{
 "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 socket\n",
    "import time\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": [
    "#Finally, import our simulator\n",
    "from GPUSimulators import Common, LxF, FORCE, HLL, HLL2, KP07, KP07_dimsplit, WAF, IPythonMagic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Console logger using level INFO\n",
      "File logger using level DEBUG to output.log\n",
      "Python version 3.6.5 |Anaconda custom (64-bit)| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]\n",
      "Registering cuda_context in user workspace\n",
      "PyCUDA version 2017.1.1\n",
      "CUDA version (9, 1, 0)\n",
      "Driver version 9010\n",
      "Using 'GeForce 840M' GPU\n",
      "Created context handle <759106976560>\n",
      "Using CUDA cache dir c:\\Users\\anbro\\Documents\\projects\\GPUSimulators\\GPUSimulators\\cuda_cache\n",
      "Autotuning enabled. It may take several minutes to run the code the first time: have patience\n"
     ]
    }
   ],
   "source": [
    "%setup_logging\n",
    "%cuda_context_handler cuda_context"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def save_figure(fig, stem):\n",
    "    if (not os.path.isdir(\"figures\")):\n",
    "        os.mkdir(\"figures\")\n",
    "    \n",
    "    fig_filename = os.path.join(\"figures\", \"convergence_smooth1d_\" + stem + \".pdf\")\n",
    "    \n",
    "    metadata = {\n",
    "        'created': time.strftime(\"%Y_%m_%d-%H_%M_%S\"),\n",
    "        'hostname': socket.gethostname()\n",
    "    }\n",
    "        \n",
    "    legend = fig.gca().legend_\n",
    "    if (legend != None):\n",
    "        fig.savefig(fig_filename, dpi=300,format='pdf',\n",
    "                transparent=True, pad_inches=0.0, frameon=None, \n",
    "                metadata=metadata, \n",
    "                bbox_extra_artists=(legend, ), bbox_inches='tight')\n",
    "    else:\n",
    "        fig.savefig(fig_filename, dpi=300,format='pdf',\n",
    "                transparent=True, pad_inches=0.0, frameon=None, \n",
    "                metadata=metadata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 11300 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 61812 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def downsample(highres_solution, factor):\n",
    "    if (len(highres_solution.shape) == 1):\n",
    "        highres_solution = highres_solution.reshape((1, highres_solution.size))\n",
    "\n",
    "    assert(highres_solution.shape[1] % factor == 0)\n",
    "    ny = highres_solution.shape[0] \n",
    "    nx = highres_solution.shape[1] / factor\n",
    "\n",
    "    if (factor == 1):\n",
    "        return highres_solution\n",
    "    else:\n",
    "        \n",
    "        return highres_solution.reshape([int(ny), int(1), int(nx), int(factor)]).mean(3).mean(1)\n",
    "    \n",
    "\n",
    "# Test 2D downsample\n",
    "a = np.arange(60).reshape((6, 10))\n",
    "b = downsample(a, 2)\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(1,2,1)\n",
    "plt.imshow(a, extent=[0, 1, 0, 1])\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.imshow(b, extent=[0, 1, 0, 1])\n",
    "plt.show()\n",
    "\n",
    "# Test 1D downsample\n",
    "a = np.sin(np.linspace(0, 2*np.pi, 40))\n",
    "b = downsample(a, 4)\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(np.linspace(0, 1, a.size), a.flatten(), 'x-')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(np.linspace(0, 1, b.size), b.flatten(), 'x-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wall_boundary_conditions(data, num_ghost_cells):\n",
    "    data[0:num_ghost_cells,:] = data[2*num_ghost_cells-1:num_ghost_cells-1:-1,:]\n",
    "    data[-num_ghost_cells:,:] = data[-num_ghost_cells-1:-2*num_ghost_cells-1:-1,:]\n",
    "    data[:,0:num_ghost_cells] = data[:,2*num_ghost_cells-1:num_ghost_cells-1:-1]\n",
    "    data[:,-num_ghost_cells:] = data[:,-num_ghost_cells-1:-2*num_ghost_cells-1:-1]\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 25296 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 50.0, 0.27710612593755635]\n"
     ]
    }
   ],
   "source": [
    "def gen_test_data(nx, ref_nx, g, num_ghost_cells):\n",
    "    assert(num_ghost_cells >= 1)\n",
    "    ref_ny = num_ghost_cells\n",
    "    ny = ref_ny\n",
    "    \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)\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",
    "    \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",
    "    #Fix boundary conditions\n",
