "      7           0           -0    0.381023  3.3482E-15  0.401251\n",
       "      8           0 -6.37589E-16   -0.238604    0.273454  0.404641\n",
       "      9           0     -6.8E-16    0.182264    0.357982 -0.309095\n",
       "  \n",
       "  Eigenvalues:     0.908849     0.950925     0.975309     0.912008 \n",
       "              -- 6 --      -- 7 --      -- 8 --      -- 9 --\n",
       "      1            -0            0    0.0896964  4.08276E-15\n",
       "      2   1.33506E-15 -3.60646E-15     -1.51213 -6.87142E-14\n",
       "      3     -0.759946     0.656011 -2.25085E-15 -1.25628E-14\n",
       "                  ...          ...          ...          ...\n",
       "      7      0.836375    -0.602939  2.17188E-15  1.39379E-14\n",
       "      8     -0.523755    -0.608033 -2.87741E-14     0.655571\n",
       "      9      0.400083     0.464461 -3.95033E-14     0.858218\n",
       "  \n",
       "  \n"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let hf =  HartreeFock.make ~guess:`Hcore ~max_scf:10 simulation  ;;\n",
    "\n",
    "let mo_basis = MOBasis.of_hartree_fock hf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " FCI-F12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notations:\n",
    "\n",
    "* $\\langle ij || kl \\rangle = \\int \\phi_i(r_1) \\phi_j(r_2) \\frac{1}{r_{12}} \\phi_k(r1) \\phi_l(r2) $ \n",
    "* $\\left[ ij || kl \\right] = \\int \\phi_i(r_1) \\phi_j(r_2) f_{12} \\phi_k(r1) \\phi_l(r2) $ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val f12 : F12factor.t =\n",
       "  {F12factor.expo_s = 1.;\n",
       "   gaussian =\n",
       "    {GaussianOperator.coef_g =\n",
       "      [  -0.314400  -0.303700  -0.168100  -0.098110  -0.060240  -0.037260 ];\n",
       "     expo_sg =\n",
       "      [   0.220900   1.004000   3.622000  12.160000  45.870000 254.400000 ];\n",
       "     expo_sg_inv =\n",
       "      [   4.526935   0.996016   0.276091   0.082237   0.021801   0.003931 ]}}\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mo_num : int = 9\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = <fun>\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val pp_det : Format.formatter -> Determinant.t -> unit = <fun>\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val simulation_aux : Simulation.t = <abstr>\n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "66 significant shell pairs computed in 0.050789 seconds\n",
      "1\n",
      "2\n",
      "5\n",
      "6\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "15\n",
      "18\n",
      "Computed ERIs in 0.889029 seconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis : MOBasis.t =\n",
       "  Eigenvalues:   -15.681404    -0.961606    -0.451178    -0.195149     0.040479 \n",
       "               -- 1 --      -- 2 --      -- 3 --      -- 4 --      -- 5 --\n",
       "       1      0.995805    -0.228629 -1.04121E-12 -1.20393E-11 -7.74166E-12\n",
       "       2     0.0207488     0.523688 -3.08871E-13 -4.88506E-13  -3.2349E-13\n",
       "       3   2.26649E-12 -2.08563E-12     0.516899  3.82452E-12     0.306901\n",
       "                   ...          ...          ...          ...          ...\n",
       "      22             0            0            0            0           -0\n",
       "      23             0            0            0            0           -0\n",
       "      24             0            0            0            0           -0\n",
       "  \n",
       "  Eigenvalues:     0.908849     0.950925     0.975309     0.912008     2.032635 \n",
       "                -- 6 --      -- 7 --      -- 8 --      -- 9 -- -- 10 --\n",
       "       1   -1.59863E-11  1.67271E-11    0.0896964  8.01274E-12        0\n",
       "       2    7.28187E-13 -1.60327E-12     -1.51213 -2.11029E-13        0\n",
       "       3      -0.759946     0.656011 -6.79771E-13 -6.65308E-12        0\n",
       "                    ...          ...          ...          ...      ...\n",
       "      22             -0           -0            0            0        0\n",
       "      23             -0           -0            0            0        1\n",
       "      24             -0           -0            0            0        0\n",
       "  \n",
       "  Eigenvalues:     2.209274     2.205946     2.198723     2.627905    18.044176 \n",
       "               -- 11 --     -- 12 --     -- 13 --     -- 14 --     -- 15 --\n",
       "       1     4.4959E-10 -2.92245E-09 -6.60522E-10      7.27202        39.53\n",
       "       2   -2.27871E-11  1.81557E-11  8.06971E-11     -19.3218     -84.1067\n",
       "       3       -8.99756     -28.2245      -4.1365 -1.31641E-12 -1.85784E-10\n",
       "                    ...          ...          ...          ...          ...\n",
       "      22             -0           -0  2.75019E-14            0            0\n",
       "      23             -0           -0            0            0            0\n",
       "      24   -3.45546E-14 -7.00504E-14            0            0            0\n",
       "  \n",
       "  Eigenvalues:    31.400935    31.392955    31.387019   476.102993     2.036553 \n",
       "               -- 16 --     -- 17 --    -- 18 --    -- 19 --     -- 20 --\n",
       "       1   -2.50732E-08 -1.36441E-09 1.64713E-08     416.882 -2.63792E-11\n",
       "       2    5.37419E-10 -1.14011E-10 5.52992E-10    -1.46938  4.55954E-13\n",
       "       3       -190.497      18.1424     30.0485 -1.1041E-08 -1.61968E-10\n",
       "                    ...          ...         ...         ...          ...\n",
       "      22    1.51034E-13  2.01121E-13 1.28118E-13           0    -0.128674\n",
       "      23             -0           -0          -0           0           -0\n",
       "      24   -7.82065E-13           -0          -0           0     0.923094\n",
       "  \n",
       "  Eigenvalues:     2.033307     2.036684     2.036990 \n",
       "               -- 21 --     -- 22 --     -- 23 --\n",
       "       1   -5.67082E-11  1.56263E-12   3.6287E-10\n",
       "       2    9.80094E-13 -2.68735E-14 -6.29775E-12\n",
       "       3   -4.74932E-12  1.67489E-13           -0\n",
       "                    ...          ...          ...\n",
       "      22       0.986223    -0.103886  -0.00379526\n",
       "      23              0            0           -0\n",
       "      24      -0.383449    0.0293605   0.00152471\n",
       "  \n",
       "  \n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_num : int = 23\n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "66 significant shell pairs computed in 0.842000 seconds\n",
      "1\n",
      "2\n",
      "5\n",
      "6\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "15\n",
      "18\n",
      "Computed ERIs in 17.257765 seconds\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "4-idx transformation \n",
      "23 / 23\n",
      "4-idx transformation \n",
      "23 / 23\n"
     ]
    }
   ],
   "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": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val cancel_singles : bool = false\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_cabs : int list =\n",
       "  [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_abs : int list =\n",
       "  [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21;\n",
       "   22; 23]\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_in : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9]\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_a : Determinant.t -> int list = <fun>\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_b : Determinant.t -> int list = <fun>\n"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val h_one : int -> int -> '_weak2 -> float = <fun>\n"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val h_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = <fun>\n"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val f_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = <fun>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f_one : 'a -> 'b -> 'c -> float = <fun>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f_one : int -> int -> '_weak2 -> float = <fun>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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",
    "\n",
    "let f_one = h_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determinant-based functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val f12_integrals :\n",
       "  'a ->\n",
       "  (int -> int -> '_weak2 -> float) *\n",
       "  (int -> int -> int -> int -> Spin.t -> Spin.t -> float) * 'b option = <fun>\n"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val h_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f_ij : 'a -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val hf_ij :\n",
       "  MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float list =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val is_a_double : DeterminantSpace.t -> Determinant.t -> bool = <fun>\n"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of determinants : 56 28 1568\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val in_space : DeterminantSpace.t = <abstr>\n"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of determinants : 1540 231 355740\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val aux_space : DeterminantSpace.t = <abstr>\n"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val det_space_in : unit -> Determinant.t Stream.t = <fun>\n"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val det_space_out : unit -> (Determinant.t * Determinant.t) Stream.t = <fun>\n"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ci : CI.t =\n",
       "  {CI.e_shift = -54.2419683633284677; det_space = <abstr>; m_H = <lazy>;\n",
       "   m_S2 = <lazy>; eigensystem = <lazy>; n_states = 1}\n"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1     0.0000000000    5.38465905e-01\n",
      "  2    -0.0538262193    1.87217169e-01\n",
      "  3    -0.0657011468    6.52524404e-02\n",
      "  4    -0.0682884307    4.47790537e-02\n",
      "  5    -0.0722202576    2.28670803e-02\n",
      "  6    -0.0732730385    5.26351716e-03\n",
      "  7    -0.0733234182    9.38250052e-04\n",
      "  8    -0.0733249420    2.14671657e-04\n",
      "  0    -0.0733250301    7.26676403e-05\n",
      "  1    -0.0733250395    2.46738965e-05\n",
      "  2    -0.0733250400    1.50948498e-05\n",
      "  3    -0.0733250400    4.00236940e-06\n",
      "  4    -0.0733250400    1.38596264e-06\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val ci_coef : Lacaml.D.Mat.t =\n",
       "  \n",
       "\n",
       "            -- 1 --\n",
       "           1   0.701258\n",
       "           2          0\n",
       "           3          0\n",
       "                    ...\n",
       "        1566          0\n",
       "        1567          0\n",
       "        1568          0\n",
       "  \n",
       "val ci_energy : Lacaml.D.Vec.t =\n",
       "        R1       R2       R3           R5       R6       R7\n",
       "  -54.3153 -54.1549 -53.2726 ... -51.7367 -51.4918 -50.3061\n"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  5    -0.0733250400    7.40047633e-07\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val randomize : bool = false\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val out_list : (Determinant.t * Determinant.t) list =\n",
       "  [(phase:+1\n",
       "    a:+1 +++------+------------------------------------------------------\n",
       "    b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +++------+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-+-----+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-+-----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-++-----+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-++-----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++--+----+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++--+----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+-+----+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+-+----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--++----+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--++----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++---+---+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++---+---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+--+---+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+--+---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+-+---+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+-+---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---++---+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---++---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++----+--+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++----+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+---+--+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+---+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+--+--+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+--+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+-+--+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+-+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----++--+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----++--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-----+-+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-----+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+----+-+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+----+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