grogu/test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Mac:23435] shmem: mmap: an error occurred while determining whether or not /var/folders/yh/dx7xl94n3g52ts3td8qcxjcc0000gn/T//ompi.Mac.501/jf.0/46137344/sm_segment.Mac.501.2c00000.0 could be created.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'0.14.3'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "from tqdm import tqdm\n",
    "from timeit import default_timer as timer\n",
    "\n",
    "os.environ[\"OMP_NUM_THREADS\"] = \"1\"  # export OMP_NUM_THREADS=4\n",
    "os.environ[\"OPENBLAS_NUM_THREADS\"] = \"1\"  # export OPENBLAS_NUM_THREADS=4\n",
    "os.environ[\"MKL_NUM_THREADS\"] = \"1\"  # export MKL_NUM_THREADS=6\n",
    "os.environ[\"VECLIB_MAXIMUM_THREADS\"] = \"1\"  # export VECLIB_MAXIMUM_THREADS=4\n",
    "os.environ[\"NUMEXPR_NUM_THREADS\"] = \"1\"  # export NUMEXPR_NUM_THREADS=6\n",
    "\n",
    "import numpy as np\n",
    "import sisl\n",
    "from src.grogu_magn.useful import *\n",
    "from mpi4py import MPI\n",
    "from numpy.linalg import inv\n",
    "import warnings\n",
    "\n",
    "# runtime information\n",
    "times = dict()\n",
    "times[\"start_time\"] = timer()\n",
    "########################\n",
    "# it works if data is in downloads folder\n",
    "########################\n",
    "sisl.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "================================================================================================================================================================\n",
      "Input file: \n",
      "Not yet specified.\n",
      "Number of nodes in the parallel cluster:  1\n",
      "================================================================================================================================================================\n",
      "Cell [Ang]: \n",
      "[[ 3.79100000e+00  0.00000000e+00  0.00000000e+00]\n",
      " [-1.89550000e+00  3.28310231e+00  0.00000000e+00]\n",
      " [ 1.25954923e-15  2.18160327e-15  2.05700000e+01]]\n",
      "================================================================================================================================================================\n",
      "DFT axis: \n",
      "[0 0 1]\n",
      "Quantization axis and perpendicular rotation directions:\n",
      "[1 0 0]  --»  [array([0, 1, 0]), array([0, 0, 1])]\n",
      "[0 1 0]  --»  [array([1, 0, 0]), array([0, 0, 1])]\n",
      "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
      "================================================================================================================================================================\n",
      "Parameters for the contour integral:\n",
      "Number of k points:  10\n",
      "k point directions:  xy\n",
      "Ebot:  -15\n",
      "Eset:  50\n",
      "Esetp:  1000\n",
      "================================================================================================================================================================\n"
     ]
    }
   ],
   "source": [
    "# this cell mimicks an input file\n",
    "fdf = sisl.get_sile(\n",
    "    \"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\"\n",
    ")  # ./Jij_for_Marci_6p45ang/CrBr.fdf\n",
    "# this information needs to be given at the input!!\n",
    "scf_xcf_orientation = np.array([0, 0, 1])  # z\n",
    "# list of reference directions for around which we calculate the derivatives\n",
    "# o is the quantization axis, v and w are two axes perpendicular to it\n",
    "# at this moment the user has to supply o,v,w on the input.\n",
    "# we can have some default for this\n",
    "ref_xcf_orientations = [\n",
    "    dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),\n",
    "    dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),\n",
    "    dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),\n",
    "]\n",
    "\n",
    "\n",
    "# human readable definition of magnetic entities ./lat3_791/Fe3GeTe2.fdf\n",
    "magnetic_entities = [\n",
    "    dict(atom=3, l=2),\n",
    "    dict(atom=4, l=2),\n",
    "    dict(atom=5, l=2),\n",
    "    #    dict(atom=[3, 4],),\n",
    "]\n",
    "# pair information ./lat3_791/Fe3GeTe2.fdf\n",
    "pairs = [\n",
    "    # isotropic should be -82 meV\n",
    "    dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),\n",
    "    #    dict(ai=1, aj=0, Ruc=np.array([0, 0, 0])),\n",
    "    dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n",
    "    #    dict(ai=2, aj=1, Ruc=np.array([0, 0, 0])),\n",
    "    dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n",
    "    #    dict(ai=2, aj=0, Ruc=np.array([0, 0, 0])),\n",
    "    # these should all be around -41.9 in the isotropic part\n",
    "    #    dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n",
    "    #    dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n",
    "    #    dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),\n",
    "    #    dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),\n",
    "]\n",
    "\n",
    "\"\"\"\n",
    "# human readable definition of magnetic entities ./Jij_for_Marci_6p45ang/CrBr.fdf\n",
    "magnetic_entities = [\n",
    "    dict(atom=0, l=2),\n",
    "    dict(atom=1, l=2),\n",
    "    dict(atom=2, l=2),\n",
    "]\n",
    "# pair information ./Jij_for_Marci_6p45ang/CrBr.fdf\n",
    "pairs = [\n",
    "    dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),\n",
    "    dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n",
    "    dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n",
    "    dict(ai=0, aj=1, Ruc=np.array([1, 0, 0])),\n",
    "    dict(ai=0, aj=2, Ruc=np.array([1, 0, 0])),\n",
    "    dict(ai=0, aj=1, Ruc=np.array([-1, 0, 0])),\n",
    "    dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),\n",
    "    dict(ai=0, aj=1, Ruc=np.array([0, 1, 0])),\n",
    "    dict(ai=0, aj=2, Ruc=np.array([0, 1, 0])),\n",
    "    dict(ai=0, aj=1, Ruc=np.array([0, 1, 0])),\n",
    "    dict(ai=0, aj=2, Ruc=np.array([0, 1, 0])),\n",
    "]\n",
    "\"\"\"\n",
    "\n",
    "# Brilloun zone sampling and Green function contour integral\n",
    "kset = 10\n",
    "kdirs = \"xy\"\n",
    "ebot = -15\n",
    "eset = 50\n",
    "esetp = 1000\n",
    "\n",
    "\n",
    "# MPI parameters\n",
    "comm = MPI.COMM_WORLD\n",
    "size = comm.Get_size()\n",
    "rank = comm.Get_rank()\n",
    "root_node = 0\n",
    "\n",
    "simulation_parameters = dict(\n",
    "    path=\"Not yet specified.\",\n",
    "    scf_xcf_orientation=scf_xcf_orientation,\n",
    "    ref_xcf_orientations=ref_xcf_orientations,\n",
    "    kset=kset,\n",
    "    kdirs=kdirs,\n",
    "    ebot=ebot,\n",
    "    eset=eset,\n",
    "    esetp=esetp,\n",
    "    parallel_size=size,\n",
    ")\n",
    "\n",
    "# digestion of the input\n",
    "# read in hamiltonian\n",
    "dh = fdf.read_hamiltonian()\n",
    "simulation_parameters[\"cell\"] = fdf.read_geometry().cell\n",
    "\n",
    "# unit cell index\n",
    "uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])\n",
    "\n",
    "print_parameters(simulation_parameters)\n",
    "times[\"setup_time\"] = timer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/danielpozsar/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/matplotlib/cbook.py:1762: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return math.isfinite(val)\n",
