{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0312a407-6c50-49e9-8bcf-afdabc0a3834",
   "metadata": {},
   "source": [
    "# Example-33: Orbit (sextupole shift)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f74fd88d-4914-4cdb-9701-5106b4e36ff6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# In this example effects of transverse sextupole shifts on closed orbit are illustrated\n",
    "# Surrogate model from derivatives is compared with direct tracking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "09fc259e-2c50-49d8-90dd-2f508b22c2eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import\n",
    "\n",
    "from pprint import pprint\n",
    "\n",
    "import torch\n",
    "\n",
    "from pathlib import Path\n",
    "\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.patches import Rectangle\n",
    "matplotlib.rcParams['text.usetex'] = True\n",
    "\n",
    "from twiss import twiss\n",
    "\n",
    "from model.library.line import Line\n",
    "\n",
    "from model.command.util import chop\n",
    "from model.command.util import evaluate\n",
    "from model.command.util import series\n",
    "\n",
    "from model.command.external import load_lattice\n",
    "\n",
    "from model.command.build import build\n",
    "\n",
    "from model.command.wrapper import group\n",
    "\n",
    "from model.command.orbit import orbit\n",
    "from model.command.orbit import parametric_orbit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "41e56250-9338-4e66-a70d-52f8da57bcf7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build and setup lattice\n",
    "\n",
    "path = Path('ic.lte')\n",
    "data = load_lattice(path)\n",
    "\n",
    "ring:Line = build('RING', 'ELEGANT', data)\n",
    "ring.propagate = True\n",
    "ring.flatten()\n",
    "ring.merge()\n",
    "ring.split((None, ['BPM'], None, None))\n",
    "ring.roll(1)\n",
    "ring.splice()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fae8ae86-11df-400f-96ec-31fd7ca156f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "# Compute closed orbit\n",
    "\n",
    "fp = 1.0E-3*torch.randn(4, dtype=torch.float64)\n",
    "fp, *_ = orbit(ring, fp, [], alignment=True, limit=8, epsilon=1.0E-12)\n",
    "\n",
    "# Chop small values\n",
    "\n",
    "fp = [fp]\n",
    "chop(fp)\n",
    "fp, *_ = fp\n",
    "\n",
    "print(fp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4da1780e-2a71-402e-ab4a-07455c3bde03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[tensor([0., 0., 0., 0.], dtype=torch.float64),\n",
      "  tensor([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]],\n",
      "       dtype=torch.float64)]]\n",
      "\n",
      "[[tensor([0., 0., 0., 0.], dtype=torch.float64),\n",
      "  tensor([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]],\n",
      "       dtype=torch.float64)]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Compute 1st order parametric closed orbit at the first BPM\n",
    "# Note, all 1st order derivatives are zero\n",
    "\n",
    "n_sext = ring.describe['Sextupole']\n",
    "\n",
    "dx = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "dy = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "\n",
    "data, *_ = parametric_orbit(ring, fp, [dx], (1, 'dx', ['Sextupole'], None, None), alignment=True, advance=False,  full=False,  jacobian=torch.func.jacrev)\n",
    "chop(data)\n",
    "pprint(data)\n",
    "print()\n",
    "\n",
    "data, *_ = parametric_orbit(ring, fp, [dy], (1, 'dy', ['Sextupole'], None, None), alignment=True, advance=False,  full=False,  jacobian=torch.func.jacrev)\n",
    "chop(data)\n",
    "pprint(data)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5c269c2e-e628-47fd-a9e5-ebdefbc6da07",
   "metadata": {},