+---+-+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+---+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+--+-+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+--+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+-+-+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+-+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----++-+------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----++-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++------++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++------++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+-----++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+-----++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+----++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+----++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+---++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+---++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+--++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+--++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----+-++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----+-++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +------+++------------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +------+++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +++-------+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +++-------+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-+------+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-+------+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-++------+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-++------+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++--+-----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++--+-----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+-+-----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+-+-----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--++-----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--++-----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++---+----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++---+----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+--+----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+--+----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+-+----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+-+----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---++----+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---++----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++----+---+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++----+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+---+---+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+---+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+--+---+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+--+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+-+---+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+-+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----++---+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----++---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-----+--+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-----+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+----+--+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+----+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+---+--+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+---+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+--+--+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+--+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+-+--+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+-+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----++--+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----++--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++------+-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++------+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+-----+-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+-----+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+----+-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+----+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+---+-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+---+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+--+-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+--+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----+-+-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----+-+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +------++-+-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +------++-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-------++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-------++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+------++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+------++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+-----++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+-----++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+----++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+----++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+---++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+---++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----+--++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----+--++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +------+-++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +------+-++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-------+++-----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-------+++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +++--------+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +++--------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-+-------+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-+-------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-++-------+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-++-------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++--+------+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++--+------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+-+------+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+-+------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--++------+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--++------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++---+-----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++---+-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+--+-----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+--+-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+-+-----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+-+-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---++-----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---++-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++----+----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++----+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+---+----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+---+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+--+----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+--+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+-+----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+-+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----++----+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----++----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-----+---+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-----+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+----+---+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+----+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+---+---+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+---+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+--+---+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+--+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+-+---+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+-+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----++---+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----++---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++------+--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++------+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+-----+--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+-----+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+----+--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+----+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+---+--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+---+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+--+--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+--+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----+-+--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----+-+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +------++--+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +------++--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 ++-------+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 ++-------+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-+------+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-+------+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +--+-----+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +--+-----+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +---+----+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +---+----+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +----+---+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +----+---+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-----+--+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +-----+--+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +------+-+-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ",\n",
       "phase:+1\n",
       "a:+1 +------+-+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ");\n",
       "(phase:+1\n",
       " a:+1 +-------++-+----------------------------------------------------\n",
       " b:+1 +++-------------------------------------------------------------\n",
       ", ...);\n",
       "...]\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val in_list : Determinant.t list =\n",
       "  [phase:+1\n",
       "   a:+1 ++++------------------------------------------------------------\n",
       "   b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "...]\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val det_a : Determinant.t array =\n",
       "  [|phase:+1\n",
       "    a:+1 +++------+------------------------------------------------------\n",
       "    b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++----+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++---+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++--+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-+-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----++-+------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+++------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-------+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+------+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++------+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++----+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++---+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-+--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----++--+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-+-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------++-+-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-------++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+------++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-----++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+----++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+---++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+--++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+-++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+++-----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++------+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----++---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------++--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-------+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+------+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-----+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+----+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+---+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+--+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+-+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------++-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-----++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+----++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+---++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+--++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+-++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----++----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------++---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-------+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+------+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-----+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+----+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+---+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+--+