{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "This notebook sets up and runs a set of benchmarks to compare\n",
    "different numerical discretizations of the SWEs\n",
    "\n",
    "Copyright (C) 2016  SINTEF ICT\n",
    "\n",
    "This program is free software: you can redistribute it and/or modify\n",
    "it under the terms of the GNU General Public License as published by\n",
    "the Free Software Foundation, either version 3 of the License, or\n",
    "(at your option) any later version.\n",
    "\n",
    "This program is distributed in the hope that it will be useful,\n",
    "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
    "GNU General Public License for more details.\n",
    "\n",
    "You should have received a copy of the GNU General Public License\n",
    "along with this program.  If not, see <http://www.gnu.org/licenses/>.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets have matplotlib \"inline\"\n",
    "%matplotlib inline\n",
    "\n",
    "#Python 2.7 compatibility\n",
    "from __future__ import print_function\n",
    "\n",
    "#Import packages we need\n",
    "import numpy as np\n",
    "from matplotlib import animation, rc\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import gridspec\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "#import mpld3\n",
    "\n",
    "import subprocess\n",
    "import os\n",
    "import gc\n",
    "import datetime\n",
    "import logging\n",
    "\n",
    "import pycuda.driver as cuda\n",
    "\n",
    "try:\n",
    "    from StringIO import StringIO\n",
    "except ImportError:\n",
    "    from io import StringIO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Get root logger\n",
    "logger = logging.getLogger('')\n",
    "logger.setLevel(logging.DEBUG)\n",
    "\n",
    "#Add log to file\n",
    "fh = logging.FileHandler('output.log')\n",
    "formatter = logging.Formatter('%(asctime)s:%(name)s:%(levelname)s: %(message)s')\n",
    "fh.setFormatter(formatter)\n",
    "fh.setLevel(logging.DEBUG)\n",
    "logger.addHandler(fh)\n",
    "\n",
    "#Add log to screen\n",
    "ch = logging.StreamHandler()\n",
    "ch.setLevel(logging.INFO)\n",
    "logger.addHandler(ch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Registering automatic CUDA context handling\n"
     ]
    }
   ],
   "source": [
    "#Finally, import our simulator\n",
    "from SWESimulators import Common, LxF, FORCE, HLL, HLL2, KP07, KP07_dimsplit, WAF, IPythonMagic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "CUDA version (9, 1, 0)\n",
      "Driver version 9010\n",
      "Using 'GeForce 840M' GPU\n",
      "Created context handle <498737660208>\n"
     ]
    }
   ],
   "source": [
    "%cuda_context_handler cuda_context"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Misc plotting setup\n",
    "def setBwStyles(ax):\n",
    "    from cycler import cycler\n",
    "\n",
    "    ax.set_prop_cycle( cycler('marker', ['.', 'x', 4, '+', '*', '1', 5]) +\n",
    "                       cycler('linestyle', ['-.', '--', ':', '-.', '--', ':', '-.']) +\n",
    "                       #cycler('markersize', [5, 5, 5, 5, 5, 5]) +\n",
    "                       cycler('color', ['k', 'k', 'k', 'k', 'k', 'k', 'k']) )    \n",
    "\n",
    "#Set large figure sizes\n",
    "plt.rcParams['figure.figsize'] = [12, 8]\n",
    "plt.rcParams['figure.dpi'] = 100\n",
    "plt.rcParams['animation.html'] = 'html5'\n",
    "#plt.rcParams['legend.markerscale'] = 1.0\n",
    "#plt.rcParams['lines.markersize'] = 6\n",
    "plt.rcParams['lines.markeredgewidth'] = 1.5\n",
    "#plt.rcParams['savefig.dpi'] = 400"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def save_figure(fig, stem):\n",
    "    fig_filename = \"convergence_smooth2d_\" + stem + \".pdf\"\n",
    "    \n",
    "    image_text = fig_filename + \"\\nCreated \" + str(datetime.datetime.now().strftime(\"%Y-%m-%d %H:%M:%S\"))\n",
    "    \n",
    "    #ax = fig.gca()\n",
    "    #pos1 = ax.get_position() # get the original position \n",
    "    #pos2 = [pos1.x0 + 0.3, pos1.y0 + 0.3,  pos1.width / 2.0, pos1.height / 2.0] \n",
    "    #ax.set_position(pos2) # set a new position\n",
    "    \n",
    "    #fig.gca().annotate(image_text, xy=(1.1, 0), xycoords='figure fraction', fontsize=10,\n",
    "    #                   horizontalalignment='right', verticalalignment='bottom')\n",
    "    t = plt.figtext(-0.1, .9, image_text, rotation='vertical')\n",
    "    \n",
    "    legend = fig.gca().legend_\n",
    "    if (legend != None):\n",
