docs/Bogacki_Shampine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bogacki Shampine method & Duffing's equation\n",
    "\n",
    "[Bogacki-Shampine's](https://doi.org/10.1016/0898-1221%2896%2900141-1) method of order (4,5) is used to solve Duffing's equation (E3 from the [DETEST](http://perso.ensta-paristech.fr/~chapoutot/integration/docs/p1-enright.pdf) set).\n",
    "\n",
    "The class `BS45` codes the method as intended by Bogacki and Shampine. It contains a highly accurate fifth order interpolant. The class `BS45_i` is a variation with a fourth order interpolant of lower accuracy. This interpolant is free: it does not require extra fucntion evaluations. The difference between the two methods will be demonstrated.\n",
    "\n",
    "## Problem definition\n",
    "\n",
    "Duffing's equation models a mass spring system with a non-linear spring. In this case, the system is undamped, with a softening spring and a sinusoidal exitation force."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin\n",
    "\n",
    "problem = {'fun' : lambda t, y: [y[1], y[0]**3/6 - y[0] + 2*sin(2.78535*t)],\n",
    "            'y0' : [0., 0.],\n",
    "        't_span' : [0., 20.]}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reference solution\n",
    "\n",
    "First, a reference solution is created by solving this problem with low tolerance and the high order method `DOP853`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "reference = solve_ivp(**problem, atol=1e-12, rtol=1e-12, method='DOP853', dense_output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution plot\n",
    "\n",
    "A plot gives an idea about the solution. The response appears to have two sine components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<!-- Created with matplotlib (https://matplotlib.org/) -->\r\n<svg height=\"263.63625pt\" version=\"1.1\" viewBox=\"0 0 380.482813 263.63625\" width=\"380.482813pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-02-10T08:19:09.593838</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.3.2, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n </defs>\r\n <g id=\"figure_1\">\r\n  <g id=\"patch_1\">\r\n   <path d=\"M -0 263.63625 \r\nL 380.482813 263.63625 \r\nL 380.482813 0 \r\nL -0 0 \r\nz\r\n\" style=\"fill:none;\"/>\r\n  </g>\r\n  <g id=\"axes_1\">\r\n   <g id=\"patch_2\">\r\n    <path d=\"M 38.482813 239.758125 \r\nL 373.282813 239.758125 \r\nL 373.282813 22.318125 \r\nL 38.482813 22.318125 \r\nz\r\n\" style=\"fill:#ffffff;\"/>\r\n   </g>\r\n   <g id=\"matplotlib.axis_1\">\r\n    <g id=\"xtick_1\">\r\n     <g id=\"line2d_1\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL 0 3.5 \r\n\" id=\"mf77fefe674\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"53.700994\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_1\">\r\n      <!-- 0.0 -->\r\n      <g transform=\"translate(45.749432 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 31.78125 66.40625 \r\nQ 24.171875 66.40625 20.328125 58.90625 \r\nQ 16.5 51.421875 16.5 36.375 \r\nQ 16.5 21.390625 20.328125 13.890625 \r\nQ 24.171875 6.390625 31.78125 6.390625 \r\nQ 39.453125 6.390625 43.28125 13.890625 \r\nQ 47.125 21.390625 47.125 36.375 \r\nQ 47.125 51.421875 43.28125 58.90625 \r\nQ 39.453125 66.40625 31.78125 66.40625 \r\nz\r\nM 31.78125 74.21875 \r\nQ 44.046875 74.21875 50.515625 64.515625 \r\nQ 56.984375 54.828125 56.984375 36.375 \r\nQ 56.984375 17.96875 50.515625 8.265625 \r\nQ 44.046875 -1.421875 31.78125 -1.421875 \r\nQ 19.53125 -1.421875 13.0625 8.265625 \r\nQ 6.59375 17.96875 6.59375 36.375 \r\nQ 6.59375 54.828125 13.0625 64.515625 \r\nQ 19.53125 74.21875 31.78125 74.21875 \r\nz\r\n\" id=\"DejaVuSans-48\"/>\r\n        <path d=\"M 10.6875 12.40625 \r\nL 21 12.40625 \r\nL 21 0 \r\nL 10.6875 0 \r\nz\r\n\" id=\"DejaVuSans-46\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_2\">\r\n     <g id=\"line2d_2\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"91.746449\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_2\">\r\n      <!-- 2.5 -->\r\n      <g transform=\"translate(83.794886 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 19.1875 8.296875 \r\nL 53.609375 8.296875 \r\nL 53.609375 0 \r\nL 7.328125 0 \r\nL 7.328125 8.296875 \r\nQ 12.9375 14.109375 22.625 23.890625 \r\nQ 32.328125 33.6875 34.8125 36.53125 \r\nQ 39.546875 41.84375 41.421875 45.53125 \r\nQ 43.3125 49.21875 43.3125 52.78125 \r\nQ 43.3125 58.59375 39.234375 62.25 \r\nQ 35.15625 65.921875 28.609375 65.921875 \r\nQ 23.96875 65.921875 18.8125 64.3125 \r\nQ 13.671875 62.703125 7.8125 59.421875 \r\nL 7.8125 69.390625 \r\nQ 13.765625 71.78125 18.9375 73 \r\nQ 24.125 74.21875 28.421875 74.21875 \r\nQ 39.75 74.21875 46.484375 68.546875 \r\nQ 53.21875 62.890625 53.21875 53.421875 \r\nQ 53.21875 48.921875 51.53125 44.890625 \r\nQ 49.859375 40.875 45.40625 35.40625 \r\nQ 44.1875 33.984375 37.640625 27.21875 \r\nQ 31.109375 20.453125 19.1875 8.296875 \r\nz\r\n\" id=\"DejaVuSans-50\"/>\r\n        <path d=\"M 10.796875 72.90625 \r\nL 49.515625 72.90625 \r\nL 49.515625 64.59375 \r\nL 19.828125 64.59375 \r\nL 19.828125 46.734375 \r\nQ 21.96875 47.46875 24.109375 47.828125 \r\nQ 26.265625 48.1875 28.421875 48.1875 \r\nQ 40.625 48.1875 47.75 41.5 \r\nQ 54.890625 34.8125 54.890625 23.390625 \r\nQ 54.890625 11.625 47.5625 5.09375 \r\nQ 40.234375 -1.421875 26.90625 -1.421875 \r\nQ 22.3125 -1.421875 17.546875 -0.640625 \r\nQ 12.796875 0.140625 7.71875 1.703125 \r\nL 7.71875 11.625 \r\nQ 12.109375 9.234375 16.796875 8.0625 \r\nQ 21.484375 6.890625 26.703125 6.890625 \r\nQ 35.15625 6.890625 40.078125 11.328125 \r\nQ 45.015625 15.765625 45.015625 23.390625 \r\nQ 45.015625 31 40.078125 35.4375 \r\nQ 35.15625 39.890625 26.703125 39.890625 \r\nQ 22.75 39.890625 18.8125 39.015625 \r\nQ 14.890625 38.140625 10.796875 36.28125 \r\nz\r\n\" id=\"DejaVuSans-53\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_3\">\r\n     <g id=\"line2d_3\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"129.791903\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_3\">\r\n      <!