{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test of F12 matrix elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:15:59.908500Z",
     "start_time": "2020-03-30T10:15:58.731Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val png_image : string -> unit = <fun>\n"
      ]
     },
     "execution_count": 5,
     "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"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val png_image : string -> Jupyter_notebook.display_id = <fun>\n"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": {
    "hidden": true
   },
   "source": [
    "### Modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:00.033900Z",
     "start_time": "2020-03-30T10:15:58.750Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "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": {
    "hidden": true
   },
   "source": [
    "### Printers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:00.095400Z",
     "start_time": "2020-03-30T10:15:58.760Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val pp_mo : Format.formatter -> MOBasis.t -> unit = <fun>\n"
      ]
     },
     "execution_count": 7,
     "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": {
    "heading_collapsed": true
   },
   "source": [
    "## Run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Simulation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:00.287500Z",
     "start_time": "2020-03-30T10:15:58.769Z"
    },
    "hidden": true,
    "init_cell": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val basis_filename : string = \"/home/scemama/qp2/data/basis/6-31g\"\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val nuclei : Nuclei.t = [|(Element.C,   0.0000   0.0000   0.0000)|]\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val frozen_core : bool = false\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val multiplicity : int = 1\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val state : int = 1\n"
      ]
     },
     "execution_count": 10,
     "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_g =\n",
       "      [   0.220900   1.004000   3.622000  12.160000  45.870000 254.400000 ];\n",
       "     expo_g_inv =\n",
       "      [   4.526935   0.996016   0.276091   0.082237   0.021801   0.003931 ]}}\n"
      ]
     },
     "execution_count": 10,
     "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   3.04752488e+03    1.83473713e-03\n",
       "                                      4.57369518e+02    1.40373228e-02\n",
       "                                      1.03948685e+02    6.88426223e-02\n",
       "                                      2.92101553e+01    2.32184443e-01\n",
       "                                      9.28666296e+00    4.67941348e-01\n",
       "                                      3.16392696e+00    3.62311985e-01\n",
       "                                    \n",
       "                                      7.86827235e+00   -1.19332420e-01\n",
       "                                      1.88128854e+00   -1.60854152e-01\n",
       "                                      5.44249258e-01    1.14345644e+00\n",
       "                                    \n",
       "                                      1.68714478e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "  4-9  P   0.0000   0.0000   0.0000   7.86827235e+00    6.89990666e-02\n",
       "                                      1.88128854e+00    3.16423961e-01\n",
       "                                      5.44249258e-01    7.44308291e-01\n",
       "                                    \n",
       "                                      1.68714478e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 10,
     "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   3.04752488e+03    1.83473713e-03\n",
       "                                      4.57369518e+02    1.40373228e-02\n",
       "                                      1.03948685e+02    6.88426223e-02\n",
       "                                      2.92101553e+01    2.32184443e-01\n",
       "                                      9.28666296e+00    4.67941348e-01\n",
       "                                      3.16392696e+00    3.62311985e-01\n",
       "                                    \n",
       "                                      7.86827235e+00   -1.19332420e-01\n",
       "                                      1.88128854e+00   -1.60854152e-01\n",
       "                                      5.44249258e-01    1.14345644e+00\n",
       "                                    \n",
       "                                      1.68714478e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      6.66500000e+03    6.92000000e-04\n",
       "                                      1.00000000e+03    5.32900000e-03\n",
       "                                      2.28000000e+02    2.70770000e-02\n",
       "                                      6.47100000e+01    1.01718000e-01\n",
       "                                      2.10600000e+01    2.74740000e-01\n",
       "                                      7.49500000e+00    4.48564000e-01\n",
       "                                      2.79700000e+00    2.85074000e-01\n",
       "                                      5.21500000e-01    1.52040000e-02\n",
       "                                      1.59600000e-01   -3.19100000e-03\n",
       "                                    \n",
       "                                      6.66500000e+03   -1.46000000e-04\n",
       "                                      1.00000000e+03   -1.15400000e-03\n",
       "                                      2.28000000e+02   -5.72500000e-03\n",
       "                                      6.47100000e+01   -2.33120000e-02\n",
       "                                      2.10600000e+01   -6.39550000e-02\n",
       "                                      7.49500000e+00   -1.49981000e-01\n",
       "                                      2.79700000e+00   -1.27262000e-01\n",
       "                                      5.21500000e-01    5.44529000e-01\n",
       "                                      1.59600000e-01    5.80496000e-01\n",
       "                                    \n",
       "                                      1.59600000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "  4-15 P   0.0000   0.0000   0.0000   7.86827235e+00    6.89990666e-02\n",
       "                                      1.88128854e+00    3.16423961e-01\n",
       "                                      5.44249258e-01    7.44308291e-01\n",
       "                                    \n",
       "                                      1.68714478e-01    1.00000000e+00\n",
       "                                    \n",
       "                                      9.43900000e+00    3.81090000e-02\n",
       "                                      2.00200000e+00    2.09480000e-01\n",
       "                                      5.45600000e-01    5.08557000e-01\n",
       "                                      1.51700000e-01    4.68842000e-01\n",
       "                                    \n",
       "                                      1.51700000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       " 19-24 D   0.0000   0.0000   0.0000   5.50000000e-01    1.00000000e+00\n",
       "                                    \n",
       "                                    \n",
       "-----------------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val charge : int = 0\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val simulation : Simulation.t = <abstr>\n"
      ]
     },
     "execution_count": 10,
     "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 \"c\" \n",
    "let frozen_core = false\n",
    "let multiplicity = 1\n",
    "let state = 1\n",
    "\n",
    "let f12 = F12factor.gaussian_geminal 1.0 \n",
    "let basis =  Basis.of_nuclei_and_basis_filenames ~f12 ~nuclei [basis_filename] \n",
    "let aux_basis =  Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n",
    "let charge = 0 \n",
    "\n",
    "\n",
    "let simulation =\n",
    "    Simulation.make \n",
    "        ~charge ~multiplicity ~nuclei\n",
    "        ~cartesian:true\n",
    "        basis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:00.298200Z",
     "start_time": "2020-03-30T10:15:58.778Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val n_elec_alfa : int = 3\n",
       "val n_elec_beta : int = 3\n",
       "val n_elec : int = 6\n"
      ]
     },
     "execution_count": 11,
     "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": {
    "hidden": true
   },
   "source": [
    "### Hartree-Fock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:00.474000Z",
     "start_time": "2020-03-30T10:15:58.786Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15 significant shell pairs computed in 0.030632 seconds\n",
      "1\n",
      "2\n",
      "3\n",
      "6\n",
      "Computed ERIs in 0.141639 seconds\n",
      "MOs =\n",
      "\n",
      "\n",
      "            -- 1 --     -- 2 --    -- 3 --      -- 4 --   -- 5 --\n",
      "            1      0.995189   -0.236456         -0           -0         0\n",
      "            2     0.0272807    0.573253         -0           -0         0\n",
      "            3   -0.00753288     0.50151         -0 -6.64951E-16         0\n",
      "                        ...         ...        ...          ...       ...\n",
      "            7            -0          -0 -0.0346136    -0.103467  0.874392\n",