   "outputs": [],
   "source": [
    "# d^2(qx,px,qy,py)/d^2(dx)\n",
    "\n",
    "n_sext = ring.describe['Sextupole']\n",
    "\n",
    "dx = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "dy = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "\n",
    "data_xx, *_ = parametric_orbit(ring, fp, [dx], (1 + 1, 'dx', ['Sextupole'], None, None), alignment=True, advance=True,  full=False,  jacobian=torch.func.jacfwd)\n",
    "chop(data_xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f3c48a7e-b9c7-4f1f-a5b4-6750098c2bbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# d^2(qx,px,qy,py)/d^2(dy)\n",
    "\n",
    "n_sext = ring.describe['Sextupole']\n",
    "\n",
    "dx = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "dy = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "\n",
    "data_yy, *_ = parametric_orbit(ring, fp, [dy], (1 + 1, 'dy', ['Sextupole'], None, None), alignment=True, advance=True,  full=False,  jacobian=torch.func.jacfwd)\n",
    "chop(data_yy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d81a3aaf-03bb-4bf4-a7e7-b51aaaf192a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# d^2(qx,px,qy,py)/d(dx)d(dy)\n",
    "\n",
    "n_sext = ring.describe['Sextupole']\n",
    "\n",
    "dx = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "dy = torch.tensor(n_sext*[0.0], dtype=torch.float64)\n",
    "\n",
    "data_xy, *_ = parametric_orbit(ring, fp, [dx, dy], (1, 'dx', ['Sextupole'], None, None), (1, 'dy', ['Sextupole'], None, None), alignment=True, advance=True,  full=False,  jacobian=torch.func.jacfwd)\n",
    "chop(data_xy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "14535f61-85f9-4197-a0b1-3396606d4318",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1.0033e-07, -1.1509e-06, -6.3080e-07, -9.2672e-07],\n",
      "       dtype=torch.float64)\n",
      "tensor([ 1.0033e-07, -1.1509e-06, -6.3080e-07, -9.2672e-07],\n",
      "       dtype=torch.float64)\n",
      "True\n",
      "\n",
      "tensor([ 9.5113e-08, -1.1528e-06, -6.3283e-07, -9.3303e-07],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 5.2183e-09,  2.1902e-08, -2.7206e-08,  2.2594e-08,  3.1393e-08,\n",
      "        -2.2313e-08,  2.3693e-08, -3.3437e-09, -1.3831e-08, -1.1931e-08,\n",
      "         2.4838e-08, -2.8452e-08, -2.4680e-08,  2.7076e-08, -1.9813e-08,\n",
      "        -7.3490e-09], dtype=torch.float64)\n",
      "\n",
      "tensor([ 1.9981e-09, -4.2481e-08, -4.5641e-08,  4.3854e-08, -4.9479e-08,\n",
      "         3.5591e-08,  4.2046e-08, -1.6313e-08,  1.6608e-08,  2.8780e-08,\n",
      "         3.1764e-08, -4.6591e-08,  4.4813e-08, -3.7277e-08, -4.0012e-08,\n",
      "        -2.4356e-09], dtype=torch.float64)\n",
      "\n",
      "tensor([ 2.0286e-09,  5.3450e-09,  5.4072e-09, -3.5832e-09, -1.2731e-08,\n",
      "         7.8904e-10,  6.6626e-09,  1.5498e-08,  1.2892e-09, -8.5067e-09,\n",
      "        -1.0284e-08,  4.1416e-09,  1.9376e-08, -1.4913e-09, -4.8998e-09,\n",
      "        -7.5837e-09], dtype=torch.float64)\n",
      "\n",
      "tensor([ 6.3099e-09,  9.0244e-09, -6.9332e-09, -4.2968e-09, -1.6105e-08,\n",
      "         1.0479e-08, -2.5487e-09, -2.5606e-08, -3.8375e-09, -1.7324e-08,\n",
      "         1.0369e-08,  8.5195e-09,  2.5380e-08, -1.5626e-08,  4.4680e-09,\n",
      "         1.3444e-08], dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Compare orbit response for a single random realization\n",
    "\n",
    "# Set errors\n",
    "\n",
    "dx = 100.0E-6*torch.randn(n_sext, dtype=torch.float64)\n",
    "dy = 100.0E-6*torch.randn(n_sext, dtype=torch.float64)\n",
    "\n",
    "# Compute closed orbit at all BPMs\n",
    "# Note, alignment is on\n",
    "\n",