    "        fig.savefig(fig_filename, bbox_extra_artists=(legend,t, ), bbox_inches='tight')\n",
    "    else:\n",
    "        fig.savefig(fig_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def downsample(highres_solution, factor):\n",
    "    assert(highres_solution.shape[0] % factor == 0)\n",
    "    assert(highres_solution.shape[1] % factor == 0)\n",
    "    ny = highres_solution.shape[0] / factor\n",
    "    nx = highres_solution.shape[1] / factor\n",
    "    \n",
    "    if (factor == 1):\n",
    "        return highres_solution\n",
    "    else:\n",
    "        return highres_solution.reshape([int(ny), int(factor), int(nx), int(factor)]).mean(3).mean(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 22336 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 2.0, 0.2726356370001644]\n"
     ]
    }
   ],
   "source": [
    "def wall_boundary_conditions(data):\n",
    "    data[0:2,:] = data[4:2:-1,:]\n",
    "    data[-2:,:] = data[-3:-5:-1,:]\n",
    "    data[:,0:2] = data[:,4:2:-1]\n",
    "    data[:,-2:] = data[:,-3:-5:-1]\n",
    "    return data\n",
    "    \n",
    "\n",
    "def gen_test_data(nx, ny, ref_nx, ref_ny, g, num_ghost_cells):\n",
    "    width = 100.0\n",
    "    height = 100.0\n",
    "    ref_dx = width / float(ref_nx)\n",
    "    ref_dy = height / float(ref_ny)\n",
    "\n",
    "    x_center = ref_dx*ref_nx/2.0\n",
    "    y_center = ref_dy*ref_ny/2.0\n",
    "\n",
    "    #Create a gaussian \"dam break\" that will not form shocks\n",
    "    size = width / 5.0\n",
    "    dt = 10**10\n",
    "    \n",
    "    h  = np.zeros((ny+2*num_ghost_cells, nx+2*num_ghost_cells), dtype=np.float32); \n",
    "    hu = np.zeros((ny+2*num_ghost_cells, nx+2*num_ghost_cells), dtype=np.float32);\n",
    "    hv = np.zeros((ny+2*num_ghost_cells, nx+2*num_ghost_cells), dtype=np.float32);\n",
    "    \n",
    "    x = ref_dx*(np.arange(0, ref_nx, dtype=np.float32)+0.5) - x_center\n",
    "    y = ref_dy*(np.arange(0, ref_ny, dtype=np.float32)+0.5) - y_center\n",
    "    xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "    r = np.sqrt(xv**2 + yv**2)\n",
    "    xv = None\n",
    "    yv = None\n",
    "    gc.collect()\n",
    "    \n",
    "    #Make sure that the wanted resolution is suitable\n",
    "    assert(ref_nx >= nx)\n",
    "    assert(ref_ny >= ny)\n",
    "    assert(nx/ref_nx == ny/ref_ny)\n",
    "    \n",
    "    #Generate highres then downsample\n",
    "    #h_highres = 0.5 + 0.1*np.exp(-(xv**2/size + yv**2/size))\n",
    "    h_highres = 0.5 + 0.1*0.5*(1.0 + np.cos(np.pi*r/size)) * (r < size)\n",
    "    h[num_ghost_cells:-num_ghost_cells, num_ghost_cells:-num_ghost_cells] = downsample(h_highres, ref_nx/nx)\n",
    "    h_highres = None\n",
    "    gc.collect()\n",
    "    \n",
    "    #hu_highres = 0.1*np.exp(-(xv**2/size + yv**2/size))\n",
    "    hu_highres = 0.1*0.5*(1.0 + np.cos(np.pi*r/size)) * (r < size)\n",
    "    hu[num_ghost_cells:-num_ghost_cells, num_ghost_cells:-num_ghost_cells] = downsample(hu_highres, ref_nx/nx)\n",
    "    hu_highres = None\n",
    "    gc.collect()\n",
    "    \n",
    "    #hv_highres = 0.1*np.exp(-(xv**2/size + yv**2/size))\n",
    "    hv_highres = 0.1*0.5*(1.0 + np.cos(np.pi*r/size)) * (r < size)\n",
    "    hv[num_ghost_cells:-num_ghost_cells, num_ghost_cells:-num_ghost_cells] = downsample(hv_highres, ref_nx/nx)\n",
    "    hv_highres = None\n",
    "    gc.collect()\n",
    "    \n",
    "    #Fix boundary conditions\n",
    "    h = wall_boundary_conditions(h);\n",
    "    hu = wall_boundary_conditions(hu);\n",
    "    hv = wall_boundary_conditions(hv);\n",
    "    \n",
    "    scale = 0.7\n",
    "    max_h_estimate = 0.6\n",
    "    max_u_estimate = 0.1*np.sqrt(2.0)\n",
    "    dx = width/nx\n",
    "    dy = height/ny\n",
    "    dt = scale * min(dx, dy) / (max_u_estimate + np.sqrt(g*max_h_estimate))\n",
    "    \n",
    "    return h, hu, hv, dx, dy, dt\n",
    "\n",
    "h, hu, hv, dx, dy, dt = gen_test_data(nx=100, ny=50, ref_nx=1000, ref_ny=500, g=9.81, num_ghost_cells=2)\n",
    "\n",
    "plt.figure()\n",
    "ax=plt.subplot(1,3,1)\n",
    "im=plt.imshow(h, extent=[0, 100, 0, 100])\n",
    "divider = make_axes_locatable(ax)\n",
    "cax = divider.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "ax=plt.subplot(1,3,2)\n",
    "im=plt.imshow(hu, extent=[0, 100, 0, 100])\n",
    "divider = make_axes_locatable(ax)\n",
    "cax = divider.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "ax=plt.subplot(1,3,3)\n",
    "im=plt.imshow(hv, extent=[0, 100, 0, 100])\n",
    "divider = make_axes_locatable(ax)\n",