-- 5.0 -->\r\n      <g transform=\"translate(121.840341 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-53\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_4\">\r\n     <g id=\"line2d_4\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"167.837358\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_4\">\r\n      <!-- 7.5 -->\r\n      <g transform=\"translate(159.885795 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 8.203125 72.90625 \r\nL 55.078125 72.90625 \r\nL 55.078125 68.703125 \r\nL 28.609375 0 \r\nL 18.3125 0 \r\nL 43.21875 64.59375 \r\nL 8.203125 64.59375 \r\nz\r\n\" id=\"DejaVuSans-55\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-55\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_5\">\r\n     <g id=\"line2d_5\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"205.882812\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_5\">\r\n      <!-- 10.0 -->\r\n      <g transform=\"translate(194.75 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 12.40625 8.296875 \r\nL 28.515625 8.296875 \r\nL 28.515625 63.921875 \r\nL 10.984375 60.40625 \r\nL 10.984375 69.390625 \r\nL 28.421875 72.90625 \r\nL 38.28125 72.90625 \r\nL 38.28125 8.296875 \r\nL 54.390625 8.296875 \r\nL 54.390625 0 \r\nL 12.40625 0 \r\nz\r\n\" id=\"DejaVuSans-49\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_6\">\r\n     <g id=\"line2d_6\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"243.928267\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_6\">\r\n      <!-- 12.5 -->\r\n      <g transform=\"translate(232.795455 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_7\">\r\n     <g id=\"line2d_7\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"281.973722\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_7\">\r\n      <!-- 15.0 -->\r\n      <g transform=\"translate(270.840909 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_8\">\r\n     <g id=\"line2d_8\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"320.019176\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_8\">\r\n      <!-- 17.5 -->\r\n      <g transform=\"translate(308.886364 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-55\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_9\">\r\n     <g id=\"line2d_9\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"358.064631\" xlink:href=\"#mf77fefe674\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_9\">\r\n      <!-- 20.0 -->\r\n      <g transform=\"translate(346.931818 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"matplotlib.axis_2\">\r\n    <g id=\"ytick_1\">\r\n     <g id=\"line2d_10\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL -3.5 0 \r\n\" id=\"mcac9c9e303\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#mcac9c9e303\" y=\"208.368324\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_10\">\r\n      <!-- −1.0 -->\r\n      <g transform=\"translate(7.2 212.167542)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 10.59375 35.5 \r\nL 73.1875 35.5 \r\nL 73.1875 27.203125 \r\nL 10.59375 27.203125 \r\nz\r\n\" id=\"DejaVuSans-8722\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_2\">\r\n     <g id=\"line2d_11\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#mcac9c9e303\" y=\"169.420835\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_11\">\r\n      <!-- −0.5 -->\r\n      <g transform=\"translate(7.2 173.220054)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_3\">\r\n     <g id=\"line2d_12\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#mcac9c9e303\" y=\"130.473347\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_12\">\r\n      <!-- 0.0 -->\r\n      <g transform=\"translate(15.579688 134.272566)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_4\">\r\n     <g id=\"line2d_13\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#mcac9c9e303\" y=\"91.525859\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_13\">\r\n      <!-- 0.5 -->\r\n      <g transform=\"translate(15.579688 95.325077)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_5\">\r\n     <g id=\"line2d_14\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#mcac9c9e303\" y=\"52.57837\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_14\">\r\n      <!