    "points, *_ = orbit(ring, fp, [dx, dy], ('dx', ['Sextupole'], None, None), ('dy', ['Sextupole'], None, None), alignment=True, advance=True, full=False, limit=16, epsilon=1.0E-12)\n",
    "\n",
    "\n",
    "# Test closed orbit\n",
    "\n",
    "# Set parametric ring\n",
    "\n",
    "start, *_, end = ring.names\n",
    "mapping, *_ = group(ring, start, end, ('dx', ['Sextupole'], None, None), ('dy', ['Sextupole'], None, None), alignment=True)\n",
    "\n",
    "# Propagate estimated closed orbit\n",
    "\n",
    "point, *_ = points\n",
    "print(point)\n",
    "print(mapping(point, dx, dy))\n",
    "print(torch.allclose(point, mapping(point, dx, dy), rtol=1.0E-12, atol=1.0E-12))\n",
    "print()\n",
    "\n",
    "# Evaluate parametric fixed point for given deviations\n",
    "\n",
    "def taylor(lxx, lxy, lyy, dx, dy):\n",
    "    return evaluate(lxx, [fp, dx]) + evaluate(lxy, [fp, dx, dy]) + evaluate(lyy, [fp, dy])\n",
    "\n",
    "lxx, *_ = data_xx\n",
    "lxy, *_ = data_xy\n",
    "lyy, *_ = data_yy\n",
    "\n",
    "print(taylor(lxx, lxy, lyy, dx, dy))\n",
    "print()\n",
    "\n",
    "# Plot orbit at all locations\n",
    "\n",
    "qx, px, qy, py = points.T\n",
    "Qx, Px, Qy, Py = torch.stack([taylor(lxx, lxy, lyy, dx, dy) for lxx, lxy, lyy in zip(data_xx, data_xy, data_yy)]).T\n",
    "\n",
    "# qx vs Qx\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.errorbar(ring.locations().cpu().numpy(), qx.cpu().numpy(), fmt='-', color='blue', marker='o', ms=8, alpha=0.75)\n",
    "plt.errorbar(ring.locations().cpu().numpy(), Qx.cpu().numpy(), fmt=' ', color='black', marker='x', ms=8, alpha=1)\n",
    "plt.xticks(ticks=ring.locations(), labels=dict.fromkeys([name for name, kind, *_ in ring.layout() if kind == 'BPM']))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# px vs Px\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.errorbar(ring.locations().cpu().numpy(), px.cpu().numpy(), fmt='-', color='blue', marker='o', ms=8, alpha=0.75)\n",
    "plt.errorbar(ring.locations().cpu().numpy(), Px.cpu().numpy(), fmt=' ', color='black', marker='x', ms=8, alpha=1)\n",
    "plt.xticks(ticks=ring.locations(), labels=dict.fromkeys([name for name, kind, *_ in ring.layout() if kind == 'BPM']))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# qy vs Qy\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.errorbar(ring.locations().cpu().numpy(), qy.cpu().numpy(), fmt='-', color='blue', marker='o', ms=8, alpha=0.75)\n",
    "plt.errorbar(ring.locations().cpu().numpy(), Qy.cpu().numpy(), fmt=' ', color='black', marker='x', ms=8, alpha=1)\n",
    "plt.xticks(ticks=ring.locations(), labels=dict.fromkeys([name for name, kind, *_ in ring.layout() if kind == 'BPM']))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# py vs Py\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.errorbar(ring.locations().cpu().numpy(), py.cpu().numpy(), fmt='-', color='blue', marker='o', ms=8, alpha=0.75)\n",
    "plt.errorbar(ring.locations().cpu().numpy(), Py.cpu().numpy(), fmt=' ', color='black', marker='x', ms=8, alpha=1)\n",
    "plt.xticks(ticks=ring.locations(), labels=dict.fromkeys([name for name, kind, *_ in ring.layout() if kind == 'BPM']))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Accuracy\n",
    "\n",
    "print(qx - Qx)\n",
    "print()\n",
    "\n",
    "print(px - Px)\n",
    "print()\n",
    "\n",
    "print(qy - Qy)\n",
    "print()\n",
    "\n",
    "print(py - Py)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "602f29e1-42dc-4ec4-a79d-2f4d5023d08e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Estimate center and spread at all BPM using direct tracking and MC sampling\n",
    "# Note, epsilon should be None for vmap, convergence not checked\n",
    "\n",
    "def fn(dx, dy):\n",