    "cax = divider.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print([dx, dy, dt])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_filename(simulator, nx):\n",
    "    return \"shock1d_\" + str(simulator.__name__) + \"_\" + str(nx) + \".npz\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sanity_check(variable, variable_name):\n",
    "    maxval = np.amax(variable)\n",
    "    minval = np.amin(variable)\n",
    "    if (np.isnan(maxval) or np.isnan(minval)):\n",
    "        print(\"=== WARNING ===\")\n",
    "        print(variable_name + \" contains NaN values\")\n",
    "        print(\"=== WARNING ===\")\n",
    "\n",
    "def run_benchmark(simulator, courant_number, nx, ny, ref_nx, ref_ny, num_ghost_cells, g=9.81, force_rerun=False, datafilename=None):\n",
    "\n",
    "    if (datafilename and os.path.isfile(datafilename) and force_rerun == False):\n",
    "        print(\"=== WARNING ===\")\n",
    "        print(\"Existing simulation exists, skipping simulation\")\n",
    "        print(\"=== WARNING ===\")\n",
    "        return[0, 0, 0]\n",
    "    else:\n",
    "        #Generate high-res initial conditions\n",
    "        h0, hu0, hv0, dx, dy, dt = gen_test_data(nx=nx, ny=ny, ref_nx=ref_nx, ref_ny=ref_ny, g=g, num_ghost_cells=num_ghost_cells)\n",
    "        dt = dt * courant_number\n",
    "\n",
    "        #Initialize simulator\n",
    "        with Common.Timer(simulator.__name__ + \"_\" + str(nx)) as timer:\n",
    "            sim = simulator(cuda_context, \\\n",
    "                            h0, hu0, hv0, \\\n",
    "                            nx, ny, \\\n",
    "                            dx, dy, dt, \\\n",
    "                            g)\n",
    "\n",
    "            t, nt = sim.simulate(1.0)\n",
    "            \n",
    "            h, hu, hv = sim.download()\n",
    "\n",
    "        h = h[num_ghost_cells:-num_ghost_cells, num_ghost_cells:-num_ghost_cells]\n",
    "        hu = hu[num_ghost_cells:-num_ghost_cells, num_ghost_cells:-num_ghost_cells]\n",
    "        hv = hv[num_ghost_cells:-num_ghost_cells, num_ghost_cells:-num_ghost_cells]\n",
    "\n",
    "        sanity_check(h, \"h\")\n",
    "        sanity_check(hu, \"hu\")\n",
    "        sanity_check(hv, \"hv\")\n",
    "\n",
    "        if (datafilename):\n",
    "            np.savez_compressed(datafilename, h=h, hu=hu, hv=hv, nt=nt, t=t, elapsed=timer.secs)\n",
    "        else:\n",
    "            print(\"=== WARNING ===\")\n",
    "            print(\"No datafilename supplied - no data saved to disk!\")\n",
    "            print(\"=== WARNING ===\")\n",
    "            \n",
    "        \n",
    "    gc.collect() # Force run garbage collection to free up memory\n",
    "    \n",
    "    return [timer.secs, nt, dt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "KP07 simulated 1.000000 seconds to 1.000000 with 5 steps in 0.004979 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 17260 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "3367"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datafilename = \"temp_data.npz\"\n",
    "elapsed, nt, dt = run_benchmark(KP07.KP07, \n",
    "                                courant_number=0.9, \n",
    "                                ref_nx=500, ref_ny=1000,\n",
    "                                nx=50, ny=100, \n",
    "                                num_ghost_cells=2, force_rerun=True,\n",
    "                                datafilename=datafilename)\n",
    "\n",
    "with np.load(datafilename) as data:\n",
    "    rh = downsample(data['h'], 2)\n",
    "\n",
    "    plt.figure()\n",
    "    plt.imshow(rh, extent=[0, 100, 0, 100])\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    \n",
    "gc.collect()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "LxF simulated 1.000000 seconds to 1.000000 with 1 steps in 0.001006 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "FORCE simulated 1.000000 seconds to 1.000000 with 1 steps in 0.000000 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "HLL simulated 1.000000 seconds to 1.000000 with 1 steps in 0.001000 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "HLL2 simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WAF simulated 1.000000 seconds to 1.000000 with 2 steps in 0.000000 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "KP07 simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== WARNING ===\n",
      "No datafilename supplied - no data saved to disk!\n",
      "=== WARNING ===\n",