-- 1.0 -->\r\n      <g transform=\"translate(15.579688 56.377589)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_15\">\r\n    <path clip-path=\"url(#pe6af7aa235)\" d=\"M 53.700994 130.473347 \r\nL 55.133632 130.413243 \r\nL 56.401771 130.074644 \r\nL 57.685595 129.213645 \r\nL 58.995953 127.584959 \r\nL 60.341133 124.948956 \r\nL 61.726785 121.091715 \r\nL 63.155632 115.858235 \r\nL 64.617412 109.24343 \r\nL 66.073585 101.553745 \r\nL 68.87937 84.695379 \r\nL 71.632559 67.764122 \r\nL 73.053692 59.831944 \r\nL 74.550013 52.629496 \r\nL 76.170842 46.599041 \r\nL 77.963806 42.519322 \r\nL 79.84505 41.492881 \r\nL 81.660367 43.740088 \r\nL 83.512464 49.118238 \r\nL 85.199981 56.355085 \r\nL 86.887498 65.304972 \r\nL 89.839535 83.206213 \r\nL 92.58741 99.76086 \r\nL 93.969729 107.193096 \r\nL 95.384687 113.823519 \r\nL 96.837924 119.422741 \r\nL 98.304364 123.745225 \r\nL 99.742681 126.715333 \r\nL 101.13955 128.518057 \r\nL 102.495849 129.43815 \r\nL 103.814613 129.778925 \r\nL 106.372838 129.873364 \r\nL 107.639552 130.146618 \r\nL 108.919692 130.897926 \r\nL 110.224469 132.372982 \r\nL 111.562522 134.814003 \r\nL 112.93974 138.441578 \r\nL 114.359427 143.424813 \r\nL 115.815747 149.811082 \r\nL 117.275812 157.362652 \r\nL 120.094577 174.193252 \r\nL 122.843575 191.295033 \r\nL 124.25356 199.387635 \r\nL 125.730535 206.823433 \r\nL 127.320959 213.202936 \r\nL 129.078723 217.839992 \r\nL 130.95905 219.6277 \r\nL 132.790838 218.082458 \r\nL 134.624981 213.41999 \r\nL 136.524792 205.723062 \r\nL 138.064028 197.804907 \r\nL 141.045681 180.011742 \r\nL 143.80124 163.346029 \r\nL 145.179057 155.808361 \r\nL 146.586084 149.028629 \r\nL 148.032349 143.223779 \r\nL 149.500821 138.64279 \r\nL 150.948624 135.417214 \r\nL 152.355044 133.40654 \r\nL 153.719822 132.334544 \r\nL 155.045742 131.897945 \r\nL 158.878044 131.539823 \r\nL 160.155106 130.881315 \r\nL 161.454845 129.542699 \r\nL 162.786256 127.27967 \r\nL 164.155494 123.865819 \r\nL 165.566219 119.120198 \r\nL 167.015798 112.962066 \r\nL 168.477861 105.560406 \r\nL 171.310136 88.766878 \r\nL 174.057837 71.493512 \r\nL 175.45824 63.245575 \r\nL 176.918127 55.587053 \r\nL 178.481169 48.881854 \r\nL 180.203618 43.734685 \r\nL 182.075844 41.205534 \r\nL 183.924106 42.027875 \r\nL 185.743059 45.977465 \r\nL 187.646486 53.080608 \r\nL 189.219212 60.798661 \r\nL 192.253558 78.556292 \r\nL 195.019884 95.317859 \r\nL 196.394285 102.9517 \r\nL 197.794019 109.869291 \r\nL 199.232531 115.865522 \r\nL 200.700731 120.695987 \r\nL 202.157479 124.183588 \r\nL 203.573884 126.414896 \r\nL 204.947467 127.65333 \r\nL 206.280871 128.201527 \r\nL 210.122263 128.602405 \r\nL 211.396974 129.188259 \r\nL 212.692368 130.412283 \r\nL 214.017893 132.520662 \r\nL 215.379801 135.744483 \r\nL 216.782035 140.274652 \r\nL 218.224098 146.217383 \r\nL 219.68608 153.466563 \r\nL 221.127736 161.615101 \r\nL 228.117344 203.948424 \r\nL 229.656192 210.960567 \r\nL 231.345138 216.575123 \r\nL 233.202451 219.810101 \r\nL 235.065683 219.724028 \r\nL 236.875592 216.472253 \r\nL 238.774948 210.012596 \r\nL 240.385143 202.517993 \r\nL 241.995337 193.676385 \r\nL 247.630585 160.277061 \r\nL 249.024159 153.24336 \r\nL 250.455009 147.082619 \r\nL 251.921002 142.029663 \r\nL 253.385505 138.292629 \r\nL 254.811949 135.842761 \r\nL 256.194286 134.434413 \r\nL 257.535065 133.765985 \r\nL 258.840282 133.534177 \r\nL 261.387049 133.269674 \r\nL 262.660318 132.729699 \r\nL 263.952407 131.588388 \r\nL 265.273143 129.597985 \r\nL 266.628906 126.523516 \r\nL 268.023677 122.166595 \r\nL 269.458267 116.402762 \r\nL 270.91826 109.287055 \r\nL 272.365254 101.181595 \r\nL 275.15551 83.706628 \r\nL 277.911793 66.349586 \r\nL 279.344609 58.267552 \r\nL 280.863364 50.969287 \r\nL 282.523295 44.935337 \r\nL 284.362011 41.061993 \r\nL 286.237467 40.437007 \r\nL 288.048105 43.041029 \r\nL 289.940551 48.870443 \r\nL 291.58935 56.129195 \r\nL 293.238149 64.903066 \r\nL 298.910559 98.361554 \r\nL 300.299585 105.476535 \r\nL 301.72389 111.759145 \r\nL 303.186784 116.986059 \r\nL 304.657451 120.932994 \r\nL 306.093348 123.575906 \r\nL 307.483769 125.139354 \r\nL 308.831134 125.924022 \r\nL 310.141512 126.235495 \r\nL 312.693891 126.563272 \r\nL 313.966792 127.09201 \r\nL 315.257014 128.195157 \r\nL 316.57461 130.121901 \r\nL 317.926373 133.111039 \r\nL 319.315411 137.364165 \r\nL 320.743546 143.017633 \r\nL 322.200352 150.051875 \r\nL 323.650604 158.148285 \r\nL 326.448843 175.77153 \r\nL 329.200175 193.412406 \r\nL 330.623957 201.695115 \r\nL 332.127848 209.255873 \r\nL 333.766098 215.655075 \r\nL 335.588261 220.068927 \r\nL 337.472462 221.321319 \r\nL 339.288031 219.283431 \r\nL 341.175685 214.008112 \r\nL 342.860026 206.980523 \r\nL 344.544367 198.288853 \r\nL 351.639367 157.733874 \r\nL 353.058988 151.38358 \r\nL 354.519199 146.046198 \r\nL 355.994767 141.950727 \r\nL 357.439052 139.162111 \r\nL 358.064631 138.295396 \r\nL 358.064631 138.295396 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_16\">\r\n    <path clip-path=\"url(#pe6af7aa235)\" d=\"M 53.700994 130.473347 \r\nL 53.869916 130.446617 \r\nL 55.133632 128.562945 \r\nL 56.401771 123.795671 \r\nL 57.685595 116.330131 \r\nL 58.995953 106.455847 \r\nL 61.726785 81.516602 \r\nL 63.155632 68.04919 \r\nL 64.617412 55.463549 \r\nL 66.073585 45.224085 \r\nL 67.49317 38.3624 \r\nL 68.87937 35.294488 \r\nL 70.251179 36.192802 \r\nL 71.632559 41.20251 \r\nL 73.053692 50.545828 \r\nL 74.550013 64.561177 \r\nL 76.170842 83.750109 \r\nL 77.963806 108.395344 \r\nL 81.660367 162.303754 \r\nL 83.512464 186.398778 \r\nL 85.199981 204.31192 \r\nL 86.887498 217.128146 \r\nL 88.413109 223.674954 \r\nL 89.839535 225.260745 \r\nL 91.2192 222.737579 \r\nL 92.58741 216.657562 \r\nL 93.969729 207.487412 \r\nL 95.384687 195.766691 \r\nL 99.742681 155.61835 \r\nL 101.13955 144.972606 \r\nL 102.495849 137.075515 \r\nL 103.814613 132.2362 \r\nL 105.103173 130.524627 \r\nL 106.372838 131.864568 \r\nL 107.639552 136.117229 \r\nL 108.919692 143.113662 \r\nL 110.224469 152.589876 \r\nL 111.562522 164.127541 \r\nL 115.815747 203.537343 \r\nL 117.275812 214.39059 \r\nL 118.703131 222.014765 \r\nL 120.094577 225.893695 \r\nL 121.467206 