      "            8            -0 6.53154E-16   0.374215   -0.0232294 0.0788015\n",
      "            9            -0  7.4731E-16 0.00656013     0.779165  0.118461\n",
      "      \n",
      "\n",
      "             -- 6 --   -- 7 --   -- 8 --   -- 9 --\n",
      "            1              0 0.0649867        -0        -0\n",
      "            2   -1.35345E-15  -1.62901        -0        -0\n",
      "            3    7.04525E-16   1.63955        -0        -0\n",
      "                         ...       ...       ...       ...\n",
      "            7      -0.106576        -0  0.122185 -0.823344\n",
      "            8        1.15222        -0 0.0274317 -0.074201\n",
      "            9      0.0201988        -0 -0.920122 -0.111546\n",
      "      \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val hf : HartreeFock.t = \n",
       "======================================================================\n",
       "                        Restricted Hartree-Fock                      \n",
       "======================================================================\n",
       "\n",
       "    ------------------------------------------------------------\n",
       "        #     HF energy       Convergence  HOMO-LUMO\n",
       "    ------------------------------------------------------------\n",
       "        1    -36.54848150      7.4861e-01     0.2723\n",
       "    ------------------------------------------------------------\n",
       "\n",
       "\n",
       "    ============================================================\n",
       "               One-electron energy  -52.6699343629\n",
       "                           Kinetic   42.4526846308\n",
       "                         Potential  -95.1226189937\n",
       "      --------------------------------------------------------  \n",
       "               Two-electron energy   16.1214528647\n",
       "                           Coulomb   21.8535626014\n",
       "                          Exchange   -5.7321097367\n",
       "      --------------------------------------------------------  \n",
       "                           HF HOMO    0.8237527941\n",
       "                           HF LUMO    8.2337246898\n",
       "                      HF LUMO-LUMO    7.4099718957\n",
       "      --------------------------------------------------------  \n",
       "               Electronic   energy  -36.5484814981\n",
       "               Nuclear   repulsion    0.0000000000\n",
       "               Hartree-Fock energy  -36.5484814981\n",
       "    ============================================================\n",
       "    \n",
       "\n"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mo_basis : MOBasis.t =\n",
       "  Eigenvalues:   -11.127416    -0.632049    -0.269831     0.131526     0.151773 \n",
       "              -- 1 --     -- 2 --    -- 3 --      -- 4 --   -- 5 --\n",
       "      1      0.995189   -0.236456         -0           -0         0\n",
       "      2     0.0272807    0.573253         -0           -0         0\n",
       "      3   -0.00753288     0.50151         -0 -6.64951E-16         0\n",
       "                  ...         ...        ...          ...       ...\n",
       "      7            -0          -0 -0.0346136    -0.103467  0.874392\n",
       "      8            -0 6.53154E-16   0.374215   -0.0232294 0.0788015\n",
       "      9            -0  7.4731E-16 0.00656013     0.779165  0.118461\n",
       "  \n",
       "  Eigenvalues:     0.786913     0.828232     0.869410     0.849164 \n",
       "               -- 6 --   -- 7 --   -- 8 --   -- 9 --\n",
       "      1              0 0.0649867        -0        -0\n",
       "      2   -1.35345E-15  -1.62901        -0        -0\n",
       "      3    7.04525E-16   1.63955        -0        -0\n",
       "                   ...       ...       ...       ...\n",
       "      7      -0.106576        -0  0.122185 -0.823344\n",
       "      8        1.15222        -0 0.0274317 -0.074201\n",
       "      9      0.0201988        -0 -0.920122 -0.111546\n",
       "  \n",
       "  \n"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let hf =  HartreeFock.make ~guess:`Hcore ~max_scf:1 simulation  ;;\n",
    "\n",
    "let mo_basis = MOBasis.of_hartree_fock hf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# FCI-F12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Common functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:00.507100Z",
     "start_time": "2020-03-30T10:15:58.791Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "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_g =\n",
       "      [   0.220900   1.004000   3.622000  12.160000  45.870000 254.400000 ];\n",
       "     expo_g_inv =\n",
       "      [   4.526935   0.996016   0.276091   0.082237   0.021801   0.003931 ]}}\n"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mo_num : int = 9\n"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = <fun>\n"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val pp_det : Format.formatter -> Determinant.t -> unit = <fun>\n"
      ]
     },
     "execution_count": 13,
     "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": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:03.181400Z",
     "start_time": "2020-03-30T10:15:58.799Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val simulation_aux : Simulation.t = <abstr>\n"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "66 significant shell pairs computed in 0.170052 seconds\n",
      "1\n",
      "2\n",
      "3\n",
      "6\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "15\n",
      "18\n",
      "Computed ERIs in 3.375684 seconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val aux_basis : MOBasis.t =\n",
       "  Eigenvalues:   -11.127416    -0.632049    -0.269831     0.131526     0.151773 \n",
       "               -- 1 --   -- 2 --      -- 3 --     -- 4 --      -- 5 --\n",
       "       1      0.995189 -0.236456 -6.99905E-13 3.74871E-12 -1.80137E-11\n",
       "       2     0.0272807  0.573253   1.6881E-12 1.54414E-12  2.46497E-12\n",
       "       3   -0.00753288   0.50151  2.32851E-13 4.16589E-13  1.21024E-12\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:     0.786913     0.828232     0.869410     0.849164     1.480837 \n",
       "               -- 6 --   -- 7 --      -- 8 --      -- 9 --  -- 10 --\n",
       "       1   2.65719E-12 0.0649867  3.37785E-12  1.73781E-11         0\n",
       "       2   2.11976E-13  -1.62901  3.37812E-13   3.5811E-12         0\n",
       "       3    -1.352E-13   1.63955 -1.27564E-13 -8.81657E-13         0\n",
       "                   ...       ...          ...          ...       ...\n",
       "      22             0         0            0            0 -0.866025\n",
       "      23             0         0            0            0         0\n",
       "      24             0         0            0            0         0\n",
       "  \n",
       "  Eigenvalues:     1.033846     1.027840     1.023514     1.247024    25.958539 \n",
       "               -- 11 --     -- 12 --     -- 13 -- -- 14 --     -- 15 --\n",
       "       1   -3.09588E-10  2.21922E-10 -9.52402E-10  3.79632 -6.98298E-09\n",
       "       2    1.67373E-10  1.08424E-10  1.58507E-10 -10.5897  1.20079E-09\n",
       "       3    3.96217E-11   1.2302E-11  6.11965E-11  53.7881  5.40421E-10\n",
       "                    ...          ...          ...      ...          ...\n",
       "      22             -0            0            0       -0           -0\n",
       "      23     1.4274E-14            0            0       -0  2.39877E-13\n",
       "      24   -1.04644E-14 -1.17777E-14            0       -0           -0\n",
       "  \n",
       "  Eigenvalues:    25.891758    25.895674    18.767112   377.619959     1.478100 \n",
       "               -- 16 --     -- 17 -- -- 18 -- -- 19 --     -- 20 --\n",
       "       1    9.02237E-09 -1.52394E-08  27.2935  436.547  1.14358E-12\n",
       "       2    1.49437E-09  4.31003E-09 -127.494 -10.9671  -4.3086E-14\n",
       "       3   -2.24755E-10  1.44203E-09 -21.2025 -23.8199 -6.40841E-14\n",
       "                    ...          ...      ...      ...          ...\n",
       "      22    1.08099E-13  1.08791E-13       -0        0    -0.210667\n",
       "      23    1.28809E-13            0       -0        0      0.86485\n",
       "      24   -2.16198E-13 -2.17582E-13       -0        0     0.421334\n",
       "  \n",
       "  Eigenvalues:     1.480427     1.470884     1.461621 \n",
       "               -- 21 --     -- 22 --     -- 23 --\n",
       "       1   -7.95748E-13  1.61942E-12  5.76543E-10\n",
       "       2    2.98909E-14  -6.0852E-14 -2.17012E-11\n",
       "       3    4.43594E-14 -9.03033E-14 -3.22277E-11\n",
       "                    ...          ...          ...\n",
       "      22      -0.188927     0.412218  -0.00158824\n",
       "      23        0.10621     0.490651  -0.00399134\n",
       "      24       0.377853    -0.824436   0.00317648\n",
       "  \n",
       "  \n"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val aux_num : int = 23\n"
      ]
     },
     "execution_count": 17,
     "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 ~f12 nuclei\n",
    "    |> Simulation.make ~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": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-30T10:16:41.349200Z",