    "    h = wall_boundary_conditions(h, num_ghost_cells);\n",
    "    hu = wall_boundary_conditions(hu, num_ghost_cells);\n",
    "    \n",
    "    scale = 0.7\n",
    "    max_h_estimate = 0.6\n",
    "    max_u_estimate = 0.1\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, ref_nx=1000, 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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: created\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n",
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: hostname\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 44888 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot initial conditions            \n",
    "fig = plt.figure()\n",
    "setBwStyles(fig.gca())\n",
    "\n",
    "for nx in [128, 1024, 16384]:\n",
    "    h0, hu0, hv0, dx, dy, dt = gen_test_data(nx, nx, 9.81, 1)\n",
    "    x = np.linspace(0.0, nx*dx, nx)\n",
    "    \n",
    "    #plt.subplot(211)\n",
    "    plt.plot(x, h0[1:-1, 1:-1].flatten(), marker=' ', label='h_' + str(nx))\n",
    "    plt.plot(x, hu0[1:-1, 1:-1].flatten(), marker=' ', label='hu_' + str(nx))\n",
    "    #plt.subplot(212)\n",
    "    #setBwStyles(fig.gca())\n",
    "    #plt.plot(x, hu0.T, marker=\" \", label='hu_' + str(nx))\n",
    "    #plt.legend(loc='upper left')\n",
    "    \n",
    "#plt.xlim([47, 53])\n",
    "#plt.ylim([0.58, 0.61])\n",
    "plt.legend(loc='upper left')\n",
    "save_figure(fig, 'initial_conditions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_filename(simulator, nx):\n",
    "    return os.path.abspath(os.path.join(\"data\", \"smooth1d\", str(simulator.__name__) + \"_\" + str(nx) + \".npz\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sanity_check(variable, variable_name):\n",
    "    maxval = np.amax(variable)\n",
    "    minval = np.amin(variable)\n",
    "    assert np.isnan(maxval) == False and np.isnan(minval) == False, variable_name + \" contains NaN values\"\n",
    "\n",
    "def run_benchmark(datafilename, simulator, courant_number, nx, reference_nx, \n",
    "                  ghost_cells, g=9.81, force_rerun=False, transpose=False):\n",
    "\n",
    "    if (datafilename and os.path.isfile(datafilename) and force_rerun == False):\n",
    "        print(\"WARNING: Existing simulation exists, skipping simulation\")\n",
    "        return [0, 0, 0]\n",
    "    else:\n",
    "        h0, hu0, hv0, dx, dy, dt = gen_test_data(nx, reference_nx, g, ghost_cells)\n",
    "        ny = ghost_cells\n",
    "        dt = dt * courant_number\n",
    "\n",
    "        #Initialize simulator\n",
    "        with Common.Timer(simulator.__name__ + \"_\" + str(nx)) as timer:\n",
    "            if (transpose):\n",
    "                h0 = np.ascontiguousarray(np.transpose(h0))\n",
    "                hu0, hv0 = np.ascontiguousarray(np.transpose(hv0)), np.ascontiguousarray(np.transpose(hu0))\n",
    "                dx, dy = dy, dx\n",
    "                nx, ny = ny, nx\n",
    "\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",
    "            if (transpose):\n",
    "                h = np.ascontiguousarray(np.transpose(h))\n",
    "                hu, hv = np.ascontiguousarray(np.transpose(hv)), np.ascontiguousarray(np.transpose(hu))\n",
    "            \n",
    "            sanity_check(h, \"h\")\n",
    "            sanity_check(hu, \"hu\")\n",
    "            sanity_check(hv, \"hv\")\n",
    "\n",
    "            if (datafilename):\n",
    "                dirname = os.path.dirname(datafilename)\n",
    "                if (dirname and not os.path.isdir(dirname)):\n",
    "                    os.makedirs(dirname)\n",
    "                np.savez_compressed(datafilename, h=h, hu=hu, hv=hv)\n",
    "        \n",
    "    gc.collect() # Force run garbage collection to free up memory\n",
    "    \n",
    "    return [timer.secs, nt, dt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "LxF [1x16] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "FORCE [1x16] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "HLL [1x16] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "HLL2 [2x16] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "KP07 [2x16] simulated 1.000000 seconds to 1.000000 with 1 steps (RK2)\n",
      "KP07_dimsplit [2x16] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "WAF [2x16] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Completed warmup in 0.9176511764526367 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "LxF [1x8] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "LxF [1x16] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "LxF [1x32] simulated 1.000000 seconds to 1.000000 with 2 steps (Euler)\n",
