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   "cell_type": "markdown",
   "id": "a4b94702-66e7-49be-9a8a-72843377ab5c",
   "metadata": {},
   "source": [
    "# Hyperfine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "84f09f29-b0da-48af-b496-57d6ecf502be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hyperfine .id: example parameter\n",
      "  .weight =               1.0\n",
      "  .isomer_shift =         -0.11    \t dist points: 1\n",
      "  .magnetic_field =       33.0    \t dist points: 1\n",
      "  .magnetic_theta =       0.0    \t dist points: 1\n",
      "  .magnetic_phi =         45.0    \t dist points: 1\n",
      "  .quadrupole =           0.8    \t dist points: 1\n",
      "  .quadrupole_alpha =     90.0    \t dist points: 1\n",
      "  .quadrupole_beta =      45.0    \t dist points: 1\n",
      "  .quadrupole_gamma =     0.0    \t dist points: 1\n",
      "  .quadrupole_asymmetry = 0.05    \t dist points: 1\n",
      "  .isotropic =            False    \t 3D distribution in mag and efg. Random mag or efg distributions are ignored.\n",
      "  random magnetic distribution: none\t dist points: 1\n",
      "  random quadrupole distribution: none\t dist points: 1\n",
      "  total number of distribution points: 1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import nexus as nx\n",
    "\n",
    "hyperfine = nx.Hyperfine(\n",
    "      id = \"example parameter\",\n",
    "      weight = 1,                  # relative weight of the site in the material\n",
    "      isomer = -0.11,              # isomer shift in mm/s\n",
    "      magnetic_field = 33,         # magnetic field in T\n",
    "      magnetic_theta = 0,          # polar angle\n",
    "      magnetic_phi = 45,           # azimuthal angle\n",
    "      quadrupole = 0.8,            # quadrupole slitting in mm/s\n",
    "      quadrupole_alpha = 90,       # ZYZ extrinsic Euler angle alpha\n",
    "      quadrupole_beta = 45,        # ZYZ extrinsic Euler angle beta\n",
    "      quadrupole_gamma = 0,        # ZYZ extrinsic Euler angle gamma\n",
    "      quadrupole_asymmetry = 0.05, # Asymmetry parameter\n",
    "      isomer_dist = None,\n",
    "      magnetic_field_dist = None,\n",
    "      magnetic_theta_dist = None,\n",
    "      magnetic_phi_dist = None,\n",
    "      quadrupole_dist = None,\n",
    "      quadrupole_alpha_dist = None,\n",
    "      quadrupole_beta_dist = None,\n",
    "      quadrupole_gamma_dist = None,\n",
    "      quadrupole_asymmetry_dist = None,\n",
    "      isotropic = False)           # 3D distribution in mag and EFG\n",
    "\n",
    "print(hyperfine)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5b3bf740-be7b-4a7c-a4f1-4d0ff25b3645",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(33.0, 90.0, 90.0)\n",
      "(0.0, 0.0, 33.0)\n"
     ]
    }
   ],
   "source": [
    "# Nexus frame (sigma, pi, k)\n",
    "# spherical (mag, polar, azimuthal)\n",
    "\n",
    "# convert a magnetic field along pi direction to spherical coordinates\n",
    "print(nx.MagVectorToSpherical(0, 33, 0))\n",
    "\n",
    "# convert a magnetic field along k direction to Nexus frame\n",
    "print(nx.MagSphericalToVector(33, 0, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "88c8fec5-6aef-46ba-a7b6-4028b0dfb913",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.024215767587424 1.5707963267948966 1.5707963267948966\n"
     ]
    }
   ],
   "source": [
    "# input vector in the nexus coordinate system [sigma,pi,k]\n",
    "alpha, beta, gamma = nx.euler.VectorsToAngles([0,1,0])\n",
    "\n",
    "print(alpha, beta, gamma)  # the return value of alpha is random here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "12687849-5f01-40f9-b273-3d99a01966f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 1.5707963267948966 3.141592653589793\n"
     ]
    }
   ],
   "source": [
    "# input vector in the nexus coordinate system.\n",
    "# vectors must be orthogonal, but do not have to be normalized\n",
    "Vzz = [1,0,0]\n",
    "Vxx = [0,0,1]\n",
    "Vyy = [0,1,0]\n",
    "alpha, beta, gamma = nx.euler.VectorsToAngles(Vzz, Vxx, Vyy)\n",
    "\n",
    "print(alpha, beta, gamma)"
   ]
  }
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