docs/tutorials/mixing_ICM_structured_field.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/me-manu/gammaALPs/blob/master/docs/tutorials/mixing_ICM_structured_field.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example to calculate photon-ALP oscillations from NGC 1275 in a cavity field"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook demonstrates how to calculate the photon-ALP transition probability for NGC 1275, the central AGN of the Perseus cluster. The assumed B-field environments are the same as in https://arxiv.org/abs/1908.03084, and include the cluster field and the magnetic field of the Milky Way. Electron density model parameters taken from https://iopscience.iop.org/article/10.1086/374923/fulltext/57155.text.html.\n",
    "\n",
    "Note that in order to obtain the field used in 1908.03084, you have to set $\\theta$ to 225° instead of 45° (adding 180°). This effectively inverts the sign of all field components. While this change of $\\theta$ and the sign is irrelevant for the conversion probability, it changes the field along the line of sight and inverts the sign of the RM, as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you haven't installed `gammaALPs` already, you can do so using `pip`. Just uncomment the line below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install gammaALPs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gammaALPs.core import Source, ALP, ModuleList\n",
    "from gammaALPs.base import environs, transfer\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "from ebltable.tau_from_model import OptDepth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set the ALP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize an ALP object, that stores the ALP mass $m$ (in neV) and the coupling $g$ (in $10^{-11}\\mathrm{GeV}^{-1}$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "m, g = 2, 100\n",
    "alp = ALP(m,g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set the source"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the source properties (redshift and sky coordinates) in the ```Source``` containier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ngc1275 = Source(z = 0.017559, ra = '03h19m48.1s', dec = '+41d30m42s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Init the module list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the list of transfer modules that will store the different magnetic field environments. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Energies are supplied in GeV as ```numpy.ndarray```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "logEMeV = np.linspace(0.46709351, 6.53207135, num=183, endpoint=True)\n",
    "EGeV = np.power(10, logEMeV - 3.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now initialize the initial photon polarization. Since we are dealing with a gamma-ray source, no ALPs are initially present in the beam (third diagonal element is zero). The polarization density matrix is normalized such that its trace is equal to one, $\\mathrm{Tr}(\\rho_\\mathrm{in}) = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "pin = np.diag((1.,1.,0.)) * 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add modules:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we add propagation modules for the cluster, the EBL, and the Galactic magnetic field; run the module. Repeat for only the ICM field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[0;36menvirons.py:\u001b[0;35m 578\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Using inputted chi\n",
      "\u001b[0;36menvirons.py:\u001b[0;35m1196\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Using inputted chi\n",
      "\u001b[0;36m   core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 0: <class 'gammaALPs.base.environs.MixICMStructured'>\n",
      "\u001b[0;36m   core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 2: <class 'gammaALPs.base.environs.MixGMF'>\n",
      "/Users/mey/Python/gammaALPs/gammaALPs/base/transfer.py:799: UserWarning: Not all values of linear polarization are real values!\n",
      "  warnings.warn(\"Not all values of linear polarization are real values!\")\n",
      "/Users/mey/Python/gammaALPs/gammaALPs/base/transfer.py:802: UserWarning: Not all values of circular polarization are real values!\n",
      "  warnings.warn(\"Not all values of circular polarization are real values!\")\n",
      "\u001b[0;36menvirons.py:\u001b[0;35m 578\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Using inputted chi\n",
      "\u001b[0;36m   core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Running Module 0: <class 'gammaALPs.base.environs.MixICMStructured'>\n"
     ]
    }
   ],
   "source": [
    "alp = ALP(m, g)\n",
    "ml = ModuleList(alp, ngc1275, pin = pin, EGeV = EGeV)\n",
    "ml.add_propagation(\"ICMStructured\", \n",
    "                   0, # position of module counted from the source. \n",
    "                   B0 = 8.3,  # rms of B field\n",
    "                   R = 93,\n",
    "                   theta = 225,\n",
    "                   theta_rad=False,\n",
    "                   pa=147,\n",
    "                   pa_rad=False,\n",
    "                   n0 = 3.9e-2,  # normalization of electron density\n",
    "                   n2 = 4.05e-3, # second normalization of electron density, see Churazov et al. 2003, Eq. 4\n",
    "                   r_abell = 500., # extension of the cluster\n",
    "                   r_core = 80.,   # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   r_core2 = 280., # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   beta = 1.2,  # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   beta2= 0.58, # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   eta = 0 # scaling of B-field with electron denstiy\n",
    "                   )\n",
    "ml.add_propagation(\"EBL\",1, eblmodel = 'dominguez') # EBL attenuation comes second, after beam has left cluster\n",
    "ml.add_propagation(\"GMF\",2, model = 'pshirkov', model_sym = 'BSS') # finally, the beam enters the Milky Way Field\n",
    "px, py, pa = ml.run()\n",
    "\n",
    "\n",
    "\n",
    "# again with only structured field\n",
    "\n",
    "ml2 = ModuleList(alp, ngc1275, pin = pin, EGeV = EGeV)\n",
    "ml2.add_propagation(\"ICMStructured\", \n",
    "                   0, # position of module counted from the source. \n",
    "                   B0 = 8.3,  # rms of B field\n",
    "                   R = 93,\n",