      "/Users/danielpozsar/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/matplotlib/cbook.py:1398: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-12.806739"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(np.sort(dh.eig()))\n",
    "plt.ylim(None, 20)\n",
    "np.real(dh.eig()).min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "NO = dh.no  # shorthand for number of orbitals in the unit cell\n",
    "\n",
    "# preprocessing Hamiltonian and overlap matrix elements\n",
    "h11 = dh.tocsr(dh.M11r)\n",
    "h11 += dh.tocsr(dh.M11i) * 1.0j\n",
    "h11 = h11.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype(\"complex128\")\n",
    "\n",
    "h22 = dh.tocsr(dh.M22r)\n",
    "h22 += dh.tocsr(dh.M22i) * 1.0j\n",
    "h22 = h22.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype(\"complex128\")\n",
    "\n",
    "h12 = dh.tocsr(dh.M12r)\n",
    "h12 += dh.tocsr(dh.M12i) * 1.0j\n",
    "h12 = h12.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype(\"complex128\")\n",
    "\n",
    "h21 = dh.tocsr(dh.M21r)\n",
    "h21 += dh.tocsr(dh.M21i) * 1.0j\n",
    "h21 = h21.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype(\"complex128\")\n",
    "\n",
    "sov = (\n",
    "    dh.tocsr(dh.S_idx)\n",
    "    .toarray()\n",
    "    .reshape(NO, dh.n_s, NO)\n",
    "    .transpose(0, 2, 1)\n",
    "    .astype(\"complex128\")\n",
    ")\n",
    "\n",
    "\n",
    "# Reorganization of Hamiltonian and overlap matrix elements to SPIN BOX representation\n",
    "U = np.vstack(\n",
    "    [np.kron(np.eye(NO, dtype=int), [1, 0]), np.kron(np.eye(NO, dtype=int), [0, 1])]\n",
    ")\n",
    "# This is the permutation that transforms ud1ud2 to u12d12\n",
    "# That is this transforms FROM SPIN BOX to ORBITAL BOX => U\n",
    "# the inverse transformation is U.T u12d12 to ud1ud2\n",
    "# That is FROM ORBITAL BOX to SPIN BOX => U.T\n",
    "\n",
    "# From now on everything is in SPIN BOX!!\n",
    "hh, ss = np.array(\n",
    "    [\n",
    "        U.T @ np.block([[h11[:, :, i], h12[:, :, i]], [h21[:, :, i], h22[:, :, i]]]) @ U\n",
    "        for i in range(dh.lattice.nsc.prod())\n",
    "    ]\n",
    "), np.array(\n",
    "    [\n",
    "        U.T\n",
    "        @ np.block([[sov[:, :, i], sov[:, :, i] * 0], [sov[:, :, i] * 0, sov[:, :, i]]])\n",
    "        @ U\n",
    "        for i in range(dh.lattice.nsc.prod())\n",
    "    ]\n",
    ")\n",
    "\n",
    "\n",
    "# symmetrizing Hamiltonian and overlap matrix to make them hermitian\n",
    "for i in range(dh.lattice.sc_off.shape[0]):\n",
    "    j = dh.lattice.sc_index(-dh.lattice.sc_off[i])\n",
    "    h1, h1d = hh[i], hh[j]\n",
    "    hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2\n",
    "    s1, s1d = ss[i], ss[j]\n",
    "    ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2\n",
    "\n",
    "# identifying TRS and TRB parts of the Hamiltonian\n",
    "TAUY = np.kron(np.eye(NO), tau_y)\n",
    "hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])\n",
    "hTRS = (hh + hTR) / 2\n",
    "hTRB = (hh - hTR) / 2\n",
    "\n",
    "# extracting the exchange field\n",
    "traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())]  # equation 77\n",
    "XCF = np.array(\n",
    "    [\n",
    "        np.array([f[\"x\"] for f in traced]),\n",
    "        np.array([f[\"y\"] for f in traced]),\n",
    "        np.array([f[\"z\"] for f in traced]),\n",
    "    ]\n",
    ")  # equation 77\n",
    "\n",
    "# Check if exchange field has scalar part\n",
    "max_xcfs = abs(np.array(np.array([f[\"c\"] for f in traced]))).max()\n",
    "if max_xcfs > 1e-12:\n",
    "    warnings.warn(\n",
    "        f\"Exchange field has non negligible scalar part. Largest value is {max_xcfs}\"\n",
    "    )\n",
    "\n",
    "times[\"H_and_XCF_time\"] = timer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for every site we have to store 3 Greens function (and the associated _tmp-s) in the 3 reference directions\n",
    "for i, mag_ent in enumerate(magnetic_entities):\n",
    "    parsed = parse_magnetic_entity(dh, **mag_ent)  # parse orbital indexes\n",
    "    magnetic_entities[i][\"orbital_indeces\"] = parsed\n",
    "    # calculate spin box indexes\n",
    "    magnetic_entities[i][\"spin_box_indeces\"] = blow_up_orbindx(parsed)\n",
    "    # if orbital is not set use all\n",
    "    if \"l\" not in mag_ent.keys():\n",
    "        mag_ent[\"l\"] = \"all\"\n",
    "    if isinstance(mag_ent[\"atom\"], int):\n",
    "        mag_ent[\"tags\"] = [\n",
    "            f\"[{mag_ent['atom']}]{dh.atoms[mag_ent['atom']].tag}({mag_ent['l']})\"\n",
    "        ]\n",
    "        mag_ent[\"xyz\"] = [dh.xyz[mag_ent[\"atom\"]]]\n",
    "    if isinstance(mag_ent[\"atom\"], list):\n",
    "        mag_ent[\"tags\"] = []\n",
    "        mag_ent[\"xyz\"] = []\n",
    "        # iterate over atoms\n",
    "        for atom_idx in mag_ent[\"atom\"]:\n",
    "            mag_ent[\"tags\"].append(\n",
    "                f\"[{atom_idx}]{dh.atoms[atom_idx].tag}({mag_ent['l']})\"\n",
    "            )\n",
    "            mag_ent[\"xyz\"].append(dh.xyz[atom_idx])\n",
    "\n",
    "    # calculate size for Greens function generation\n",
    "    spin_box_shape = len(mag_ent[\"spin_box_indeces\"])\n",
    "\n",
    "    mag_ent[\"energies\"] = []  # we will store the second order energy derivations here\n",
    "\n",
    "    mag_ent[\"Gii\"] = []  # Greens function\n",
    "    mag_ent[\"Gii_tmp\"] = []  # Greens function for parallelization\n",
    "    # These will be the perturbed potentials from eq. 100\n",
    "    mag_ent[\"Vu1\"] = [list([]) for _ in range(len(ref_xcf_orientations))]\n",
    "    mag_ent[\"Vu2\"] = [list([]) for _ in range(len(ref_xcf_orientations))]\n",
    "    for i in ref_xcf_orientations:\n",
    "        # Greens functions for every quantization axis\n",
    "        mag_ent[\"Gii\"].append(\n",
    "            np.zeros((eset, spin_box_shape, spin_box_shape), dtype=\"complex128\")\n",
    "        )\n",
    "        mag_ent[\"Gii_tmp\"].append(\n",
    "            np.zeros((eset, spin_box_shape, spin_box_shape), dtype=\"complex128\")\n",
    "        )\n",
    "\n",
    "# for every site we have to store 2x3 Greens function (and the associated _tmp-s)\n",
    "# in the 3 reference directions, because G_ij and G_ji are both needed\n",
    "for pair in pairs:\n",
    "    # calculate size for Greens function generation\n",
    "    spin_box_shape_i = len(magnetic_entities[pair[\"ai\"]][\"spin_box_indeces\"])\n",
    "    spin_box_shape_j = len(magnetic_entities[pair[\"aj\"]][\"spin_box_indeces\"])\n",
    "    pair[\"tags\"] = []\n",
    "    for mag_ent in [magnetic_entities[pair[\"ai\"]], magnetic_entities[pair[\"aj\"]]]:\n",
    "        tag = \"\"\n",
    "        # get atoms of magnetic entity\n",
    "        atoms_idx = mag_ent[\"atom\"]\n",
    "        orbitals = mag_ent[\"l\"]\n",
    "\n",
    "        # if magnetic entity contains one atoms\n",
    "        if isinstance(atoms_idx, int):\n",
    "            tag += f\"[{atoms_idx}]{dh.atoms[atoms_idx].tag}({orbitals})\"\n",
    "\n",
    "        # if magnetic entity contains more than one atoms\n",
    "        if isinstance(atoms_idx, list):\n",
    "            # iterate over atoms\n",
    "            atom_group = \"{\"\n",
    "            for atom_idx in atoms_idx:\n",
    "                atom_group += f\"[{atom_idx}]{dh.atoms[atom_idx].tag}({orbitals})--\"\n",