     "start_time": "2020-03-30T10:15:58.806Z"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "66 significant shell pairs computed in 2.944168 seconds\n",
      "1\n",
      "2\n",
      "3\n",
      "6\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "15\n",
      "18\n",
      "Computed ERIs in 47.577040 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": {
    "hidden": true
   },
   "source": [
    "## Integral-based functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "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": 19,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val cancel_singles : bool = false\n"
      ]
     },
     "execution_count": 19,
     "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": 19,
     "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": 19,
     "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": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_a : Determinant.t -> int list = <fun>\n"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val mos_b : Determinant.t -> int list = <fun>\n"
      ]
     },
     "execution_count": 19,
     "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": {
    "hidden": true
   },
   "source": [
    "### H integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val h_one : int -> int -> '_weak1 -> float = <fun>\n"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val h_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = <fun>\n"
      ]
     },
     "execution_count": 20,
     "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": {
    "hidden": true
   },
   "source": [
    "### F12 integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val f_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = <fun>\n"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f_one : 'a -> 'b -> 'c -> float = <fun>\n"
      ]
     },
     "execution_count": 21,
     "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",
    "let f_one = h_one\n",
    "*)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Determinant-based functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val f12_integrals :\n",
       "  'a ->\n",
       "  ('b -> 'c -> 'd -> float) *\n",
       "  (int -> int -> int -> int -> Spin.t -> Spin.t -> float) * 'e option = <fun>\n"
      ]
     },
     "execution_count": 22,
     "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val f_ij : 'a -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 22,
     "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": 22,
     "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": {
    "hidden": true
   },
   "source": [
    "### Determinant space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val is_a_double : DeterminantSpace.t -> Determinant.t -> bool = <fun>\n"
      ]
     },
     "execution_count": 23,
     "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": 24,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of determinants : 84 84 7056\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val in_space : DeterminantSpace.t = <abstr>\n"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of determinants : 1771 1771 3136441\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val aux_space : DeterminantSpace.t = <abstr>\n"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val det_space_in : unit -> Determinant.t Stream.t = <fun>\n"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val det_space_out : unit -> (Determinant.t * Determinant.t) Stream.t = <fun>\n"
      ]
     },
     "execution_count": 24,
     "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": 25,
   "metadata": {
    "hidden": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ci : CI.t =\n",
       "  {CI.e_shift = -37.5503734698766749; det_space = <abstr>; m_H = <lazy>;\n",
       "   m_S2 = <lazy>; eigensystem = <lazy>; n_states = 1}\n"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1     0.0000000000    4.27876562e-01\n",
      "  2    -0.0892428622    1.30475694e-01\n",
      "  3    -0.0992140908    8.74622552e-02\n",
      "  4    -0.1022422166    2.82063810e-02\n",
      "  5    -0.1043598897    3.75067379e-02\n",
      "  6    -0.1065557159    4.71900677e-02\n",
      "  7    -0.1080257508    1.17050850e-02\n",
      "  8    -0.1082438353    4.19578665e-03\n",
      "  0    -0.1082636845    1.74312819e-03\n",
      "  1    -0.1082673418    7.12907013e-04\n",
      "  2    -0.1082677387    3.29773623e-04\n",
      "  3    -0.1082678068    1.62017164e-04\n",
      "  4    -0.1082678363    1.97376384e-04\n",
      "  5    -0.1082678767    1.65667212e-04\n",
      "  6    -0.1082678966    1.24231166e-04\n",
      "  7    -0.1082679014    1.06697750e-05\n",
      "  8    -0.1082679016    5.05286931e-06\n",
      "  0    -0.1082679016    2.52890819e-06\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "val ci_coef : Lacaml.D.Mat.t =\n",
       "  \n",
       "\n",
       "                -- 1 --\n",
       "           1      -0.780949\n",
       "           2             -0\n",
       "           3             -0\n",
       "                        ...\n",
       "        7054             -0\n",
       "        7055             -0\n",
       "        7056   -3.12865E-06\n",
       "  \n",
       "val ci_energy : Lacaml.D.Vec.t =\n",
       "        R1       R2       R3\n",
       "  -37.6586 -36.7238 -36.2286\n"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1    -0.1082679016    4.37907116e-07\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 25,
     "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": {
    "hidden": true
   },
   "source": [
    "Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "hidden": true
   },
   "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": {
    "hidden": true
   },
   "source": [
    "## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val randomize : bool = false\n"
      ]
     },
     "execution_count": 26,
     "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": 26,
     "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": 26,
     "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",
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       "a:+1 -+----+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+---+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+--+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+-+----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -----++----+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +------+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+-----+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+----+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+---+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----+--+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+-+---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------++---+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+-----+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+----+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+---+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+--+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+-+--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------++--+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +--------+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+------+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+-----+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+----+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+---+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+--+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -------+-+-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --------++-+----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+--------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+-------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+------++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+-----++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+----++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+---++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------+--++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --------+-++----------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++----------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +-+---------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -++---------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +---+-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+--+-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+-+-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---++-------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+---+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+--+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+-+------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----++------+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +-----+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+----+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+---+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+--+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+-+-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -----++-----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+----+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+---+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+--+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+-+----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------++