225.830352 \r\nL 122.843575 221.68728 \r\nL 124.25356 213.262044 \r\nL 125.730535 200.245383 \r\nL 127.320959 182.164525 \r\nL 129.078723 158.57576 \r\nL 132.790838 104.350146 \r\nL 134.624981 79.771431 \r\nL 136.524792 58.785023 \r\nL 138.064028 46.345846 \r\nL 139.603264 38.698235 \r\nL 141.045681 36.143527 \r\nL 142.432693 37.839148 \r\nL 143.80124 43.18843 \r\nL 145.179057 51.718679 \r\nL 146.586084 62.915753 \r\nL 150.948624 103.004341 \r\nL 152.355044 114.087518 \r\nL 153.719822 122.512336 \r\nL 155.045742 127.918439 \r\nL 156.33954 130.19782 \r\nL 157.612079 129.404533 \r\nL 158.878044 125.669817 \r\nL 160.155106 119.149776 \r\nL 161.454845 110.084945 \r\nL 162.786256 98.860004 \r\nL 167.015798 59.340969 \r\nL 168.477861 47.928266 \r\nL 169.912711 39.56595 \r\nL 171.310136 34.888158 \r\nL 172.684568 34.127734 \r\nL 174.057837 37.421986 \r\nL 175.45824 44.952095 \r\nL 176.918127 57.002395 \r\nL 178.481169 74.014297 \r\nL 180.203618 96.515851 \r\nL 185.743059 175.783724 \r\nL 187.646486 197.88345 \r\nL 189.219212 211.668035 \r\nL 190.791937 220.577389 \r\nL 192.253558 224.138912 \r\nL 193.649692 223.29223 \r\nL 195.019884 218.690052 \r\nL 196.394285 210.81868 \r\nL 197.794019 200.175375 \r\nL 200.700731 173.631036 \r\nL 202.157479 160.345397 \r\nL 203.573884 148.866144 \r\nL 204.947467 139.94683 \r\nL 206.280871 133.999365 \r\nL 207.580352 131.171401 \r\nL 208.856341 131.433156 \r\nL 210.122263 134.662926 \r\nL 211.396974 140.715497 \r\nL 212.692368 149.37123 \r\nL 214.017893 160.277056 \r\nL 218.224098 199.792676 \r\nL 219.68608 211.699035 \r\nL 221.127736 220.758665 \r\nL 222.531583 226.20833 \r\nL 223.90866 227.766817 \r\nL 225.279971 225.292554 \r\nL 226.67232 218.62203 \r\nL 228.117344 207.493279 \r\nL 229.656192 191.49539 \r\nL 231.345138 170.064756 \r\nL 236.875592 90.627376 \r\nL 238.774948 67.599241 \r\nL 240.385143 52.446199 \r\nL 241.995337 42.25536 \r\nL 243.478466 37.696394 \r\nL 244.885192 37.714252 \r\nL 246.25831 41.590095 \r\nL 247.630585 48.816689 \r\nL 249.024159 58.905411 \r\nL 250.455009 71.242892 \r\nL 253.385505 98.287526 \r\nL 254.811949 110.092316 \r\nL 256.194286 119.43622 \r\nL 257.535065 125.858596 \r\nL 258.840282 129.174174 \r\nL 260.120036 129.388237 \r\nL 261.387049 126.609884 \r\nL 262.660318 120.977044 \r\nL 263.952407 112.69124 \r\nL 265.273143 102.078827 \r\nL 268.023677 76.176446 \r\nL 269.458267 62.630645 \r\nL 270.91826 50.316234 \r\nL 272.365254 40.639297 \r\nL 273.775322 34.488 \r\nL 275.15551 32.201761 \r\nL 276.52582 33.930447 \r\nL 277.911793 39.824083 \r\nL 279.344609 50.125576 \r\nL 280.863364 65.219584 \r\nL 282.523295 85.67862 \r\nL 286.237467 139.278549 \r\nL 288.048105 165.106902 \r\nL 289.940551 188.867131 \r\nL 291.58935 205.306371 \r\nL 293.238149 216.69766 \r\nL 294.743413 222.164583 \r\nL 296.161323 222.888497 \r\nL 297.539064 219.65742 \r\nL 298.910559 213.008531 \r\nL 300.299585 203.428477 \r\nL 301.72389 191.499029 \r\nL 304.657451 164.632552 \r\nL 306.093348 152.607981 \r\nL 307.483769 142.958108 \r\nL 308.831134 136.184561 \r\nL 310.141512 132.502615 \r\nL 311.424892 131.928189 \r\nL 312.693891 134.365734 \r\nL 313.966792 139.6826 \r\nL 315.257014 147.691261 \r\nL 316.57461 158.084923 \r\nL 319.315411 183.826518 \r\nL 320.743546 197.486651 \r\nL 322.200352 210.108437 \r\nL 323.650604 220.274682 \r\nL 325.065747 226.996101 \r\nL 326.448843 229.874489 \r\nL 327.818793 228.749561 \r\nL 329.200175 223.480665 \r\nL 330.623957 213.839406 \r\nL 332.127848 199.459826 \r\nL 333.766098 179.76839 \r\nL 335.588261 154.460282 \r\nL 339.288031 100.438224 \r\nL 341.175685 76.124497 \r\nL 342.860026 58.603875 \r\nL 344.544367 46.210624 \r\nL 346.070067 40.009774 \r\nL 347.498543 38.697283 \r\nL 348.881191 41.416964 \r\nL 350.25309 47.60161 \r\nL 351.639367 56.75998 \r\nL 353.058988 68.327682 \r\nL 357.439052 107.018363 \r\nL 358.064631 111.689751 \r\nL 358.064631 111.689751 \r\n\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"patch_3\">\r\n    <path d=\"M 38.482813 239.758125 \r\nL 38.482813 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_4\">\r\n    <path d=\"M 373.282813 239.758125 \r\nL 373.282813 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_5\">\r\n    <path d=\"M 38.482813 239.758125 \r\nL 373.282813 239.758125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_6\">\r\n    <path d=\"M 38.482813 22.318125 \r\nL 373.282813 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"text_15\">\r\n    <!-- Duffing's equation -->\r\n    <g transform=\"translate(150.802813 16.318125)scale(0.12 -0.12)\">\r\n     <defs>\r\n      <path d=\"M 19.671875 64.796875 \r\nL 19.671875 8.109375 \r\nL 31.59375 8.109375 \r\nQ 46.6875 8.109375 53.6875 14.9375 \r\nQ 60.6875 21.78125 60.6875 36.53125 \r\nQ 60.6875 51.171875 53.6875 57.984375 \r\nQ 46.6875 64.796875 31.59375 64.796875 \r\nz\r\nM 9.8125 72.90625 \r\nL 30.078125 72.90625 \r\nQ 51.265625 72.90625 61.171875 64.09375 \r\nQ 71.09375 55.28125 71.09375 36.53125 \r\nQ 71.09375 17.671875 61.125 8.828125 \r\nQ 51.171875 0 30.078125 0 \r\nL 9.8125 0 \r\nz\r\n\" id=\"DejaVuSans-68\"/>\r\n      <path d=\"M 8.5 21.578125 \r\nL 8.5 54.6875 \r\nL 17.484375 54.6875 \r\nL 17.484375 21.921875 \r\nQ 17.484375 14.15625 20.5 10.265625 \r\nQ 23.53125 6.390625 29.59375 6.390625 \r\nQ 36.859375 6.390625 41.078125 11.03125 \r\nQ 45.3125 15.671875 45.3125 23.6875 \r\nL 45.3125 54.6875 \r\nL 54.296875 54.6875 \r\nL 54.296875 0 \r\nL 45.3125 0 \r\nL 45.3125 8.40625 \r\nQ 42.046875 3.421875 