      "Completed warmup in 3.976818323135376 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "LxF simulated 1.000000 seconds to 1.000000 with 1 steps in 0.001001 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 1 steps in 0.000000 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 2 steps in 0.000000 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 3 steps in 0.001001 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 6 steps in 0.000000 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 11 steps in 0.001001 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 21 steps in 0.001001 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 42 steps in 0.006009 seconds\n",
      "LxF simulated 1.000000 seconds to 1.000000 with 84 steps in 0.009007 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 1 steps in 0.000000 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 1 steps in 0.000000 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001000 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 3 steps in 0.000000 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 6 steps in 0.001002 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 11 steps in 0.001002 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 21 steps in 0.002020 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 42 steps in 0.007006 seconds\n",
      "FORCE simulated 1.000000 seconds to 1.000000 with 84 steps in 0.007004 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 1 steps in 0.000000 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 1 steps in 0.000000 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001000 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 3 steps in 0.001001 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 6 steps in 0.001001 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 11 steps in 0.002001 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 21 steps in 0.001002 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 42 steps in 0.002001 seconds\n",
      "HLL simulated 1.000000 seconds to 1.000000 with 84 steps in 0.011009 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001002 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 2 steps in 0.000000 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 4 steps in 0.001001 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 6 steps in 0.001025 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 12 steps in 0.002002 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 22 steps in 0.004003 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 42 steps in 0.001987 seconds\n",
      "HLL2 simulated 1.000000 seconds to 1.000000 with 84 steps in 0.025019 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 2 steps in 0.000000 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 4 steps in 0.000000 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 6 steps in 0.001001 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 12 steps in 0.001001 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 22 steps in 0.000984 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 42 steps in 0.002001 seconds\n",
      "WAF simulated 1.000000 seconds to 1.000000 with 84 steps in 0.009979 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 1 steps in 0.001002 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 2 steps in 0.000999 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 3 steps in 0.001002 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 6 steps in 0.001000 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 11 steps in 0.003003 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 21 steps in 0.005004 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 42 steps in 0.009985 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 84 steps in 0.016012 seconds\n",
      "KP07 simulated 1.000000 seconds to 1.000000 with 167 steps in 0.031051 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001000 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 2 steps in 0.000000 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 2 steps in 0.001001 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 4 steps in 0.000000 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 6 steps in 0.001001 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 12 steps in 0.002002 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 22 steps in 0.003002 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 42 steps in 0.008007 seconds\n",