      "LxF [1x64] simulated 1.000000 seconds to 1.000000 with 3 steps (Euler)\n",
      "LxF [1x128] simulated 1.000000 seconds to 1.000000 with 6 steps (Euler)\n",
      "LxF [1x256] simulated 1.000000 seconds to 1.000000 with 11 steps (Euler)\n",
      "LxF [1x512] simulated 1.000000 seconds to 1.000000 with 21 steps (Euler)\n",
      "LxF [1x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (Euler)\n",
      "LxF [1x2048] simulated 1.000000 seconds to 1.000000 with 83 steps (Euler)\n",
      "LxF [1x4096] simulated 1.000000 seconds to 1.000000 with 165 steps (Euler)\n",
      "LxF [1x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (Euler)\n",
      "FORCE [1x8] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "FORCE [1x16] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "FORCE [1x32] simulated 1.000000 seconds to 1.000000 with 2 steps (Euler)\n",
      "FORCE [1x64] simulated 1.000000 seconds to 1.000000 with 3 steps (Euler)\n",
      "FORCE [1x128] simulated 1.000000 seconds to 1.000000 with 6 steps (Euler)\n",
      "FORCE [1x256] simulated 1.000000 seconds to 1.000000 with 11 steps (Euler)\n",
      "FORCE [1x512] simulated 1.000000 seconds to 1.000000 with 21 steps (Euler)\n",
      "FORCE [1x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (Euler)\n",
      "FORCE [1x2048] simulated 1.000000 seconds to 1.000000 with 83 steps (Euler)\n",
      "FORCE [1x4096] simulated 1.000000 seconds to 1.000000 with 165 steps (Euler)\n",
      "FORCE [1x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (Euler)\n",
      "HLL [1x8] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "HLL [1x16] simulated 1.000000 seconds to 1.000000 with 1 steps (Euler)\n",
      "HLL [1x32] simulated 1.000000 seconds to 1.000000 with 2 steps (Euler)\n",
      "HLL [1x64] simulated 1.000000 seconds to 1.000000 with 3 steps (Euler)\n",
      "HLL [1x128] simulated 1.000000 seconds to 1.000000 with 6 steps (Euler)\n",
      "HLL [1x256] simulated 1.000000 seconds to 1.000000 with 11 steps (Euler)\n",
      "HLL [1x512] simulated 1.000000 seconds to 1.000000 with 21 steps (Euler)\n",
      "HLL [1x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (Euler)\n",
      "HLL [1x2048] simulated 1.000000 seconds to 1.000000 with 83 steps (Euler)\n",
      "HLL [1x4096] simulated 1.000000 seconds to 1.000000 with 165 steps (Euler)\n",
      "HLL [1x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (Euler)\n",
      "HLL2 [2x8] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "HLL2 [2x16] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "HLL2 [2x32] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "HLL2 [2x64] simulated 1.000000 seconds to 1.000000 with 4 steps (dimsplit)\n",
      "HLL2 [2x128] simulated 1.000000 seconds to 1.000000 with 6 steps (dimsplit)\n",
      "HLL2 [2x256] simulated 1.000000 seconds to 1.000000 with 12 steps (dimsplit)\n",
      "HLL2 [2x512] simulated 1.000000 seconds to 1.000000 with 22 steps (dimsplit)\n",
      "HLL2 [2x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (dimsplit)\n",
      "HLL2 [2x2048] simulated 1.000000 seconds to 1.000000 with 84 steps (dimsplit)\n",
      "HLL2 [2x4096] simulated 1.000000 seconds to 1.000000 with 166 steps (dimsplit)\n",
      "HLL2 [2x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (dimsplit)\n",
      "KP07 [2x8] simulated 1.000000 seconds to 1.000000 with 1 steps (RK2)\n",
      "KP07 [2x16] simulated 1.000000 seconds to 1.000000 with 1 steps (RK2)\n",
      "KP07 [2x32] simulated 1.000000 seconds to 1.000000 with 2 steps (RK2)\n",
      "KP07 [2x64] simulated 1.000000 seconds to 1.000000 with 3 steps (RK2)\n",
      "KP07 [2x128] simulated 1.000000 seconds to 1.000000 with 6 steps (RK2)\n",
      "KP07 [2x256] simulated 1.000000 seconds to 1.000000 with 11 steps (RK2)\n",
      "KP07 [2x512] simulated 1.000000 seconds to 1.000000 with 21 steps (RK2)\n",
      "KP07 [2x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (RK2)\n",
      "KP07 [2x2048] simulated 1.000000 seconds to 1.000000 with 83 steps (RK2)\n",
      "KP07 [2x4096] simulated 1.000000 seconds to 1.000000 with 165 steps (RK2)\n",
      "KP07 [2x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (RK2)\n",
      "KP07_dimsplit [2x8] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "KP07_dimsplit [2x16] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "KP07_dimsplit [2x32] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "KP07_dimsplit [2x64] simulated 1.000000 seconds to 1.000000 with 4 steps (dimsplit)\n",