    "                   theta = 225,\n",
    "                   theta_rad=False,\n",
    "                   pa=147,\n",
    "                   pa_rad=False,\n",
    "                   n0 = 3.9e-2,  # normalization of electron density\n",
    "                   n2 = 4.05e-3, # second normalization of electron density, see Churazov et al. 2003, Eq. 4\n",
    "                   r_abell = 500., # extension of the cluster\n",
    "                   r_core = 80.,   # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   r_core2 = 280., # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   beta = 1.2,  # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   beta2= 0.58, # electron density parameter, see Churazov et al. 2003, Eq. 4\n",
    "                   eta = 0 # scaling of B-field with electron denstiy\n",
    "                   )\n",
    "px2, py2, pa2 = ml2.run()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the output "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(EGeV, px[0] + py[0], label='ICM + EBL + GMF')\n",
    "plt.plot(EGeV, px2[0] + py2[0], label='ICM')\n",
    "plt.xscale('log')\n",
    "plt.yscale('linear')\n",
    "plt.ylim(0.4, 1.05)\n",
    "plt.xlim(3e-2, 1e2)\n",
    "plt.xlabel('Energy (GeV)')\n",
    "plt.ylabel('Photon survival probability')\n",
    "plt.legend(loc = 0, fontsize = 'medium')\n",
    "\n",
    "plt.annotate(r'$m_a = {0:.1f}\\,\\mathrm{{neV}}, g_{{a\\gamma}} = {1:.1f} \\times 10^{{-11}}\\,\\mathrm{{GeV}}^{{-1}}$'.format(ml.alp.m,ml.alp.g),\n",
    "             xy = (0.95,0.1), size = 'x-large', xycoords = 'axes fraction', ha = 'right')\n",
    "\n",
    "plt.subplots_adjust(left = 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the B fields\n",
    "\n",
    "Plot r vs B field components of structured field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13eeaab50>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error in callback <function _draw_all_if_interactive at 0x1396e8af0> (for post_execute):\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "\nr [\\SI{}{\\kilo\\parsec}]\n   ^\nParseFatalException: Unknown symbol: \\SI, found '\\'  (at char 3), (line:1, col:4)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/pyplot.py:197\u001b[0m, in \u001b[0;36m_draw_all_if_interactive\u001b[0;34m()\u001b[0m\n\u001b[1;32m    195\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_draw_all_if_interactive\u001b[39m() \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    196\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m matplotlib\u001b[38;5;241m.\u001b[39mis_interactive():\n\u001b[0;32m--> 197\u001b[0m         \u001b[43mdraw_all\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/_pylab_helpers.py:132\u001b[0m, in \u001b[0;36mGcf.draw_all\u001b[0;34m(cls, force)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m manager \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mcls\u001b[39m\u001b[38;5;241m.\u001b[39mget_all_fig_managers():\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m force \u001b[38;5;129;01mor\u001b[39;00m manager\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39mstale:\n\u001b[0;32m--> 132\u001b[0m         \u001b[43mmanager\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcanvas\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw_idle\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/backend_bases.py:1893\u001b[0m, in \u001b[0;36mFigureCanvasBase.draw_idle\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1891\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_is_idle_drawing:\n\u001b[1;32m   1892\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_idle_draw_cntx():\n\u001b[0;32m-> 1893\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:388\u001b[0m, in \u001b[0;36mFigureCanvasAgg.draw\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    385\u001b[0m \u001b[38;5;66;03m# Acquire a lock on the shared font cache.\u001b[39;00m\n\u001b[1;32m    386\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m (\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtoolbar\u001b[38;5;241m.\u001b[39m_wait_cursor_for_draw_cm() \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtoolbar\n\u001b[1;32m    387\u001b[0m       \u001b[38;5;28;01melse\u001b[39;00m nullcontext()):\n\u001b[0;32m--> 388\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfigure\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    389\u001b[0m     \u001b[38;5;66;03m# A GUI class may be need to update a window using this draw, so\u001b[39;00m\n\u001b[1;32m    390\u001b[0m     \u001b[38;5;66;03m# don't forget to call the superclass.\u001b[39;00m\n\u001b[1;32m    391\u001b[0m     \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mdraw()\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:95\u001b[0m, in \u001b[0;36m_finalize_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m     93\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(draw)\n\u001b[1;32m     94\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdraw_wrapper\u001b[39m(artist, renderer, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m---> 95\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     96\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m renderer\u001b[38;5;241m.\u001b[39m_rasterizing:\n\u001b[1;32m     97\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstop_rasterizing()\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/figure.py:3154\u001b[0m, in \u001b[0;36mFigure.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   3151\u001b[0m         \u001b[38;5;66;03m# ValueError can occur when resizing a window.\u001b[39;00m\n\u001b[1;32m   3153\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpatch\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[0;32m-> 3154\u001b[0m \u001b[43mmimage\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_draw_list_compositing_images\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   3155\u001b[0m \u001b[43m    \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43martists\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msuppressComposite\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3157\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m sfig \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msubfigs:\n\u001b[1;32m   3158\u001b[0m     sfig\u001b[38;5;241m.\u001b[39mdraw(renderer)\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m         \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     image_group \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/axes/_base.py:3070\u001b[0m, in \u001b[0;36m_AxesBase.