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+-+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------++--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--------+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-------+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+------+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-----+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+----+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+---+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+--+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+-+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-----++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+----++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+---++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+--++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----++-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------++----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-------+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+------+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-----+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+----+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+---+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+--+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+-+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------++---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--------+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-------+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+------+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-----+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+----+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+---+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+--+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+-+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-----+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+----+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+---+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+--+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-----++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+----++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+---++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----++------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------+-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----+-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----+-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---+-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--+-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-+-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------++-----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-------+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+------+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-----+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+----+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+---+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+--+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+-+----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------++----+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--------+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-------+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+------+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-----+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+----+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+---+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+--+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+-+---+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---------+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--------+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-------+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+------+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-----+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+----+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+---+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+--+--+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----------+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---------+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--------+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-------+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+------+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-----+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+----+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+---+-+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----------++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----------++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---------++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--------++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-------++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+------++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+-----++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-------+----++-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++------------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-----------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-----------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+----------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+----------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++----------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+---------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+---------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+---------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++---------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+--------+------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "...|]\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val det_I : Determinant.t array =\n",
       "  [|phase:+1\n",
       "    a:+1 ++++------------------------------------------------------------\n",
       "    b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 ++-+------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 +-++------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 ++--+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+++---------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++----+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+---+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++---+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+--+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+--+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++--+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++-+--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+++--------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-----+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+----+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++----+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+---+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+---+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++---+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---+--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--+--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-+--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---++--+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+---+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+--+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+-+-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----++-+-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+----++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+---++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+--++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+-++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+++-------------------------------------------------------\n",
       "b:+1 +-+-+-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++++------------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++-+-----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-++-----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+++-----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++--+----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+-+----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++-+----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--++----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-++----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+++----------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +++---+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-+--+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-++--+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++--+-+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-+-+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--++-+---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++---++---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+--++---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+-++---------------------------------------------------------\n",
       "b:+1 +--++-----------------------------------------------------------\n",
       ";\n",
       "...|]\n"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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 $|J\\rangle$\n",
    "* `cabs` is the number of electrons in the CABS\n",
    "* `l` is the degree of excitation between $|I\\rangle$ and $|\\alpha \\rangle$\n",
    "* `r` is the degree of excitation between $|\\alpha \\rangle$ and $|J\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val generate_alphas :\n",
       "  Determinant.t ->\n",
       "  Determinant.t -> int -> int -> int -> int -> Determinant.t list = <fun>\n"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val compute_HaaF :\n",
       "  CIMatrixElement.De.t ->\n",
       "  CIMatrixElement.De.t list -> CIMatrixElement.De.t -> float = <fun>\n"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let generate_alphas ki kj exc cabs l r =\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 = \n",
    "      match l with\n",
    "      | 1 -> all_singles ki\n",
    "      | 2 -> all_doubles ki\n",
    "      | _ -> assert false\n",
    "  in\n",
    "  let ar = \n",
    "      match r with\n",
    "      | 1 -> all_singles kj\n",
    "      | 2 -> all_doubles kj\n",
    "      | _ -> assert false\n",
    "  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",
    "      Bitstring.popcount a + Bitstring.popcount b = cabs\n",
    "  in\n",
    "  let good_lr k =\n",
    "    Determinant.degree ki k = l &&\n",
    "    Determinant.degree k kj = r \n",
    "  in\n",
    "\n",
    "\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",
    "  (* Filter out all determinants with incorrect excitation numbers *)\n",
    "  |> List.filter good_lr \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": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val check :\n",
       "  int ->\n",
       "  (CIMatrixElement.De.t -> CIMatrixElement.De.t -> float) ->\n",
       "  int -> int -> int -> int -> unit = <fun>\n"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val sum : 'a list -> ('a -> float) -> float = <fun>\n"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let check n integral_value exc cabs lexc rexc =\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 cabs lexc rexc 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": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val array_3_init :\n",
       "  int ->\n",
       "  int ->\n",
       "  int ->\n",
       "  (int -> int -> int -> float) ->\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val array_4_init :\n",
       "  int ->\n",
       "  int ->\n",
       "  int ->\n",
       "  int ->\n",
       "  (int -> int -> int -> int -> float) ->\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val array_5_init :\n",
       "  int ->\n",
       "  int ->\n",
       "  int ->\n",
       "  int ->\n",
       "  int ->\n",
       "  (int -> int -> int -> int -> int -> float) ->\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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 1 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "- : Jupyter_notebook.display_id = <abstr>\n"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let _ = png_image \"0_1_11.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
    "\n",
    "$\\sum_i \\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{i}$\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{a} \\sum_{i}\n",
    "        \\left( h_{ia} +\n",
    "            \\sum_{j} \\langle i j || a j \\rangle +\n",
    "            \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n",
    "        \\left( f_{ai} +\n",
    "            \\sum_{j}  \\left[ a j || i j \\right] + \n",
    "            \\sum_{\\bar{j}}  \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) + \\\\\n",
    "\\sum_{\\bar{a}}  \\sum_{\\bar{i}}\n",
    "        \\left( h_{ia} +\n",
    "            \\sum_{j} \\langle \\bar{i} j | \\bar{a} j \\rangle +\n",
    "            \\sum_{\\bar{j}} \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n",
    "        \\left( f_{ai} +\n",
    "            \\sum_{j}  \\left[ \\bar{a} j | \\bar{i} j \\right] + \n",
    "            \\sum_{\\bar{j}}  \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right)  \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> 'a -> float = <fun>\n"