      "KP07_dimsplit [2x128] simulated 1.000000 seconds to 1.000000 with 6 steps (dimsplit)\n",
      "KP07_dimsplit [2x256] simulated 1.000000 seconds to 1.000000 with 12 steps (dimsplit)\n",
      "KP07_dimsplit [2x512] simulated 1.000000 seconds to 1.000000 with 22 steps (dimsplit)\n",
      "KP07_dimsplit [2x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (dimsplit)\n",
      "KP07_dimsplit [2x2048] simulated 1.000000 seconds to 1.000000 with 84 steps (dimsplit)\n",
      "KP07_dimsplit [2x4096] simulated 1.000000 seconds to 1.000000 with 166 steps (dimsplit)\n",
      "KP07_dimsplit [2x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (dimsplit)\n",
      "WAF [2x8] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "WAF [2x16] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "WAF [2x32] simulated 1.000000 seconds to 1.000000 with 2 steps (dimsplit)\n",
      "WAF [2x64] simulated 1.000000 seconds to 1.000000 with 4 steps (dimsplit)\n",
      "WAF [2x128] simulated 1.000000 seconds to 1.000000 with 6 steps (dimsplit)\n",
      "WAF [2x256] simulated 1.000000 seconds to 1.000000 with 12 steps (dimsplit)\n",
      "WAF [2x512] simulated 1.000000 seconds to 1.000000 with 22 steps (dimsplit)\n",
      "WAF [2x1024] simulated 1.000000 seconds to 1.000000 with 42 steps (dimsplit)\n",
      "WAF [2x2048] simulated 1.000000 seconds to 1.000000 with 84 steps (dimsplit)\n",
      "WAF [2x4096] simulated 1.000000 seconds to 1.000000 with 166 steps (dimsplit)\n",
      "WAF [2x16384] simulated 1.000000 seconds to 1.000000 with 1314 steps (dimsplit)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Completed simulation in 19.930959224700928 s\n"
     ]
    }
   ],
   "source": [
    "reference_nx = 16384\n",
    "domain_sizes = [8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]\n",
    "#domain_sizes = [8, 16, 32, 64, 128, 256]\n",
    "#domain_sizes = [8, 16, 32]\n",
    "\n",
    "simulators = [LxF.LxF, FORCE.FORCE, HLL.HLL, HLL2.HLL2, KP07.KP07, KP07_dimsplit.KP07_dimsplit, WAF.WAF]\n",
    "simulator_ghost_cells = [1, 1, 1, 2, 2, 2, 2]\n",
    "simulator_reference = [LxF.LxF, FORCE.FORCE, HLL.HLL, HLL2.HLL2, KP07.KP07, KP07_dimsplit.KP07_dimsplit, WAF.WAF]\n",
    "simulator_courant_numbers = [0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9]\n",
    "force_rerun=True\n",
    "transpose=True\n",
    "\n",
    "#reference_nx = 4096\n",
    "#domain_sizes = [32, 64, 128, 256, 512, 1024]\n",
    "#simulators = [HLL2.HLL2, WAF.WAF]\n",
    "#simulator_ghost_cells = [2, 2]\n",
    "#simulator_reference = [HLL2.HLL2, WAF.WAF]\n",
    "#simulator_courant_numbers = [0.95, 0.95]\n",
    "#force_rerun=True\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(None, \n",
    "                      simulators[i], \n",
    "                      simulator_courant_numbers[i], \n",
    "                      16, 16, \n",
    "                      simulator_ghost_cells[i], \n",
    "                      force_rerun=force_rerun,\n",
    "                      transpose=transpose)\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(datafilename, \n",
    "                          simulators[i], \n",
    "                          simulator_courant_numbers[i], \n",
    "                          nx, reference_nx, \n",
    "                          simulator_ghost_cells[i], \n",
    "                          force_rerun=force_rerun,\n",
    "                          transpose=transpose)\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(datafilename, \n",
    "                      simulators[i], \n",
    "                      simulator_courant_numbers[i] * 0.5, \n",
    "                      reference_nx, reference_nx, \n",
    "                      simulator_ghost_cells[i], \n",
    "                      force_rerun=force_rerun,\n",
    "                      transpose=transpose)\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 0xb0c6bd1710>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "[encoded data, 115580 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 43120 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 55348 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": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: created\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n",