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   3067\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artists_rasterized:\n\u001b[1;32m   3068\u001b[0m     _draw_rasterized(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure, artists_rasterized, renderer)\n\u001b[0;32m-> 3070\u001b[0m \u001b[43mmimage\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_draw_list_compositing_images\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   3071\u001b[0m \u001b[43m    \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43martists\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfigure\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msuppressComposite\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3073\u001b[0m renderer\u001b[38;5;241m.\u001b[39mclose_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124maxes\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m   3074\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mstale \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m         \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     image_group \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/axis.py:1395\u001b[0m, in \u001b[0;36mAxis.draw\u001b[0;34m(self, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1393\u001b[0m \u001b[38;5;66;03m# Shift label away from axes to avoid overlapping ticklabels.\u001b[39;00m\n\u001b[1;32m   1394\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_label_position(renderer)\n\u001b[0;32m-> 1395\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlabel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1397\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_offset_text_position(tlb1, tlb2)\n\u001b[1;32m   1398\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moffsetText\u001b[38;5;241m.\u001b[39mset_text(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmajor\u001b[38;5;241m.\u001b[39mformatter\u001b[38;5;241m.\u001b[39mget_offset())\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:748\u001b[0m, in \u001b[0;36mText.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    745\u001b[0m renderer\u001b[38;5;241m.\u001b[39mopen_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtext\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_gid())\n\u001b[1;32m    747\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cm_set(text\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_wrapped_text()):\n\u001b[0;32m--> 748\u001b[0m     bbox, info, descent \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_layout\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    749\u001b[0m     trans \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_transform()\n\u001b[1;32m    751\u001b[0m     \u001b[38;5;66;03m# don't use self.get_position here, which refers to text\u001b[39;00m\n\u001b[1;32m    752\u001b[0m     \u001b[38;5;66;03m# position in Text:\u001b[39;00m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:381\u001b[0m, in \u001b[0;36mText._get_layout\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    379\u001b[0m clean_line, ismath \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_preprocess_math(line)\n\u001b[1;32m    380\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m clean_line:\n\u001b[0;32m--> 381\u001b[0m     w, h, d \u001b[38;5;241m=\u001b[39m \u001b[43m_get_text_metrics_with_cache\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    382\u001b[0m \u001b[43m        \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mclean_line\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_fontproperties\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    383\u001b[0m \u001b[43m        \u001b[49m\u001b[43mismath\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mismath\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfigure\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdpi\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    384\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    385\u001b[0m     w \u001b[38;5;241m=\u001b[39m h \u001b[38;5;241m=\u001b[39m d \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:69\u001b[0m, in \u001b[0;36m_get_text_metrics_with_cache\u001b[0;34m(renderer, text, fontprop, ismath, dpi)\u001b[0m\n\u001b[1;32m     66\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Call ``renderer.get_text_width_height_descent``, caching the results.\"\"\"\u001b[39;00m\n\u001b[1;32m     67\u001b[0m \u001b[38;5;66;03m# Cached based on a copy of fontprop so that later in-place mutations of\u001b[39;00m\n\u001b[1;32m     68\u001b[0m \u001b[38;5;66;03m# the passed-in argument do not mess up the cache.\u001b[39;00m\n\u001b[0;32m---> 69\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_get_text_metrics_with_cache_impl\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m     70\u001b[0m \u001b[43m    \u001b[49m\u001b[43mweakref\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mref\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtext\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontprop\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mismath\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:77\u001b[0m, in \u001b[0;36m_get_text_metrics_with_cache_impl\u001b[0;34m(renderer_ref, text, fontprop, ismath, dpi)\u001b[0m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;129m@functools\u001b[39m\u001b[38;5;241m.\u001b[39mlru_cache(\u001b[38;5;241m4096\u001b[39m)\n\u001b[1;32m     74\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_get_text_metrics_with_cache_impl\u001b[39m(\n\u001b[1;32m     75\u001b[0m         renderer_ref, text, fontprop, ismath, dpi):\n\u001b[1;32m     76\u001b[0m     \u001b[38;5;66;03m# dpi is unused, but participates in cache invalidation (via the renderer).