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   "id": "2d39e1ec-6a49-49f0-be16-7d87e66b4b33",
   "metadata": {},
   "source": [
    "# Example-14: Linear (element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "14d8b935-fb14-4f1d-86e7-4295e92f95f1",
   "metadata": {},
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   "source": [
    "# Can be used to model elements as linear transformations\n",
    "# Constant offset can be used to model first order dispersion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ca2e02c9-b50f-4a35-9904-51de96328925",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from model.library.quadrupole import Quadrupole\n",
    "from model.library.dipole import Dipole\n",
    "from model.library.linear import Linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4e047ffc-924d-4e4f-8d5d-208e7b9fa77f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.012284014325104016, 0.013015328226371463, 0.005866573649483532, 0.01748719571870364]\n",
      "[0.012284330668424102, 0.013015814342968814, 0.005867420763768485, 0.01748647747810468]\n",
      "[-3.163433200861071e-07, -4.861165973507608e-07, -8.471142849530294e-07, 7.182405989576701e-07]\n"
     ]
    }
   ],
   "source": [
    "# Linear quadrupole\n",
    "\n",
    "length = 1.0\n",
    "kn = - 2.0\n",
    "ks = + 1.5\n",
    "dp = 0.0\n",
    "Q = Quadrupole('Q', length, kn, ks, dp)\n",
    "\n",
    "state = torch.tensor([0.0, 0.0, 0.0, 0.0], dtype=torch.float64)\n",
    "\n",
    "matrix = torch.func.jacrev(lambda state, dp: Q(state, data={**Q.data(), **{'dp': dp}}), 0)(state, Q.dp)\n",
    "vector = torch.func.jacrev(lambda state, dp: Q(state, data={**Q.data(), **{'dp': dp}}), 1)(state, Q.dp)\n",
    "\n",
    "length = 1.0\n",
    "kn = - 2.0\n",
    "ks = + 1.5\n",
    "dp = 0.0001\n",
    "Q = Quadrupole('Q', length, kn, ks, dp)\n",
    "\n",
    "L = Linear('L', (dp*vector).tolist(), matrix.tolist())\n",
    "\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(Q(state).tolist())\n",
    "print(L(state).tolist())\n",
    "print((Q(state) - L(state)).tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6157af5d-0dea-43ed-9264-c939a9d42135",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.8326139356223135e-06, -0.005001000818821848, -0.002994615078158236, 0.001004198140800915]\n",
      "[9.165104284458664e-06, -0.004994998958072864, -0.002993748697591074, 0.001004997134048961]\n",
      "[-6.33249034883635e-06, -6.001860748984511e-06, -8.663805671619597e-07, -7.989932480460815e-07]\n"
     ]
    }
   ],
   "source": [
    "# Linear dipole\n",
    "\n",
    "length = 2.0\n",
    "angle = 0.05\n",
    "e1 = 0.025\n",
    "e2 = 0.025\n",
    "dp = 0.0\n",
    "D = Dipole('D', length, angle, e1, e2, dp)\n",
    "\n",
    "state = torch.tensor([0.0, 0.0, 0.0, 0.0], dtype=torch.float64)\n",
    "\n",
    "matrix = torch.func.jacrev(lambda state, dp: D(state, data={**D.data(), **{'dp': dp}}), 0)(state, D.dp)\n",
    "vector = torch.func.jacrev(lambda state, dp: D(state, data={**D.data(), **{'dp': dp}}), 1)(state, D.dp)\n",
    "\n",
    "length = 2.0\n",
    "angle = 0.05\n",
    "e1 = 0.025\n",
    "e2 = 0.025\n",
    "dp = 0.0001\n",
    "D = Dipole('D', length, angle, e1, e2, dp)\n",
    "\n",
    "L = Linear('L', (dp*vector).tolist(), matrix.tolist())\n",
    "\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(D(state).tolist())\n",
    "print(L(state).tolist())\n",
    "print((D(state) - L(state)).tolist())"
   ]
  }
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