----+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+-----+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+----+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+---+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+--+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+-+---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------++---+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+------+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+-----+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----+----+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+---+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+--+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------+-+--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --------++--+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +---------+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+-------+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+------+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+-----+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+----+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+---+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------+--+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --------+-+-+---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +----------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+---------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+-------++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --------+--++---------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++-----------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -++----------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+-+---------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --++---------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---++--------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+--+-------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+-+-------+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+----+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+---+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+--+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+-+-----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+-----+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+----+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+---+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+-+----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------++----+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+------+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ---+-----+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+----+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+---+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ------+--+---+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 ----+-----+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -----+----+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -------+--+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --------+-+--+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 +----------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 -+---------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
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       "a:+1 --+--------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---+-------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----+------+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -----+-----+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ------+----+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -------+---+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --------+--+-+--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -+----------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --+---------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---+--------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----+-------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -----+------++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ------+-----++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -------+----++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --------+---++--------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ++------------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-+-----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -++-----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +--+----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -+-+----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --++----------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +---+---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -+--+---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --+-+---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---++---------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +----+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -+---+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --+--+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---+-+--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----++--------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +-----+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -+----+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --+---+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---+--+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----+-+-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -----++-------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 +------+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -+-----+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 --+----+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ---+---+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 ----+--+------+-------------------------------------------------\n",
       "b:+1 +++-------------------------------------------------------------\n",
       ";\n",
       "phase:+1\n",
       "a:+1 -----+-+------+-------------------------------------------------\n",
       "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": 26,
     "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": 26,
     "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": {
    "hidden": true,
    "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": {
    "hidden": true
   },
   "source": [
    "Function to generate all intermediate external determinants $|\\alpha \\rangle$ between $|I\\rangle$ and $|J\\rangle$, with a positive phase factor.\n",
    "\n",
    "* `exc` is the degree of excitation between $|I\\rangle$ and $|J\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val generate_alphas :\n",
       "  Determinant.t -> Determinant.t -> int -> Determinant.t list = <fun>\n"
      ]
     },
     "execution_count": 27,
     "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": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let generate_alphas ki kj exc =\n",
    "  (* Check input excitation degree *)\n",
    "  let d = Determinant.degree ki kj in\n",
    "  if d <> exc then\n",
    "    Printf.sprintf \"Invalid excitation degree. Expected %d and found %d.\" exc d\n",
    "    |> failwith;\n",
    "    \n",
    "  (* Generate single excitations *)\n",
    "  let all_singles ki =\n",
    "      let mos_a, mos_b = Determinant.to_lists ki in\n",
    "      [ List.map (fun hole -> \n",
    "          List.map (fun particle ->\n",
    "               if hole = particle then None else\n",
    "                  Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n",
    "              ) mos_abs\n",
    "          ) mos_a\n",
    "      ;\n",
    "        List.map (fun hole -> \n",
    "          List.map (fun particle ->\n",
    "               if hole = particle then None else\n",
    "                 Some (Determinant.single_excitation Spin.Beta hole particle ki)\n",
    "              ) mos_abs\n",
    "          ) mos_b \n",
    "      ]\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> Util.list_some\n",
    "      |> List.filter (fun x -> Determinant.is_none x = false)\n",
    "      |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
    "  in\n",
    "  \n",
    "  (* Generate double excitations *)\n",
    "  let all_doubles ki =\n",
    "      let mos_a, mos_b = Determinant.to_lists ki in\n",
    "      [ List.map (fun hole ->  (* Alpha-Alpha *)\n",
    "          List.map (fun particle ->\n",
    "            List.map (fun hole' -> \n",
    "              List.map (fun particle' ->\n",
    "                if hole = particle || hole' = particle' then None else\n",
    "                if hole' > hole && particle' < particle then\n",
    "                  Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
    "                else None\n",
    "                      ) mos_abs\n",
    "                  ) mos_a \n",
    "              ) mos_abs\n",
    "          ) mos_a\n",
    "        ; \n",
    "        List.map (fun hole ->  (* Beta-Beta *)\n",
    "          List.map (fun particle ->\n",
    "            List.map (fun hole' -> \n",
    "              List.map (fun particle' ->\n",
    "                if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then\n",
    "                  Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n",
    "                else None\n",
    "                      ) mos_abs\n",
    "                  ) mos_b \n",