    "            # end {} of the atoms in the magnetic entity\n",
    "            tag += atom_group[:-2] + \"}\"\n",
    "        pair[\"tags\"].append(tag)\n",
    "    pair[\"energies\"] = []  # we will store the second order energy derivations here\n",
    "\n",
    "    pair[\"Gij\"] = []  # Greens function\n",
    "    pair[\"Gji\"] = []\n",
    "    pair[\"Gij_tmp\"] = []  # Greens function for parallelization\n",
    "    pair[\"Gji_tmp\"] = []\n",
    "    for i in ref_xcf_orientations:\n",
    "        # Greens functions for every quantization axis\n",
    "        pair[\"Gij\"].append(\n",
    "            np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype=\"complex128\")\n",
    "        )\n",
    "        pair[\"Gij_tmp\"].append(\n",
    "            np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype=\"complex128\")\n",
    "        )\n",
    "        pair[\"Gji\"].append(\n",
    "            np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype=\"complex128\")\n",
    "        )\n",
    "        pair[\"Gji_tmp\"].append(\n",
    "            np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype=\"complex128\")\n",
    "        )\n",
    "\n",
    "times[\"site_and_pair_dictionaries_time\"] = timer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "k loop:   0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    }
   ],
   "source": [
    "kset = make_kset(dirs=kdirs, NUMK=kset)  # generate k space sampling\n",
    "wkset = np.ones(len(kset)) / len(kset)  # generate weights for k points\n",
    "kpcs = np.array_split(kset, size)  # split the k points based on MPI size\n",
    "kpcs[root_node] = tqdm(kpcs[root_node], desc=\"k loop\")\n",
    "\n",
    "times[\"k_set_time\"] = timer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this will contain the three hamiltonians in the reference directions needed to calculate the energy variations upon rotation\n",
    "hamiltonians = []\n",
    "\n",
    "# iterate over the reference directions (quantization axes)\n",
    "for i, orient in enumerate(ref_xcf_orientations):\n",
    "    # obtain rotated exchange field\n",
    "    R = RotMa2b(scf_xcf_orientation, orient[\"o\"])\n",
    "    rot_XCF = np.einsum(\"ij,jklm->iklm\", R, XCF)\n",
    "    rot_H_XCF = sum(\n",
    "        [np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]\n",
    "    )\n",
    "    rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]\n",
    "\n",
    "    # obtain total Hamiltonian with the rotated exchange field\n",
    "    rot_H = (\n",
    "        hTRS + rot_H_XCF\n",
    "    )  # equation 76 #######################################################################################\n",
    "\n",
    "    hamiltonians.append(\n",
    "        dict(orient=orient[\"o\"], H=rot_H)\n",
    "    )  # store orientation and rotated Hamiltonian\n",
    "\n",
    "    # these are the infinitezimal rotations (for now) perpendicular to the quantization axis\n",
    "    for u in orient[\"vw\"]:\n",
    "        Tu = np.kron(np.eye(NO, dtype=int), tau_u(u))  # section 2.H\n",
    "\n",
    "        Vu1 = 1j / 2 * commutator(rot_H_XCF_uc, Tu)  # equation 100\n",
    "        Vu2 = 1 / 8 * commutator(commutator(Tu, rot_H_XCF_uc), Tu)  # equation 100\n",
    "\n",
    "        for mag_ent in magnetic_entities:\n",
    "            # fill up the perturbed potentials (for now) based on the on-site projections\n",
    "            mag_ent[\"Vu1\"][i].append(\n",
    "                Vu1[:, mag_ent[\"spin_box_indeces\"]][mag_ent[\"spin_box_indeces\"], :]\n",
    "            )\n",
    "            mag_ent[\"Vu2\"][i].append(\n",
    "                Vu2[:, mag_ent[\"spin_box_indeces\"]][mag_ent[\"spin_box_indeces\"], :]\n",
    "            )\n",
    "\n",
    "times[\"reference_rotations_time\"] = timer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of k points: 100\n",
      "Total number of directions: 3\n",
      "Total number of matrix inversions: 300\n",
      "The shape of the Hamiltonian and the Greens function is 84x84=7056\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "k loop: 100%|██████████| 100/100 [00:27<00:00,  3.70it/s]\n"
     ]
    }
   ],
   "source": [
    "if rank == root_node:\n",
    "    print(\"Starting matrix inversions\")\n",
    "    print(f\"Total number of k points: {kset.shape[0]}\")\n",
    "    print(f\"Total number of directions: {len(hamiltonians)}\")\n",
    "    print(f\"Total number of matrix inversions: {kset.shape[0] * len(hamiltonians)}\")\n",
    "    print(f\"The shape of the Hamiltonian and the Greens function is {NO}x{NO}={NO*NO}\")\n",
    "    print(\n",
    "        \"================================================================================================================================================================\"\n",
    "    )\n",
    "\n",
    "comm.Barrier()\n",
    "# ----------------------------------------------------------------------\n",
    "\n",
    "# make energy contour\n",
    "# we are working in eV now  !\n",
    "# and sisil shifts E_F to 0 !\n",
    "cont = make_contour(emin=ebot, enum=eset, p=esetp)\n",
    "eran = cont.ze\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# sampling the integrand on the contour and the BZ\n",
    "for k in kpcs[rank]:\n",
    "    wk = wkset[rank]  # weight of k point in BZ integral\n",
    "    # iterate over reference directions\n",
    "    for i, hamiltonian_orientation in enumerate(hamiltonians):\n",
    "        # calculate Greens function\n",
    "        H = hamiltonian_orientation[\"H\"]\n",
    "        HK, SK = hsk(H, ss, dh.sc_off, k)\n",
    "        # Gk = inv(SK * eran.reshape(eset, 1, 1) - HK)\n",
    "\n",
    "        # solve Greens function sequentially for the energies, because of memory bound\n",
    "        Gk = np.zeros(shape=(eset, HK.shape[0], HK.shape[1]), dtype=\"complex128\")\n",
    "        for j in range(eset):\n",
    "            Gk[j] = inv(SK * eran[j] - HK)\n",
    "\n",
    "        # store the Greens function slice of the magnetic entities (for now) based on the on-site projections\n",
    "        for mag_ent in magnetic_entities:\n",
    "            mag_ent[\"Gii_tmp\"][i] += (\n",
    "                Gk[:, mag_ent[\"spin_box_indeces\"]][..., mag_ent[\"spin_box_indeces\"]]\n",
    "                * wk\n",
    "            )\n",
    "\n",
    "        for pair in pairs:\n",
    "            # add phase shift based on the cell difference\n",
    "            phase = np.exp(1j * 2 * np.pi * k @ pair[\"Ruc\"].T)\n",
    "\n",
    "            # get the pair orbital sizes from the magnetic entities\n",
    "            ai = magnetic_entities[pair[\"ai\"]][\"spin_box_indeces\"]\n",
    "            aj = magnetic_entities[pair[\"aj\"]][\"spin_box_indeces\"]\n",
    "\n",
    "            # store the Greens function slice of the magnetic entities (for now) based on the on-site projections\n",
    "            pair[\"Gij_tmp\"][i] += Gk[:, ai][..., aj] * phase * wk\n",
    "            pair[\"Gji_tmp\"][i] += Gk[:, aj][..., ai] * phase * wk\n",
    "\n",
    "# summ reduce partial results of mpi nodes\n",
    "for i in range(len(hamiltonians)):\n",
    "    for mag_ent in magnetic_entities:\n",
    "        comm.Reduce(mag_ent[\"Gii_tmp\"][i], mag_ent[\"Gii\"][i], root=root_node)\n",
    "\n",
    "    for pair in pairs:\n",
    "        comm.Reduce(pair[\"Gij_tmp\"][i], pair[\"Gij\"][i], root=root_node)\n",