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: hostname\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 132724 characters]\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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'].astype(np.float64)\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'].astype(np.float64)\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\n",
    "        conservation[i, j] = (np.sum(h_ref) - 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",
    "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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</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",
       "      <th>1024</th>\n",
       "      <th>2048</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LxF</th>\n",
       "      <td>2.046113</td>\n",
       "      <td>1.074352</td>\n",
       "      <td>1.834396</td>\n",
       "      <td>1.165695</td>\n",
       "      <td>1.413403</td>\n",
       "      <td>1.434256</td>\n",
       "      <td>1.528817</td>\n",
       "      <td>1.582837</td>\n",
       "      <td>-0.651759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FORCE</th>\n",
       "      <td>1.843822</td>\n",
       "      <td>0.964271</td>\n",
       "      <td>1.528033</td>\n",
       "      <td>1.060319</td>\n",
       "      <td>1.226514</td>\n",
       "      <td>1.207009</td>\n",
       "      <td>1.225253</td>\n",
       "      <td>1.552378</td>\n",
       "      <td>1.701265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL</th>\n",
       "      <td>0.959727</td>\n",
       "      <td>1.222380</td>\n",
       "      <td>1.098404</td>\n",
       "      <td>1.174641</td>\n",
       "      <td>1.077480</td>\n",
       "      <td>1.167240</td>\n",
       "      <td>1.380064</td>\n",
       "      <td>1.709250</td>\n",
       "      <td>0.591226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL2</th>\n",
       "      <td>2.108358</td>\n",
       "      <td>2.912787</td>\n",
       "      <td>2.417060</td>\n",
       "      <td>1.994055</td>\n",
       "      <td>0.793664</td>\n",
       "      <td>0.095366</td>\n",
       "      <td>0.006444</td>\n",
       "      <td>0.001872</td>\n",
       "      <td>0.001645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07</th>\n",
       "      <td>1.469653</td>\n",
       "      <td>1.925581</td>\n",
       "      <td>1.846695</td>\n",
       "      <td>2.178919</td>\n",
       "      <td>2.111979</td>\n",
       "      <td>0.766464</td>\n",
       "      <td>0.002079</td>\n",
       "      <td>-0.026937</td>\n",
       "      <td>-0.005820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07_dimsplit</th>\n",
       "      <td>2.133728</td>\n",
       "      <td>2.334123</td>\n",
       "      <td>2.387310</td>\n",
       "      <td>1.989174</td>\n",
       "      <td>1.251513</td>\n",
       "      <td>0.217078</td>\n",
       "      <td>0.025907</td>\n",
       "      <td>0.006118</td>\n",
       "      <td>0.000582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WAF</th>\n",
       "      <td>2.095988</td>\n",
       "      <td>2.662524</td>\n",
       "      <td>1.904090</td>\n",
       "      <td>2.028226</td>\n",
       "      <td>1.823600</td>\n",
       "      <td>0.581859</td>\n",
       "      <td>0.125404</td>\n",
       "      <td>0.007799</td>\n",
       "      <td>-0.000888</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   8         16        32        64        128       256   \\\n",
       "LxF            2.046113  1.074352  1.834396  1.165695  1.413403  1.434256   \n",
       "FORCE          1.843822  0.964271  1.528033  1.060319  1.226514  1.207009   \n",
       "HLL            0.959727  1.222380  1.098404  1.174641  1.077480  1.167240   \n",
       "HLL2           2.108358  2.912787  2.417060  1.994055  0.793664  0.095366   \n",
       "KP07           1.469653  1.925581  1.846695  2.178919  2.111979  0.766464   \n",
       "KP07_dimsplit  2.133728  2.334123  2.387310  1.989174  1.251513  0.217078   \n",
       "WAF            2.095988  2.662524  1.904090  2.028226  1.823600  0.581859   \n",
       "\n",
       "                   512       1024      2048  \n",
       "LxF            1.528817  1.582837 -0.651759  \n",
       "FORCE          1.225253  1.552378  1.701265  \n",
       "HLL            1.380064  1.709250  0.591226  \n",
       "HLL2           0.006444  0.001872  0.001645  \n",
       "KP07           0.002079 -0.026937 -0.005820  \n",
       "KP07_dimsplit  0.025907  0.006118  0.000582  \n",
       "WAF            0.125404  0.007799 -0.000888  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Max</th>\n",