\u001b[39;00m\n\u001b[0;32m---> 77\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mrenderer_ref\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_text_width_height_descent\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtext\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontprop\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mismath\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:217\u001b[0m, in \u001b[0;36mRendererAgg.get_text_width_height_descent\u001b[0;34m(self, s, prop, ismath)\u001b[0m\n\u001b[1;32m    213\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mget_text_width_height_descent(s, prop, ismath)\n\u001b[1;32m    215\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m ismath:\n\u001b[1;32m    216\u001b[0m     ox, oy, width, height, descent, font_image \u001b[38;5;241m=\u001b[39m \\\n\u001b[0;32m--> 217\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmathtext_parser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdpi\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprop\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    218\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m width, height, descent\n\u001b[1;32m    220\u001b[0m font \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_prepare_font(prop)\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/mathtext.py:79\u001b[0m, in \u001b[0;36mMathTextParser.parse\u001b[0;34m(self, s, dpi, prop, antialiased)\u001b[0m\n\u001b[1;32m     77\u001b[0m prop \u001b[38;5;241m=\u001b[39m prop\u001b[38;5;241m.\u001b[39mcopy() \u001b[38;5;28;01mif\u001b[39;00m prop \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m     78\u001b[0m antialiased \u001b[38;5;241m=\u001b[39m mpl\u001b[38;5;241m.\u001b[39m_val_or_rc(antialiased, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtext.antialiased\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m---> 79\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_parse_cached\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprop\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mantialiased\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/mathtext.py:100\u001b[0m, in \u001b[0;36mMathTextParser._parse_cached\u001b[0;34m(self, s, dpi, prop, antialiased)\u001b[0m\n\u001b[1;32m     97\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_parser \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:  \u001b[38;5;66;03m# Cache the parser globally.\u001b[39;00m\n\u001b[1;32m     98\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__class__\u001b[39m\u001b[38;5;241m.\u001b[39m_parser \u001b[38;5;241m=\u001b[39m _mathtext\u001b[38;5;241m.\u001b[39mParser()\n\u001b[0;32m--> 100\u001b[0m box \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_parser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontset\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontsize\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    101\u001b[0m output \u001b[38;5;241m=\u001b[39m _mathtext\u001b[38;5;241m.\u001b[39mship(box)\n\u001b[1;32m    102\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_output_type \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mvector\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/_mathtext.py:2165\u001b[0m, in \u001b[0;36mParser.parse\u001b[0;34m(self, s, fonts_object, fontsize, dpi)\u001b[0m\n\u001b[1;32m   2162\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_expression\u001b[38;5;241m.\u001b[39mparseString(s)\n\u001b[1;32m   2163\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m ParseBaseException \u001b[38;5;28;01mas\u001b[39;00m err:\n\u001b[1;32m   2164\u001b[0m     \u001b[38;5;66;03m# explain becomes a plain method on pyparsing 3 (err.explain(0)).\u001b[39;00m\n\u001b[0;32m-> 2165\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m+\u001b[39m ParseException\u001b[38;5;241m.\u001b[39mexplain(err, \u001b[38;5;241m0\u001b[39m)) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m   2166\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_state_stack \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m   2167\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_in_subscript_or_superscript \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n",
      "\u001b[0;31mValueError\u001b[0m: \nr [\\SI{}{\\kilo\\parsec}]\n   ^\nParseFatalException: Unknown symbol: \\SI, found '\\'  (at char 3), (line:1, col:4)"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "\nr [\\SI{}{\\kilo\\parsec}]\n   ^\nParseFatalException: Unknown symbol: \\SI, found '\\'  (at char 3), (line:1, col:4)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/IPython/core/formatters.py:340\u001b[0m, in \u001b[0;36mBaseFormatter.__call__\u001b[0;34m(self, obj)\u001b[0m\n\u001b[1;32m    338\u001b[0m     \u001b[38;5;28;01mpass\u001b[39;00m\n\u001b[1;32m    339\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 340\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mprinter\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobj\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    341\u001b[0m \u001b[38;5;66;03m# Finally look for special method names\u001b[39;00m\n\u001b[1;32m    342\u001b[0m method \u001b[38;5;241m=\u001b[39m get_real_method(obj, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mprint_method)\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/IPython/core/pylabtools.py:152\u001b[0m, in \u001b[0;36mprint_figure\u001b[0;34m(fig, fmt, bbox_inches, base64, **kwargs)\u001b[0m\n\u001b[1;32m    149\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_bases\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m FigureCanvasBase\n\u001b[1;32m    150\u001b[0m     FigureCanvasBase(fig)\n\u001b[0;32m--> 152\u001b[0m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcanvas\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mprint_figure\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbytes_io\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkw\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    153\u001b[0m data \u001b[38;5;241m=\u001b[39m bytes_io\u001b[38;5;241m.\u001b[39mgetvalue()\n\u001b[1;32m    154\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m fmt \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124msvg\u001b[39m\u001b[38;5;124m'\u001b[39m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/backend_bases.py:2158\u001b[0m, in \u001b[0;36mFigureCanvasBase.print_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m   2155\u001b[0m     \u001b[38;5;66;03m# we do this instead of `self.figure.draw_without_rendering`\u001b[39;00m\n\u001b[1;32m   2156\u001b[0m     \u001b[38;5;66;03m# so that we can inject the orientation\u001b[39;00m\n\u001b[1;32m   2157\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(renderer, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m_draw_disabled\u001b[39m\u001b[38;5;124m\"\u001b[39m, nullcontext)():\n\u001b[0;32m-> 2158\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfigure\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2159\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m bbox_inches:\n\u001b[1;32m   2160\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m bbox_inches \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtight\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:95\u001b[0m, in \u001b[0;36m_finalize_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m     93\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(draw)\n\u001b[1;32m     94\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdraw_wrapper\u001b[39m(artist, renderer, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m---> 95\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     96\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m renderer\u001b[38;5;241m.