    "        comm.Reduce(pair[\"Gji_tmp\"][i], pair[\"Gji\"][i], root=root_node)\n",
    "\n",
    "times[\"green_function_inversion_time\"] = timer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##################################################################### GROGU OUTPUT #############################################################################\n",
      "================================================================================================================================================================\n",
      "Input file: \n",
      "Not yet specified.\n",
      "Number of nodes in the parallel cluster:  1\n",
      "================================================================================================================================================================\n",
      "Cell [Ang]: \n",
      "[[ 3.79100000e+00  0.00000000e+00  0.00000000e+00]\n",
      " [-1.89550000e+00  3.28310231e+00  0.00000000e+00]\n",
      " [ 1.25954923e-15  2.18160327e-15  2.05700000e+01]]\n",
      "================================================================================================================================================================\n",
      "DFT axis: \n",
      "[0 0 1]\n",
      "Quantization axis and perpendicular rotation directions:\n",
      "[1 0 0]  --»  [array([0, 1, 0]), array([0, 0, 1])]\n",
      "[0 1 0]  --»  [array([1, 0, 0]), array([0, 0, 1])]\n",
      "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
      "================================================================================================================================================================\n",
      "Parameters for the contour integral:\n",
      "Number of k points:  10\n",
      "k point directions:  xy\n",
      "Ebot:  -15\n",
      "Eset:  50\n",
      "Esetp:  1000\n",
      "================================================================================================================================================================\n",
      "Atomic information: \n",
      "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
      "[atom index]Element(orbitals)        x [Ang]        y [Ang]        z [Ang]        Sx        Sy        Sz        Q        Lx        Ly        Lz        Jx        Jy        Jz\n",
      "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
      "[3]Fe(2)        -7.339158738013707e-06        4.149278510690423e-06        11.657585837928032\n",
      "\n",
      "[4]Fe(2)        -7.326987662162937e-06        4.158274523275774e-06        8.912422537596708\n",
      "\n",
      "[5]Fe(2)        1.8954667088117545        1.0943913231921656        10.285002698393109\n",
      "\n",
      "================================================================================================================================================================\n",
      "Exchange [meV]\n",
      "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Magnetic entity1        Magnetic entity2       [i  j  k]       d [Ang]\n",
      "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
      "[3]Fe(2)        [4]Fe(2)        [0 0 0]        d [Ang] Not yet.\n",
      "Isotropic:  -39.33305904162077\n",
      "DMI:  [-3.49132045e-01  2.55180589e-04 -2.79328031e-07]\n",
      "Symmetric-anisotropy:  [-3.25353129e-02 -1.12520210e-01 -2.11441543e-05  2.53477251e-04\n",
      " -6.21351953e-07]\n",
      "Energies for debugging: \n",
      "array([[-3.94455793e-02, -3.49131423e-04,  3.49132666e-04,\n",
      "        -3.91880035e-02],\n",
      "       [-3.96260920e-02, -2.53477251e-07,  2.56883927e-07,\n",
      "        -3.93655944e-02],\n",
      "       [-3.24859133e-02,  2.08648262e-08,  2.14234823e-08,\n",
      "        -3.24858874e-02]])\n",
      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
      "array([-0.03936559, -0.03248591, -0.03944558])\n",
      "Test J_xx = E(y,z) = E(z,y)\n",
      "-0.03936559435457027 -0.03248588738966994\n",
      "\n",
      "[4]Fe(2)        [5]Fe(2)        [0 0 0]        d [Ang] Not yet.\n",
      "Isotropic:  -65.55485507687138\n",
      "DMI:  [-3.57652832e+00  6.16350266e+00  1.76417146e-05]\n",
      "Symmetric-anisotropy:  [0.08815647 0.19563304 0.03702482 6.25899263 0.04349251]\n",
      "Energies for debugging: \n",
      "array([[-6.53592220e-02, -3.62002083e-03,  3.53303581e-03,\n",
      "        -6.58386446e-02],\n",
      "       [-6.51008759e-02, -6.25899263e-03,  6.06801268e-03,\n",
      "        -6.54666986e-02],\n",
      "       [-6.59577470e-02, -3.70071792e-05, -3.70424626e-05,\n",
      "        -6.59146548e-02]])\n",
      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
      "array([-0.0654667 , -0.06595775, -0.06535922])\n",
      "Test J_xx = E(y,z) = E(z,y)\n",
      "-0.06546669860888496 -0.06591465478729451\n",
      "\n",
      "[3]Fe(2)        [5]Fe(2)        [0 0 0]        d [Ang] Not yet.\n",
      "Isotropic:  -65.55361001040538\n",
      "DMI:  [ 3.55870825e+00 -6.14744383e+00  2.20064459e-05]\n",
      "Symmetric-anisotropy:  [ 0.08580243  0.19612473  0.03702668 -6.24894432 -0.04979181]\n",
      "Energies for debugging: \n",
      "array([[-6.53574853e-02,  3.60850006e-03, -3.50891645e-03,\n",
      "        -6.58355372e-02],\n",
      "       [-6.51026555e-02,  6.24894432e-03, -6.04594334e-03,\n",
      "        -6.54678076e-02],\n",
      "       [-6.59577277e-02, -3.70046728e-05, -3.70486857e-05,\n",
      "        -6.59146327e-02]])\n",
      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
      "array([-0.06546781, -0.06595773, -0.06535749])\n",
      "Test J_xx = E(y,z) = E(z,y)\n",
      "-0.06546780758377949 -0.06591463268052017\n",
      "\n",
      "================================================================================================================================================================\n",
      "Runtime information: \n",
      "Total runtime: 28.020738958 s\n",
      "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Initial setup: 0.16348762500000014 s\n",
      "Hamiltonian conversion and XC field extraction: 0.739 s\n",
      "Pair and site datastructure creatrions: 0.016 s\n",
      "k set cration and distribution: 0.018 s\n",
      "Rotating XC potential: 0.216 s\n",
      "Greens function inversion: 26.841 s\n",
      "Calculate energies and magnetic components: 0.027 s\n"
     ]
    }
   ],
   "source": [
    "if rank == root_node:\n",
    "    # iterate over the magnetic entities\n",
    "    for tracker, mag_ent in enumerate(magnetic_entities):\n",
    "        # iterate over the quantization axes\n",
    "        for i, Gii in enumerate(mag_ent[\"Gii\"]):\n",
    "            storage = []\n",
    "            # iterate over the first and second order local perturbations\n",
    "            for Vu1, Vu2 in zip(mag_ent[\"Vu1\"][i], mag_ent[\"Vu2\"][i]):\n",
    "                # The Szunyogh-Lichtenstein formula\n",
    "                traced = np.trace((Vu2 @ Gii + 0.5 * Gii @ Vu1 @ Gii), axis1=1, axis2=2)\n",
    "                # evaluation of the contour integral\n",
    "                storage.append(np.trapz(-1 / np.pi * np.imag(traced * cont.we)))\n",
    "\n",
    "            # fill up the magnetic entities dictionary with the energies\n",
    "            magnetic_entities[tracker][\"energies\"].append(storage)\n",
    "\n",
    "    # iterate over the pairs\n",
    "    for tracker, pair in enumerate(pairs):\n",