      ]
     },
     "execution_count": 41,
     "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",
      "Failed: (135, 135) | 2.284769e+00 2.284769e+00 | 1.776357e-15  |  cpu : 2.160390 0.491860\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let integral_value ki kj = \n",
    "   (* Alpha-Beta *)\n",
    "   let s, s' = Spin.(Alfa, Beta) in \n",
    "   let mos_a, mos_b = mos_a ki, mos_b ki in\n",
    "   \n",
    "   sum mos_cabs (fun a ->\n",
    "      sum mos_a (fun i -> \n",
    "           (h_one i a s  +.\n",
    "               sum mos_a (fun j -> h_two i j a j s s ) +.\n",
    "               sum mos_b (fun j -> h_two i j a j s s')\n",
    "               ) *. \n",
    "           (f_one a i s  +.\n",
    "               sum mos_a (fun j -> f_two a j i j s s ) +.\n",
    "               sum mos_b (fun j -> f_two a j i j s s')\n",
    "               )\n",
    "         )\n",
    "       +.\n",
    "       sum mos_b (fun i -> \n",
    "           (h_one i a s'  +.\n",
    "               sum mos_b (fun j -> h_two i j a j s' s') +.\n",
    "               sum mos_a (fun j -> h_two i j a j s' s )\n",
    "               ) *. \n",
    "           (f_one a i s'  +.\n",
    "               sum mos_b (fun j -> f_two a j i j s' s') +.\n",
    "               sum mos_a (fun j -> f_two a j i j s' s )\n",
    "               )\n",
    "         ) \n",
    "     ) \n",
    "     \n",
    "let _ =\n",
    "  check 0 integral_value 0 1 1 1\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_0111_1H_1F : Lacaml.D.vec =\n",
       "       R1       R2       R3          R7       R8      R9\n",
       "  1.23163 0.512679 0.379158 ... 1.15717 0.783246 0.94134\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_1H_2Fa : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "          -- 1 --     -- 2 --     -- 3 --    -- 4 --     -- 5 --\n",
       "        1           0 9.54805E-05 0.000949414 0.00102124 0.000612123\n",
       "        2   0.0157601           0  0.00387182  0.0040609  0.00288411\n",
       "        3   0.0123451  0.00482411           0 0.00262065  0.00153994\n",
       "                  ...         ...         ...        ...         ...\n",
       "        7   0.0638665   0.0309407   0.0280828  0.0291155   0.0201909\n",
       "        8    0.035099  0.00993291   0.0123105  0.0128627   0.0095454\n",
       "        9   0.0546496   0.0268732   0.0249878  0.0209954     0.02047\n",
       "  \n",
       "\n",
       "            -- 6 --    -- 7 --      -- 8 --    -- 9 --\n",
       "        1    0.00135039 0.00168769 -2.50132E-05 0.00127857\n",
       "        2    0.00164244 0.00263016   -0.0049468 0.00145336\n",
       "        3   -0.00786828 0.00262225  0.000307787 0.00154154\n",
       "                    ...        ...          ...        ...\n",
       "        7     0.0210255          0    0.0169901  0.0199928\n",
       "        8     0.0097481  0.0125132            0 0.00919583\n",
       "        9     0.0187406  0.0232584    0.0154703          0\n",
       "  \n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_1H_2Fb : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "           -- 1 --     -- 2 --     -- 3 --     -- 4 --     -- 5 --\n",
       "        1   0.00838947 0.000802512 0.000774268 0.000824527 0.000531664\n",
       "        2    0.0167558  0.00284141  0.00289398  0.00311638  0.00181881\n",
       "        3    0.0138217  0.00142914 0.000717031  0.00205097  0.00097096\n",
       "                   ...         ...         ...         ...         ...\n",
       "        7    0.0672127   0.0297099   0.0280681    0.029107    0.022267\n",
       "        8    0.0361343   0.0135355   0.0127802   0.0133849  0.00974314\n",
       "        9    0.0572555   0.0267995   0.0251558   0.0264006    0.020602\n",
       "  \n",
       "\n",
       "            -- 6 --    -- 7 --     -- 8 --     -- 9 --\n",
       "        1   0.000838226 0.00108083 0.000590322 0.000787968\n",
       "        2    0.00312393  0.0041991  0.00210452  0.00290152\n",
       "        3    0.00156923 0.00296985 0.000876672  0.00188984\n",
       "                    ...        ...         ...         ...\n",
       "        7     0.0206994  0.0254055   0.0187116   0.0196605\n",
       "        8    0.00965382  0.0126909  0.00818378  0.00904916\n",
       "        9     0.0183365  0.0228903   0.0168998   0.0166274\n",
       "  \n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_2Ha_1F : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "          -- 1 --    -- 2 --     -- 3 --    -- 4 --     -- 5 --\n",
       "        1           0 0.00346355 -0.00957818 -0.0103791 -0.00586334\n",
       "        2   -0.121634          0   -0.019873 -0.0209946  -0.0141534\n",
       "        3   -0.115395 -0.0247239           0  -0.017339  -0.0100747\n",
       "                  ...        ...         ...        ...         ...\n",
       "        7   -0.405587  -0.140299   -0.129164  -0.134263  -0.0844326\n",
       "        8   -0.207751 -0.0414479  -0.0574012 -0.0601297  -0.0438726\n",
       "        9   -0.335499  -0.120993   -0.113422 -0.0875797   -0.091945\n",
       "  \n",
       "\n",
       "           -- 6 --    -- 7 --     -- 8 --    -- 9 --\n",
       "        1   -0.0155848 -0.0192997  0.00228062 -0.0147839\n",
       "        2   -0.0112498 -0.0169694   0.0224836 -0.0101282\n",
       "        3    0.0322167 -0.0204013 -0.00423111  -0.013137\n",
       "                   ...        ...         ...        ...\n",
       "        7    -0.106147          0  -0.0844097  -0.101048\n",
       "        8   -0.0490936 -0.0626221           0 -0.0463651\n",
       "        9   -0.0928575  -0.114335  -0.0760592          0\n",
       "  \n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_2Hb_1F : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "          -- 1 --    -- 2 --     -- 3 --     -- 4 --     -- 5 --\n",
       "        1   -0.267262 -0.0092275 -0.00385375 -0.00417671 -0.00235846\n",
       "        2   -0.165952 -0.0180838  -0.0197588  -0.0214917  -0.0115557\n",
       "        3   -0.149576 -0.0113644   -0.010116  -0.0155245 -0.00736965\n",
       "                  ...        ...         ...         ...         ...\n",
       "        7   -0.487134  -0.140774    -0.13287   -0.138318   -0.111128\n",
       "        8   -0.253633 -0.0687529  -0.0664679  -0.0700869  -0.0486229\n",
       "        9   -0.399565  -0.125537   -0.117439   -0.133629  -0.0946778\n",
       "  \n",
       "\n",
       "            -- 6 --     -- 7 --     -- 8 --     -- 9 --\n",
       "        1   -0.00636217 -0.00785747 -0.00673128 -0.00603921\n",
       "        2    -0.0272961  -0.0354992  -0.0184917  -0.0255632\n",
       "        3    -0.0207391  -0.0252065  -0.0100414  -0.0170516\n",
       "                    ...         ...         ...         ...\n",
       "        7     -0.111178   -0.151723  -0.0978176    -0.10573\n",
       "        8    -0.0587109  -0.0765558  -0.0468344  -0.0550919\n",
       "        9    -0.0962035   -0.118965  -0.0866369  -0.0978307\n",
       "  \n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0111_2Hb_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> 'a -> float = <fun>\n"
      ]
     },
     "execution_count": 42,
     "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",
      "Failed: (225, 225) | 2.333780e+00 2.333780e+00 | 1.776357e-15  |  cpu : 2.156856 0.039502\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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",
    "    \n",
    "let m_0111_1H_2Fa = \n",
    "  Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
    "    h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa  ))\n",
    "\n",
    "    \n",
    "let m_0111_1H_2Fb = \n",
    "  Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
    "    h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta  ))\n",
    "\n",
    "\n",
    "let m_0111_2Ha_1F = \n",
    "  Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
    "    h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa ))\n",
    "\n",
    "    \n",
    "let m_0111_2Hb_1F = \n",
    "  Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n",
    "    h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa ))\n",
    "\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",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_0111_2Hb_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.Beta *.\n",
    "      f_two a k i k Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\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",
    "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 i j a j Spin.Alfa Spin.Beta *.\n",
    "      f_two a k i k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "let integral_value ki kj = \n",
    "\n",
    "   let mos_a, mos_b = mos_a ki, mos_b ki in\n",
    "   \n",
    "   sum mos_a (fun i ->\n",
    "     m_0111_1H_1F.{i} +. \n",
    "     sum mos_a (fun j ->\n",
    "       m_0111_2Ha_1F.{i,j} +.\n",
    "       m_0111_1H_2Fa.{i,j} +.\n",
    "       sum mos_a (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n",
    "       sum mos_b (fun k -> m_0111_2Ha_2Fb.{i,j,k})\n",
    "       ) +.\n",
    "     sum mos_b (fun j ->\n",
    "       m_0111_2Hb_1F.{i,j} +.\n",
    "       m_0111_1H_2Fb.{i,j} +.\n",
    "       sum mos_a (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n",
    "       sum mos_b (fun k -> m_0111_2Hb_2Fb.{i,j,k})\n",
    "       )\n",
    "     )\n",
    "   +.\n",
    "   sum mos_b (fun i ->\n",
    "     m_0111_1H_1F.{i} +. \n",
    "     sum mos_b (fun j ->\n",
    "       m_0111_2Ha_1F.{i,j} +.\n",
    "       m_0111_1H_2Fa.{i,j} +.\n",
    "       sum mos_b (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n",
    "       sum mos_a (fun k -> m_0111_2Ha_2Fb.{i,j,k})\n",
    "       ) +.\n",
    "     sum mos_a (fun j ->\n",
    "       m_0111_2Hb_1F.{i,j} +.\n",
    "       m_0111_1H_2Fb.{i,j} +.\n",
    "       sum mos_b (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n",
    "       sum mos_a (fun k -> m_0111_2Hb_2Fb.{i,j,k})\n",
    "       )\n",
    "     )\n",
    "   \n",
    "let _ =\n",
    "  check 0 integral_value 0 1 1 1\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. 0 1 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "- : Jupyter_notebook.display_id = <abstr>\n"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let _ = png_image \"0_1_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$i,j$ : orbital indices of MOs   occupied in $|I\\rangle$.\n",
    "\n",
    "$k$   : orbital indices of MOs unoccupied in $|I\\rangle$.\n",
    "\n",
    "$\\sum_i \\sum_a \\sum_j \\sum_k \\hat{T}_{ij}^{ak} \\hat{T}_{ak}^{ij}$\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{a} \\sum_{k} \\sum_{i} \\sum_{j<i}\n",
    "            \\langle i j || a k \\rangle \n",
    "             \\left[ a k || i j \\right] + \n",
    "\\sum_{a} \\sum_{\\bar{k}} \\sum_{i} \\sum_{\\bar{j}}\n",
    "            \\langle i \\bar{j} | a \\bar{k} \\rangle \n",
    "             \\left[ a \\bar{k} | i \\bar{j} \\right]  + \\\\\n",
    "\\sum_{\\bar{a}} \\sum_{k} \\sum_{\\bar{i}} \\sum_{j}\n",
    "            \\langle \\bar{i} j | \\bar{a} k \\rangle \n",
    "             \\left[ \\bar{a} k | \\bar{i} j \\right] + \n",
    "\\sum_{\\bar{a}} \\sum_{\\bar{k}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
    "            \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{k} \\rangle \n",
    "             \\left[ \\bar{a} \\bar{k} || \\bar{i} \\bar{j} \\right] \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 44,
     "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: (22, 22) | -3.896807e-02 -3.896807e-02 | 6.245005e-17  |  cpu : 2.708850  0.154509\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let integral_value ki kj = \n",
    "   (* mos unoccupied in both I and J *)\n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.init mo_num (fun i -> Some (i+1)) , \n",
    "     Array.init mo_num (fun i -> Some (i+1)) \n",
    "   in\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
    "   \n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.to_list mos_virt_a |> Util.list_some,\n",
    "     Array.to_list mos_virt_b |> Util.list_some\n",
    "   in\n",
    "   \n",
    "   (* Alpha-Beta *)\n",
    "   let s, s' = Spin.(Alfa, Beta) in\n",
    "   sum mos_cabs   (fun a ->\n",
    "   sum (mos_b ki) (fun j ->  \n",
    "   sum (mos_a ki) (fun i ->  \n",
    "   sum mos_virt_b (fun k ->  \n",
    "       h_two i j a k s s'  *. f_two a k i j s s'\n",
    "   )))\n",
    "   +.\n",
    "   sum (mos_a ki) (fun j ->  \n",
    "   sum (mos_b ki) (fun i ->  \n",
    "   sum mos_virt_a (fun k ->  \n",
    "       h_two i j a k s s'  *. f_two a k i j s s'\n",
    "   )))) \n",
    "   +.\n",
    "   (* Alpha-Alpha / Beta-Beta *)\n",
    "   List.fold_left (fun accu (mos_virt,mos,s) -> \n",
    "     let s' = s in accu +.\n",
    "     sum mos (fun j ->  \n",
    "     sum mos (fun i -> if i < j then 0. else\n",
    "     sum mos_virt (fun k ->  \n",
    "     sum mos_cabs (fun a -> \n",
    "       h_two i j a k s s'  *. f_two a k i j s s'\n",
    "     )))) \n",
    "   ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)]\n",
    "     \n",
    "let _ =\n",
    "  check 100 integral_value 0 1 2 2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_0122_Haa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0122_Hab :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 46,