\u001b[39m_rasterizing:\n\u001b[1;32m     97\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstop_rasterizing()\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/figure.py:3154\u001b[0m, in \u001b[0;36mFigure.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   3151\u001b[0m         \u001b[38;5;66;03m# ValueError can occur when resizing a window.\u001b[39;00m\n\u001b[1;32m   3153\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpatch\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[0;32m-> 3154\u001b[0m \u001b[43mmimage\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_draw_list_compositing_images\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   3155\u001b[0m \u001b[43m    \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43martists\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msuppressComposite\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3157\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m sfig \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msubfigs:\n\u001b[1;32m   3158\u001b[0m     sfig\u001b[38;5;241m.\u001b[39mdraw(renderer)\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m         \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     image_group \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/axes/_base.py:3070\u001b[0m, in \u001b[0;36m_AxesBase.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   3067\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artists_rasterized:\n\u001b[1;32m   3068\u001b[0m     _draw_rasterized(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure, artists_rasterized, renderer)\n\u001b[0;32m-> 3070\u001b[0m \u001b[43mmimage\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_draw_list_compositing_images\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   3071\u001b[0m \u001b[43m    \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43martists\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfigure\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msuppressComposite\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3073\u001b[0m renderer\u001b[38;5;241m.\u001b[39mclose_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124maxes\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m   3074\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mstale \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m         \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     image_group \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/axis.py:1395\u001b[0m, in \u001b[0;36mAxis.draw\u001b[0;34m(self, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1393\u001b[0m \u001b[38;5;66;03m# Shift label away from axes to avoid overlapping ticklabels.\u001b[39;00m\n\u001b[1;32m   1394\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_label_position(renderer)\n\u001b[0;32m-> 1395\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlabel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1397\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_offset_text_position(tlb1, tlb2)\n\u001b[1;32m   1398\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moffsetText\u001b[38;5;241m.\u001b[39mset_text(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmajor\u001b[38;5;241m.\u001b[39mformatter\u001b[38;5;241m.\u001b[39mget_offset())\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:748\u001b[0m, in \u001b[0;36mText.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    745\u001b[0m renderer\u001b[38;5;241m.\u001b[39mopen_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtext\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_gid())\n\u001b[1;32m    747\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cm_set(text\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_wrapped_text()):\n\u001b[0;32m--> 748\u001b[0m     bbox, info, descent \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_layout\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    749\u001b[0m     trans \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_transform()\n\u001b[1;32m    751\u001b[0m     \u001b[38;5;66;03m# don't use self.get_position here, which refers to text\u001b[39;00m\n\u001b[1;32m    752\u001b[0m     \u001b[38;5;66;03m# position in Text:\u001b[39;00m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:381\u001b[0m, in \u001b[0;36mText._get_layout\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    379\u001b[0m clean_line, ismath \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_preprocess_math(line)\n\u001b[1;32m    380\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m clean_line:\n\u001b[0;32m--> 381\u001b[0m     w, h, d \u001b[38;5;241m=\u001b[39m \u001b[43m_get_text_metrics_with_cache\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    382\u001b[0m \u001b[43m        \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mclean_line\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_fontproperties\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    383\u001b[0m \u001b[43m        \u001b[49m\u001b[43mismath\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mismath\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfigure\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdpi\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    384\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    385\u001b[0m     w \u001b[38;5;241m=\u001b[39m h \u001b[38;5;241m=\u001b[39m d \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:69\u001b[0m, in \u001b[0;36m_get_text_metrics_with_cache\u001b[0;34m(renderer, text, fontprop, ismath, dpi)\u001b[0m\n\u001b[1;32m     66\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Call ``renderer.get_text_width_height_descent``, caching the results.