    "        # iterate over the quantization axes\n",
    "        for i, (Gij, Gji) in enumerate(zip(pair[\"Gij\"], pair[\"Gji\"])):\n",
    "            site_i = magnetic_entities[pair[\"ai\"]]\n",
    "            site_j = magnetic_entities[pair[\"aj\"]]\n",
    "\n",
    "            storage = []\n",
    "            # iterate over the first order local perturbations in all possible orientations for the two sites\n",
    "            for Vui in site_i[\"Vu1\"][i]:\n",
    "                for Vuj in site_j[\"Vu1\"][i]:\n",
    "                    # The Szunyogh-Lichtenstein formula\n",
    "                    traced = np.trace((Vui @ Gij @ Vuj @ Gji), axis1=1, axis2=2)\n",
    "                    # evaluation of the contour integral\n",
    "                    storage.append(np.trapz(-1 / np.pi * np.imag(traced * cont.we)))\n",
    "            # fill up the pairs dictionary with the energies\n",
    "            pairs[tracker][\"energies\"].append(storage)\n",
    "\n",
    "    # calculate magnetic parameters\n",
    "    for pair in pairs:\n",
    "        J_iso, J_S, D = calculate_exchange_tensor(pair)\n",
    "        pair[\"J_iso\"] = J_iso * sisl.unit_convert(\"eV\", \"meV\")\n",
    "        pair[\"J_S\"] = J_S * sisl.unit_convert(\"eV\", \"meV\")\n",
    "        pair[\"D\"] = D * sisl.unit_convert(\"eV\", \"meV\")\n",
    "\n",
    "    times[\"end_time\"] = timer()\n",
    "    print(\n",
    "        \"##################################################################### GROGU OUTPUT #############################################################################\"\n",
    "    )\n",
    "\n",
    "    print_parameters(simulation_parameters)\n",
    "    print_atoms_and_pairs(magnetic_entities, pairs)\n",
    "    print_runtime_informations(times)\n",
    "\n",
    "    # remove clutter to save magnetic entities and pair information\n",
    "    for pair in pairs:\n",
    "        del pair[\"Gij\"]\n",
    "        del pair[\"Gij_tmp\"]\n",
    "        del pair[\"Gji\"]\n",
    "        del pair[\"Gji_tmp\"]\n",
    "    for mag_ent in magnetic_entities:\n",
    "        del mag_ent[\"Gii\"]\n",
    "        del mag_ent[\"Gii_tmp\"]\n",
    "        del mag_ent[\"Vu1\"]\n",
    "        del mag_ent[\"Vu2\"]\n",
    "    results = dict(\n",
    "        parameters=simulation_parameters,\n",
    "        magnetic_entities=magnetic_entities,\n",
    "        pairs=pairs,\n",
    "        runtime=times,\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'parameters': {'path': 'Not yet specified.',\n",
       "  'scf_xcf_orientation': array([0, 0, 1]),\n",
       "  'ref_xcf_orientations': [{'o': array([1, 0, 0]),\n",
       "    'vw': [array([0, 1, 0]), array([0, 0, 1])]},\n",
       "   {'o': array([0, 1, 0]), 'vw': [array([1, 0, 0]), array([0, 0, 1])]},\n",
       "   {'o': array([0, 0, 1]), 'vw': [array([1, 0, 0]), array([0, 1, 0])]}],\n",
       "  'kset': 10,\n",
       "  'kdirs': 'xy',\n",
       "  'ebot': -15,\n",
       "  'eset': 50,\n",
       "  'esetp': 1000,\n",
       "  'parallel_size': 1,\n",
       "  'cell': array([[ 3.79100000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "         [-1.89550000e+00,  3.28310231e+00,  0.00000000e+00],\n",
       "         [ 1.25954923e-15,  2.18160327e-15,  2.05700000e+01]])},\n",
       " 'magnetic_entities': [{'atom': 3,\n",
       "   'l': 2,\n",
       "   'orbital_indeces': array([41, 42, 43, 44, 45, 46, 47, 48, 49, 50], dtype=int32),\n",
       "   'spin_box_indeces': array([ 82,  83,  84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,\n",
       "           95,  96,  97,  98,  99, 100, 101]),\n",
       "   'tags': ['[3]Fe(2)'],\n",
       "   'xyz': [array([-7.33915874e-06,  4.14927851e-06,  1.16575858e+01])],\n",
       "   'energies': [[3.734465086018773, 3.7345045132387904],\n",
       "    [3.734496010868627, 3.7344992971735755],\n",
       "    [3.744098645200186, 3.744096314352881]]},\n",
       "  {'atom': 4,\n",
       "   'l': 2,\n",
       "   'orbital_indeces': array([56, 57, 58, 59, 60, 61, 62, 63, 64, 65], dtype=int32),\n",
       "   'spin_box_indeces': array([112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,\n",
       "          125, 126, 127, 128, 129, 130, 131]),\n",
       "   'tags': ['[4]Fe(2)'],\n",
       "   'xyz': [array([-7.32698766e-06,  4.15827452e-06,  8.91242254e+00])],\n",
       "   'energies': [[3.734489896651657, 3.7345163491510975],\n",
       "    [3.7346033722527983, 3.73451361626319],\n",
       "    [3.744120742400213, 3.744123051274557]]},\n",
       "  {'atom': 5,\n",
       "   'l': 2,\n",
       "   'orbital_indeces': array([71, 72, 73, 74, 75, 76, 77, 78, 79, 80], dtype=int32),\n",
       "   'spin_box_indeces': array([142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154,\n",
       "          155, 156, 157, 158, 159, 160, 161]),\n",
       "   'tags': ['[5]Fe(2)'],\n",
       "   'xyz': [array([ 1.89546671,  1.09439132, 10.2850027 ])],\n",
       "   'energies': [[2.1707567909611734, 2.170785438112471],\n",
       "    [2.1708196859983695, 2.1707887369208603],\n",
       "    [2.171678783995076, 2.1716787861431013]]}],\n",
       " 'pairs': [{'ai': 0,\n",
       "   'aj': 1,\n",
       "   'Ruc': array([0, 0, 0]),\n",
       "   'tags': ['[3]Fe(2)', '[4]Fe(2)'],\n",
       "   'energies': [[-0.03944557925189693,\n",
       "     -0.0003491314233520734,\n",
       "     0.00034913266605597995,\n",
       "     -0.03918800351839513],\n",
       "    [-0.03962609204615879,\n",
       "     -2.5347725119651397e-07,\n",
       "     2.5688392741602586e-07,\n",
       "     -0.03936559435457027],\n",
       "    [-0.032485913309031784,\n",
       "     2.086482622369864e-08,\n",
       "     2.1423482286665388e-08,\n",
       "     -0.03248588738966994]],\n",
       "   'J_iso': -39.33305904162077,\n",
       "   'J_S': array([-3.25353129e-02, -1.12520210e-01, -2.11441543e-05,  2.53477251e-04,\n",
       "          -6.21351953e-07]),\n",
       "   'D': array([-3.49132045e-01,  2.55180589e-04, -2.79328031e-07])},\n",
       "  {'ai': 1,\n",
       "   'aj': 2,\n",
       "   'Ruc': array([0, 0, 0]),\n",
       "   'tags': ['[4]Fe(2)', '[5]Fe(2)'],\n",
       "   'energies': [[-0.06535922203590024,\n",
       "     -0.003620020827251614,\n",
       "     0.0035330358091578322,\n",
       "     -0.06583864458582893],\n",
       "    [-0.065100875948478,\n",
       "     -0.006258992627124543,\n",
       "     0.0060680126832299295,\n",
       "     -0.06546669860888496],\n",
       "    [-0.06595774697036409,\n",
       "     -3.700717915377913e-05,\n",
       "     -3.7042462582999624e-05,\n",
       "     -0.06591465478729451]],\n",
       "   'J_iso': -65.55485507687138,\n",
       "   'J_S': array([0.08815647, 0.19563304, 0.03702482, 6.25899263, 0.04349251]),\n",
       "   'D': array([-3.57652832e+00,  6.16350266e+00,  1.76417146e-05])},\n",
       "  {'ai': 0,\n",
       "   'aj': 2,\n",
       "   'Ruc': array([0, 0, 0]),\n",
       "   'tags': ['[3]Fe(2)', '[5]Fe(2)'],\n",
       "   'energies': [[-0.0653574852836104,\n",
       "     0.003608500059552775,\n",
       "     -0.0035089164454806124,\n",
       "     -0.06583553716382626],\n",
       "    [-0.06510265546673727,\n",
       "     0.006248944319269189,\n",
       "     -0.006045943341346723,\n",
       "     -0.06546780758377949],\n",
       "    [-0.0659577276970226,\n",
       "     -3.700467282282758e-05,\n",
