{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1D AMRVAC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a Magritte model from a snapshot of 1D AMRVAC hydrodynamics simulation.\n",
    "The hydro model was kindly provided by Jan Bolte.\n",
    "Currently, the AMRVAC binary files can not yet be used directly to extract the snapshot data.\n",
    "Hence we use the corresponding `.vtu` files."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the required functionalty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import magritte.setup    as setup                 # Model setup\n",
    "import magritte.core     as magritte              # Core functionality\n",
    "import numpy             as np                    # Data structures\n",
    "import matplotlib.pyplot as plt                   # Plotting\n",
    "import vtk                                        # Reading the model\n",
    "import os\n",
    "\n",
    "from tqdm                   import tqdm           # Progress bars\n",
    "from astropy                import constants      # Unit conversions\n",
    "from vtk.util.numpy_support import vtk_to_numpy   # Converting data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a working directory (you will have to change this; it must be an **absolute path**)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "wdir = \"/lhome/thomasc/Magritte-examples/AMRVAC_1D/\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the working directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "!mkdir -p $wdir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define file names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_file = os.path.join(wdir, 'model_AMRVAC_1D.vtu' )   # AMRVAC snapshot\n",
    "model_file = os.path.join(wdir, 'model_AMRVAC_1D.hdf5')   # Resulting Magritte model\n",
    "lamda_file = os.path.join(wdir, 'co.txt'              )   # Line data file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use a snapshot and data file that can be downloaded with the following links."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_link = \"https://owncloud.ster.kuleuven.be/index.php/s/NpPG88x5LCbaZNC/download\"\n",
    "lamda_link = \"https://home.strw.leidenuniv.nl/~moldata/datafiles/co.dat\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dowload the snapshot and the linedata (``%%capture`` is just used to suppress the output)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "!wget $input_link --output-document $input_file\n",
    "!wget $lamda_link --output-document $lamda_file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The script below extracts the required data from the snapshot `.vtu` file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████| 85/85 [00:00<00:00, 346468.26it/s]\n",
      "100%|███████████████████████████████████| 2000/2000 [00:00<00:00, 220677.35it/s]\n"
     ]
    }
   ],
   "source": [
    "# Create a vtk reader to read the AMRVAC file and extract its contents.\n",
    "reader = vtk.vtkXMLUnstructuredGridReader()\n",
    "reader.SetFileName(input_file)\n",
    "reader.Update()\n",
    "\n",
    "# Extract the grid output\n",
    "grid = reader.GetOutput()\n",
    "\n",
    "# Extract the number of cells\n",
    "ncells = grid.GetNumberOfCells() \n",
    "\n",
    "# Extract cell data\n",
    "cellData = grid.GetCellData()\n",
    "for i in tqdm(range(cellData.GetNumberOfArrays())):\n",
    "    array = cellData.GetArray(i)\n",
    "    if (array.GetName() == 'rho'):\n",
    "        rho = vtk_to_numpy(array)\n",
    "    if (array.GetName() == 'temperature'):\n",
    "        tmp = vtk_to_numpy(array)\n",
    "    if (array.GetName() == 'v1'):\n",
    "        v_x = vtk_to_numpy(array)\n",
    "\n",
    "# Convert rho (total density) to abundances\n",
    "nH2 = rho * 1.0e+6 * constants.N_A.si.value / 2.02\n",
    "nCO = nH2 * 1.0e-4\n",
    "\n",
    "# Convenience arrays\n",
    "zeros = np.zeros(ncells)\n",
    "ones  = np.ones (ncells)\n",
    "\n",
    "# Since it is a 1D model there is no y or z data.\n",
    "v_y = v_z = zeros\n",
    "\n",
    "# Convert to fractions of the speed of light\n",
    "velocity = np.array((v_x, v_y, v_z)).transpose() / constants.c.cgs.value\n",
    "\n",
    "# Define turbulence at 150 m/s\n",
    "trb = (150.0/constants.c.si.value)**2 * ones\n",
    "\n",
    "# Extract cell centres to use as positions of the Magritte points.\n",
    "centres = []\n",
    "for c in tqdm(range(ncells)):\n",
    "    cell = grid.GetCell(c)\n",
    "    centre = np.zeros(3)\n",
    "    for i in range(2):\n",
    "        centre = centre + np.array(cell.GetPoints().GetPoint(i))\n",
    "    centre = 0.5 * centre\n",
    "    centres.append(centre)\n",
    "centres  = np.array(centres)\n",