\"\"\"\u001b[39;00m\n\u001b[1;32m     67\u001b[0m \u001b[38;5;66;03m# Cached based on a copy of fontprop so that later in-place mutations of\u001b[39;00m\n\u001b[1;32m     68\u001b[0m \u001b[38;5;66;03m# the passed-in argument do not mess up the cache.\u001b[39;00m\n\u001b[0;32m---> 69\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_get_text_metrics_with_cache_impl\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m     70\u001b[0m \u001b[43m    \u001b[49m\u001b[43mweakref\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mref\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtext\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontprop\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcopy\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mismath\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/text.py:77\u001b[0m, in \u001b[0;36m_get_text_metrics_with_cache_impl\u001b[0;34m(renderer_ref, text, fontprop, ismath, dpi)\u001b[0m\n\u001b[1;32m     73\u001b[0m \u001b[38;5;129m@functools\u001b[39m\u001b[38;5;241m.\u001b[39mlru_cache(\u001b[38;5;241m4096\u001b[39m)\n\u001b[1;32m     74\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_get_text_metrics_with_cache_impl\u001b[39m(\n\u001b[1;32m     75\u001b[0m         renderer_ref, text, fontprop, ismath, dpi):\n\u001b[1;32m     76\u001b[0m     \u001b[38;5;66;03m# dpi is unused, but participates in cache invalidation (via the renderer).\u001b[39;00m\n\u001b[0;32m---> 77\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mrenderer_ref\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_text_width_height_descent\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtext\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontprop\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mismath\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:217\u001b[0m, in \u001b[0;36mRendererAgg.get_text_width_height_descent\u001b[0;34m(self, s, prop, ismath)\u001b[0m\n\u001b[1;32m    213\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mget_text_width_height_descent(s, prop, ismath)\n\u001b[1;32m    215\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m ismath:\n\u001b[1;32m    216\u001b[0m     ox, oy, width, height, descent, font_image \u001b[38;5;241m=\u001b[39m \\\n\u001b[0;32m--> 217\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmathtext_parser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdpi\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprop\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    218\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m width, height, descent\n\u001b[1;32m    220\u001b[0m font \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_prepare_font(prop)\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/mathtext.py:79\u001b[0m, in \u001b[0;36mMathTextParser.parse\u001b[0;34m(self, s, dpi, prop, antialiased)\u001b[0m\n\u001b[1;32m     77\u001b[0m prop \u001b[38;5;241m=\u001b[39m prop\u001b[38;5;241m.\u001b[39mcopy() \u001b[38;5;28;01mif\u001b[39;00m prop \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m     78\u001b[0m antialiased \u001b[38;5;241m=\u001b[39m mpl\u001b[38;5;241m.\u001b[39m_val_or_rc(antialiased, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtext.antialiased\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m---> 79\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_parse_cached\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprop\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mantialiased\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/mathtext.py:100\u001b[0m, in \u001b[0;36mMathTextParser._parse_cached\u001b[0;34m(self, s, dpi, prop, antialiased)\u001b[0m\n\u001b[1;32m     97\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_parser \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:  \u001b[38;5;66;03m# Cache the parser globally.\u001b[39;00m\n\u001b[1;32m     98\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__class__\u001b[39m\u001b[38;5;241m.\u001b[39m_parser \u001b[38;5;241m=\u001b[39m _mathtext\u001b[38;5;241m.\u001b[39mParser()\n\u001b[0;32m--> 100\u001b[0m box \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_parser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontset\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfontsize\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    101\u001b[0m output \u001b[38;5;241m=\u001b[39m _mathtext\u001b[38;5;241m.\u001b[39mship(box)\n\u001b[1;32m    102\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_output_type \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mvector\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n",
      "File \u001b[0;32m~/Python/miniconda3/envs/gammaALPs-0.4/lib/python3.9/site-packages/matplotlib/_mathtext.py:2165\u001b[0m, in \u001b[0;36mParser.parse\u001b[0;34m(self, s, fonts_object, fontsize, dpi)\u001b[0m\n\u001b[1;32m   2162\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_expression\u001b[38;5;241m.\u001b[39mparseString(s)\n\u001b[1;32m   2163\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m ParseBaseException \u001b[38;5;28;01mas\u001b[39;00m err:\n\u001b[1;32m   2164\u001b[0m     \u001b[38;5;66;03m# explain becomes a plain method on pyparsing 3 (err.explain(0)).\u001b[39;00m\n\u001b[0;32m-> 2165\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m+\u001b[39m ParseException\u001b[38;5;241m.\u001b[39mexplain(err, \u001b[38;5;241m0\u001b[39m)) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m   2166\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_state_stack \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m   2167\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_in_subscript_or_superscript \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n",
      "\u001b[0;31mValueError\u001b[0m: \nr [\\SI{}{\\kilo\\parsec}]\n   ^\nParseFatalException: Unknown symbol: \\SI, found '\\'  (at char 3), (line:1, col:4)"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = ml.modules[0].r\n",
    "b_r = ml.modules[0]._Bfield_model.b_r\n",
    "b_theta = ml.modules[0]._Bfield_model.b_theta\n",
    "b_phi = ml.modules[0]._Bfield_model.b_phi\n",
    "plt.plot(r, b_r, label='$B_r$')\n",
    "plt.plot(r, b_theta, label=r'$B_\\theta$')\n",
    "plt.plot(r, b_phi, label=r'$B_\\phi$')\n",
    "plt.xlabel(r'$r [\\SI{}{\\kilo\\parsec}]$')\n",
    "plt.ylabel(r'$B [\\SI{}{\\micro\\gauss}]$')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot electron density\n",
    "\n",