       "      <th>Min</th>\n",
       "      <th>Mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LxF</th>\n",
       "      <td>2.046113</td>\n",
       "      <td>-0.651759</td>\n",
       "      <td>1.269790</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FORCE</th>\n",
       "      <td>1.843822</td>\n",
       "      <td>0.964271</td>\n",
       "      <td>1.367651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL</th>\n",
       "      <td>1.709250</td>\n",
       "      <td>0.591226</td>\n",
       "      <td>1.153379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HLL2</th>\n",
       "      <td>2.912787</td>\n",
       "      <td>0.001645</td>\n",
       "      <td>1.147917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07</th>\n",
       "      <td>2.178919</td>\n",
       "      <td>-0.026937</td>\n",
       "      <td>1.140957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KP07_dimsplit</th>\n",
       "      <td>2.387310</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>1.149504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WAF</th>\n",
       "      <td>2.662524</td>\n",
       "      <td>-0.000888</td>\n",
       "      <td>1.247623</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                    Max       Min      Mean\n",
       "LxF            2.046113 -0.651759  1.269790\n",
       "FORCE          1.843822  0.964271  1.367651\n",
       "HLL            1.709250  0.591226  1.153379\n",
       "HLL2           2.912787  0.001645  1.147917\n",
       "KP07           2.178919 -0.026937  1.140957\n",
       "KP07_dimsplit  2.387310  0.000582  1.149504\n",
       "WAF            2.662524 -0.000888  1.247623"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from IPython.display import display\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), 3)), columns=['Max', 'Min', 'Mean'], 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",
    "display(order_summary)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: created\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n",
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: hostname\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 135004 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",
    "for i, simulator in enumerate(simulators):\n",
    "    plt.plot(order[i,:], label=simulator.__name__)\n",
    "    \n",
    "plt.ylim([0, 3])\n",
    "plt.xlabel('Number of cells')\n",
    "plt.ylabel('Order')\n",
    "plt.legend()\n",
    "plt.title(\"Numerical order\")\n",
    "save_figure(fig, 'numerical_order')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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",
    "        \n",
    "    x = np.linspace(0.5, nx-0.5, nx)*100.0/float(nx)\n",
    "    y = h[0,:]\n",
    "    \n",
    "    plt.plot(x, y, 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": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: created\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n",
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: hostname\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 168772 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": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: created\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n",
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: hostname\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 89472 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": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: created\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n",
      "c:\\Users\\anbro\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_pdf.py:1579: UserWarning: Unknown infodict keyword: hostname\n",
      "  warnings.warn('Unknown infodict keyword: %s' % k)\n"
     ]
    },
    {
     "data": {
      "image/png": "[encoded data, 195592 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 201600 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 193252 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 175520 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 179104 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 176892 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "[encoded data, 175828 characters]\n",
      "text/plain": [
       "<Figure size 1200x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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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