    "              ) mos_abs\n",
    "          ) mos_b\n",
    "        ;\n",
    "        List.map (fun hole ->  (* Alpha-Beta *)\n",
    "          List.map (fun particle ->\n",
    "            List.map (fun hole' -> \n",
    "              List.map (fun particle' ->\n",
    "                  if hole = particle || hole' = particle' then None else\n",
    "                  Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n",
    "                      ) mos_abs\n",
    "                  ) mos_b \n",
    "              ) mos_abs\n",
    "          ) mos_a\n",
    "      ]\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> List.concat\n",
    "      |> Util.list_some\n",
    "      |> List.filter (fun x -> Determinant.is_none x = false)\n",
    "      |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
    "  in\n",
    "\n",
    "  (* Generate left and right excitations *)\n",
    "  let al = List.concat [ all_singles ki ; all_doubles ki ] in\n",
    "  let ar = List.concat [ all_singles kj ; all_doubles kj ] in\n",
    "  \n",
    "  let mo_class = DeterminantSpace.mo_class in_space in\n",
    "  let m l =\n",
    "    List.fold_left (fun accu i ->\n",
    "        let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n",
    "      ) (Bitstring.zero mo_num) l\n",
    "  in\n",
    "  let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n",
    "  let good_cabs k = \n",
    "      let alfa =\n",
    "        Determinant.alfa k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let beta =\n",
    "        Determinant.beta k\n",
    "        |> Spindeterminant.bitstring\n",
    "      in\n",
    "      let a = Bitstring.logand aux_mask alfa\n",
    "      and b = Bitstring.logand aux_mask beta\n",
    "      in\n",
    "      match Bitstring.popcount a + Bitstring.popcount b with\n",
    "      | 1 | 2 -> true\n",
    "      | _ -> false\n",
    "  in\n",
    "  \n",
    "  (* Merge lists in a set of unique determinants *)\n",
    "  List.concat [ al; ar ]\n",
    "  |> List.sort_uniq compare\n",
    "  \n",
    "  (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n",
    "  |> List.filter good_cabs \n",
    "  \n",
    "  \n",
    "let compute_HaaF ki alphas kj =\n",
    "   List.fold_left (fun accu alpha -> accu\n",
    "      +. h_ij aux_basis ki alpha\n",
    "      *. f_ij aux_basis alpha kj\n",
    "    ) 0. alphas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val check :\n",
       "  int ->\n",
       "  (CIMatrixElement.De.t -> CIMatrixElement.De.t -> float) -> int -> unit =\n",
       "  <fun>\n"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val sum : 'a list -> ('a -> float) -> float = <fun>\n"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let check n integral_value exc =\n",
    "  let cpudet, cpuint = ref 0., ref 0. in\n",
    "  let det_list =\n",
    "      match n with\n",
    "        | 0 -> det_I\n",
    "        | n -> Array.sub det_I 0 n\n",
    "  in\n",
    "  let result =\n",
    "        Printf.printf \"Checking ... \\n%!\";\n",
    "        let percent = ref 0 in\n",
    "        let task (i,ki) =\n",
    "            (let p = (10 * (i+1))/(Array.length det_list) in\n",
    "            if p <> !percent then\n",
    "                ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) ));\n",
    "            Array.mapi (fun j kj -> \n",
    "                if i > j || Determinant.degree ki kj <> exc then\n",
    "                    (0,0,0.,0.)\n",
    "                else\n",
    "                  begin\n",
    "                    let alphas = generate_alphas ki kj exc in\n",
    "                    let det_value =\n",
    "                      let t0 = Unix.gettimeofday () in\n",
    "                      let result = compute_HaaF ki alphas kj in\n",
    "                      cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n",
    "                      result\n",
    "                    in\n",
    "                    let int_value = \n",
    "                      let t0 = Unix.gettimeofday () in\n",
    "                      let result = integral_value ki kj in\n",
    "                      cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n",
    "                      result\n",
    "                    in\n",
    "(*   Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value;  *)\n",
    "                    (i,j,det_value,int_value)\n",
    "                  end\n",
    "            ) det_list\n",
    "        in\n",
    "        det_list\n",
    "        |> Array.mapi (fun i ki -> (i,ki))\n",
    "        |> Array.to_list\n",
    "        |> Stream.of_list\n",
    "        |> Farm.run ~f:task\n",
    "        |> Util.stream_to_list\n",
    "        |> Array.concat\n",
    "  in\n",
    "  let i,j,d,v = \n",
    "      let rec aux k imax jmax emax dmax vmax = \n",
    "        if k = -1 then\n",
    "          imax, jmax, dmax, vmax\n",
    "        else\n",
    "          let i, j, d, v = result.(k) in\n",
    "          let e = abs_float (d -. v) in\n",
    "          if e >= emax then\n",
    "            aux (k-1) i j e d v\n",
    "          else\n",
    "            aux (k-1) imax jmax emax dmax vmax\n",
    "      in\n",
    "      aux (Array.length result - 1) 0 0 0. 0. 0.\n",
    "  in\n",
    "  let error = abs_float (d -. v) in\n",
    "  if error < epsilon_float then\n",
    "  (*\n",
    "      Printf.printf \"OK: %e\\n%!\" error\n",
    "      *)\n",
    "      Printf.printf \"OK: (%d, %d) | %e %e | %e  |  cpu : %f  %f\\n%!\" i j d v error !cpudet !cpuint\n",
    "  else\n",
    "      Printf.printf \"Failed: (%d, %d) | %e %e | %e  |  cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n",
    "\n",
    "    \n",
    "let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hidden": true
   },
   "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": 29,
     "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": 29,
     "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": 29,
     "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": {
    "hidden": true
   },
   "source": [
    "******"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# 1. 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_0111_1H_1F : Lacaml.D.vec = R1 R2 R3     R7 R8 R9\n",
       "                                   0  0  0 ...  0  0  0\n"
      ]
     },
     "execution_count": 30,
     "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 4.14783E-05 0.000191898   5.819E-05 3.17034E-05\n",
       "        2    0.00285395           0  0.00130169 0.000700753 0.000516776\n",
       "        3     0.0048103 0.000752348           0  0.00113768 0.000719116\n",
       "                    ...         ...         ...         ...         ...\n",
       "        7   -0.00384068 -0.00136624 -0.00343863 -0.00255958 -0.00227812\n",
       "        8     0.0164152   0.0118156   0.0104307  0.00609247  0.00526221\n",
       "        9     0.0169861   0.0119274    0.010345  0.00631195  0.00505777\n",
       "  \n",
       "\n",
       "            -- 6 --      -- 7 --     -- 8 --     -- 9 --\n",
       "        1   0.000201004 -1.30762E-06 0.000334712 0.000361198\n",
       "        2   0.000232139  -0.00168234  0.00083308  0.00101706\n",
       "        3   -0.00387497  0.000450355  0.00302132  0.00343988\n",
       "                    ...          ...         ...         ...\n",
       "        7   -0.00166296            0  0.00138345  0.00154153\n",
       "        8    0.00316903   0.00287547           0   0.0177299\n",
       "        9     0.0026978   0.00232342  0.00673081           0\n",
       "  \n",
       "val m_0111_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 30,
     "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    0.00296502  0.00298831  0.00488797 0.000118822 -0.000472343\n",
       "        2    0.00298831 -0.00136007 -0.00413131  -0.0063196  -0.00598212\n",
       "        3    0.00488797 -0.00413131 -0.00712707 -0.00508589  -0.00503032\n",
       "                    ...         ...         ...         ...          ...\n",
       "        7   -0.00407169 -0.00213075  -0.0040668 -0.00417519  -0.00370227\n",
       "        8     0.0160284   0.0113906   0.0122954  0.00422564   0.00433285\n",
       "        9     0.0166196   0.0110531   0.0122398  0.00511694    0.0023468\n",
       "  \n",
       "\n",
       "           -- 6 --     -- 7 --   -- 8 --    -- 9 --\n",
       "        1    0.0112593 -0.00407169 0.0160284  0.0166196\n",
       "        2   0.00920231 -0.00213075 0.0113906  0.0110531\n",
       "        3   0.00825183  -0.0040668 0.0122954  0.0122398\n",
       "                   ...         ...       ...        ...\n",
       "        7    0.0043954 -0.00205631 0.0045038 0.00403087\n",
       "        8    0.0150589   0.0045038 0.0198249  0.0230215\n",
       "        9    0.0158986  0.00403087 0.0230215  0.0220599\n",
       "  \n",
       "val m_0111_2Hb_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 30,
     "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": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> 'a -> float = <fun>\n"
      ]
     },
     "execution_count": 30,
     "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: (5594, 5594) | -2.621269e-01 -2.621269e-01 | 9.992007e-16  |  cpu : 605.920079 0.214178\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 30,
     "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",
    "let m_0111_1H_2Fa, m_0111_2Ha_2Fa =\n",
    "\n",