      "KP07_dimsplit simulated 1.000000 seconds to 1.000000 with 84 steps in 0.014010 seconds\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Completed simulation in 144.15734195709229 s\n"
     ]
    }
   ],
   "source": [
    "reference_nx = 2048\n",
    "force_rerun=True\n",
    "domain_sizes = [8, 16, 32, 64, 128, 256, 512, 1024]\n",
    "simulators = [LxF.LxF, FORCE.FORCE, HLL.HLL, HLL2.HLL2, WAF.WAF, KP07.KP07, KP07_dimsplit.KP07_dimsplit]\n",
    "simulator_ghost_cells = [1, 1, 1, 2, 2, 2, 2]\n",
    "simulator_names = ['LxF', 'FORCE', 'HLL', 'HLL2', 'WAF', 'KP07', 'KP07 dimsplit']\n",
    "simulator_courant_numbers = [0.9, 0.9, 0.9, 0.9, 0.9, 0.45, 0.9]\n",
    "\n",
    "\n",
    "\n",
    "sim_elapsed_time = np.zeros((len(simulators), len(domain_sizes)))\n",
    "sim_dt = np.zeros((len(simulators), len(domain_sizes)))\n",
    "sim_nt = np.zeros((len(simulators), len(domain_sizes)))\n",
    "\n",
    "#Warmup to compile kernels\n",
    "with Common.Timer(\"warmup\") as timer:\n",
    "    for i in range(len(simulators)):\n",
    "        run_benchmark(simulator=simulators[i], \n",
    "                      courant_number=simulator_courant_numbers[i], \n",
    "                      nx=16, ny=16, ref_nx=16, ref_ny=16,\n",
    "                      num_ghost_cells=simulator_ghost_cells[i], \n",
    "                      force_rerun=force_rerun)\n",
    "print(\"Completed warmup in {:} s\".format(timer.secs))\n",
    "    \n",
    "with Common.Timer(\"simulation\") as timer:\n",
    "    for i in range(len(simulators)):        \n",
    "        # Run the simulation for all the domain sizes\n",
    "        for j, nx in enumerate(domain_sizes):\n",
    "            datafilename = gen_filename(simulators[i], nx)\n",
    "            [secs, nt, dt] = run_benchmark(simulator=simulators[i], \n",
    "                          courant_number=simulator_courant_numbers[i], \n",
    "                          nx=nx, ny=nx, ref_nx=reference_nx, ref_ny=reference_nx,\n",
    "                          num_ghost_cells=simulator_ghost_cells[i], \n",
    "                          force_rerun=force_rerun, \n",
    "                          datafilename=datafilename)\n",
    "            sim_elapsed_time[i, j] = secs\n",
    "            sim_dt[i, j] = dt\n",
    "            sim_nt[i, j] = nt\n",
    "\n",
    "        # Run reference with a low CFL-number\n",
    "        datafilename = gen_filename(simulators[i], reference_nx)\n",
    "        run_benchmark(simulator=simulators[i], \n",
    "                      courant_number=simulator_courant_numbers[i], \n",
    "                      nx=reference_nx, ny=reference_nx, ref_nx=reference_nx, ref_ny=reference_nx,\n",
    "                      num_ghost_cells=simulator_ghost_cells[i], \n",
    "                      force_rerun=force_rerun, \n",
    "                      datafilename=datafilename)\n",
    "print(\"Completed simulation in {:} s\".format(timer.secs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7423fb7780>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "[encoded data, 87176 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 56780 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 66200 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "setBwStyles(fig.gca())\n",
    "plt.title(\"Elapsed time vs number of cells\")\n",
    "for i, simulator in enumerate(simulators):\n",
    "    plt.plot(domain_sizes, sim_elapsed_time[i,:], label=simulator.__name__)\n",
    "plt.legend()\n",
    "    \n",
    "fig = plt.figure()\n",
    "setBwStyles(fig.gca())\n",
    "plt.title(\"Dt vs number of cells\")\n",
    "for i, simulator in enumerate(simulators):\n",
    "    plt.loglog(domain_sizes, sim_dt[i,:], label=simulator.__name__)\n",
    "plt.legend()\n",
    "    \n",
    "fig = plt.figure()\n",
    "setBwStyles(fig.gca())\n",
    "plt.title(\"Number of timesteps vs number of cells\")\n",
    "for i, simulator in enumerate(simulators):\n",
    "    plt.plot(domain_sizes, sim_nt[i,:], label=simulator.__name__)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>8</th>\n",
       "      <th>16</th>\n",
       "      <th>32</th>\n",
       "      <th>64</th>\n",
       "      <th>128</th>\n",
       "      <th>256</th>\n",
       "      <th>512</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LxF</th>\n",
       "      <td>2.109998</td>\n",
       "      <td>1.117344</td>\n",
       "      <td>1.770541</td>\n",
       "      <td>1.130174</td>\n",
       "      <td>1.398593</td>\n",
       "      <td>1.459872</td>\n",
       "      <td>1.585554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FORCE</th>\n",