    "centres *= 1.0e-2   # convert [cm] to [m]\n",
    "\n",
    "# Define AMRVAC cell centres as Magritte point positions\n",
    "position = centres"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Downsample the data by a factor 20. (Check whether this is a reasonable approximation for your radiative transfer model!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "reduction_factor = 20\n",
    "\n",
    "position = position[::reduction_factor]\n",
    "velocity = velocity[::reduction_factor]\n",
    "nCO      = nCO     [::reduction_factor]\n",
    "nH2      = nH2     [::reduction_factor]\n",
    "tmp      = tmp     [::reduction_factor]\n",
    "trb      = trb     [::reduction_factor]\n",
    "zeros    = zeros   [::reduction_factor]\n",
    "ones     = ones    [::reduction_factor]\n",
    "\n",
    "ncells = len(position)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now all data is read, we can use it to construct a Magritte model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing parameters...\n",
      "Writing points...\n",
      "Writing rays...\n",
      "Writing boundary...\n",
      "Writing chemistry...\n",
      "Writing species...\n",
      "Writing thermodynamics...\n",
      "Writing temperature...\n",
      "Writing turbulence...\n",
      "Writing lines...\n",
      "Writing lineProducingSpecies...\n",
      "Writing linedata...\n",
      "ncolpoar = 2\n",
      "--- colpoar = 0\n",
      "Writing collisionPartner...\n",
      "(l, c) = 0, 0\n",
      "--- colpoar = 1\n",
      "Writing collisionPartner...\n",
      "(l, c) = 0, 1\n",
      "Writing quadrature...\n",
      "Writing populations...\n",
      "Writing radiation...\n",
      "Writing frequencies...\n"
     ]
    }
   ],
   "source": [
    "model = magritte.Model ()                              # Create model object\n",
    "\n",
    "model.parameters.set_model_name         (model_file)   # Magritte model file\n",
    "model.parameters.set_spherical_symmetry (True)         # Assume spherical symmetry\n",
    "model.parameters.set_dimension          (1)            # Spherical symmetry is 1D\n",
    "model.parameters.set_npoints            (ncells)       # Number of points\n",
    "model.parameters.set_nrays              (50)           # Number of rays  \n",
    "model.parameters.set_nspecs             (3)            # Number of species (min. 5)\n",
    "model.parameters.set_nlspecs            (1)            # Number of line species\n",
    "model.parameters.set_nquads             (11)           # Number of quadrature points\n",
    "\n",
    "model.geometry.points.position.set (position)\n",
    "model.geometry.points.velocity.set (velocity)\n",
    "\n",
    "model.chemistry.species.abundance = np.array((nCO, nH2, zeros)).T\n",
    "model.chemistry.species.symbol    = ['CO', 'H2', 'e-']\n",
    "\n",
    "model.thermodynamics.temperature.gas  .set(tmp)\n",
    "model.thermodynamics.turbulence.vturb2.set(trb)\n",
    "\n",
    "setup.set_Delaunay_neighbor_lists  (model)\n",
    "setup.set_Delaunay_boundary        (model)\n",
    "setup.set_boundary_condition_CMB   (model)\n",
    "setup.set_uniform_rays             (model)\n",
    "setup.set_linedata_from_LAMDA_file (model, lamda_file)\n",
    "setup.set_quadrature               (model)\n",
    "\n",
    "model.write()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data can be extracted from the Magritte model by casting it into numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "position  = np.array(model.geometry.points.position)\n",
    "velocity  = np.array(model.geometry.points.velocity)\n",
    "abundance = np.array(model.chemistry.species.abundance)\n",
    "\n",
    "rs  = np.linalg.norm(position, axis=1)\n",
    "vs  = np.linalg.norm(velocity, axis=1)\n",
    "nCO = abundance[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot of the CO number density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CO number density [m$^{-3}$]')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 832x624 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=130)\n",
    "plt.title('CO number density')\n",
    "plt.plot(rs, nCO)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'r [m]')\n",
    "plt.ylabel(r'CO number density [m$^{-3}$]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot of the lengths of the velocity vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '|velocity| [m/s]')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 832x624 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=130)\n",
    "plt.title('|velocity|')\n",
    "plt.plot(rs, vs*magritte.CC)\n",
    "plt.xscale('log')\n",
    "plt.xlabel(r'r [m]')\n",
    "plt.ylabel(r'|velocity| [m/s]')"
   ]
  }
 ],
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