    "    let m_0122_Haa = \n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "          sum mos_cabs (fun a ->\n",
    "            h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa\n",
    "            ) )\n",
    "    in      \n",
    "    \n",
    "    let m_0111_1H_2Fa = \n",
    "      Mat.init_cols mo_num mo_num (fun i j ->\n",
    "          sum mos_cabs (fun a ->\n",
    "            h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa +.\n",
    "            h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa\n",
    "          ) +.\n",
    "          if i < j then 0. else\n",
    "              begin\n",
    "                  sum mos_cabs (fun a ->\n",
    "                      sum mos_cabs (fun b -> if b >= a then 0. else\n",
    "                        h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa\n",
    "                      )\n",
    "                  ) +.\n",
    "                  sum mos_in (fun k -> m_0122_Haa.{i,j,k}) \n",
    "              end\n",
    "      )\n",
    "    in\n",
    "    \n",
    "    let m_0111_2Ha_2Fa =\n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "          f_two a k i k Spin.Alfa Spin.Alfa \n",
    "        ) -. if i < j then 0. else m_0122_Haa.{i,j,k}\n",
    "      )\n",
    "    in m_0111_1H_2Fa, m_0111_2Ha_2Fa\n",
    "\n",
    "\n",
    "    \n",
    "let m_0111_1H_2Fb, m_0111_2Hb_2Fb =\n",
    "    let m_0122_Hab = \n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "          sum mos_cabs (fun a ->\n",
    "             h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta\n",
    "          ) )\n",
    "    in\n",
    "    \n",
    "    let m_0111_1H_2Fb = \n",
    "      Mat.init_cols mo_num mo_num (fun i j ->\n",
    "          sum mos_cabs (fun a ->\n",
    "            h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta +. \n",
    "            h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa +.\n",
    "            h_one j a Spin.Alfa *. f_two a i j i Spin.Alfa Spin.Beta +. \n",
    "            h_two j i a i Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa\n",
    "          ) +.\n",
    "        sum mos_in (fun k -> m_0122_Hab.{i,j,k} +. m_0122_Hab.{j,i,k} ) +.\n",
    "        sum mos_cabs (fun a ->\n",
    "            sum mos_cabs (fun b ->\n",
    "            h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta\n",
    "            )\n",
    "          )\n",
    "        )\n",
    "    in    \n",
    "    \n",
    "    let m_0111_2Hb_2Fb =\n",
    "      array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two k i a i Spin.Alfa Spin.Beta *.\n",
    "          f_two a j k j Spin.Alfa Spin.Beta +.\n",
    "          h_two i k a k Spin.Alfa Spin.Beta *.\n",
    "          f_two a j i j Spin.Alfa Spin.Alfa \n",
    "        ) -. m_0122_Hab.{k,i,j}\n",
    "      )\n",
    "    in\n",
    "    m_0111_1H_2Fb, m_0111_2Hb_2Fb\n",
    "    \n",
    "\n",
    "let m_0111_2Ha_2Fb =\n",
    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "      f_two a k i k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "let integral_value ki kj = \n",
    "\n",
    "   let mos_i, mos_i' = mos_a ki, mos_b ki in\n",
    "   let same = (mos_i = mos_i') in\n",
    "   \n",
    "   (* Alpha *)\n",
    "   let a = \n",
    "       sum mos_i  (fun i -> m_0111_1H_1F.{i}) \n",
    "   in\n",
    "   \n",
    "   let b = \n",
    "       if same then a else\n",
    "       sum mos_i' (fun i -> m_0111_1H_1F.{i})\n",
    "   in\n",
    "   \n",
    "   let aa = \n",
    "       sum mos_i (fun j ->\n",
    "         sum mos_i (fun i -> m_0111_1H_2Fa.{i,j} ))\n",
    "   in\n",
    "   \n",
    "   let bb = \n",
    "     if same then aa else\n",
    "     sum mos_i' (fun j ->\n",
    "       sum mos_i' (fun i -> m_0111_1H_2Fa.{i,j} ))\n",
    "   in\n",
    "   \n",
    "   let ab = \n",
    "     sum mos_i' (fun j ->\n",
    "       sum mos_i (fun i -> m_0111_1H_2Fb.{i,j}  )) \n",
    "   in\n",
    "   \n",
    "   let aaa = \n",
    "       sum mos_i (fun k ->\n",
    "         sum mos_i (fun j ->\n",
    "           sum mos_i (fun i -> m_0111_2Ha_2Fa.{i,j,k} ))) \n",
    "   in\n",
    "   \n",
    "   let bbb = \n",
    "     if same then aaa else\n",
    "       sum mos_i' (fun k ->\n",
    "         sum mos_i' (fun j ->\n",
    "           sum mos_i' (fun i -> m_0111_2Ha_2Fa.{i,j,k} )))\n",
    "   in\n",
    "   \n",
    "   let baa = \n",
    "       sum mos_i' (fun k ->\n",
    "         sum mos_i (fun j ->\n",
    "           sum mos_i (fun i ->\n",
    "             m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{i,j,k}\n",
    "       )))\n",
    "   in\n",
    "   \n",
    "   let bba = \n",
    "       sum mos_i  (fun k ->\n",
    "         sum mos_i' (fun j ->\n",
    "           sum mos_i' (fun i ->\n",
    "             m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{j,i,k} \n",
    "       ))) \n",
    "   in\n",
    "\n",
    "   a +. b +. aa +. bb +. ab +. aaa +. baa +. bba +. bbb\n",
    "   \n",
    "     \n",
    "let _ =\n",
    "  check 0 integral_value 0 \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# 2. 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "hidden": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_1111_1H_1F : Lacaml.D.mat =\n",
       "  \n",
       "\n",
       "        -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n",
       "        1         0       0       0       0       0\n",
       "        2         0       0       0       0       0\n",
       "        3         0       0       0       0       0\n",
       "                ...     ...     ...     ...     ...\n",
       "        7         0       0       0       0       0\n",
       "        8         0       0       0       0       0\n",
       "        9         0       0       0       0       0\n",
       "  \n",
       "\n",
       "        -- 6 -- -- 7 -- -- 8 -- -- 9 --\n",
       "        1         0       0       0       0\n",
       "        2         0       0       0       0\n",
       "        3         0       0       0       0\n",
       "                ...     ...     ...     ...\n",
       "        7         0       0       0       0\n",
       "        8         0       0       0       0\n",
       "        9         0       0       0       0\n",
       "  \n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1111_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1111_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1111_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1111_2Hb_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1121_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1121_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1121_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1121_2Hb_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1122_va :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1111_1H_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1122_v2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1122_v3 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1111_1H_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1122_oa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_1122_o :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 31,
     "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: (1, 35) | 1.340491e-02 1.340491e-02 | 2.775558e-17  |  cpu : 79.129396  0.030664\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let m_1111_1H_1F = \n",
    "  Mat.init_cols mo_num mo_num (fun i k -> \n",
    "        sum mos_cabs (fun a -> h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "let m_1111_2Ha_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    if l=i then\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two j l a l Spin.Alfa Spin.Alfa *.\n",
    "          f_two a i j k Spin.Alfa Spin.Alfa \n",
    "        )\n",
    "    else\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "          f_two a l k l Spin.Alfa Spin.Alfa +.\n",
    "          h_two j l a l Spin.Alfa Spin.Alfa *.\n",
    "          f_two a i j k Spin.Alfa Spin.Alfa )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "let m_1111_2Hb_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    if l=i then\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two j l a l Spin.Alfa Spin.Beta *.\n",
    "          f_two a i j k Spin.Alfa Spin.Beta \n",
    "        )\n",
    "    else\n",
    "        sum mos_cabs (fun a ->\n",
    "          h_two i j a j Spin.Alfa Spin.Beta *.\n",
    "          f_two a l k l Spin.Alfa Spin.Alfa +.\n",
    "          h_two j l a l Spin.Alfa Spin.Beta *.\n",
    "          f_two a i j k Spin.Alfa Spin.Beta \n",
    "        )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1111_2Ha_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a j Spin.Alfa Spin.Alfa *.\n",
    "      f_two a l k l Spin.Alfa Spin.Beta +.\n",
    "      h_two j l a l Spin.Alfa Spin.Beta *.\n",
    "      f_two a i j k Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "let m_1111_2Hb_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a j Spin.Alfa Spin.Beta *.\n",
    "      f_two a l k l Spin.Alfa Spin.Beta +.\n",
    "      h_two j l a l Spin.Alfa Spin.Alfa *.\n",
    "      f_two a i j k Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "\n",
    "let m_1121_2Ha_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