     "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: (22, 22) | -3.896807e-02 -3.896807e-02 | 6.938894e-17  |  cpu : 2.688957  0.003098\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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",
    "      \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",
    "\n",
    "\n",
    "let integral_value ki kj = \n",
    "   (* mos unoccupied in both I and J *)\n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.init mo_num (fun i -> Some (i+1)) , \n",
    "     Array.init mo_num (fun i -> Some (i+1)) \n",
    "   in\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
    "   \n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.to_list mos_virt_a |> Util.list_some,\n",
    "     Array.to_list mos_virt_b |> Util.list_some\n",
    "   in\n",
    "   \n",
    "   let result = \n",
    "   sum (mos_a ki) (fun i ->  \n",
    "   sum (mos_b ki) (fun j ->  \n",
    "   sum mos_virt_b (fun k ->  m_0122_Hab.{i,j,k} )))\n",
    "   +.\n",
    "   sum (mos_b ki) (fun i ->  \n",
    "   sum (mos_a ki) (fun j ->  \n",
    "   sum mos_virt_a (fun k ->  m_0122_Hab.{i,j,k} )))\n",
    "   +.\n",
    "   (* Alpha-Alpha / Beta-Beta *)\n",
    "   List.fold_left (fun accu (mos_virt,mos) -> \n",
    "     accu +.\n",
    "     sum mos (fun j ->  \n",
    "     sum mos (fun i -> if i <= j then 0. else\n",
    "     sum mos_virt (fun k -> m_0122_Haa.{i,j,k} )))\n",
    "   ) 0. [ (mos_virt_a,mos_a ki) ; (mos_virt_b,mos_b ki)]\n",
    "   in \n",
    "   result\n",
    "     \n",
    "let _ =\n",
    "  check 100 integral_value 0 1 2 2\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. 0 2 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV4AAAGeCAMAAADrHZmcAAAJJmlDQ1BpY2MAAEiJlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBWXDfGZ33HT+8/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3yiMn5bC8fR0A9/VuxEArcR7ut/P+a4IEZFp/OW4uLxy+SmCdACg7GXWzEpPWeGjy0wPj//CZ1dYsFzgMt9Y4eh/eexLzr8s+pLj681dfhUKABwp+hsO/4b/c++KVDiC9NioyGymT3JUelaYIJKZttIJHpfL9BQkR8UmRH5T8P+V/B2lR2anr0RucsomQWx0TDrzfw41MjA0BF9n8cbrS48hRv9/z2dFX73kegDYcwAg+7564ZUAdO4CQPrRV09tua+UfAA67vAzBJn/eqiVDQ0IgALoQAYoAlWgCXSBETADlsAWOAAX4AF8QRDYAPggBiQCAcgCuWAHKABFYB84CKpALWgATaAVnAad4Dy4Aq6D2+AuGAaPgRBMgpdABN6BBQiCsBAZokEykBKkDulARhAbsoYcIDfIGwqCQqFoKAnKgHKhnVARVApVQXVQE/QLdA66At2EBqGH0Dg0A/0NfYQRmATTYQVYA9aH2TAHdoV94fVwNJwK58D58F64Aq6HT8Id8BX4NjwMC+GX8BwCECLCQJQRXYSNcBEPJBiJQgTIVqQQKUfqkVakG+lD7iFCZBb5gMKgaCgmShdliXJG+aH4qFTUVlQxqgp1AtWB6kXdQ42jRKjPaDJaHq2DtkDz0IHoaHQWugBdjm5Et6OvoYfRk+h3GAyGgWFhzDDOmCBMHGYzphhzGNOGuYwZxExg5rBYrAxWB2uF9cCGYdOxBdhK7EnsJewQdhL7HkfEKeGMcI64YFwSLg9XjmvGXcQN4aZwC3hxvDreAu+Bj8BvwpfgG/Dd+Dv4SfwCQYLAIlgRfAlxhB2ECkIr4RphjPCGSCSqEM2JXsRY4nZiBfEU8QZxnPiBRCVpk7ikEFIGaS/pOOky6SHpDZlM1iDbkoPJ6eS95CbyVfJT8nsxmpieGE8sQmybWLVYh9iQ2CsKnqJO4VA2UHIo5ZQzlDuUWXG8uIY4VzxMfKt4tfg58VHxOQmahKGEh0SiRLFEs8RNiWkqlqpBdaBGUPOpx6hXqRM0hKZK49L4tJ20Bto12iQdQ2fRefQ4ehH9Z/oAXSRJlTSW9JfMlqyWvCApZCAMDQaPkcAoYZxmjDA+SilIcaQipfZItUoNSc1Ly0nbSkdKF0q3SQ9Lf5RhyjjIxMvsl+mUeSKLktWW9ZLNkj0ie012Vo4uZynHlyuUOy33SB6W15b3lt8sf0y+X35OQVHBSSFFoVLhqsKsIkPRVjFOsUzxouKMEk3JWilWqUzpktILpiSTw0xgVjB7mSJleWVn5QzlOuUB5QUVloqfSp5Km8oTVYIqWzVKtUy1R1WkpqTmrpar1qL2SB2vzlaPUT+k3qc+r8HSCNDYrdGpMc2SZvFYOawW1pgmWdNGM1WzXvO+FkaLrRWvdVjrrjasbaIdo12tfUcH1jHVidU5rDO4Cr3KfFXSqvpVo7okXY5upm6L7rgeQ89NL0+vU++Vvpp+sP5+/T79zwYmBgkGDQaPDamGLoZ5ht2GfxtpG/GNqo3uryavdly9bXXX6tfGOsaRxkeMH5jQTNxNdpv0mHwyNTMVmLaazpipmYWa1ZiNsulsT3Yx+4Y52tzOfJv5efMPFqYW6RanLf6y1LWMt2y2nF7DWhO5pmHNhJWKVZhVnZXQmmkdan3UWmijbBNmU2/zzFbVNsK20XaKo8WJ45zkvLIzsBPYtdvNcy24W7iX7RF7J/tC+wEHqoOfQ5XDU0cVx2jHFkeRk4nTZqfLzmhnV+f9zqM8BR6f18QTuZi5bHHpdSW5+rhWuT5z03YTuHW7w+4u7gfcx9aqr01a2+kBPHgeBzyeeLI8Uz1/9cJ4eXpVez33NvTO9e7zofls9Gn2eedr51vi+9hP0y/Dr8ef4h/i3+Q/H2AfUBogDNQP3BJ4O0g2KDaoKxgb7B/cGDy3zmHdwXWTISYhBSEj61nrs9ff3CC7IWHDhY2UjWEbz4SiQwNCm0MXwzzC6sPmwnnhNeEiPpd/iP8ywjaiLGIm0iqyNHIqyiqqNGo62ir6QPRMjE1MecxsLDe2KvZ1nHNcbdx8vEf88filhICEtkRcYmjiuSRqUnxSb7JicnbyYIpOSkGKMNUi9WCqSOAqaEyD0tandaXTlz/F/gzNjF0Z45nWmdWZ77P8s85kS2QnZfdv0t60Z9NUjmPOT5tRm/mbe3KVc3fkjm/hbKnbCm0N39qzTXVb/rbJ7U7bT+wg7Ijf8VueQV5p3tudATu78xXyt+dP7HLa1VIgViAoGN1tubv2B9QPsT8M7Fm9p3LP58KIwltFBkXlRYvF/OJbPxr+WPHj0t6ovQMlpiVH9mH2Je0b2W+z/0SpRGlO6cQB9wMdZcyywrK3BzcevFluXF57iHAo45Cwwq2iq1Ktcl/lYlVM1XC1XXVbjXzNnpr5wxGHh47YHmmtVagtqv14NPbogzqnuo56jfryY5hjmceeN/g39P3E/qmpUbaxqPHT8aTjwhPeJ3qbzJqamuWbS1rgloyWmZMhJ+/+bP9zV6tua10bo63oFDiVcerFL6G/jJx2Pd1zhn2m9az62Zp2WnthB9SxqUPUGdMp7ArqGjzncq6n27K7/Ve9X4+fVz5ffUHyQslFwsX8i0uXci7NXU65PHsl+spEz8aex1cDr97v9eoduOZ67cZ1x+tX+zh9l25Y3Th/0+LmuVvsW523TW939Jv0t/9m8lv7gOlAxx2zO113ze92D64ZvDhkM3Tlnv296/d5928Prx0eHPEbeTAaMip8EPFg+mHCw9ePMh8tPN4+hh4rfCL+pPyp/NP637V+bxOaCi+M24/3P/N59niCP/Hyj7Q/Fifzn5Ofl08pTTVNG02fn3Gcufti3YvJlykvF2YL/pT4s+aV5quzf9n+1S8KFE2+Frxe+rv4jcyb42+N3/bMec49fZf4bmG+8L3M+xMf2B/6PgZ8nFrIWsQuVnzS+tT92fXz2FLi0tI/QiyQvpNzTVQAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAANJQTFRF////y8vLy8vLy8vLy8vLy8vL/wAAAK7vAK7v/wAAAK7vAK7v/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA/wAA9icn61dXJ7TpV7zhAK7vAK7vAK7vAK7vAK7vAK7vAK7vAK7vAK7vAK7vAAAAAAAAAAAAAAAAAAAAAAAArgAAaAAAAHejAEdhAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAy8vL/wAAAK7v519f2ZWVX7zelcPVAAAAiAAARAAAAF1/AC5A////3OYwygAAADl0Uk5TAIi7RCIziDOqRIhEM92ZZu4RqrvMIlWndad1IlXdZhHuzHeZu0QiM4i7Zsenx6eq3ZnuEcxVx6d3OXniWQAAAAFiS0dEAIgFHUgAAAAJcEhZcwAAASwAAAEsAHOI6VIAAAAHdElNRQfjDAMPAxy/McnSAAAJYklEQVR42u2daXPiVhpGlUxiYtqNTbudZKbbgOMILbOgBWYYaZY7y///TSMwBi1XLDX3lUCc8yFVVqp08jygFwmUK8uq5a+n8Y1lhG9Ps357sVbqpd7Lrfc3p/GdmaDfn2b9/pKtAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAnc6Pd2vuBZkxwm2g399MPdGPizZvcUa8cH5MB9YpxnyQPQ+oVYviQJMkn6hXiMfmUPCb31CvCILm/SW51/VLv/83d56zXrN7h5+RmSL2Gyx0kq3dtVq81HCQPN0/Ua46nj9lH2pP1Vq9l/Zj9+Ui95t67j5u361u9WcED6hW5arvlsoJ6qReurd7WF9r6KflZJ/pt+rsuLLTV+jJxf0v+rhP9I/0nq/BRL/W2WS+zt9uLHHJiRr3UC9Tbdr1f+r1SvV/7dGSs3g9p+jza1TvuT9KUjswNh17/OX3pber9OklfRmM6Mjp7f5lMeut6R+kzA9j8R1vvedLL6h2lr7xzJc4cxpNJP+2nr7Qjc2LWSzNeeO9Knff2s3qZu2L1jifpr3Qjd9X2mo7oRq7eUcrkNcG99vZe68sL1QAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAS9inMTVjdU6zOhdrVafhmgnqnWb1LtZKvdR7ufUye6WtAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA0AostMUih6zCR73U27zVPQ3bTFD/NKt/yVYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAuGhutFt7P1xPVsmwt4l2cz/90L12a7JKhr1J7q6m3pqskmE/JoOrqbcmq2DY+yR5GF5JvXVZ5cIOH5Ik+XQd9dZmlQv7mHxKHpP7q6i3NqtY2EFyf5Pc6pzdq7c+q1DYu8+ZK1MOPyc3w47Xuy+rSNi7QbJ6JTOlNRwkDzdPHa53f1aBsE8fszH/ZL0pLevH7M/HrtZ7KKtA2LvHzUv4psykg87Weyir7FXb7RVdtd02f1FMvdRLvdRLvY3Um1sW7V/Jv3Wrpf0n/W/3lomryVoI61Ev9V51vblF/X6f/EG31t8f0z91b5HDmqyFsH4j456PNuqlXuql3sbq/dLvlYxf+52tt4mwReWHNH0e7Yzj/iRNO1tvE2FLyl7/OX3pbYxfJ+nLaNzd4dBA2Oo8+mUy6a2No/S5WwNYM3ulw2qUvedJLzOO0tex1fV6pcPqlOPJpJ/209erOHOQDatV9tKMl/FV1CsbVq/sZ8bunfjWnuPLhdUrx5P016u5rJA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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "- : Jupyter_notebook.display_id = <abstr>\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let _ = png_image \"0_2_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$i,j$ : orbital indices of MOs   occupied in $|I\\rangle$.\n",
    "\n",
    "$\\sum_i \\sum_a \\sum_j \\sum_b \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{ij}$\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{a} \\sum_{b>a} \\sum_{i} \\sum_{j<i}\n",
    "            \\langle i j || a b \\rangle \n",
    "             \\left[ a b || i j \\right] + \n",
    "\\sum_{a} \\sum_{\\bar{b}} \\sum_{i} \\sum_{\\bar{j}}\n",
    "            \\langle i \\bar{j} | a \\bar{b} \\rangle  \n",
    "             \\left[ a \\bar{b} | i \\bar{j} \\right]  + \\\\\n",
    "\\sum_{\\bar{a}} \\sum_{b} \\sum_{\\bar{i}} \\sum_{j}\n",
    "            \\langle \\bar{i} j | \\bar{a} b \\rangle  \n",
    "             \\left[ \\bar{a} b | \\bar{i} j \\right] + \n",
    "\\sum_{\\bar{a}} \\sum_{\\bar{b}>\\bar{a}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
    "            \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{b} \\rangle \n",
    "             \\left[ \\bar{a} \\bar{b} || \\bar{i} \\bar{j} \\right] \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> 'a -> float = <fun>\n"
      ]
     },
     "execution_count": 48,
     "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: (95, 95) | -1.697991e-02 -1.697991e-02 | 2.775558e-17  |  cpu : 3.329183  0.257722\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let integral_value ki kj = \n",
    "   (* Alpha-Beta *)\n",
    "   let s, s' = Spin.(Alfa, Beta) in\n",
    "   sum  mos_cabs  (fun a -> \n",
    "   sum  mos_cabs  (fun b ->  \n",
    "   sum (mos_a ki) (fun i ->  \n",
    "   sum (mos_b ki) (fun j ->  \n",
    "       h_two i j a b s s'  *. f_two a b i j s s'\n",
    "   ))))\n",
    "   +.\n",
    "   (* Alpha-Alpha / Beta-Beta *)\n",
    "   List.fold_left (fun accu (mos,s) -> \n",
    "     let s' = s in accu +.\n",
    "     sum mos_cabs (fun b ->  \n",
    "     sum mos_cabs (fun a -> if b > a then 0. else\n",
    "     sum   mos    (fun j ->  \n",
    "     sum   mos    (fun i -> if i < j then 0. else\n",
    "        h_two i j a b s s'  *. f_two a b i j s s'\n",
    "     ))))\n",
    "   ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
    "     \n",
    "let _ =\n",
    "  check 100 integral_value 0 2 2 2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_0222_Haa : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "             -- 1 --      -- 2 --      -- 3 --      -- 4 --      -- 5 --\n",
       "        1              0  -1.0063E-05 -0.000334496 -0.000347188 -0.000267608\n",
       "        2    -1.0063E-05            0  -0.00016695 -0.000173345 -0.000134367\n",
       "        3   -0.000334496  -0.00016695            0  -0.00370788  -0.00334839\n",
       "                     ...          ...          ...          ...          ...\n",
       "        7   -0.000232416 -0.000151236 -0.000542986 -0.000572891  -2.9266E-05\n",
       "        8   -4.11752E-05 -3.98219E-05 -0.000454591  -0.00047264 -0.000369248\n",
       "        9   -0.000152836 -0.000112257 -0.000183496  -2.9266E-05 -0.000103812\n",
       "  \n",
       "\n",
       "             -- 6 --      -- 7 --      -- 8 --      -- 9 --\n",
       "        1   -0.000165528 -0.000232416 -4.11752E-05 -0.000152836\n",
       "        2   -0.000118652 -0.000151236 -3.98219E-05 -0.000112257\n",
       "        3    -2.9266E-05 -0.000542986 -0.000454591 -0.000183496\n",
       "                     ...          ...          ...          ...\n",
       "        7    -0.00083789            0 -0.000621663 -0.000807984\n",
       "        8    -0.00053632 -0.000621663            0 -0.000518271\n",
       "        9   -0.000728301 -0.000807984 -0.000518271            0\n",
       "  \n"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_0222_Hab : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "             -- 1 --      -- 2 --      -- 3 --      -- 4 --      -- 5 --\n",
       "        1     -0.0026356 -8.37274E-05 -0.000318312 -0.000329372 -0.000258412\n",
       "        2   -8.37274E-05  -0.00329888  -0.00055028  -0.00055898 -0.000498185\n",
       "        3   -0.000318312  -0.00055028  -0.00651939  -0.00351919  -0.00318906\n",
       "                     ...          ...          ...          ...          ...\n",
       "        7   -0.000177876 -0.000280993 -0.000526737 -0.000561143 -0.000637823\n",
       "        8   -7.32564E-05 -0.000232089  -0.00062993 -0.000653508 -0.000521154\n",
       "        9   -0.000106915 -0.000220198 -0.000196607 -0.000319215 -0.000105067\n",
       "  \n",
       "\n",
       "             -- 6 --      -- 7 --      -- 8 --      -- 9 --\n",
       "        1   -0.000117975 -0.000177876 -7.32564E-05 -0.000106915\n",
       "        2   -0.000228899 -0.000280993 -0.000232089 -0.000220198\n",
       "        3   -0.000355709 -0.000526737  -0.00062993 -0.000196607\n",
       "                     ...          ...          ...          ...\n",
       "        7    -0.00104342  -0.00180231 -0.000934604  -0.00100902\n",
       "        8   -0.000825828 -0.000934604 -0.000964699  -0.00080225\n",
       "        9   -0.000917478  -0.00100902  -0.00080225  -0.00135053\n",
       "  \n"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> 'a -> float = <fun>\n"
      ]
     },
     "execution_count": 49,
     "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: (58, 58) | -2.336186e-02 -2.336186e-02 | 3.122502e-17  |  cpu : 3.329266  0.000941\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let m_0222_Haa = \n",
    "  Mat.init_cols mo_num mo_num (fun i j ->\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",
    "        \n",
    "let m_0222_Hab = \n",
    "  Mat.init_cols mo_num mo_num (fun i j ->\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",
    "let integral_value ki kj = \n",
    "   (* Alpha-Beta *)\n",
    "   sum (mos_a ki) (fun i ->  \n",
    "       sum (mos_b ki) (fun j ->  \n",
    "          m_0222_Hab.{i,j}  \n",
    "       ))\n",
    "   +.\n",
    "   (* Alpha-Alpha / Beta-Beta *)\n",
    "   List.fold_left (fun accu (mos) -> \n",
    "     accu +.\n",
    "     sum mos (fun j ->  \n",
    "         sum mos (fun i -> if i < j then 0. else\n",
    "           m_0222_Haa.{i,j}  \n",
    "     ))\n",
    "   ) 0. [ (mos_a ki) ; (mos_b ki)]\n",
    "     \n",
    "let _ =\n",
    "  check 100 integral_value 0 2 2 2\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. 1 1 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "- : Jupyter_notebook.display_id = <abstr>\n"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let _ = png_image \"1_1_11.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