       "     -3.704868571469545e-05,\n",
       "     -0.06591463268052017]],\n",
       "   'J_iso': -65.55361001040538,\n",
       "   'J_S': array([ 0.08580243,  0.19612473,  0.03702668, -6.24894432, -0.04979181]),\n",
       "   'D': array([ 3.55870825e+00, -6.14744383e+00,  2.20064459e-05])}],\n",
       " 'runtime': {'start_time': 3.2424505,\n",
       "  'setup_time': 3.405938125,\n",
       "  'H_and_XCF_time': 4.145158916,\n",
       "  'site_and_pair_dictionaries_time': 4.161620875,\n",
       "  'k_set_time': 4.179151,\n",
       "  'reference_rotations_time': 4.395303708,\n",
       "  'green_function_inversion_time': 31.236585666,\n",
       "  'end_time': 31.263189458}}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (4136980242.py, line 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Cell \u001b[0;32mIn[11], line 2\u001b[0;36m\u001b[0m\n\u001b[0;31m    ================================================================================================================================================================\u001b[0m\n\u001b[0m    ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "##################################################################### GROGU OUTPUT #############################################################################\n",
    "================================================================================================================================================================\n",
    "Input file: \n",
    "Not yet specified.\n",
    "Number of nodes in the parallel cluster:  1\n",
    "================================================================================================================================================================\n",
    "Cell [Ang]: \n",
    "[[ 3.79100000e+00  0.00000000e+00  0.00000000e+00]\n",
    " [-1.89550000e+00  3.28310231e+00  0.00000000e+00]\n",
    " [ 1.25954923e-15  2.18160327e-15  2.05700000e+01]]\n",
    "================================================================================================================================================================\n",
    "DFT axis: \n",
    "[0 0 1]\n",
    "Quantization axis and perpendicular rotation directions:\n",
    "[1 0 0]  --»  [array([0, 1, 0]), array([0, 0, 1])]\n",
    "[0 1 0]  --»  [array([1, 0, 0]), array([0, 0, 1])]\n",
    "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
    "================================================================================================================================================================\n",
    "number of k points:  20\n",
    "k point directions:  xy\n",
    "================================================================================================================================================================\n",
    "Parameters for the contour integral:\n",
    "Ebot:  -15\n",
    "Eset:  50\n",
    "Esetp:  10000\n",
    "================================================================================================================================================================\n",
    "Atomic informations: \n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[atom index]Element(orbitals)        x [Ang]        y [Ang]        z [Ang]        Sx        Sy        Sz        Q        Lx        Ly        Lz        Jx        Jy        Jz\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[3]Fe(2)        -7.339158738013707e-06        4.149278510690423e-06        11.657585837928032\n",
    "\n",
    "[4]Fe(2)        -7.326987662162937e-06        4.158274523275774e-06        8.912422537596708\n",
    "\n",
    "[5]Fe(2)        1.8954667088117545        1.0943913231921656        10.285002698393109\n",
    "\n",
    "================================================================================================================================================================\n",
    "Exchange [meV]\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Magnetic entity1        Magnetic entity2       [i  j  k]       d [Ang]\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[3]Fe(2)        [4]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -63.47396322818869\n",
    "DMI:  [-9.32946318e-01 -7.94980656e-04 -1.68626155e-06]\n",
    "Symmetric-anisotropy:  [-3.28657093e+00  1.26919731e+00 -5.25251097e-04 -7.51662131e-04\n",
    " -1.69771318e-05]\n",
    "Energies for debugging: \n",
    "array([[-6.22047659e-02, -9.32929341e-04,  9.32963295e-04,\n",
    "        -6.14565896e-02],\n",
    "       [-6.75292273e-02,  7.51662131e-07, -8.38299181e-07,\n",
    "        -6.67605342e-02],\n",
    "       [-5.46814050e-02,  5.23564835e-07,  5.26937358e-07,\n",
    "        -5.46808408e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06676053, -0.0546814 , -0.06220477])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06676053415896452 -0.05468084079537627\n",
    "\n",
    "[4]Fe(2)        [5]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -60.97346468960899\n",
    "DMI:  [-3.79957858e+00  6.15341580e+00  1.98171298e-03]\n",
    "Symmetric-anisotropy:  [0.10023044 0.10625949 0.07113812 6.2430436  0.03640581]\n",
    "Energies for debugging: \n",
    "array([[-6.08672052e-02, -3.83598439e-03,  3.76317277e-03,\n",
    "        -6.11799546e-02],\n",
    "       [-6.06363005e-02, -6.24304360e-03,  6.06378800e-03,\n",
    "        -6.08732343e-02],\n",
    "       [-5.98939156e-02, -6.91564033e-05, -7.31198293e-05,\n",
    "        -5.98115156e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06087323, -0.05989392, -0.06086721])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06087323425105703 -0.05981151560602731\n",
    "\n",
    "[3]Fe(2)        [5]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -60.97783221534475\n",
    "DMI:  [ 3.78495282e+00 -6.14017205e+00  1.98157781e-03]\n",
    "Symmetric-anisotropy:  [ 0.09115149  0.10676698  0.07113987 -6.23329445 -0.04250828]\n",
    "Energies for debugging: \n",
    "array([[-6.08710652e-02,  3.82746110e-03, -3.74244454e-03,\n",
    "        -6.11757507e-02],\n",
    "       [-6.06489192e-02,  6.23329445e-03, -6.04704964e-03,\n",
    "        -6.08866807e-02],\n",
    "       [-5.98938645e-02, -6.91582962e-05, -7.31214518e-05,\n",
    "        -5.98114592e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06088668, -0.05989386, -0.06087107])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06088668072635317 -0.05981145916679715\n",
    "\n",
    "================================================================================================================================================================\n",
    "Runtime information: \n",
    "Total runtime: 106.24268275 s\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Initial setup: 0.12151341699999985 s\n",
    "Hamiltonian conversion and XC field extraction: 0.664 s\n",
    "Pair and site datastructure creatrions: 0.008 s\n",
    "k set cration and distribution: 0.013 s\n",
    "Rotating XC potential: 0.209 s\n",
    "Greens function inversion: 105.202 s\n",
    "Calculate energies and magnetic components: 0.025 s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##################################################################### GROGU OUTPUT #############################################################################\n",
    "================================================================================================================================================================\n",