37.71875 1 \r\nQ 33.40625 -1.421875 27.6875 -1.421875 \r\nQ 18.265625 -1.421875 13.375 4.4375 \r\nQ 8.5 10.296875 8.5 21.578125 \r\nz\r\nM 31.109375 56 \r\nz\r\n\" id=\"DejaVuSans-117\"/>\r\n      <path d=\"M 37.109375 75.984375 \r\nL 37.109375 68.5 \r\nL 28.515625 68.5 \r\nQ 23.6875 68.5 21.796875 66.546875 \r\nQ 19.921875 64.59375 19.921875 59.515625 \r\nL 19.921875 54.6875 \r\nL 34.71875 54.6875 \r\nL 34.71875 47.703125 \r\nL 19.921875 47.703125 \r\nL 19.921875 0 \r\nL 10.890625 0 \r\nL 10.890625 47.703125 \r\nL 2.296875 47.703125 \r\nL 2.296875 54.6875 \r\nL 10.890625 54.6875 \r\nL 10.890625 58.5 \r\nQ 10.890625 67.625 15.140625 71.796875 \r\nQ 19.390625 75.984375 28.609375 75.984375 \r\nz\r\n\" id=\"DejaVuSans-102\"/>\r\n      <path d=\"M 9.421875 54.6875 \r\nL 18.40625 54.6875 \r\nL 18.40625 0 \r\nL 9.421875 0 \r\nz\r\nM 9.421875 75.984375 \r\nL 18.40625 75.984375 \r\nL 18.40625 64.59375 \r\nL 9.421875 64.59375 \r\nz\r\n\" id=\"DejaVuSans-105\"/>\r\n      <path d=\"M 54.890625 33.015625 \r\nL 54.890625 0 \r\nL 45.90625 0 \r\nL 45.90625 32.71875 \r\nQ 45.90625 40.484375 42.875 44.328125 \r\nQ 39.84375 48.1875 33.796875 48.1875 \r\nQ 26.515625 48.1875 22.3125 43.546875 \r\nQ 18.109375 38.921875 18.109375 30.90625 \r\nL 18.109375 0 \r\nL 9.078125 0 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.1875 \r\nQ 21.34375 51.125 25.703125 53.5625 \r\nQ 30.078125 56 35.796875 56 \r\nQ 45.21875 56 50.046875 50.171875 \r\nQ 54.890625 44.34375 54.890625 33.015625 \r\nz\r\n\" id=\"DejaVuSans-110\"/>\r\n      <path d=\"M 45.40625 27.984375 \r\nQ 45.40625 37.75 41.375 43.109375 \r\nQ 37.359375 48.484375 30.078125 48.484375 \r\nQ 22.859375 48.484375 18.828125 43.109375 \r\nQ 14.796875 37.75 14.796875 27.984375 \r\nQ 14.796875 18.265625 18.828125 12.890625 \r\nQ 22.859375 7.515625 30.078125 7.515625 \r\nQ 37.359375 7.515625 41.375 12.890625 \r\nQ 45.40625 18.265625 45.40625 27.984375 \r\nz\r\nM 54.390625 6.78125 \r\nQ 54.390625 -7.171875 48.1875 -13.984375 \r\nQ 42 -20.796875 29.203125 -20.796875 \r\nQ 24.46875 -20.796875 20.265625 -20.09375 \r\nQ 16.0625 -19.390625 12.109375 -17.921875 \r\nL 12.109375 -9.1875 \r\nQ 16.0625 -11.328125 19.921875 -12.34375 \r\nQ 23.78125 -13.375 27.78125 -13.375 \r\nQ 36.625 -13.375 41.015625 -8.765625 \r\nQ 45.40625 -4.15625 45.40625 5.171875 \r\nL 45.40625 9.625 \r\nQ 42.625 4.78125 38.28125 2.390625 \r\nQ 33.9375 0 27.875 0 \r\nQ 17.828125 0 11.671875 7.65625 \r\nQ 5.515625 15.328125 5.515625 27.984375 \r\nQ 5.515625 40.671875 11.671875 48.328125 \r\nQ 17.828125 56 27.875 56 \r\nQ 33.9375 56 38.28125 53.609375 \r\nQ 42.625 51.21875 45.40625 46.390625 \r\nL 45.40625 54.6875 \r\nL 54.390625 54.6875 \r\nz\r\n\" id=\"DejaVuSans-103\"/>\r\n      <path d=\"M 17.921875 72.90625 \r\nL 17.921875 45.796875 \r\nL 9.625 45.796875 \r\nL 9.625 72.90625 \r\nz\r\n\" id=\"DejaVuSans-39\"/>\r\n      <path d=\"M 44.28125 53.078125 \r\nL 44.28125 44.578125 \r\nQ 40.484375 46.53125 36.375 47.5 \r\nQ 32.28125 48.484375 27.875 48.484375 \r\nQ 21.1875 48.484375 17.84375 46.4375 \r\nQ 14.5 44.390625 14.5 40.28125 \r\nQ 14.5 37.15625 16.890625 35.375 \r\nQ 19.28125 33.59375 26.515625 31.984375 \r\nL 29.59375 31.296875 \r\nQ 39.15625 29.25 43.1875 25.515625 \r\nQ 47.21875 21.78125 47.21875 15.09375 \r\nQ 47.21875 7.46875 41.1875 3.015625 \r\nQ 35.15625 -1.421875 24.609375 -1.421875 \r\nQ 20.21875 -1.421875 15.453125 -0.5625 \r\nQ 10.6875 0.296875 5.421875 2 \r\nL 5.421875 11.28125 \r\nQ 10.40625 8.6875 15.234375 7.390625 \r\nQ 20.0625 6.109375 24.8125 6.109375 \r\nQ 31.15625 6.109375 34.5625 8.28125 \r\nQ 37.984375 10.453125 37.984375 14.40625 \r\nQ 37.984375 18.0625 35.515625 20.015625 \r\nQ 33.0625 21.96875 24.703125 23.78125 \r\nL 21.578125 24.515625 \r\nQ 13.234375 26.265625 9.515625 29.90625 \r\nQ 5.8125 33.546875 5.8125 39.890625 \r\nQ 5.8125 47.609375 11.28125 51.796875 \r\nQ 16.75 56 26.8125 56 \r\nQ 31.78125 56 36.171875 55.265625 \r\nQ 40.578125 54.546875 44.28125 53.078125 \r\nz\r\n\" id=\"DejaVuSans-115\"/>\r\n      <path id=\"DejaVuSans-32\"/>\r\n      <path d=\"M 56.203125 29.59375 \r\nL 56.203125 25.203125 \r\nL 14.890625 25.203125 \r\nQ 15.484375 15.921875 20.484375 11.0625 \r\nQ 25.484375 6.203125 34.421875 6.203125 \r\nQ 39.59375 6.203125 44.453125 7.46875 \r\nQ 49.3125 8.734375 54.109375 11.28125 \r\nL 54.109375 2.78125 \r\nQ 49.265625 0.734375 44.1875 -0.34375 \r\nQ 39.109375 -1.421875 33.890625 -1.421875 \r\nQ 20.796875 -1.421875 13.15625 6.1875 \r\nQ 5.515625 13.8125 5.515625 26.8125 \r\nQ 5.515625 40.234375 12.765625 48.109375 \r\nQ 20.015625 56 32.328125 56 \r\nQ 43.359375 56 49.78125 48.890625 \r\nQ 56.203125 41.796875 56.203125 29.59375 \r\nz\r\nM 47.21875 32.234375 \r\nQ 47.125 39.59375 43.09375 43.984375 \r\nQ 39.0625 48.390625 32.421875 48.390625 \r\nQ 24.90625 48.390625 20.390625 44.140625 \r\nQ 15.875 39.890625 15.1875 32.171875 \r\nz\r\n\" id=\"DejaVuSans-101\"/>\r\n      <path d=\"M 14.796875 27.296875 \r\nQ 14.796875 17.390625 18.875 11.75 \r\nQ 22.953125 6.109375 30.078125 6.109375 \r\nQ 37.203125 6.109375 41.296875 11.75 \r\nQ 45.40625 17.390625 45.40625 27.296875 \r\nQ 45.40625 37.203125 41.296875 42.84375 \r\nQ 37.203125 48.484375 30.078125 48.484375 \r\nQ 22.953125 48.484375 18.875 42.84375 \r\nQ 14.796875 37.203125 14.796875 27.296875 \r\nz\r\nM 45.40625 8.203125 \r\nQ 42.578125 3.328125 38.25 0.953125 \r\nQ 33.9375 -1.421875 27.875 -1.421875 \r\nQ 17.96875 -1.421875 11.734375 6.484375 \r\nQ 5.515625 14.40625 5.515625 27.296875 \r\nQ 