    "\n",
    "$j$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$\\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{k}$\n",
    "\n",
    "\\begin{align}\n",
    "    \\sum_{a} \n",
    "    \\left( h_{ia} +\\sum_{j} \\langle i j || a j \\rangle +\n",
    "    \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle  \\right)\n",
    "    \\left( f_{ak} +\\sum_{j}  \\left[ a j || k j \\right] + \n",
    "    \\sum_{\\bar{j}}  \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 51,
     "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: (0, 0) | 0.000000e+00 0.000000e+00 | 0.000000e+00  |  cpu : 4.151429  1.045428\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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_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",
    "    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",
    "       let s' = Spin.other s in\n",
    "       \n",
    "       sum mos_cabs (fun a -> \n",
    "           (h_one i a s +. \n",
    "              sum mos_i  (fun j ->  h_two i j a j s s ) +.\n",
    "              sum mos_i' (fun j ->  h_two i j a j s s') ) *.\n",
    "           (f_one a k s +. \n",
    "              sum mos_j  (fun j ->  f_two a j k j s s ) +.\n",
    "              sum mos_j' (fun j ->  f_two a j k j s s') )  \n",
    "         )\n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 0 integral_value 1 1 1 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let ki = det_I.(77)\n",
    "let kj = det_I.(83)\n",
    "\n",
    "let _ = integral_value ki kj"
   ]
  },
  {
   "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 ->\n",
    "            h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n",
    "\n",
    "\n",
    "let m_1111_1H_2Fa = \n",
    "  array_3_init mo_num mo_num mo_num (fun i j 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",
    "\n",
    "    \n",
    "let m_1111_1H_2Fb = \n",
    "  array_3_init mo_num mo_num mo_num (fun i j 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",
    "\n",
    "\n",
    "let m_1111_2Ha_1F = \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 *. f_one a k Spin.Alfa ))\n",
    "\n",
    "    \n",
    "let m_1111_2Hb_1F = \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.Beta *. f_one a k Spin.Alfa ))\n",
    "\n",
    "\n",
    "let m_1111_2Ha_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_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "      f_two a l k l 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 i j k l ->\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",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1111_2Ha_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_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "      f_two a l k l Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1111_2Hb_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_two i j a j Spin.Alfa Spin.Beta *.\n",
    "      f_two a l k l Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let integral_value_11 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_a, mos_b =\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 result = \n",
    "     m_1111_1H_1F.{i,k} +. \n",
    "     sum mos_a (fun j -> if j = i then 0. else\n",
    "       m_1111_1H_2Fa.{i,j,k} +. m_1111_2Ha_1F.{i,j,k} +.\n",
    "       sum mos_a (fun l -> if l = i then 0. else m_1111_2Ha_2Fa.{i,j,k,l}) +.\n",
    "       sum mos_b (fun l -> m_1111_2Ha_2Fb.{i,j,k,l})) +.\n",
    "     sum mos_b (fun j ->\n",
    "       m_1111_1H_2Fb.{i,j,k} +. m_1111_2Hb_1F.{i,j,k} +.\n",
    "       sum mos_a (fun l -> if l = i then 0. else m_1111_2Hb_2Fa.{i,j,k,l}) +.\n",
    "       sum mos_b (fun l -> m_1111_2Hb_2Fb.{i,j,k,l}))\n",
    "    in\n",
    "    \n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "    \n",
    "let _ =\n",
    "  check 0 integral_value_11 1 1 1 1\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. 1 1 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"1_1_12.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
    "\n",
    "$\\sum_{j} \\sum_a \\hat{T}_{j}^{a} \\hat{T}_{ai}^{jk}$\n",
    "\n",
    "$j$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "\\begin{align}\n",
    "    \\sum_{a} \\sum_{j} \n",
    "    \\left( h_{ja} +\\sum_{m} \\langle j m || a m \\rangle +\n",
    "    \\sum_{\\bar{m}} \\langle j \\bar{m} | a \\bar{m} \\rangle  \\right)\n",
    "    \\left[ a i || j k \\right] + \\\\\n",
    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n",
    "    \\left( h_{\\bar{j}\\bar{a}} +\\sum_{m} \\langle \\bar{j} m | \\bar{a} m \\rangle +\n",
    "    \\sum_{\\bar{m}} \\langle \\bar{j} \\bar{m} || \\bar{a} \\bar{m} \\rangle  \\right)\n",
    "    \\left[ \\bar{a} i | \\bar{j} k \\right] \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "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_j, mos_j' =\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 result = \n",
    "       let s' = Spin.other s in\n",
    "       sum mos_cabs (fun a -> \n",
    "           sum mos_j (fun j -> \n",
    "               (h_one j a s +. \n",
    "                  sum mos_i  (fun m -> h_two j m a m s s )  +.\n",
    "                  sum mos_i' (fun m -> h_two j m a m s s')  ) *.\n",
    "               (f_two a i j k s s )\n",
    "             ) \n",
    "           +.\n",
    "           sum mos_j' (fun j -> \n",
    "               (h_one j a s +. \n",
    "                  sum mos_i  (fun m ->  h_two j m a m s' s ) +.\n",
    "                  sum mos_i' (fun m ->  h_two j m a m s' s') ) *.\n",
    "               (f_two a i j k s' s )\n",
    "             ) \n",
    "         ) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 1 1 1 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let m_1112_1H_2Fa = \n",
    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "      sum mos_cabs (fun a ->\n",
    "        h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa ))\n",
    "\n",
    "    \n",
    "let m_1112_1H_2Fb = \n",
    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "      sum mos_cabs (fun a ->\n",
    "        h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta ))\n",
    "\n",
    "\n",
    "let m_1112_2Ha_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j m a m Spin.Alfa Spin.Alfa *.\n",
    "      f_two a i j k Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1112_2Hb_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j m a m Spin.Alfa Spin.Beta *.\n",
    "      f_two a i j k Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1112_2Ha_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j m a m Spin.Alfa Spin.Alfa *.\n",
    "      f_two a i j k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1112_2Hb_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j m a m Spin.Alfa Spin.Beta *.\n",
    "      f_two a i j k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let integral_value_12 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_j, mos_j' =\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 result = \n",
    "     sum mos_j (fun j -> \n",
    "       m_1112_1H_2Fa.{i,j,k} +. \n",
    "       sum mos_i  (fun m -> m_1112_2Ha_2Fa.{i,j,k,m}) +.\n",
    "       sum mos_i' (fun m -> m_1112_2Hb_2Fa.{i,j,k,m})) +.\n",
    "     sum mos_j' (fun j ->\n",
    "       m_1112_1H_2Fb.{i,j,k} +. \n",
    "       sum mos_i  (fun m -> m_1112_2Hb_2Fb.{i,j,k,m}) +.\n",
    "       sum mos_i' (fun m -> m_1112_2Ha_2Fb.{i,j,k,m}))\n",
    "    in\n",
    "    \n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "   \n",
    "   \n",
    "\n",
    "let _ = check 100 integral_value_12 1 1 1 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. 1 1 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let _ = png_image \"1_1_21.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
    "\n",
    "$\\sum_{j} \\sum_a \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{j}$\n",
    "\n",
    "$j$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "\\begin{align}\n",
    "    \\sum_{a} \\sum_{j} \n",
    "    \\langle i j || k a \\rangle \n",
    "    \\left( f_{aj} +\\sum_{m} \\left[ m a || m j \\right] +\n",
    "    \\sum_{\\bar{m}} \\left[ \\bar{m} a | \\bar{m} j \\right] \\right) + \\\\\n",
    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n",
    "    \\langle i \\bar{j} | k \\bar{a} \\rangle\n",
    "    \\left( f_{\\bar{a}\\bar{j}} +\\sum_{m} \\left[ m \\bar{a} | m \\bar{j} \\right] +\n",
    "    \\sum_{\\bar{m}} \\left[ \\bar{m} \\bar{a} || \\bar{m} \\bar{j} \\right]  \\right)\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "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_j, mos_j' =\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 kj, mos_b kj\n",
    "      | Spin.Beta -> mos_b kj, mos_a kj\n",
    "    in\n",
    "\n",
    "    let result = \n",
    "       let s' = Spin.other s in\n",
    "       sum mos_cabs (fun a -> \n",
    "       sum mos_j    (fun j -> \n",
    "               (h_two i j k a s s ) *.\n",
    "               (f_one a j s  +. \n",
    "                  sum mos_i  (fun m -> f_two m a m j s  s) +.\n",
    "                  sum mos_i' (fun m -> f_two m a m j s' s) ) \n",
    "             ) \n",
    "       +.\n",
    "       sum mos_j' (fun j -> \n",
    "               (h_two i j k a s s') *.\n",
    "               (f_one a j s' +. \n",
    "                  sum mos_i  (fun m -> f_two m a m j s  s') +.\n",
    "                  sum mos_i' (fun m -> f_two m a m j s' s') ) \n",
    "       )) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 1 1 2 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let m_1121_2Ha_1F = \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 k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa))\n",
    "\n",
    "    \n",
    "let m_1121_2Hb_1F = \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 k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta))\n",
    "\n",
    "\n",
    "let m_1121_2Ha_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
    "      f_two m a m 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 i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two m a m 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 i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
    "      f_two m a m 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 i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two m a m j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let integral_value_21 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_j, mos_j' =\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 kj, mos_b kj\n",
    "      | Spin.Beta -> mos_b kj, mos_a kj\n",
    "    in\n",
    "   \n",
    "    let result = \n",
    "     sum mos_j (fun j -> \n",
    "       m_1121_2Ha_1F.{i,j,k} +. \n",
    "       sum mos_i  (fun m -> m_1121_2Ha_2Fa.{i,j,k,m}) +.\n",
    "       sum mos_i' (fun m -> m_1121_2Ha_2Fb.{i,j,k,m})) +.\n",
    "     sum mos_j' (fun j ->\n",
    "       m_1121_2Hb_1F.{i,j,k} +. \n",
    "       sum mos_i  (fun m -> m_1121_2Hb_2Fb.{i,j,k,m}) +.\n",
    "       sum mos_i' (fun m -> m_1121_2Hb_2Fa.{i,j,k,m}))\n",
    "    in\n",
    "    \n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "   \n",
    "   \n",
    "\n",
    "let _ = check 100 integral_value_21 1 1 2 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. 1 1 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"1_1_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
    "\n",
    "$\\sum_{j} \\sum_{a} \\sum_{m}\n",
    "    \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kj} - \n",
    "    \\hat{T}_{lj}^{ka} \\hat{T}_{ia}^{lj} + \\\\\n",
    "\\sum_{\\bar{j}} \\sum_{\\bar{a}} \\sum_{m}\n",
    "    \\hat{T}_{i\\bar{j}}^{m\\bar{a}} \\hat{T}_{m\\bar{a}}^{k\\bar{j}} - \n",
    "    \\hat{T}_{l\\bar{j}}^{k\\bar{a}} \\hat{T}_{i\\bar{a}}^{l\\bar{j}} +\n",
    "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{m}}\n",
    "    \\hat{T}_{i\\bar{j}}^{a\\bar{m}} \\hat{T}_{a\\bar{m}}^{k\\bar{j}} \n",
    "$\n",
    "\n",
    "$j,l$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$m$ : orbital indices of virtual MOs, unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$a$ : orbital indices of CABS MOs\n",
    "\n",
    "\\begin{align}\n",
    "    \\sum_{a} \\sum_{j} \\sum_{m}\n",
    "      \\langle i j || m a \\rangle  \\left[ m a || k j \\right]  - \\\\\n",
    "    \\sum_{a} \\sum_{j} \\sum_{l}\n",
    "      \\langle l j || k a \\rangle  \\left[ i a || l j \\right]  + \\\\\n",
    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m}\n",
    "      \\langle i \\bar{j} | m \\bar{a} \\rangle  \\left[ m \\bar{a} | k \\bar{j} \\right]  + \\\\\n",
    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l}\n",
    "      \\langle l \\bar{j} | k \\bar{a} \\rangle  \\left[ i \\bar{a} | l \\bar{j} \\right] - \\\\\n",
    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{\\bar{m}}\n",
    "      \\langle i \\bar{j} | a \\bar{m} \\rangle  \\left[ a \\bar{m} | k \\bar{j} \\right]  \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(*\n",
    "let ki = det_I.(6)\n",
    "let kj = det_I.(58)\n",
    "\n",
    "let _ = \n",
    "    Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
    "generate_alphas ki kj 1 1 2 2\n",
    "|> Array.of_list\n",
    "|> Array.mapi (fun kk alpha -> \n",
    "\n",
    "(*\n",
    "let _ = Determinant.to_lists ki\n",
    "let _ = Determinant.to_lists alpha\n",
    "let _ = Determinant.to_lists kj\n",
    "\n",
    "   \n",
    "let _ = \n",