    "Input file: \n",
    "Not yet specified.\n",
    "Number of nodes in the parallel cluster:  1\n",
    "================================================================================================================================================================\n",
    "Cell [Ang]: \n",
    "[[ 3.79100000e+00  0.00000000e+00  0.00000000e+00]\n",
    " [-1.89550000e+00  3.28310231e+00  0.00000000e+00]\n",
    " [ 1.25954923e-15  2.18160327e-15  2.05700000e+01]]\n",
    "================================================================================================================================================================\n",
    "DFT axis: \n",
    "[0 0 1]\n",
    "Quantization axis and perpendicular rotation directions:\n",
    "[1 0 0]  --»  [array([0, 1, 0]), array([0, 0, 1])]\n",
    "[0 1 0]  --»  [array([1, 0, 0]), array([0, 0, 1])]\n",
    "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
    "================================================================================================================================================================\n",
    "number of k points:  20\n",
    "k point directions:  xy\n",
    "================================================================================================================================================================\n",
    "Parameters for the contour integral:\n",
    "Ebot:  -15\n",
    "Eset:  50\n",
    "Esetp:  1000\n",
    "================================================================================================================================================================\n",
    "Atomic informations: \n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[atom index]Element(orbitals)        x [Ang]        y [Ang]        z [Ang]        Sx        Sy        Sz        Q        Lx        Ly        Lz        Jx        Jy        Jz\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[3]Fe(2)        -7.339158738013707e-06        4.149278510690423e-06        11.657585837928032\n",
    "\n",
    "[4]Fe(2)        -7.326987662162937e-06        4.158274523275774e-06        8.912422537596708\n",
    "\n",
    "[5]Fe(2)        1.8954667088117545        1.0943913231921656        10.285002698393109\n",
    "\n",
    "================================================================================================================================================================\n",
    "Exchange [meV]\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Magnetic entity1        Magnetic entity2       [i  j  k]       d [Ang]\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[3]Fe(2)        [4]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -63.613204102235464\n",
    "DMI:  [-9.33066197e-01 -9.12173634e-04 -2.66552375e-06]\n",
    "Symmetric-anisotropy:  [-3.41993761e+00  1.35139766e+00 -4.15748909e-03 -8.08118347e-04\n",
    "  5.75970072e-05]\n",
    "Energies for debugging: \n",
    "array([[-6.22618064e-02, -9.33123794e-04,  9.33008600e-04,\n",
    "        -6.15446642e-02],\n",
    "       [-6.76703372e-02,  8.08118347e-07, -1.01622892e-06,\n",
    "        -6.70331417e-02],\n",
    "       [-5.07756491e-02,  4.15482357e-06,  4.16015462e-06,\n",
    "        -5.07708822e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06703314, -0.05077565, -0.06226181])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06703314171283804 -0.05077088224506824\n",
    "\n",
    "[4]Fe(2)        [5]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -60.981389719594276\n",
    "DMI:  [-3.79876136e+00  6.14996306e+00  4.52338839e-03]\n",
    "Symmetric-anisotropy:  [0.07285133 0.12581883 0.07081179 6.23894685 0.0361525 ]\n",
    "Energies for debugging: \n",
    "array([[-6.08555709e-02, -3.83491386e-03,  3.76260887e-03,\n",
    "        -6.11800599e-02],\n",
    "       [-6.06231936e-02, -6.23894685e-03,  6.06097927e-03,\n",
    "        -6.09085384e-02],\n",
    "       [-5.99055239e-02, -6.62883987e-05, -7.53351755e-05,\n",
    "        -5.98235127e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06090854, -0.05990552, -0.06085557])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06090853838909634 -0.05982351269907684\n",
    "\n",
    "[3]Fe(2)        [5]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -60.99043921106905\n",
    "DMI:  [ 3.78566701e+00 -6.13454413e+00  4.52301283e-03]\n",
    "Symmetric-anisotropy:  [ 0.06072775  0.1281154   0.07081275 -6.22754151 -0.04243893]\n",
    "Energies for debugging: \n",
    "array([[-6.08623238e-02,  3.82810594e-03, -3.74322808e-03,\n",
    "        -6.11792824e-02],\n",
    "       [-6.06338592e-02,  6.22754151e-03, -6.04154675e-03,\n",
    "        -6.09297115e-02],\n",
    "       [-5.99054929e-02, -6.62897359e-05, -7.53357616e-05,\n",
    "        -5.98234762e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06092971, -0.05990549, -0.06086232])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06092971146100409 -0.05982347618612315\n",
    "\n",
    "================================================================================================================================================================\n",
    "Runtime information: \n",
    "Total runtime: 107.15435087500009 s\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Initial setup: 0.11759866600004898 s\n",
    "Hamiltonian conversion and XC field extraction: 0.737 s\n",
    "Pair and site datastructure creatrions: 0.012 s\n",
    "k set cration and distribution: 0.005 s\n",
    "Rotating XC potential: 0.241 s\n",
    "Greens function inversion: 106.014 s\n",
    "Calculate energies and magnetic components: 0.028 s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##################################################################### GROGU OUTPUT #############################################################################\n",
    "================================================================================================================================================================\n",
    "Input file: \n",
    "Not yet specified.\n",
    "Number of nodes in the parallel cluster:  1\n",
    "================================================================================================================================================================\n",
    "Cell [Ang]: \n",
    "[[ 3.79100000e+00  0.00000000e+00  0.00000000e+00]\n",
    " [-1.89550000e+00  3.28310231e+00  0.00000000e+00]\n",
    " [ 1.25954923e-15  2.18160327e-15  2.05700000e+01]]\n",
    "================================================================================================================================================================\n",
    "DFT axis: \n",
    "[0 0 1]\n",
    "Quantization axis and perpendicular rotation directions:\n",
    "[1 0 0]  --»  [array([0, 1, 0]), array([0, 0, 1])]\n",
    "[0 1 0]  --»  [array([1, 0, 0]), array([0, 0, 1])]\n",
    "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
    "================================================================================================================================================================\n",
    "number of k points:  20\n",
    "k point directions:  xy\n",
    "================================================================================================================================================================\n",
    "Parameters for the contour integral:\n",
    "Ebot:  -15\n",