5.515625 40.1875 11.734375 48.09375 \r\nQ 17.96875 56 27.875 56 \r\nQ 33.9375 56 38.25 53.625 \r\nQ 42.578125 51.265625 45.40625 46.390625 \r\nL 45.40625 54.6875 \r\nL 54.390625 54.6875 \r\nL 54.390625 -20.796875 \r\nL 45.40625 -20.796875 \r\nz\r\n\" id=\"DejaVuSans-113\"/>\r\n      <path d=\"M 34.28125 27.484375 \r\nQ 23.390625 27.484375 19.1875 25 \r\nQ 14.984375 22.515625 14.984375 16.5 \r\nQ 14.984375 11.71875 18.140625 8.90625 \r\nQ 21.296875 6.109375 26.703125 6.109375 \r\nQ 34.1875 6.109375 38.703125 11.40625 \r\nQ 43.21875 16.703125 43.21875 25.484375 \r\nL 43.21875 27.484375 \r\nz\r\nM 52.203125 31.203125 \r\nL 52.203125 0 \r\nL 43.21875 0 \r\nL 43.21875 8.296875 \r\nQ 40.140625 3.328125 35.546875 0.953125 \r\nQ 30.953125 -1.421875 24.3125 -1.421875 \r\nQ 15.921875 -1.421875 10.953125 3.296875 \r\nQ 6 8.015625 6 15.921875 \r\nQ 6 25.140625 12.171875 29.828125 \r\nQ 18.359375 34.515625 30.609375 34.515625 \r\nL 43.21875 34.515625 \r\nL 43.21875 35.40625 \r\nQ 43.21875 41.609375 39.140625 45 \r\nQ 35.0625 48.390625 27.6875 48.390625 \r\nQ 23 48.390625 18.546875 47.265625 \r\nQ 14.109375 46.140625 10.015625 43.890625 \r\nL 10.015625 52.203125 \r\nQ 14.9375 54.109375 19.578125 55.046875 \r\nQ 24.21875 56 28.609375 56 \r\nQ 40.484375 56 46.34375 49.84375 \r\nQ 52.203125 43.703125 52.203125 31.203125 \r\nz\r\n\" id=\"DejaVuSans-97\"/>\r\n      <path d=\"M 18.3125 70.21875 \r\nL 18.3125 54.6875 \r\nL 36.8125 54.6875 \r\nL 36.8125 47.703125 \r\nL 18.3125 47.703125 \r\nL 18.3125 18.015625 \r\nQ 18.3125 11.328125 20.140625 9.421875 \r\nQ 21.96875 7.515625 27.59375 7.515625 \r\nL 36.8125 7.515625 \r\nL 36.8125 0 \r\nL 27.59375 0 \r\nQ 17.1875 0 13.234375 3.875 \r\nQ 9.28125 7.765625 9.28125 18.015625 \r\nL 9.28125 47.703125 \r\nL 2.6875 47.703125 \r\nL 2.6875 54.6875 \r\nL 9.28125 54.6875 \r\nL 9.28125 70.21875 \r\nz\r\n\" id=\"DejaVuSans-116\"/>\r\n      <path d=\"M 30.609375 48.390625 \r\nQ 23.390625 48.390625 19.1875 42.75 \r\nQ 14.984375 37.109375 14.984375 27.296875 \r\nQ 14.984375 17.484375 19.15625 11.84375 \r\nQ 23.34375 6.203125 30.609375 6.203125 \r\nQ 37.796875 6.203125 41.984375 11.859375 \r\nQ 46.1875 17.53125 46.1875 27.296875 \r\nQ 46.1875 37.015625 41.984375 42.703125 \r\nQ 37.796875 48.390625 30.609375 48.390625 \r\nz\r\nM 30.609375 56 \r\nQ 42.328125 56 49.015625 48.375 \r\nQ 55.71875 40.765625 55.71875 27.296875 \r\nQ 55.71875 13.875 49.015625 6.21875 \r\nQ 42.328125 -1.421875 30.609375 -1.421875 \r\nQ 18.84375 -1.421875 12.171875 6.21875 \r\nQ 5.515625 13.875 5.515625 27.296875 \r\nQ 5.515625 40.765625 12.171875 48.375 \r\nQ 18.84375 56 30.609375 56 \r\nz\r\n\" id=\"DejaVuSans-111\"/>\r\n     </defs>\r\n     <use xlink:href=\"#DejaVuSans-68\"/>\r\n     <use x=\"77.001953\" xlink:href=\"#DejaVuSans-117\"/>\r\n     <use x=\"140.380859\" xlink:href=\"#DejaVuSans-102\"/>\r\n     <use x=\"175.585938\" xlink:href=\"#DejaVuSans-102\"/>\r\n     <use x=\"210.791016\" xlink:href=\"#DejaVuSans-105\"/>\r\n     <use x=\"238.574219\" xlink:href=\"#DejaVuSans-110\"/>\r\n     <use x=\"301.953125\" xlink:href=\"#DejaVuSans-103\"/>\r\n     <use x=\"365.429688\" xlink:href=\"#DejaVuSans-39\"/>\r\n     <use x=\"392.919922\" xlink:href=\"#DejaVuSans-115\"/>\r\n     <use x=\"445.019531\" xlink:href=\"#DejaVuSans-32\"/>\r\n     <use x=\"476.806641\" xlink:href=\"#DejaVuSans-101\"/>\r\n     <use x=\"538.330078\" xlink:href=\"#DejaVuSans-113\"/>\r\n     <use x=\"601.806641\" xlink:href=\"#DejaVuSans-117\"/>\r\n     <use x=\"665.185547\" xlink:href=\"#DejaVuSans-97\"/>\r\n     <use x=\"726.464844\" xlink:href=\"#DejaVuSans-116\"/>\r\n     <use x=\"765.673828\" xlink:href=\"#DejaVuSans-105\"/>\r\n     <use x=\"793.457031\" xlink:href=\"#DejaVuSans-111\"/>\r\n     <use x=\"854.638672\" xlink:href=\"#DejaVuSans-110\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"legend_1\">\r\n    <g id=\"patch_7\">\r\n     <path d=\"M 182.582813 44.99625 \r\nL 366.282812 44.99625 \r\nQ 368.282812 44.99625 368.282812 42.99625 \r\nL 368.282812 29.318125 \r\nQ 368.282812 27.318125 366.282812 27.318125 \r\nL 182.582813 27.318125 \r\nQ 180.582813 27.318125 180.582813 29.318125 \r\nL 180.582813 42.99625 \r\nQ 180.582813 44.99625 182.582813 44.99625 \r\nz\r\n\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\r\n    </g>\r\n    <g id=\"line2d_17\">\r\n     <path d=\"M 184.582813 35.416562 \r\nL 204.582813 35.416562 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_18\"/>\r\n    <g id=\"text_16\">\r\n     <!-- dispacement -->\r\n     <g transform=\"translate(212.582813 38.916562)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 45.40625 46.390625 \r\nL 45.40625 75.984375 \r\nL 54.390625 75.984375 \r\nL 54.390625 0 \r\nL 45.40625 0 \r\nL 45.40625 8.203125 \r\nQ 42.578125 3.328125 38.25 0.953125 \r\nQ 33.9375 -1.421875 27.875 -1.421875 \r\nQ 17.96875 -1.421875 11.734375 6.484375 \r\nQ 5.515625 14.40625 5.515625 27.296875 \r\nQ 5.515625 40.1875 11.734375 48.09375 \r\nQ 17.96875 56 27.875 56 \r\nQ 33.9375 56 38.25 53.625 \r\nQ 42.578125 51.265625 45.40625 46.390625 \r\nz\r\nM 14.796875 27.296875 \r\nQ 14.796875 17.390625 18.875 11.75 \r\nQ 22.953125 6.109375 30.078125 6.109375 \r\nQ 37.203125 6.109375 41.296875 11.75 \r\nQ 45.40625 17.390625 45.40625 27.296875 \r\nQ 45.40625 37.203125 41.296875 42.84375 \r\nQ 37.203125 48.484375 30.078125 48.484375 \r\nQ 22.953125 48.484375 18.875 42.84375 \r\nQ 14.796875 37.203125 14.796875 27.296875 \r\nz\r\n\" id=\"DejaVuSans-100\"/>\r\n       <path d=\"M 