    "    Format.printf \"|I> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det ki kj);\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",
    "\n",
    "    let integral_value ki kj = \n",
    "    \n",
    "      let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
    "      let exc1 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n",
    "      let exc2 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n",
    " \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",
    "      let spin = function\n",
    "        | Spin.Alfa -> 0\n",
    "        | _ -> 1\n",
    "      in\n",
    "        exc0.(i).(spin s ) <- \"i\" \n",
    "      ; exc0.(k).(spin s ) <- \"k\" \n",
    "      ;\n",
    "      let s0 = 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 ) <- \"n\";\n",
    "      if exc0.(j).(spin s') =  \"-\" then exc0.(j).(spin s') <- \"n\";\n",
    "      if exc0.(k).(spin s ) =  \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n",
    "      if exc0.(l).(spin s') =  \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\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 \"s'\")\n",
    "            (if s' = s0 then \"s \" else \"s'\")\n",
    "            (*\n",
    "            (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s  \" else \n",
    "             if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \"s''\")\n",
    "            (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s  \" else \n",
    "             if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \"s''\")\n",
    "             *)\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",
    "            (*\n",
    "            (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s  \" else \n",
    "             if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \n",
    "             if exc0.(i).(spin s ) = \"n\" || exc0.(k).(spin s ) = \"n\" then \"s''\" else\n",
    "             if s  = s0 then \"s\" else \"s'\")\n",
    "            (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s  \" else \n",
    "             if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \n",
    "             if exc0.(j).(spin s') = \"n\" || exc0.(l).(spin s') = \"n\" then \"s''\" else\n",
    "             if s' = s0 then \"s\" else \"s'\")\n",
    "             *)\n",
    "            (if s  = s0 then \"s \" else \"s'\")\n",
    "            (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",
    "    let sign = \n",
    "        if Phase.add p1 p2 = phase then \"+. \" else \"-. \"\n",
    "    in\n",
    "sign ^ string_h ^ string_f\n",
    "(*\n",
    "        \n",
    "        let mos, mos' =\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 result = \n",
    "           let k=4 and l=5 in\n",
    "           let i=1 and j=2 in\n",
    "           let n=2 and a=7 in\n",
    "           let s   = Spin.Alfa\n",
    "           and s'  = Spin.Alfa\n",
    "           and s'' = Spin.Beta\n",
    "           in\n",
    "           (* \n",
    "           h_two j n l a s' s'' *. f_two a i n k s s''\n",
    "           *)\n",
    "           h_two i n k a s s'' *. f_two j a l n s s''\n",
    "        in\n",
    "\n",
    "        match phase with\n",
    "        | Phase.Pos -> result\n",
    "        | Phase.Neg -> -. result\n",
    "        *)\n",
    "\n",
    "in\n",
    "integral_value ki kj\n",
    "(*\n",
    "let a = (compute_HaaF ki [alpha] kj)\n",
    "and b = (integral_value ki kj)\n",
    "in\n",
    "if kk = 31 then\n",
    "    Format.printf \"%6d %e %e@.@.\" (kk) a b\n",
    "    *)\n",
    ")\n",
    "|> Array.to_list\n",
    "|> List.sort_uniq compare\n",
    "\n",
    "let _ = compute_HaaF ki (generate_alphas ki kj 1 1 2 2) kj\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "\n",
    "*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "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",
    "   (* MOs unoccupied in both I and J *)\n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.init mo_num (fun i -> Some (i+1)) , \n",
    "     Array.init mo_num (fun i -> Some (i+1)) \n",
    "   in\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
    "   \n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.to_list mos_virt_a |> Util.list_some,\n",
    "     Array.to_list mos_virt_b |> Util.list_some\n",
    "   in\n",
    "\n",
    "   let mos_virt, mos_virt' =\n",
    "      match s with\n",
    "      | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
    "      | Spin.Beta -> mos_virt_b, mos_virt_a\n",
    "   in\n",
    "    \n",
    "   let mos_j, mos_j' =\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",
    "   let result = \n",
    "       let s' = Spin.other s in\n",
    "        sum mos_cabs (fun a -> \n",
    "        sum mos_j    (fun n -> \n",
    "        sum mos_virt (fun m -> \n",
    "             h_two n i a m s  s  *.  f_two m a k n s  s \n",
    "        ))) +.\n",
    "        sum mos_cabs (fun a' -> \n",
    "        sum mos_j'   (fun n' -> \n",
    "        sum mos_virt (fun m -> \n",
    "             h_two i n' m a' s  s' *.  f_two m a' k n' s  s'\n",
    "        ))) +.\n",
    "        sum mos_cabs  (fun a -> \n",
    "        sum mos_j'    (fun n' -> \n",
    "        sum mos_virt' (fun m' -> \n",
    "             h_two i n' a m' s  s' *.  f_two a m' k n' s  s'\n",
    "        ))) -. \n",
    "        sum mos_cabs (fun a -> \n",
    "        sum mos_j    (fun n -> \n",
    "        sum mos_j    (fun l -> if l <=n then 0. else\n",
    "             h_two n l a k s  s  *.  f_two i a l n s  s \n",
    "        ))) -.  \n",
    "        sum mos_cabs (fun a' -> \n",
    "        sum mos_j'   (fun n' -> \n",
    "        sum mos_j    (fun l -> \n",
    "             h_two l n' k a' s s'  *.  f_two i a' l n' s s'\n",
    "        ))) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "let _ = check 100 integral_value 1 1 2 2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let m_1122_va =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j i a m Spin.Alfa Spin.Alfa *.\n",
    "      f_two m a k j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1122_v2 =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j m a Spin.Alfa Spin.Beta *.\n",
    "      f_two m a k j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1122_v3 =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a m Spin.Alfa Spin.Beta *.\n",
    "      f_two a m k j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1122_oa =\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_two j l a k Spin.Alfa Spin.Alfa *.\n",
    "      f_two i a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1122_o =\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_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",
    "let integral_value_22 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",
    "   (* MOs unoccupied in both I and J *)\n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.init mo_num (fun i -> Some (i+1)) , \n",
    "     Array.init mo_num (fun i -> Some (i+1)) \n",
    "   in\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
    "   \n",
    "   let mos_virt_a, mos_virt_b = \n",
    "     Array.to_list mos_virt_a |> Util.list_some,\n",
    "     Array.to_list mos_virt_b |> Util.list_some\n",
    "   in\n",
    "\n",
    "   let mos_virt, mos_virt' =\n",
    "      match s with\n",
    "      | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
    "      | Spin.Beta -> mos_virt_b, mos_virt_a\n",
    "   in\n",
    "    \n",
    "   let mos_j, mos_j' =\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 result = \n",
    "        sum mos_j    (fun j -> \n",
    "        sum mos_virt (fun m -> \n",
    "          m_1122_va.{i,j,k,m}\n",
    "        )) +.\n",
    "        sum mos_j'   (fun j -> \n",
    "        sum mos_virt (fun m -> \n",
    "          m_1122_v2.{i,j,k,m}\n",
    "        ))   +.\n",
    "        \n",
    "        sum mos_j'    (fun j -> \n",
    "        sum mos_virt' (fun m -> \n",
    "          m_1122_v3.{i,j,k,m}\n",
    "        ))   -.\n",
    "        sum mos_j    (fun j -> \n",
    "        sum mos_j    (fun l -> if l <= j then 0. else\n",
    "          m_1122_oa.{i,j,k,l}\n",
    "        )) -. \n",
    "        sum mos_j'   (fun j -> \n",
    "        sum mos_j    (fun l -> \n",
    "          m_1122_o.{i,j,k,l}\n",
    "        )) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value_22 1 1 2 2\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let ki = det_I.(77) and kj = det_I.(83)\n",
    "\n",
    "let _ =\n",
    "integral_value_11 ki kj\n",
    "+. integral_value_12 ki kj\n",
    "+. integral_value_21 ki kj\n",
    "+. integral_value_22 ki kj "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8. 1 2 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"1_2_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
    "\n",
    "$j$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$\\sum_{j} \\sum_{a} \\sum_{b}\n",
    "    \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{kj} +\n",
    "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{b}}\n",
    "    \\hat{T}_{i\\bar{j}}^{a\\bar{b}} \\hat{T}_{a\\bar{b}}^{k\\bar{j}} \n",
    "$\n",
    "\n",
    "\n",
    "$$\n",
    "\\sum_{j} \\sum_{b}\\sum_{a<b}\n",
    "    \\langle i j || a b \\rangle \\left[ ab || kj \\right] + \n",
    "\\sum_{\\bar{j}} \\sum_{\\bar{b}}\\sum_{a}\n",
    "    \\langle i \\bar{j} | a \\bar{b} \\rangle \\left[ a \\bar{b} | k \\bar{j} \\right] \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let integral_value ki kj = \n",
    "    let h, p, 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, mos' =\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",
    "   \n",
    "\n",
    "    let result = \n",
    "       (* Alpha-Beta *)\n",
    "       let s' = Spin.other s in\n",
    "       sum mos_cabs (fun b -> \n",
    "       sum mos_cabs (fun a -> \n",
    "       sum mos'     (fun j -> h_two h j a b s s'  *. f_two a b p j s s')\n",
    "       ))\n",
    "       +.\n",
    "       (* Alpha-Alpha / Beta-Beta *)\n",
    "       sum mos_cabs (fun b -> \n",
    "       sum mos_cabs (fun a -> if b >= a then 0. else\n",
    "       sum mos  (fun j -> h_two h j a b s s  *. f_two a b p j s s)\n",
    "       )) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 1 2 2 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let m_1222a =\n",
    "  array_3_init mo_num mo_num mo_num (fun i j k ->\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 *.\n",
    "      f_two a b k j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1222 =\n",
    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "    sum mos_cabs (fun a ->\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",
    "\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",
    "   (* MOs unoccupied in both I and J *)\n",
    "    let mos_j, mos_j' =\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 result = \n",
    "        sum mos_j    (fun j ->  m_1222a.{i,j,k} ) +.\n",
    "        sum mos_j'   (fun j ->  m_1222.{i,j,k} )\n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 1 2 2 2\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9. 2 1 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"2_1_12.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
    "\n",
    "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
    "\n",
    "$\\sum_{a} \n",
    "    \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n",
    "    \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n",
    "$\n",
    "\n",
    "\n",
    "$$\n",
    "\\sum_{a}\n",
    "    \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n",
    "\\sum_{a}\n",
    "    \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "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",
    "\n",
    "        let mos, mos' =\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 mos2, mos2' =\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 result = \n",
    "       sum mos_cabs (fun a -> \n",
    "           let s'' = Spin.other s in\n",
    "             ( h_one i a s +.\n",
    "               sum mos  (fun n -> h_two i n a n s s  ) +.\n",
    "               sum mos' (fun n -> h_two i n a n s s'') \n",
    "             ) *. f_two a j k l s s'\n",
    "             ) +.\n",
    "       sum mos_cabs (fun a -> \n",
    "           let s'' = Spin.other s' in\n",
    "             ( h_one j a s' +.\n",
    "               sum mos2 (fun n -> h_two j n a n s' s' ) +.\n",
    "               sum mos2'  (fun n -> h_two j n a n s' s'') \n",
    "             ) *. f_two i a k l s s'\n",
    "             ) \n",
    "        in\n",
    "\n",
    "        match phase with\n",
    "        | Phase.Pos -> result\n",
    "        | Phase.Neg -> -. result\n",
    "\n",
    "\n",
    "let _ = check 100 integral_value 2 1 1 2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
    "\n",
    "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
    "\n",
    "$\\sum_{a} \n",
    "    \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n",
    "    \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n",
    "$\n",
    "\n",
    "\n",
    "$$\n",
    "\\sum_{a}\n",
    "    \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n",
    "\\sum_{a}\n",
    "    \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "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",
    "    )\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",
    "    )\n",
    "\n",
    "let m_2112_2Ha_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Alfa *.\n",