    "We plot the electron density. Further, nel is used for calculating the RM at a later point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$r$ (kpc)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nel = ml.modules[0]._nelicm(r)   # in cm^-3\n",
    "plt.plot(r, nel)\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.ylabel('$n_\\mathrm{el}$ (cm$^{-3}$)')\n",
    "plt.xlabel('$r$ (kpc)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualisation of the magnetic field\n",
    "\n",
    "We can further plot a field line to illustrate that the field really is structured, opposed to a gaussian turbulence field.\n",
    "\n",
    "For this, we use the equation determining a single field line\n",
    "$\\newcommand{\\vert}{|}\\newcommand{\\vect}{\\mathbf}\\vect{x}_{i+1} =  \\vect{x}_{i} + \\frac{\\vect{B}(\\vect{x}_i)}{\\left \\vert \\vect{B}(\\vect{x}_i) \\right \\vert} \\Delta s$\n",
    "for a small $\\Delta s$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "from scipy.spatial.transform import Rotation as R\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib.collections import LineCollection\n",
    "from matplotlib.colors import ListedColormap, BoundaryNorm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions and constants\n",
    "\n",
    "In the following block, we define the neccessary functions (field components etc.), some constants and transformations of coordinates and vector fields to be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def field_line(x_0, steps, ds):\n",
    "    x = np.zeros((steps, 3))\n",
    "    x[0] = x_0\n",
    "    for i in range(steps-1):\n",
    "        x[i+1] = integrate(x[i], ds)\n",
    "    return x\n",
    "\n",
    "def integrate(x_prev, ds):\n",
    "    '''Returns next point along field line, given some starting point x_prev and a small increment ds'''\n",
    "    r, theta, phi = cart_to_sphere(x_prev[0], x_prev[1], x_prev[2])\n",
    "    B_sph = B_sphere(r, theta, phi)\n",
    "    B_cart = np.matmul(trafo(r, theta, phi), B_sph.transpose()).transpose()\n",
    "    norm = np.linalg.norm(B_cart)\n",
    "    x_new = x_prev + B_cart / norm * ds\n",
    "    return x_new\n",
    "\n",
    "\n",
    "def cart_to_sphere(x, y, z):\n",
    "    '''Coordinate transformation from cartesian to spherical.'''\n",
    "    r = np.sqrt(x**2 + y**2 + z**2)\n",
    "    theta = np.arccos(z / r)\n",
    "    phi = np.arctan2(y, x)\n",
    "    return r, theta, phi\n",
    "\n",
    "def sphere_to_cart(r, theta, phi):\n",
    "    '''Coordinate transformation from spherical to cartesian'''\n",
    "    x = r * np.sin(theta) * np.cos(phi)\n",
    "    y = r * np.sin(theta) * np.sin(phi)\n",
    "    z = r * np.cos(theta)\n",
    "    return x, y, z\n",
    "\n",
    "\n",
    "def trafo(r, theta, phi):\n",
    "    '''Returns trafo used for vector fields, i.e. Field A cartesian = S * Field A spherical. S is returned'''\n",
    "    mat = np.array([[np.sin(theta) * np.cos(phi), np.cos(theta) * np.cos(phi), -np.sin(phi)],\n",
    "                    [np.sin(theta) * np.sin(phi), np.cos(theta) * np.sin(phi), np.cos(phi)],\n",
    "                    [np.cos(theta), -np.sin(theta), 0]])\n",
    "    return mat\n",
    "\n",
    "\n",
    "'''Constants used for field definitions'''\n",
    "alpha = 5.7634591968\n",
    "c = 1\n",
    "F_0 = c * (alpha * np.cos(alpha) - np.sin(alpha)) * alpha**2\n",
    "\n",
    "\n",
    "def b_r(r, theta):\n",
    "    val = 2 * np.cos(theta) * f(r) / r**2\n",
    "    return val\n",
    "    \n",
    "\n",
    "def b_theta(r, theta):\n",
    "    val = - np.sin(theta) * f_prime(r) / r\n",
    "    return val\n",
    "\n",
    "\n",
    "def b_phi(r, theta):\n",
    "    val = alpha * np.sin(theta) * f(r) / r\n",
    "    return val\n",
    "\n",
    "\n",
    "def f(r):\n",
    "    return c * (alpha * np.cos(alpha * r) - np.sin(alpha * r) / r) \\\n",
    "           - F_0 * r**2 / alpha**2\n",
    "\n",
    "\n",
    "def f_prime(r):\n",
    "    return c * ( - alpha**2 * np.sin(alpha * r) \\\n",
    "                - alpha * np.cos(alpha * r) / r \\\n",
    "                + np.sin(alpha * r) / r**2) \\\n",
    "               - 2 * F_0 * r / alpha**2\n",
    "\n",
    "def B_sphere(r, theta, phi):\n",
    "    return np.array([[b_r(r, theta), b_theta(r, theta), b_phi(r, theta)]])\n",
    "\n",
    "\n",
    "def norm(r):\n",
    "    return np.sqrt(r[:, :, :, 0]**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the field line\n",
    "We plot an \"interactive\" field line, in the sense that you can rotate it around in space!\n",
    "\n",
    "Because pyplot lacks a proper function for coloured 3D plots, we use instead a scatter with some colormap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
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       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
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       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
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       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
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       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
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       "    this.root.setAttribute('style', 'display: inline-block');\n",
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       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
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       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
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       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
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       "    canvas_div.setAttribute('tabindex', '0');\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;' +\n",
       "            'z-index: 2;'\n",
       "    );\n",
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       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
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       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
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       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
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       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box;' +\n",
       "            'pointer-events: none;' +\n",
       "            'position: relative;' +\n",
       "            'z-index: 0;'\n",