    "    guess = torch.tensor(4*[0.0], dtype=torch.float64)\n",
    "    point, _ = orbit(ring, guess,  [dx, dy], ('dx', ['Sextupole'], None, None), ('dy', ['Sextupole'], None, None), alignment=True, advance=True, full=False, limit=16, epsilon=None)\n",
    "    return point\n",
    "\n",
    "dxs = 100.0E-6*torch.randn((8192, n_sext), dtype=torch.float64)\n",
    "dys = 100.0E-6*torch.randn((8192, n_sext), dtype=torch.float64)\n",
    "\n",
    "cqxs, cpxs, cqys, cpys = torch.vmap(fn)(dxs, dys).swapaxes(0, -1)\n",
    "\n",
    "# Plot histogram at the first BPM for qx and qy\n",
    "\n",
    "cqx, *_ = cqxs\n",
    "cqy, *_ = cqys\n",
    "\n",
    "fig, (ax, ay) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "ax.hist(cqx.cpu().numpy(), bins=100, range=(-5E-6, +5E-6), color='blue', alpha=0.7)\n",
    "ay.hist(cqy.cpu().numpy(), bins=100, range=(-5E-6, +5E-6), color='blue', alpha=0.7)\n",
    "plt.tight_layout() \n",
    "plt.show()\n",
    "\n",
    "# Estimate center and spread at all BPMs\n",
    "\n",
    "qx_center_tracking = cqxs.mean(-1)\n",
    "qy_center_tracking = cqys.mean(-1)\n",
    "\n",
    "qx_spread_tracking = cqxs.std(-1)\n",
    "qy_spread_tracking = cqys.std(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3fccf81c-7ff1-4633-9830-92c055b794c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Estimate center and spread at all BPM using series and MC sampling\n",
    "\n",
    "dxs = 100.0E-6*torch.randn((8192, n_sext), dtype=torch.float64)\n",
    "dys = 100.0E-6*torch.randn((8192, n_sext), dtype=torch.float64)\n",
    "\n",
    "def taylor(lxx, lxy, lyy, dx, dy):\n",
    "    return evaluate(lxx, [fp, dx]) + evaluate(lxy, [fp, dx, dy]) + evaluate(lyy, [fp, dy])\n",
    "\n",
    "cqxs, cpxs, cqys, cpys = torch.stack([torch.vmap(lambda dx, dy: taylor(lxx, lxy, lyy, dx, dy))(dxs, dys) for lxx, lxy, lyy in zip(data_xx, data_xy, data_yy)]).swapaxes(0, -1)\n",
    "\n",
    "# Plot histogram at the first BPM for qx and qy\n",
    "\n",
    "cqx, *_ = cqxs.T\n",
    "cqy, *_ = cqys.T\n",
    "\n",
    "fig, (ax, ay) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "ax.hist(cqx.cpu().numpy(), bins=100, range=(-5E-6, +5E-6), color='blue', alpha=0.7)\n",
    "ay.hist(cqy.cpu().numpy(), bins=100, range=(-5E-6, +5E-6), color='blue', alpha=0.7)\n",
    "plt.tight_layout() \n",
    "plt.show()\n",
    "\n",
    "# Estimate center and spread at all BPMs\n",
    "\n",
    "qx_center_taylor = cqxs.T.mean(-1)\n",
    "qy_center_taylor = cqys.T.mean(-1)\n",
    "\n",
    "qx_spread_taylor = cqxs.T.std(-1)\n",
    "qy_spread_taylor = cqys.T.std(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dba480b7-44bc-420d-90ef-bdbc12f5f82d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot (compare estimated spreads)\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(ring.locations())), qx_spread_tracking.cpu().numpy(), color='blue',alpha=0.75)\n",
    "plt.bar(range(len(ring.locations())), qx_spread_taylor.cpu().numpy(), color='red', alpha=0.50)\n",
    "plt.xticks(ticks=range(len(ring.locations())), labels=dict.fromkeys([name for name, kind, *_ in ring.layout() if kind == 'BPM']))\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(ring.locations())), qy_spread_tracking.cpu().numpy(), color='blue',alpha=0.75)\n",
    "plt.bar(range(len(ring.locations())), qy_spread_taylor.cpu().numpy(), color='red', alpha=0.50)\n",
    "plt.xticks(ticks=range(len(ring.locations())), labels=dict.fromkeys([name for name, kind, *_ in ring.layout() if kind == 'BPM']))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [
    "myt0_gMIOq7b",
    "5d97819c"
   ],
   "name": "03_frequency.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.1"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}