       "      <td>1.803550</td>\n",
       "      <td>1.058752</td>\n",
       "      <td>1.424818</td>\n",
       "      <td>0.994047</td>\n",
       "      <td>1.264049</td>\n",
       "      <td>1.354103</td>\n",
       "      <td>1.598773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL</th>\n",
       "      <td>1.271458</td>\n",
       "      <td>1.218233</td>\n",
       "      <td>1.018041</td>\n",
       "      <td>1.023368</td>\n",
       "      <td>1.120194</td>\n",
       "      <td>1.259487</td>\n",
       "      <td>1.649370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL2</th>\n",
       "      <td>2.011525</td>\n",
       "      <td>2.450778</td>\n",
       "      <td>0.885168</td>\n",
       "      <td>0.590706</td>\n",
       "      <td>0.819484</td>\n",
       "      <td>1.128430</td>\n",
       "      <td>2.156802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WAF</th>\n",
       "      <td>2.016446</td>\n",
       "      <td>2.483785</td>\n",
       "      <td>1.021645</td>\n",
       "      <td>0.705272</td>\n",
       "      <td>0.891656</td>\n",
       "      <td>0.858559</td>\n",
       "      <td>2.275014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07</th>\n",
       "      <td>1.560495</td>\n",
       "      <td>2.067524</td>\n",
       "      <td>1.738482</td>\n",
       "      <td>2.077667</td>\n",
       "      <td>2.065662</td>\n",
       "      <td>2.206142</td>\n",
       "      <td>2.172162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07_dimsplit</th>\n",
       "      <td>1.896522</td>\n",
       "      <td>2.258217</td>\n",
       "      <td>1.073543</td>\n",
       "      <td>0.676780</td>\n",
       "      <td>0.846475</td>\n",
       "      <td>1.155170</td>\n",
       "      <td>2.138188</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    8         16        32        64        128       256  \\\n",
       "LxF            2.109998  1.117344  1.770541  1.130174  1.398593  1.459872   \n",
       "FORCE          1.803550  1.058752  1.424818  0.994047  1.264049  1.354103   \n",
       "HLL            1.271458  1.218233  1.018041  1.023368  1.120194  1.259487   \n",
       "HLL2           2.011525  2.450778  0.885168  0.590706  0.819484  1.128430   \n",
       "WAF            2.016446  2.483785  1.021645  0.705272  0.891656  0.858559   \n",
       "KP07           1.560495  2.067524  1.738482  2.077667  2.065662  2.206142   \n",
       "KP07_dimsplit  1.896522  2.258217  1.073543  0.676780  0.846475  1.155170   \n",
       "\n",
       "                    512  \n",
       "LxF            1.585554  \n",
       "FORCE          1.598773  \n",
       "HLL            1.649370  \n",
       "HLL2           2.156802  \n",
       "WAF            2.275014  \n",
       "KP07           2.172162  \n",
       "KP07_dimsplit  2.138188  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Max</th>\n",
       "      <th>Min</th>\n",
       "      <th>Mean</th>\n",
       "      <th>Stdev</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LxF</th>\n",
       "      <td>2.109998</td>\n",
       "      <td>1.117344</td>\n",
       "      <td>1.510297</td>\n",
       "      <td>0.326663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FORCE</th>\n",
       "      <td>1.803550</td>\n",
       "      <td>0.994047</td>\n",
       "      <td>1.356870</td>\n",
       "      <td>0.265059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL</th>\n",
       "      <td>1.649370</td>\n",
       "      <td>1.018041</td>\n",
       "      <td>1.222879</td>\n",
       "      <td>0.199257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL2</th>\n",
       "      <td>2.450778</td>\n",
       "      <td>0.590706</td>\n",
       "      <td>1.434699</td>\n",
       "      <td>0.694177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WAF</th>\n",
       "      <td>2.483785</td>\n",
       "      <td>0.705272</td>\n",
       "      <td>1.464625</td>\n",
       "      <td>0.703906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07</th>\n",
       "      <td>2.206142</td>\n",
       "      <td>1.560495</td>\n",
       "      <td>1.984019</td>\n",
       "      <td>0.222584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07_dimsplit</th>\n",
       "      <td>2.258217</td>\n",
       "      <td>0.676780</td>\n",
       "      <td>1.434985</td>\n",
       "      <td>0.599449</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Max       Min      Mean     Stdev\n",
       "LxF            2.109998  1.117344  1.510297  0.326663\n",