       "    );\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box;' +\n",
       "            'left: 0;' +\n",
       "            'pointer-events: none;' +\n",
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       "            'z-index: 1;'\n",
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       "             * appears correct on HiDPI screens. */\n",
       "            canvas.style.width = width + 'px';\n",
       "            canvas.style.height = height + 'px';\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
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       "    this.resizeObserverInstance.observe(canvas_div);\n",
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       "    function on_mouse_event_closure(name) {\n",
       "        /* User Agent sniffing is bad, but WebKit is busted:\n",
       "         * https://bugs.webkit.org/show_bug.cgi?id=144526\n",
       "         * https://bugs.webkit.org/show_bug.cgi?id=181818\n",
       "         * The worst that happens here is that they get an extra browser\n",
       "         * selection when dragging, if this check fails to catch them.\n",
       "         */\n",
       "        var UA = navigator.userAgent;\n",
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       "                /* This prevents the web browser from automatically changing to\n",
       "                 * the text insertion cursor when the button is pressed. We\n",
       "                 * want to control all of the cursor setting manually through\n",
       "                 * the 'cursor' event from matplotlib */\n",
       "                event.preventDefault()\n",
       "                return fig.mouse_event(event, name);\n",
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       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
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       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
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       "            canvas_div.style.width = width + 'px';\n",
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       "    }\n",
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       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
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       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
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       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.canvas_div.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "function getModifiers(event) {\n",
       "    var mods = [];\n",
       "    if (event.ctrlKey) {\n",
       "        mods.push('ctrl');\n",
       "    }\n",
       "    if (event.altKey) {\n",
       "        mods.push('alt');\n",
       "    }\n",
       "    if (event.shiftKey) {\n",
       "        mods.push('shift');\n",
       "    }\n",
       "    if (event.metaKey) {\n",
       "        mods.push('meta');\n",
       "    }\n",
       "    return mods;\n",
       "}\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    // from https://stackoverflow.com/q/1114465\n",
       "    var boundingRect = this.canvas.getBoundingClientRect();\n",
       "    var x = (event.clientX - boundingRect.left) * this.ratio;\n",
       "    var y = (event.clientY - boundingRect.top) * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        modifiers: getModifiers(event),\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
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       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id='fbaf014a-33be-43f6-afc1-7a90e650100f'></div>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "TypeError",
     "evalue": "gca() got an unexpected keyword argument 'projection'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[14], line 5\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m# so that we can have an interactive plot!\u001b[39;00m\n\u001b[1;32m      4\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m----> 5\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgca\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprojection\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m3d\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      6\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_xlabel(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$x$\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m      7\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_ylabel(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$y$\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "\u001b[0;31mTypeError\u001b[0m: gca() got an unexpected keyword argument 'projection'"
     ]
    }
   ],
   "source": [
    "%matplotlib notebook    \n",
    "# so that we can have an interactive plot!\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.set_zlabel('$z$')\n",
    "\n",
    "\n",
    "# start a field line at r=0.2, theta=pi / 2 (on the equator), phi=0\n",
    "# choose some stepsize ds=0.001 and integrate 100000 steps\n",
    "\n",
    "ds = 0.001\n",
    "steps = 100000\n",
    "\n",
    "#if you want to plot multiple field lines, change this for loop\n",
    "for phi in np.linspace(0, 2 * np.pi, num=1):\n",
    "    x_0 = sphere_to_cart(0.2, np.pi / 2, phi)\n",
    "    x = field_line(x_0, steps, ds)\n",
    "    #print(x)\n",
    "    #plot only every 10th point to save memory and time\n",
    "    line = ax.scatter(x[::10, 0], x[::10, 1], x[::10, 2],\n",
    "                      c=np.linalg.norm(x[::10], axis=-1),\n",
    "                      cmap=plt.get_cmap('viridis'),\n",
    "                      s=1, marker='.')\n",
    "cbar = fig.colorbar(line, ax=ax, label='$r$')\n",
    "ax.set_xticks((-0.5, 0, 0.5))\n",
    "ax.set_yticks((-0.5, 0, 0.5))\n",
    "ax.set_zticks((-0.4, 0, 0.4))\n",
    "ax.view_init(elev=25, azim=-107)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate rotation measure\n",
    "\n",
    "Faraday RM can be calculated via a method of the structured field model, arguments areelectron density evaluated at r = structured_field.r in cm^-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml.modules[0].Bfield_model.rotation_measure(nel)   # in rad * m^-2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taylor et al. (2006) found RM values between 6500 and 7500 rad m^-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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