    "      f_two l a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1121_2Hb_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two l a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1121_2Ha_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
    "      f_two l a l j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1121_2Hb_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two l a l j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "let m_1122_va =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j i a l Spin.Alfa Spin.Alfa *.\n",
    "      f_two l a k j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  )\n",
    "  \n",
    "let m_1111_1H_2Fa = \n",
    "  array_3_init mo_num mo_num mo_num (fun j i k ->\n",
    "      sum mos_in (fun l -> m_1122_va.{l,j,i,k}) +.\n",
    "      sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa +.\n",
    "        h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n",
    "        h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa +.\n",
    "        h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa +.\n",
    "        sum mos_cabs (fun b -> if b > a then 0. else\n",
    "          h_two i j a b Spin.Alfa Spin.Alfa *.\n",
    "          f_two a b k j Spin.Alfa Spin.Alfa )\n",
    "      )\n",
    "    )\n",
    "\n",
    "\n",
    "let m_1122_v2 =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j l a Spin.Alfa Spin.Beta *.\n",
    "      f_two l a k j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "\n",
    "let m_1122_v3 =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two i j a l Spin.Alfa Spin.Beta *.\n",
    "      f_two a l k j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "\n",
    "  \n",
    "let m_1111_1H_2Fb = \n",
    "  array_3_init mo_num mo_num mo_num (fun j i k ->\n",
    "      sum mos_in (fun l -> m_1122_v2.{l,j,i,k} +. m_1122_v3.{l,j,i,k}) +.\n",
    "      sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta +.\n",
    "        h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n",
    "        h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta +.\n",
    "        h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta +.\n",
    "        sum mos_cabs (fun b ->\n",
    "          h_two i j a b Spin.Alfa Spin.Beta *.\n",
    "          f_two a b k j Spin.Alfa Spin.Beta \n",
    "        )\n",
    "      )\n",
    "    )\n",
    "  \n",
    "let m_1122_oa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "  if l > j then\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two j l a k Spin.Alfa Spin.Alfa *.\n",
    "      f_two i a l j Spin.Alfa Spin.Alfa \n",
    "    )\n",
    "  else 0.\n",
    "  )\n",
    "\n",
    "let m_1122_o =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      h_two l j k a Spin.Alfa Spin.Beta *.\n",
    "      f_two i a l j Spin.Alfa Spin.Beta \n",
    "    )\n",
    "  )\n",
    "  \n",
    "\n",
    "\n",
    "(*----*)\n",
    "\n",
    "let integral_value ki kj = \n",
    "    let i, k, s, phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
    "            hole, particle, spin, phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "    \n",
    "    let mos_novirt, mos_novirt' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      let beta  = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let mos_ij, mos_ij' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      let beta  = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let mos_i, mos_i' =\n",
    "      match s with\n",
    "      | Spin.Alfa -> mos_a ki, mos_b ki\n",
    "      | Spin.Beta -> mos_b ki, mos_a ki\n",
    "    in\n",
    "   \n",
    "    let mos_j, mos_j' =\n",
    "      match s with\n",
    "      | Spin.Alfa -> mos_a kj, mos_b kj\n",
    "      | Spin.Beta -> mos_b kj, mos_a kj\n",
    "    in\n",
    "   \n",
    "    let result = \n",
    "     m_1111_1H_1F.{i,k} +. \n",
    "     sum mos_ij (fun j -> \n",
    "          m_1111_1H_2Fa.{j,i,k} \n",
    "       +. sum mos_i  (fun l -> m_1111_2Ha_2Fa.{l,j,i,k})\n",
    "       +. sum mos_i' (fun l -> m_1111_2Ha_2Fb.{l,j,i,k})\n",
    "       +. sum mos_j  (fun l -> m_1121_2Ha_2Fa.{l,j,i,k})\n",
    "       +. sum mos_j' (fun l -> m_1121_2Ha_2Fb.{l,j,i,k})\n",
    "       -. sum mos_novirt (fun l -> m_1122_va.{l,j,i,k})\n",
    "       -. sum mos_ij (fun l -> m_1122_oa.{l,j,i,k} )\n",
    "       ) +.\n",
    "     sum mos_ij' (fun j ->\n",
    "          m_1111_1H_2Fb.{j,i,k} \n",
    "       +. sum mos_i  (fun l -> m_1111_2Hb_2Fa.{l,j,i,k})\n",
    "       +. sum mos_i' (fun l -> m_1111_2Hb_2Fb.{l,j,i,k})\n",
    "       +. sum mos_j  (fun l -> m_1121_2Hb_2Fb.{l,j,i,k})\n",
    "       +. sum mos_j' (fun l -> m_1121_2Hb_2Fa.{l,j,i,k})\n",
    "       -. sum mos_novirt  (fun l ->  m_1122_v2.{l,j,i,k}) \n",
    "       -. sum mos_novirt' (fun l ->  m_1122_v3.{l,j,i,k})\n",
    "       -. sum mos_ij    (fun l ->  m_1122_o.{l,j,i,k})\n",
    "       ) \n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "(*\n",
    "let ki = det_I.(77)\n",
    "let kj = det_I.(83)\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "let _ = \n",
    "    let alphas =  generate_alphas ki kj 1 1\n",
    "    in compute_HaaF ki alphas kj\n",
    "*)\n",
    "\n",
    "let _ = check 100 integral_value 1 \n",
    "\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Timing : 40.020974 0.019294"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# 3. 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val m_2112_1H_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_1H_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2112_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2121_2Ha_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2121_2Hb_2Fa :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2121_2Ha_2Fb :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Ha_2Fa_ij :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_ij :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_ij2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Ha_2Fa_ij2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Ha_2Fa_nv :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_nv :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_2122_2Hb_2Fb_nv2 :\n",
       "  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n",
       "  <abstr>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking ... \n",
      " -  10 %\n",
      " -  20 %\n",
      " -  30 %\n",
      " -  40 %\n",
      " -  50 %\n",
      " -  60 %\n",
      " -  70 %\n",
      " -  80 %\n",
      " -  90 %\n",
      " - 100 %\n",
      "OK: (2, 45) | 2.332967e-02 2.332967e-02 | 2.428613e-17  |  cpu : 109.679883  0.039116\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val ki : Determinant.t =\n",
       "  phase:+1\n",
       "  a:+1 +--++-----------------------------------------------------------\n",
       "  b:+1 +++-------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val kj : Determinant.t =\n",
       "  phase:+1\n",
       "  a:+1 +-+-+-----------------------------------------------------------\n",
       "  b:+1 ++-+------------------------------------------------------------\n",
       "\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : float = 0.000896378780435275082\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : float = 0.000896378780435274107\n"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let m_2112_1H_2Fa =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n",
    "        h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa +. \n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n",
    "        h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa +.\n",
    "        sum mos_in  (fun m -> -. h_two i j a m Spin.Alfa Spin.Alfa *.\n",
    "                                 f_two m a k l Spin.Alfa Spin.Alfa) +.\n",
    "        sum mos_cabs (fun b -> if b >= a then 0. else\n",
    "            h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b k l Spin.Alfa Spin.Alfa \n",
    "        )\n",
    "      )\n",
    "    )\n",
    "\n",
    "let m_2112_1H_2Fb =\n",
    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n",
    "        h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta +.\n",
    "        h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n",
    "        h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa +.\n",
    "        sum mos_in (fun m ->\n",
    "          h_two i j a m Spin.Alfa Spin.Beta *.  f_two a m k l Spin.Alfa Spin.Beta +.\n",
    "          h_two i j m a Spin.Alfa Spin.Beta *.  f_two m a k l Spin.Alfa Spin.Beta ) +.\n",
    "        sum mos_cabs (fun b -> \n",
    "            h_two i j a b Spin.Alfa Spin.Beta *. f_two a b k l Spin.Alfa Spin.Beta \n",
    "        )\n",
    "      )\n",
    "    )\n",
    "\n",
    "let m_2112_2Ha_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +. \n",
    "        h_two j n a n Spin.Alfa Spin.Alfa *. f_two a i l k Spin.Alfa Spin.Alfa \n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Hb_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Beta *. f_two a j k l Spin.Alfa Spin.Alfa +.\n",
    "        h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Alfa \n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2112_2Ha_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n",
    "        h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Beta )\n",
    "    )\n",
    "    \n",
    "    \n",
    "let m_2121_2Ha_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Alfa +.\n",
    "        h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Alfa \n",
    "      )\n",
    "    )\n",