       "FORCE          1.803550  0.994047  1.356870  0.265059\n",
       "HLL            1.649370  1.018041  1.222879  0.199257\n",
       "HLL2           2.450778  0.590706  1.434699  0.694177\n",
       "WAF            2.483785  0.705272  1.464625  0.703906\n",
       "KP07           2.206142  1.560495  1.984019  0.222584\n",
       "KP07_dimsplit  2.258217  0.676780  1.434985  0.599449"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from IPython.display import display\n",
    "\n",
    "conservation = np.zeros((len(simulators), len(domain_sizes)))\n",
    "error = np.zeros((len(simulators), len(domain_sizes)))\n",
    "order = np.zeros((len(simulators), len(domain_sizes)-1))\n",
    "\n",
    "for i, simulator in enumerate(simulators):\n",
    "    #Read the reference solution\n",
    "    datafilename = gen_filename(simulator, reference_nx)\n",
    "    with np.load(datafilename) as data:\n",
    "        h_ref = data['h']\n",
    "    \n",
    "    #Compute conservation and error for subsequent resolutions\n",
    "    for j, nx in enumerate(domain_sizes):\n",
    "        #Read current resolution\n",
    "        datafilename = gen_filename(simulator, nx)\n",
    "        with np.load(datafilename) as data:\n",
    "            h = data['h']\n",
    "        \n",
    "        #Downsample reference to current resolution\n",
    "        h_ref_downsampled = downsample(h_ref, reference_nx/nx)\n",
    "        \n",
    "        #Compute error per cell\n",
    "        error[i, j] = np.linalg.norm((h_ref_downsampled - h).flatten(), ord=1) / (nx*nx)\n",
    "        conservation[i, j] = (np.sum(h_ref_downsampled) - np.sum(h))\n",
    "    \n",
    "    #Compute the numerical order\n",
    "    a = np.arange(1, len(domain_sizes))\n",
    "    order[i,:] = np.log2(error[i, :-1] / error[i, 1:])\n",
    "\n",
    "\n",
    "table = pd.DataFrame(order, columns=domain_sizes[:-1], index=[simulator.__name__ for simulator in simulators])\n",
    "display(table)\n",
    "\n",
    "order_summary = pd.DataFrame(np.empty((len(simulators), 4)), columns=['Max', 'Min', 'Mean', 'Stdev'], index=[simulator.__name__ for simulator in simulators])\n",
    "for i, simulator in enumerate(simulators):\n",
    "    order_summary.loc[simulator.__name__] = [np.max(order[i,:]), \n",
    "        np.min(order[i,:]), \n",
    "        np.mean(order[i,:]), \n",
    "        np.std(order[i,:])]\n",
    "display(order_summary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 151188 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "setBwStyles(fig.gca())\n",
    "\n",
    "x = np.linspace(domain_sizes[0], domain_sizes[-1], 100);\n",
    "\n",
    "scaling = np.max(error[:,0]) * domain_sizes[0] * 1.5\n",
    "plt.loglog(x, scaling/x, '-', color='gray', label='Order 1')\n",
    "\n",
    "scaling = np.min(error[:,0]) * domain_sizes[0]**2 * 0.5\n",
    "plt.loglog(x, scaling/(x*x), '-', color='gray', label='Order 2')\n",
    "\n",
    "for i, simulator in enumerate(simulators):\n",
    "    plt.loglog(domain_sizes, error[i,:], label=simulators[i].__name__)\n",
    "\n",
    "plt.xlabel('Number of cells')\n",
    "plt.ylabel('Error')\n",
    "plt.title(\"Convergence\")\n",
    "plt.legend()\n",
    "save_figure(fig, 'convergence')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_solution(simulator, nx, label, **kwargs):\n",
    "    datafilename = gen_filename(simulator, nx)\n",
    "    \n",
    "    #Read the solution\n",
    "    with np.load(datafilename) as data:\n",
    "        h = data['h']\n",
    "        h = h[int(nx/2),:]\n",
    "        \n",
    "    x = np.linspace(0.5, nx-0.5, nx)*100.0/float(nx)\n",
    "    \n",
    "    plt.plot(x, h, label=label, **kwargs)\n",
    "    \n",
    "    h = None\n",
    "    x = None\n",
    "    gc.collect() # Force run garbage collection to free up memory\n",
    "    \n",
    "def plot_comparison(nx, **kwargs):\n",
    "    plot_solution(HLL2.HLL2, reference_nx, 'Reference', marker=' ', linestyle='-')\n",
    "\n",
    "    for i, simulator in enumerate(simulators):\n",
    "        plot_solution(simulator, nx, simulator.__name__, **kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 181304 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxes = np.array([\\\n",
    "         [[28, 35], [0.499, 0.516]], \\\n",
    "         [[45, 56], [0.58, 0.60]]\n",
    "         ])\n",
    "comparison_nx = 32\n",
    "\n",
    "fig = plt.figure(figsize=(12, 12))\n",
    "gs = gridspec.GridSpec(2, 2)\n",
    "    \n",
    "ax1 = fig.add_subplot(gs[0,:])\n",
    "setBwStyles(ax1)\n",