18.109375 8.203125 \r\nL 18.109375 -20.796875 \r\nL 9.078125 -20.796875 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.390625 \r\nQ 20.953125 51.265625 25.265625 53.625 \r\nQ 29.59375 56 35.59375 56 \r\nQ 45.5625 56 51.78125 48.09375 \r\nQ 58.015625 40.1875 58.015625 27.296875 \r\nQ 58.015625 14.40625 51.78125 6.484375 \r\nQ 45.5625 -1.421875 35.59375 -1.421875 \r\nQ 29.59375 -1.421875 25.265625 0.953125 \r\nQ 20.953125 3.328125 18.109375 8.203125 \r\nz\r\nM 48.6875 27.296875 \r\nQ 48.6875 37.203125 44.609375 42.84375 \r\nQ 40.53125 48.484375 33.40625 48.484375 \r\nQ 26.265625 48.484375 22.1875 42.84375 \r\nQ 18.109375 37.203125 18.109375 27.296875 \r\nQ 18.109375 17.390625 22.1875 11.75 \r\nQ 26.265625 6.109375 33.40625 6.109375 \r\nQ 40.53125 6.109375 44.609375 11.75 \r\nQ 48.6875 17.390625 48.6875 27.296875 \r\nz\r\n\" id=\"DejaVuSans-112\"/>\r\n       <path d=\"M 48.78125 52.59375 \r\nL 48.78125 44.1875 \r\nQ 44.96875 46.296875 41.140625 47.34375 \r\nQ 37.3125 48.390625 33.40625 48.390625 \r\nQ 24.65625 48.390625 19.8125 42.84375 \r\nQ 14.984375 37.3125 14.984375 27.296875 \r\nQ 14.984375 17.28125 19.8125 11.734375 \r\nQ 24.65625 6.203125 33.40625 6.203125 \r\nQ 37.3125 6.203125 41.140625 7.25 \r\nQ 44.96875 8.296875 48.78125 10.40625 \r\nL 48.78125 2.09375 \r\nQ 45.015625 0.34375 40.984375 -0.53125 \r\nQ 36.96875 -1.421875 32.421875 -1.421875 \r\nQ 20.0625 -1.421875 12.78125 6.34375 \r\nQ 5.515625 14.109375 5.515625 27.296875 \r\nQ 5.515625 40.671875 12.859375 48.328125 \r\nQ 20.21875 56 33.015625 56 \r\nQ 37.15625 56 41.109375 55.140625 \r\nQ 45.0625 54.296875 48.78125 52.59375 \r\nz\r\n\" id=\"DejaVuSans-99\"/>\r\n       <path d=\"M 52 44.1875 \r\nQ 55.375 50.25 60.0625 53.125 \r\nQ 64.75 56 71.09375 56 \r\nQ 79.640625 56 84.28125 50.015625 \r\nQ 88.921875 44.046875 88.921875 33.015625 \r\nL 88.921875 0 \r\nL 79.890625 0 \r\nL 79.890625 32.71875 \r\nQ 79.890625 40.578125 77.09375 44.375 \r\nQ 74.3125 48.1875 68.609375 48.1875 \r\nQ 61.625 48.1875 57.5625 43.546875 \r\nQ 53.515625 38.921875 53.515625 30.90625 \r\nL 53.515625 0 \r\nL 44.484375 0 \r\nL 44.484375 32.71875 \r\nQ 44.484375 40.625 41.703125 44.40625 \r\nQ 38.921875 48.1875 33.109375 48.1875 \r\nQ 26.21875 48.1875 22.15625 43.53125 \r\nQ 18.109375 38.875 18.109375 30.90625 \r\nL 18.109375 0 \r\nL 9.078125 0 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.1875 \r\nQ 21.1875 51.21875 25.484375 53.609375 \r\nQ 29.78125 56 35.6875 56 \r\nQ 41.65625 56 45.828125 52.96875 \r\nQ 50 49.953125 52 44.1875 \r\nz\r\n\" id=\"DejaVuSans-109\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-100\"/>\r\n      <use x=\"63.476562\" xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"91.259766\" xlink:href=\"#DejaVuSans-115\"/>\r\n      <use x=\"143.359375\" xlink:href=\"#DejaVuSans-112\"/>\r\n      <use x=\"206.835938\" xlink:href=\"#DejaVuSans-97\"/>\r\n      <use x=\"268.115234\" xlink:href=\"#DejaVuSans-99\"/>\r\n      <use x=\"323.095703\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"384.619141\" xlink:href=\"#DejaVuSans-109\"/>\r\n      <use x=\"482.03125\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"543.554688\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"606.933594\" xlink:href=\"#DejaVuSans-116\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_19\">\r\n     <path d=\"M 297.198438 35.416562 \r\nL 317.198438 35.416562 \r\n\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_20\"/>\r\n    <g id=\"text_17\">\r\n     <!-- velocity -->\r\n     <g transform=\"translate(325.198438 38.916562)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 2.984375 54.6875 \r\nL 12.5 54.6875 \r\nL 29.59375 8.796875 \r\nL 46.6875 54.6875 \r\nL 56.203125 54.6875 \r\nL 35.6875 0 \r\nL 23.484375 0 \r\nz\r\n\" id=\"DejaVuSans-118\"/>\r\n       <path d=\"M 9.421875 75.984375 \r\nL 18.40625 75.984375 \r\nL 18.40625 0 \r\nL 9.421875 0 \r\nz\r\n\" id=\"DejaVuSans-108\"/>\r\n       <path d=\"M 32.171875 -5.078125 \r\nQ 28.375 -14.84375 24.75 -17.8125 \r\nQ 21.140625 -20.796875 15.09375 -20.796875 \r\nL 7.90625 -20.796875 \r\nL 7.90625 -13.28125 \r\nL 13.1875 -13.28125 \r\nQ 16.890625 -13.28125 18.9375 -11.515625 \r\nQ 21 -9.765625 23.484375 -3.21875 \r\nL 25.09375 0.875 \r\nL 2.984375 54.6875 \r\nL 12.5 54.6875 \r\nL 29.59375 11.921875 \r\nL 46.6875 54.6875 \r\nL 56.203125 54.6875 \r\nz\r\n\" id=\"DejaVuSans-121\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-118\"/>\r\n      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"120.703125\" xlink:href=\"#DejaVuSans-108\"/>\r\n      <use x=\"148.486328\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use x=\"209.667969\" xlink:href=\"#DejaVuSans-99\"/>\r\n      <use x=\"264.648438\" xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"292.431641\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"331.640625\" xlink:href=\"#DejaVuSans-121\"/>\r\n     </g>\r\n    </g>\r\n   </g>\r\n  </g>\r\n </g>\r\n <defs>\r\n  <clipPath id=\"pe6af7aa235\">\r\n   <rect height=\"217.44\" width=\"334.8\" x=\"38.482813\" y=\"22.318125\"/>\r\n  </clipPath>\r\n </defs>\r\n</svg>\r\n",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(reference.t, reference.y.T)\n",
    "plt.title(\"Duffing's equation\")\n",
    "plt.legend(('dispacement', 'velocity'), ncol=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Efficiency plot\n",