    "    \n",
    "\n",
    "let m_2121_2Hb_2Fa =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Beta *. f_two a n k n Spin.Alfa Spin.Alfa +.\n",
    "        h_two j i a k Spin.Alfa Spin.Beta *. f_two a n l n Spin.Alfa Spin.Beta \n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2121_2Ha_2Fb =\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Beta +.\n",
    "        h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Beta \n",
    "      )\n",
    "    )\n",
    "    \n",
    "\n",
    "let m_2122_2Ha_2Fa_ij =\n",
    "  let s = Spin.Alfa in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "           h_two i n a k s s  *.  f_two j a n l s s \n",
    "        +. h_two i n a l s s  *.  f_two j a k n s s \n",
    "        -. h_two j n a k s s  *.  f_two i a n l s s   \n",
    "        -. h_two j n a l s s  *.  f_two i a k n s s\n",
    "      )\n",
    "    )\n",
    "    \n",
    "let m_2122_2Hb_2Fb_ij =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "          h_two n i a k s  s  *.  f_two a j n l s  s'\n",
    "       +. h_two n j a l s  s' *.  f_two i a k n s  s \n",
    "       -. h_two n j k a s  s' *.  f_two i a n l s  s'\n",
    "    )\n",
    "  )\n",
    "    \n",
    "let m_2122_2Hb_2Fb_ij2 =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "      -. h_two i n a l s  s' *.  f_two a j k n s  s' +.\n",
    "      (if n < j then\n",
    "                  h_two i n k a s  s' *.  f_two j a l n s' s'\n",
    "               +. h_two n j a l s' s' *.  f_two i a k n s  s'\n",
    "       else \n",
    "               -. h_two i n k a s  s' *.  f_two j a n l s' s' \n",
    "               -. h_two j n a l s' s' *.  f_two i a k n s  s'\n",
    "      )\n",
    "    )\n",
    "  )\n",
    "    \n",
    "let m_2122_2Ha_2Fa_ij2 =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a ->\n",
    "         h_two i n k a s s' *.  f_two j a l n s s'\n",
    "      +. h_two j n l a s s' *.  f_two i a k n s s'\n",
    "      -. h_two i n l a s s' *.  f_two j a k n s s'\n",
    "      -. h_two j n k a s s' *.  f_two i a l n s s'\n",
    "      )\n",
    "    ) \n",
    "    \n",
    "let m_2122_2Ha_2Fa_nv =\n",
    "  let s = Spin.Alfa in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a -> h_two i j a n s  s  *.  f_two n a k l s  s ) ) \n",
    "    \n",
    "    \n",
    "    \n",
    "let m_2122_2Hb_2Fb_nv =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a -> -. h_two i j a n s s'  *.  f_two a n k l s s' ) ) \n",
    "    \n",
    "let m_2122_2Hb_2Fb_nv2 =\n",
    "  let s, s' = Spin.(Alfa, Beta) in\n",
    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n",
    "    sum mos_cabs (fun a -> -. h_two i j n a s s'  *.  f_two n a k l s s' ) ) \n",
    "    \n",
    "    \n",
    "    \n",
    "let integral_value ki kj = \n",
    "    let i, j, k, l, s, s', phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
    "            hole, hole', particle, particle', spin, spin', phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "    let mos_i, mos_i' =\n",
    "       match s with\n",
    "       | Spin.Alfa -> mos_a ki, mos_b ki\n",
    "       | Spin.Beta -> mos_b ki, mos_a ki\n",
    "    in\n",
    "    \n",
    "    let mos_j, mos_j' =\n",
    "       match s with\n",
    "       | Spin.Alfa -> mos_a kj, mos_b kj\n",
    "       | Spin.Beta -> mos_b kj, mos_a kj\n",
    "    in\n",
    "    \n",
    "    let mos_ij, mos_ij' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      let beta  =  \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logand i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let mos_novirt, mos_novirt' =\n",
    "      let alfa = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      let beta  = \n",
    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
    "        Bitstring.to_list (Bitstring.logor i j)\n",
    "      in\n",
    "      match s with\n",
    "      | Spin.Alfa -> alfa, beta\n",
    "      | Spin.Beta -> beta, alfa\n",
    "    in\n",
    "    \n",
    "    let result = \n",
    "       if s = s' then\n",
    "         m_2112_1H_2Fa.{i,j,k,l} +. \n",
    "         sum mos_i      (fun n -> m_2112_2Ha_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_i'     (fun n -> m_2112_2Hb_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_j      (fun n -> m_2121_2Ha_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_j'     (fun n -> m_2121_2Ha_2Fb.{n,i,j,k,l} ) +.\n",
    "         sum mos_ij     (fun n -> m_2122_2Ha_2Fa_ij.{n,i,j,k,l} ) +. \n",
    "         sum mos_ij'    (fun n -> m_2122_2Ha_2Fa_ij2.{n,i,j,k,l} ) +. \n",
    "         sum mos_novirt (fun n -> m_2122_2Ha_2Fa_nv.{n,i,j,k,l} ) \n",
    "       else\n",
    "         m_2112_1H_2Fb.{i,j,k,l} +. \n",
    "         sum mos_i      (fun n -> m_2112_2Ha_2Fb.{n,i,j,k,l} ) +.\n",
    "         sum mos_i'     (fun n -> m_2112_2Ha_2Fb.{n,j,i,l,k} ) +.\n",
    "         sum mos_j      (fun n -> m_2121_2Hb_2Fa.{n,i,j,k,l} ) +.\n",
    "         sum mos_j'     (fun n -> m_2121_2Hb_2Fa.{n,j,i,l,k} ) +.\n",
    "         sum mos_novirt'(fun n -> m_2122_2Hb_2Fb_nv.{n,i,j,k,l} ) +.\n",
    "         sum mos_novirt (fun n -> m_2122_2Hb_2Fb_nv2.{n,i,j,k,l} )+.\n",
    "         sum mos_ij     (fun n -> m_2122_2Hb_2Fb_ij.{n,i,j,k,l} ) +. \n",
    "         sum mos_ij'    (fun n -> m_2122_2Hb_2Fb_ij2.{n,i,j,k,l} ) \n",
    "     in\n",
    "\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "let _ = check 100  integral_value 2 \n",
    "\n",
    "let ki = det_I.(7)\n",
    "let kj = det_I.(89)\n",
    "\n",
    "let _ = integral_value ki kj\n",
    "let _ = \n",
    "    let alphas =  generate_alphas ki kj 2 \n",
    "    in compute_HaaF ki alphas kj\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# 4. 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val integral_value : Determinant.t -> Determinant.t -> float = <fun>\n"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking ... \n",
      " -  10 %\n",
      " -  20 %\n",
      " -  30 %\n",
      " -  40 %\n",
      " -  50 %\n",
      " -  60 %\n",
      " -  70 %\n",
      " -  80 %\n",
      " -  90 %\n",
      " - 100 %\n",
      "OK: (13, 52) | 6.122906e-04 6.122906e-04 | 3.252607e-19  |  cpu : 77.238524  0.119682\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let integral_value ki kj = \n",
    "    let i, j, m, k, l, n, s1, s2, s3, phase =\n",
    "          match Excitation.of_det ki kj with\n",
    "          | Excitation.(Triple (phase,\n",
    "              { hole=h1 ; particle=p1 ; spin=s1 },\n",
    "              { hole=h2 ; particle=p2 ; spin=s2 },\n",
    "              { hole=h3 ; particle=p3 ; spin=s3 }) )  -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n",
    "          | _ -> assert false\n",
    "    in\n",
    "\n",
    "    let result = \n",
    "       let open Spin in \n",
    "       match s1, s2, s3 with\n",
    "       | Alfa, Alfa, Alfa\n",
    "       | Beta, Beta, Beta -> \n",
    "           sum mos_cabs (fun a -> \n",
    "                h_two i j a k s1 s2 *.  f_two m a l n s3 s3 \n",
    "             +. h_two i j a n s1 s2 *.  f_two m a k l s3 s2 \n",
    "             +. h_two i m a l s1 s3 *.  f_two j a k n s2 s3 \n",
    "             +. h_two j m a k s2 s3 *.  f_two i a l n s1 s3 \n",
    "             +. h_two j m a n s2 s3 *.  f_two i a k l s1 s2 \n",
    "             -. h_two i j a l s1 s2 *.  f_two m a k n s3 s3 \n",
    "             -. h_two i m a k s1 s3 *.  f_two j a l n s2 s3 \n",
    "             -. h_two i m a n s1 s3 *.  f_two j a k l s2 s2 \n",
    "             -. h_two j m a l s2 s3 *.  f_two i a k n s1 s3 )\n",
    "       | Alfa, Alfa, Beta\n",
    "       | Beta, Beta, Alfa -> \n",
    "           sum mos_cabs (fun a -> \n",
    "                h_two i j a l s1 s2 *.  f_two a m k n s1 s3\n",
    "             +. h_two i m k a s1 s3 *.  f_two j a l n s2 s3\n",
    "             +. h_two j m a n s2 s3 *.  f_two i a k l s1 s2 \n",
    "             +. h_two j m l a s2 s3 *.  f_two i a k n s1 s3\n",
    "             -. h_two i j a k s1 s2 *.  f_two a m l n s1 s3\n",
    "             -. h_two i m a n s1 s3 *.  f_two j a k l s2 s2 \n",
    "             -. h_two i m l a s1 s3 *.  f_two j a k n s2 s3\n",
    "             -. h_two j m k a s2 s3 *.  f_two i a l n s1 s3\n",
    "           ) \n",
    "       | Alfa, Beta, Beta\n",
    "       | Beta, Alfa, Alfa -> \n",
    "           sum mos_cabs (fun a -> \n",
    "                h_two i j a l s1 s2 *.  f_two a m k n s1 s3 \n",
    "             +. h_two i m a n s1 s3 *.  f_two a j k l s1 s2 \n",
    "             +. h_two i m k a s1 s3 *.  f_two j a l n s2 s3 \n",
    "             +. h_two j m a n s2 s3 *.  f_two i a k l s1 s2 \n",
    "             -. h_two i j a n s1 s2 *.  f_two a m k l s1 s2 \n",
    "             -. h_two i j k a s1 s2 *.  f_two m a l n s2 s3 \n",
    "             -. h_two i m a l s1 s3 *.  f_two a j k n s1 s3 \n",
    "             -. h_two j m a l s2 s3 *.  f_two i a k n s1 s3 \n",
    "           ) \n",
    "       | Beta, Alfa, Beta\n",
    "       | Alfa, Beta, Alfa ->  assert false (*TODO *)\n",
    "    in\n",
    "    match phase with\n",
    "    | Phase.Pos -> result\n",
    "    | Phase.Neg -> -. result\n",
    "     \n",
    "\n",
    "let _ = check 100 integral_value 3 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "---------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true,
    "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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