    "for simulator in simulators:\n",
    "    plot_solution(simulator, comparison_nx, simulator.__name__, marker=' ')\n",
    "for box_x, box_y in boxes:\n",
    "    x = np.kron(box_x, np.ones((2)))\n",
    "    y = np.hstack((box_y, box_y[::-1]))\n",
    "    fig.gca().fill(x, y, fill=True, linestyle='-', color='gray', alpha=0.5)\n",
    "plt.title(\"Comparison of solutions at nx=\" + str(comparison_nx))\n",
    "plt.legend()\n",
    "\n",
    "ax2 = fig.add_subplot(gs[1,0])\n",
    "setBwStyles(ax2)\n",
    "for simulator in simulators:\n",
    "    plot_solution(simulator, comparison_nx, simulator.__name__, markevery=2)\n",
    "plt.xlim(boxes[0, 0])\n",
    "plt.ylim(boxes[0, 1])\n",
    "\n",
    "ax3 = fig.add_subplot(gs[1,1])\n",
    "setBwStyles(ax3)\n",
    "setBwStyles(ax2)\n",
    "for simulator in simulators:\n",
    "    plot_solution(simulator, comparison_nx, simulator.__name__, markevery=2)\n",
    "plt.xlim(boxes[1, 0])\n",
    "plt.ylim(boxes[1, 1])\n",
    "    \n",
    "save_figure(fig, 'solution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 110808 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12, 12))\n",
    "gs = gridspec.GridSpec(2, 2)\n",
    "    \n",
    "ax1 = fig.add_subplot(gs[0,:])\n",
    "setBwStyles(ax1)\n",
    "for simulator in simulators:\n",
    "    plot_solution(simulator, reference_nx, simulator.__name__, marker=' ')\n",
    "for box_x, box_y in boxes:\n",
    "    x = np.kron(box_x, np.ones((2)))\n",
    "    y = np.hstack((box_y, box_y[::-1]))\n",
    "    fig.gca().fill(x, y, fill=True, linestyle='-', color='gray', alpha=0.5)\n",
    "plt.title(\"Comparison of reference solutions\")\n",
    "plt.legend()\n",
    "\n",
    "ax2 = fig.add_subplot(gs[1,0])\n",
    "setBwStyles(ax2)\n",
    "for simulator in simulators:\n",
    "    plot_solution(simulator, reference_nx, simulator.__name__, marker=' ')\n",
    "plt.xlim(boxes[0, 0])\n",
    "plt.ylim(boxes[0, 1])\n",
    "\n",
    "ax3 = fig.add_subplot(gs[1,1])\n",
    "setBwStyles(ax3)\n",
    "setBwStyles(ax2)\n",
    "for simulator in simulators:\n",
    "    plot_solution(simulator, reference_nx, simulator.__name__, marker=' ')\n",
    "plt.xlim(boxes[1, 0])\n",
    "plt.ylim(boxes[1, 1])\n",
    "    \n",
    "save_figure(fig, 'reference_solutions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 200616 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 200596 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 189852 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 177816 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 176048 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 178816 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 180020 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxes = np.array([\\\n",
    "         [[28, 35], [0.499, 0.516]], \\\n",
    "         [[45, 56], [0.58, 0.60]]\n",
    "         ])\n",
    "\n",
    "for simulator in simulators:\n",
    "    fig = plt.figure(figsize=(12, 12))\n",
    "    \n",
    "    gs = gridspec.GridSpec(2, 2)\n",
    "    \n",
    "    ax1 = fig.add_subplot(gs[0,:])\n",
    "    setBwStyles(ax1)\n",
    "    plot_solution(simulator, reference_nx, 'Reference', linestyle='-', marker=' ')\n",
    "    for j, nx in enumerate(domain_sizes):\n",
    "        plot_solution(simulator, nx, 'nx=' + str(nx), marker=' ')\n",
    "    for box_x, box_y in boxes:\n",
    "        x = np.kron(box_x, np.ones((2)))\n",
    "        y = np.hstack((box_y, box_y[::-1]))\n",
    "        fig.gca().fill(x, y, fill=True, linestyle='-', color='gray', alpha=0.5)\n",
    "    plt.title(str(simulator.__name__))\n",
    "    plt.legend()\n",
    "    \n",
    "    ax2 = fig.add_subplot(gs[1,0])\n",
    "    setBwStyles(ax2)\n",
    "    plot_solution(simulator, reference_nx, 'Reference', linestyle='-', marker=' ')\n",
    "    for j, nx in enumerate(domain_sizes):\n",
    "        plot_solution(simulator, nx, 'nx=' + str(nx), marker=' ')  \n",
    "    plt.xlim(boxes[0, 0])\n",
    "    plt.ylim(boxes[0, 1])\n",
    "    \n",
    "    ax3 = fig.add_subplot(gs[1,1])\n",
    "    setBwStyles(ax3)\n",
    "    plot_solution(simulator, reference_nx, 'Reference', linestyle='-', marker=' ')\n",
    "    for j, nx in enumerate(domain_sizes):\n",
    "        plot_solution(simulator, nx, 'nx=' + str(nx), marker=' ')   \n",
    "    plt.xlim(boxes[1, 0])\n",
    "    plt.ylim(boxes[1, 1])\n",
    "    \n",
    "    save_figure(fig, simulator.__name__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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