    "        f_two a j k l Spin.Alfa Spin.Alfa )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Hb_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Beta *.\n",
    "        f_two a j k l Spin.Alfa Spin.Alfa )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Ha_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Alfa *.\n",
    "        f_two a j k l Spin.Alfa Spin.Beta )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Hb_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Beta *.\n",
    "        f_two a j k l Spin.Alfa Spin.Beta )\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, mos' =\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 result = \n",
    "       if s = s' then\n",
    "         m_2112_1H_2Fa.{i,j,k,l} +. \n",
    "         sum mos  (fun n ->\n",
    "             m_2112_2Ha_2Fa.{i,j,k,l,n} +. m_2112_2Ha_2Fa.{j,i,l,k,n}\n",
    "         ) +.\n",
    "         sum mos' (fun n ->\n",
    "             m_2112_2Hb_2Fa.{i,j,k,l,n} +. m_2112_2Hb_2Fa.{j,i,l,k,n}\n",
    "         ) \n",
    "       else\n",
    "         m_2112_1H_2Fb.{i,j,k,l} +.\n",
    "         sum mos  (fun n ->\n",
    "             m_2112_2Ha_2Fb.{i,j,k,l,n} +. m_2112_2Hb_2Fb.{j,i,l,k,n}\n",
    "         ) +.\n",
    "         sum mos' (fun n ->\n",
    "             m_2112_2Hb_2Fb.{i,j,k,l,n} +. m_2112_2Ha_2Fb.{j,i,l,k,n}\n",
    "         ) \n",
    "     in\n",
    "\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "let _ = check 100 integral_value 2 1 1 2\n",
    "\n",
    "let ki = det_I.(2)\n",
    "let kj = det_I.(33)\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "let _ = \n",
    "    let alphas =  generate_alphas ki kj 2 1 1 2\n",
    "    in compute_HaaF ki alphas kj\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 10. 2 1 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"2_1_21.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
    "\n",
    "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$n$ : orbital indices of MOs occupied in $|J\\rangle$\n",
    "\n",
    "$\\sum_{a} \n",
    "    \\hat{T}_{ij}^{al} \\hat{T}_{a}^{k} +\n",
    "    \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{l} +\n",
    "    \\hat{T}_{i\\bar{j}}^{a\\bar{l}} \\hat{T}_{a}^{k} +\n",
    "    \\hat{T}_{i\\bar{j}}^{k\\bar{a}} \\hat{T}_{\\bar{a}}^{\\bar{l}}\n",
    "$\n",
    "\n",
    "\n",
    "$$\n",
    "\\sum_{a}\n",
    "    \\langle i j || a l \\rangle \\left( f_{ak} + \\sum_{n} \\left[ a n || k n \\right] + \\sum_{\\bar{n}} \\left[ a \\bar{n} | k \\bar{n} \\right] \\right) + \\\\\n",
    "\\sum_{a}\n",
    "    \\langle i j || k a \\rangle \\left( f_{al} + \\sum_{n} \\left[ n a || n l \\right] + \\sum_{\\bar{n}} \\left[ \\bar{n} a | \\bar{n} l \\right] \\right) \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "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",
    "\n",
    "        let result = \n",
    "        \n",
    "        let mos, mos', s'' =\n",
    "          match s with\n",
    "          | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n",
    "          | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n",
    "        in\n",
    "        sum mos_cabs (fun a -> \n",
    "             h_two i j a l s s' *.\n",
    "             ( f_one a k s +.\n",
    "               sum mos  (fun n -> f_two a n k n s s) +.\n",
    "               sum mos' (fun n -> f_two a n k n s s'') \n",
    "             ) ) +.\n",
    "\n",
    "        let mos, mos', s'' =\n",
    "          match s' with\n",
    "          | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n",
    "          | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n",
    "        in\n",
    "        sum mos_cabs (fun a -> \n",
    "             h_two j i a k s' s *.\n",
    "             ( f_one a l s' +.\n",
    "               sum mos  (fun n -> f_two a n l n s' s') +.\n",
    "               sum mos' (fun n -> f_two a n l n s' s'') \n",
    "             ) \n",
    "             ) \n",
    "        in\n",
    "\n",
    "        match phase with\n",
    "        | Phase.Pos -> result\n",
    "        | Phase.Neg -> -. result\n",
    "\n",
    "\n",
    "let _ = check 100 integral_value 2 1 2 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "let m_2121_2Ha_1F =\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_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",
    "    )\n",
    "\n",
    "let m_2121_2Hb_1F =\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_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",
    "    )\n",
    "\n",
    "let m_2121_2Ha_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *.\n",
    "        f_two a n k n Spin.Alfa Spin.Alfa )\n",
    "    )\n",
    "    \n",
    "let m_2121_2Hb_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Beta *.\n",
    "        f_two a n k n Spin.Alfa Spin.Alfa )\n",
    "    )\n",
    "    \n",
    "let m_2121_2Ha_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *.\n",
    "        f_two a n k n Spin.Alfa Spin.Beta )\n",
    "    )\n",
    "    \n",
    "let m_2121_2Hb_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Beta *.\n",
    "        f_two a n k n Spin.Alfa Spin.Beta )\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, mos' =\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",
    "       if s = s' then\n",
    "         m_2121_2Ha_1F.{i,j,k,l} +. \n",
    "         sum mos  (fun n ->\n",
    "             m_2121_2Ha_2Fa.{i,j,k,l,n} +. m_2121_2Ha_2Fa.{j,i,l,k,n}\n",
    "         ) +.\n",
    "         sum mos' (fun n ->\n",
    "             m_2121_2Ha_2Fb.{i,j,k,l,n} +. m_2121_2Ha_2Fb.{j,i,l,k,n}\n",
    "         ) \n",
    "       else\n",
    "         m_2121_2Hb_1F.{i,j,k,l} +.\n",
    "         sum mos  (fun n ->\n",
    "             m_2121_2Hb_2Fa.{i,j,k,l,n} +. m_2121_2Hb_2Fb.{j,i,l,k,n}\n",
    "         ) +.\n",
    "         sum mos' (fun n ->\n",
    "             m_2121_2Hb_2Fb.{i,j,k,l,n} +. m_2121_2Hb_2Fa.{j,i,l,k,n}\n",
    "         ) \n",
    "     in\n",
    "\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 2 1 2 1\n",
    "\n",
    "(*\n",
    "let ki = det_I.(2)\n",
    "let kj = det_I.(33)\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "let _ = \n",
    "    let alphas =  generate_alphas ki kj 2 1 2 1\n",
    "    in compute_HaaF ki alphas kj\n",
    "*)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11. 2 1 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"2_1_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
    "\n",
    "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
    "\n",
    "$n$ : orbital indices of MOs occupied in both $|I\\rangle$ and $|J\\rangle$ .\n",
    "\n",
    "$\\sum_{a} \n",
    "    \\hat{T}_{ij}^{am} \\hat{T}_{am}^{kl} +\n",
    "    \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kl} -\n",
    "    \\hat{T}_{in}^{al} \\hat{T}_{aj}^{kn} -\n",
    "    \\hat{T}_{nj}^{ka} \\hat{T}_{ia}^{nl} +\n",
    "    \\sum_{n}\n",
    "    \\hat{T}_{i\\bar{n}}^{k\\bar{a}} \\hat{T}_{\\bar{a}j}^{\\bar{n}l}\n",
    "$\n",
    "\n",
    "\n",
    "$$\n",
    "\\sum_{a}\n",
    "\\sum_{m} \\langle i j || a m \\rangle \\left[ a m || k l \\right] +  \\langle i j || m a \\rangle \\left[ m a || k l \\right] - \\\\\n",
    "\\sum_{n} \\langle i n || a l \\rangle \\left[ a j || k n \\right] +  \\langle n j || k a \\rangle \\left[ i a || n l \\right] \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "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",
    "\n",
    "    let mos_virt_a, mos_virt_b = \n",
    "       Array.init mo_num (fun i -> Some (i+1)) , \n",
    "       Array.init mo_num (fun i -> Some (i+1)) \n",
    "    in\n",
    "    List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
    "    List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
    "    List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
    "    List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
    "\n",
    "    let mos_virt_a, mos_virt_b = \n",
    "      Array.to_list mos_virt_a |> Util.list_some,\n",
    "      Array.to_list mos_virt_b |> Util.list_some\n",
    "    in\n",
    "   \n",
    "    let result = \n",
    "        \n",
    "        let mos_virt, mos_virt' =\n",
    "          match s with\n",
    "          | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
    "          | Spin.Beta -> mos_virt_b, mos_virt_a\n",
    "        in\n",
    "        \n",
    "        let mos, mos' =\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",
    "        if s = s' then            \n",
    "            let s'' = Spin.other s' in\n",
    "            sum mos_cabs (fun a -> \n",
    "            sum mos  (fun n ->\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",
    "            +. sum mos_virt (fun m ->\n",
    "                -. h_two i j a m s  s  *.  f_two m a k l s  s )\n",
    "            +. sum mos' (fun n ->\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",
    "        else\n",
    "            sum mos_cabs (fun a ->\n",
    "            sum mos_virt' (fun m ->\n",
    "                  h_two i j a m s  s' *.  f_two a m k l s  s' ) +.\n",
    "            sum mos_virt  (fun m ->\n",
    "                  h_two i j m a s  s' *.  f_two m a k l s  s' ) +.\n",
    "            sum mos  (fun n ->\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",
    "            sum mos' (fun n -> if n >= j then 0. else \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",
    "            sum mos' (fun n -> if n <= j then 0. 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",
    "            sum mos' (fun n -> \n",
    "               -. h_two i n a l s  s' *.  f_two a j k n s  s'\n",
    "               )\n",
    "            )\n",
    "    in\n",
    "\n",
    "    match phase with\n",
    "        | Phase.Pos -> result\n",
    "        | Phase.Neg -> -. result\n",
    "\n",
    "\n",
    "let _ = check 300 integral_value 2 1 2 2"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/markdown",
    "scrolled": false
   },
   "source": [
    "let ki = det_I.(99)\n",
    "let kj = det_I.(193)\n",
    "\n",
    "let alpha_to_string alpha = \n",
    "   \n",
    "      let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
    " \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 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",
    "      ;\n",
    "      let s0, s0' = 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 ) <- \"n\";\n",
    "      if exc0.(j).(spin s') =  \"-\" then exc0.(j).(spin s') <- \"n\";\n",
    "      if exc0.(k).(spin s ) =  \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n",
    "      if exc0.(l).(spin s') =  \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\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 \"s'\")\n",
    "            (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 \"s'\")\n",
    "            (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 2 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 2 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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 12. 2 2 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"2_2_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
    "\n",
    "$$\n",
    "\\sum_{b}\\sum_{a<b}\n",
    "    \\langle i j || a b \\rangle \n",
    "    \\left[ ab || kj \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let integral_value ki kj = \n",
    "    let h, h', p, p', s, s', phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Double (phase,\n",
    "              { hole=h ; particle=p ; spin=s },\n",
    "              { hole=h'; particle=p'; spin=s'}) )  -> h, h', p, p', s, s', phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "\n",
    "    let result = \n",
    "       if s <> s' then (* Alpha-Beta *)\n",
    "           sum mos_cabs (fun b -> \n",
    "           sum mos_cabs (fun a -> \n",
    "               h_two h h' a b s s'  *. f_two a b p p' s s'\n",
    "           )) \n",
    "       else (* Alpha-Alpha / Beta-Beta *)\n",
    "           sum mos_cabs (fun b -> \n",
    "           sum mos_cabs (fun a ->  if b >= a then 0. else\n",
    "               h_two h h' a b s s'  *. f_two a b p p' s s'\n",
    "           )) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 2 2 2 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13. 3 1 2 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let _ = png_image \"3_1_22.png\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$|J\\rangle = \\hat{T}_{ijm}^{kln}|I\\rangle$\n",
    "\n",
    "$\\sum_{a}\n",
    "    \\hat{T}_{ij}^{al} \\hat{T}_{am}^{kn}   \n",
    "  + \\hat{T}_{ij}^{ka} \\hat{T}_{am}^{ln}   \n",
    "  + \\hat{T}_{im}^{ka} \\hat{T}_{ja}^{ln}   \n",
    "  + \\hat{T}_{im}^{an} \\hat{T}_{aj}^{kl}   \n",
    "  + \\hat{T}_{jm}^{an} \\hat{T}_{ia}^{kl}  \n",
    "  + \\hat{T}_{jm}^{la} \\hat{T}_{ia}^{kn} \n",
    "$\n",
    "\n",
    "$$\n",
    "\\sum_{a} \\langle i j || a l \\rangle  \\left[ a m || k n \\right] +\n",
    "         \\langle i j || k a \\rangle  \\left[ a m || l n \\right] +\n",
    "         \\langle i m || k a \\rangle  \\left[ j a || l n \\right] +\n",
    "         \\langle i m || a n \\rangle  \\left[ a j || k l \\right] +\n",
    "         \\langle j m || a n \\rangle  \\left[ i a || k l \\right] +\n",
    "         \\langle j m || l a \\rangle  \\left[ i a || k n \\right] \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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 200 integral_value 3 1 2 2"
   ]
  },
  {
   "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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