    "Eset:  500\n",
    "Esetp:  1000\n",
    "================================================================================================================================================================\n",
    "Atomic informations: \n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[atom index]Element(orbitals)        x [Ang]        y [Ang]        z [Ang]        Sx        Sy        Sz        Q        Lx        Ly        Lz        Jx        Jy        Jz\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[3]Fe(2)        -7.339158738013707e-06        4.149278510690423e-06        11.657585837928032\n",
    "\n",
    "[4]Fe(2)        -7.326987662162937e-06        4.158274523275774e-06        8.912422537596708\n",
    "\n",
    "[5]Fe(2)        1.8954667088117545        1.0943913231921656        10.285002698393109\n",
    "\n",
    "================================================================================================================================================================\n",
    "Exchange [meV]\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Magnetic entity1        Magnetic entity2       [i  j  k]       d [Ang]\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "[3]Fe(2)        [4]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -63.440713197129476\n",
    "DMI:  [-9.32927095e-01 -6.78818440e-04 -1.30891264e-06]\n",
    "Symmetric-anisotropy:  [-3.23494810e+00  1.24125542e+00 -3.51321370e-05 -6.74519122e-04\n",
    " -2.75924032e-05]\n",
    "Energies for debugging: \n",
    "array([[-6.21994578e-02, -9.32899503e-04,  9.32954688e-04,\n",
    "        -6.14470205e-02],\n",
    "       [-6.74870164e-02,  6.74519122e-07, -6.83117758e-07,\n",
    "        -6.66756613e-02],\n",
    "       [-5.57434879e-02,  3.38232244e-08,  3.64410497e-08,\n",
    "        -5.57434496e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06667566, -0.05574349, -0.06219946])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06667566129701633 -0.05574344955698773\n",
    "\n",
    "[4]Fe(2)        [5]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -60.970992244504004\n",
    "DMI:  [-3.79968813e+00  6.15433793e+00  2.99893936e-04]\n",
    "Symmetric-anisotropy:  [0.10892357 0.1011052  0.07120461 6.24418495 0.03644165]\n",
    "Energies for debugging: \n",
    "array([[-6.08698870e-02, -3.83612979e-03,  3.76324648e-03,\n",
    "        -6.11810210e-02],\n",
    "       [-6.06394618e-02, -6.24418495e-03,  6.06449091e-03,\n",
    "        -6.08620687e-02],\n",
    "       [-5.98919690e-02, -7.09047183e-05, -7.15045062e-05,\n",
    "        -5.98094909e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06086207, -0.05989197, -0.06086989])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.06086206867258083 -0.059809490859558875\n",
    "\n",
    "[3]Fe(2)        [5]Fe(2)             [0 0 0]    d [Ang] Not yet.\n",
    "Isotropic:  -60.974228876874314\n",
    "DMI:  [ 3.78485228e+00 -6.14192269e+00  2.99131471e-04]\n",
    "Symmetric-anisotropy:  [ 0.10123774  0.10087947  0.07120733 -6.23504361 -0.04251795]\n",
    "Energies for debugging: \n",
    "array([[-6.08733494e-02,  3.82737022e-03, -3.74233433e-03,\n",
    "        -6.11763461e-02],\n",
    "       [-6.06540016e-02,  6.23504361e-03, -6.04880177e-03,\n",
    "        -6.08729911e-02],\n",
    "       [-5.98919105e-02, -7.09081946e-05, -7.15064575e-05,\n",
    "        -5.98094279e-02]])\n",
    "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
    "array([-0.06087299, -0.05989191, -0.06087335])\n",
    "Test J_xx = E(y,z) = E(z,y)\n",
    "-0.060872991134857855 -0.05980942785099304\n",
    "\n",
    "================================================================================================================================================================\n",
    "Runtime information: \n",
    "Total runtime: 995.791283916 s\n",
    "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Initial setup: 0.10009837499999819 s\n",
    "Hamiltonian conversion and XC field extraction: 0.522 s\n",
    "Pair and site datastructure creatrions: 0.025 s\n",
    "k set cration and distribution: 0.023 s\n",
    "Rotating XC potential: 0.239 s\n",
    "Greens function inversion: 994.703 s\n",
    "Calculate energies and magnetic components: 0.178 s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "========================================\n",
    " \n",
    "Atom Angstrom\n",
    "# Label,        x           y           z          Sx           Sy           Sz         #Q           Lx           Ly           Lz           Jx           Jy           Jz\n",
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "Te1         1.8955      1.0943      13.1698     -0.0000     0.0000      -0.1543    # 5.9345       -0.0000      0.0000       -0.0537      -0.0000      0.0000       -0.2080   \n",
    "Te2         1.8955      1.0943      7.4002      0.0000      -0.0000     -0.1543    # 5.9345       0.0000       -0.0000      -0.0537      0.0000       -0.0000      -0.2080   \n",
    "Ge3         -0.0000     2.1887      10.2850     0.0000      0.0000      -0.1605    # 3.1927       -0.0000      0.0000       0.0012       0.0000       0.0000       -0.1593   \n",
    "Fe4         -0.0000     0.0000      11.6576     0.0001      -0.0001     2.0466     # 8.3044       0.0000       -0.0000      0.1606       0.0001       -0.0001      2.2072    \n",
    "Fe5         -0.0000     0.0000      8.9124      -0.0001     0.0001      2.0466     # 8.3044       -0.0000      0.0000       0.1606       -0.0001      0.0001       2.2072    \n",
    "Fe6         1.8955      1.0944      10.2850     0.0000      0.0000      1.5824     # 8.3296       -0.0000      -0.0000      0.0520       -0.0000      0.0000       1.6344    \n",
    "==================================================================================================================================\n",
    " \n",
    "Exchange meV\n",
    "--------------------------------------------------------------------------------\n",
    "# at1     at2   i  j  k    #    d (Ang)\n",
    "--------------------------------------------------------------------------------\n",
    "Fe4     Fe5     0  0  0    #    2.7452\n",
    "Isotropic -82.0854\n",
    "DMI 0.12557 -0.00082199  6.9668e-08\n",
    "Symmetric-anisotropy -0.60237    -0.83842 -0.00032278 -1.2166e-05 -3.3923e-05\n",
    "--------------------------------------------------------------------------------\n",
    "Fe4     Fe6     0  0  0    #    2.5835\n",
    "Isotropic -41.9627\n",
    "DMI 1.1205     -1.9532   0.0018386\n",
    "Symmetric-anisotropy 0.26007 -0.00013243     0.12977   -0.069979   -0.042066\n",
    "--------------------------------------------------------------------------------\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "coords = dh.xyz[-3:]\n",
    "\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "plt.subplot(131)\n",
    "plt.scatter(coords[:, 0], coords[:, 2], color=[\"r\", \"g\", \"b\"])\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"z\")\n",
    "plt.subplot(132)\n",
    "plt.scatter(coords[:, 1], coords[:, 2], color=[\"r\", \"g\", \"b\"])\n",
    "plt.xlabel(\"y\")\n",
    "plt.ylabel(\"z\")\n",
    "plt.subplot(133)\n",
    "plt.scatter(coords[:, 0], coords[:, 1], color=[\"r\", \"g\", \"b\"])\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "print(\"xyz[-3:]: red, green, blue\")"
   ]
  }
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