    "The method is efficient if it can solve problems to low error with low cost. I will use the number of function evaluations as measure of cost. For the error measure I wil use the RMS of the error norm over all solution points. A function to calculate it is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rms_err_norm(solution, reference):\n",
    "    error = solution.y - reference.sol(solution.t)\n",
    "    err_norm = (error**2).mean()**0.5\n",
    "    return err_norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So how well do the methods of Bogacki and Shampine `BS45` and `BS45_i` solve the Duffing problem? To answer this question, the solution is calculated for multiple absolute tolerance values with these methods and with the `RK45` method. Plotting the number of function evaluations versus the error shows their relative efficiency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<!-- Created with matplotlib (https://matplotlib.org/) -->\r\n<svg height=\"277.73625pt\" version=\"1.1\" viewBox=\"0 0 387.478125 277.73625\" width=\"387.478125pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-02-10T08:19:11.698511</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.3.2, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n </defs>\r\n <g id=\"figure_1\">\r\n  <g id=\"patch_1\">\r\n   <path d=\"M 0 277.73625 \r\nL 387.478125 277.73625 \r\nL 387.478125 0 \r\nL 0 0 \r\nz\r\n\" style=\"fill:none;\"/>\r\n  </g>\r\n  <g id=\"axes_1\">\r\n   <g id=\"patch_2\">\r\n    <path d=\"M 45.478125 239.758125 \r\nL 380.278125 239.758125 \r\nL 380.278125 22.318125 \r\nL 45.478125 22.318125 \r\nz\r\n\" style=\"fill:#ffffff;\"/>\r\n   </g>\r\n   <g id=\"matplotlib.axis_1\">\r\n    <g id=\"xtick_1\">\r\n     <g id=\"line2d_1\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL 0 3.5 \r\n\" id=\"m6f7636d3f5\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"59.94803\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_1\">\r\n      <!-- $\\mathdefault{10^{-7}}$ -->\r\n      <g transform=\"translate(48.19803 254.356562)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 12.40625 8.296875 \r\nL 28.515625 8.296875 \r\nL 28.515625 63.921875 \r\nL 10.984375 60.40625 \r\nL 10.984375 69.390625 \r\nL 28.421875 72.90625 \r\nL 38.28125 72.90625 \r\nL 38.28125 8.296875 \r\nL 54.390625 8.296875 \r\nL 54.390625 0 \r\nL 12.40625 0 \r\nz\r\n\" id=\"DejaVuSans-49\"/>\r\n        <path d=\"M 31.78125 66.40625 \r\nQ 24.171875 66.40625 20.328125 58.90625 \r\nQ 16.5 51.421875 16.5 36.375 \r\nQ 16.5 21.390625 20.328125 13.890625 \r\nQ 24.171875 6.390625 31.78125 6.390625 \r\nQ 39.453125 6.390625 43.28125 13.890625 \r\nQ 47.125 21.390625 47.125 36.375 \r\nQ 47.125 51.421875 43.28125 58.90625 \r\nQ 39.453125 66.40625 31.78125 66.40625 \r\nz\r\nM 31.78125 74.21875 \r\nQ 44.046875 74.21875 50.515625 64.515625 \r\nQ 56.984375 54.828125 56.984375 36.375 \r\nQ 56.984375 17.96875 50.515625 8.265625 \r\nQ 44.046875 -1.421875 31.78125 -1.421875 \r\nQ 19.53125 -1.421875 13.0625 8.265625 \r\nQ 6.59375 17.96875 6.59375 36.375 \r\nQ 6.59375 54.828125 13.0625 64.515625 \r\nQ 19.53125 74.21875 31.78125 74.21875 \r\nz\r\n\" id=\"DejaVuSans-48\"/>\r\n        <path d=\"M 10.59375 35.5 \r\nL 73.1875 35.5 \r\nL 73.1875 27.203125 \r\nL 10.59375 27.203125 \r\nz\r\n\" id=\"DejaVuSans-8722\"/>\r\n        <path d=\"M 8.203125 72.90625 \r\nL 55.078125 72.90625 \r\nL 55.078125 68.703125 \r\nL 28.609375 0 \r\nL 18.3125 0 \r\nL 43.21875 64.59375 \r\nL 8.203125 64.59375 \r\nz\r\n\" id=\"DejaVuSans-55\"/>\r\n       </defs>\r\n       <use transform=\"translate(0 0.684375)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.684375)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-55\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_2\">\r\n     <g id=\"line2d_2\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"107.046256\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_2\">\r\n      <!-- $\\mathdefault{10^{-6}}$ -->\r\n      <g transform=\"translate(95.296256 254.356562)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 33.015625 40.375 \r\nQ 26.375 40.375 22.484375 35.828125 \r\nQ 18.609375 31.296875 18.609375 23.390625 \r\nQ 18.609375 15.53125 22.484375 10.953125 \r\nQ 26.375 6.390625 33.015625 6.390625 \r\nQ 39.65625 6.390625 43.53125 10.953125 \r\nQ 47.40625 15.53125 47.40625 23.390625 \r\nQ 47.40625 31.296875 43.53125 35.828125 \r\nQ 39.65625 40.375 33.015625 40.375 \r\nz\r\nM 52.59375 71.296875 \r\nL 52.59375 62.3125 \r\nQ 48.875 64.0625 45.09375 64.984375 \r\nQ 41.3125 65.921875 37.59375 65.921875 \r\nQ 27.828125 65.921875 22.671875 59.328125 \r\nQ 17.53125 52.734375 16.796875 39.40625 \r\nQ 19.671875 43.65625 24.015625 45.921875 \r\nQ 28.375 48.1875 33.59375 48.1875 \r\nQ 44.578125 48.1875 50.953125 41.515625 \r\nQ 57.328125 34.859375 57.328125 23.390625 \r\nQ 57.328125 12.15625 50.6875 5.359375 \r\nQ 44.046875 -1.421875 33.015625 -1.421875 \r\nQ 20.359375 -1.421875 13.671875 8.265625 \r\nQ 6.984375 17.96875 6.984375 36.375 \r\nQ 6.984375 53.65625 15.1875 63.9375 \r\nQ 23.390625 74.21875 37.203125 74.21875 \r\nQ 40.921875 74.21875 44.703125 73.484375 \r\nQ 48.484375 72.75 52.59375 71.296875 \r\nz\r\n\" id=\"DejaVuSans-54\"/>\r\n       </defs>\r\n       <use transform=\"translate(0 0.765625)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.765625)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_3\">\r\n     <g id=\"line2d_3\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"154.144481\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_3\">\r\n      <!-- $\\mathdefault{10^{-5}}$ -->\r\n      <g transform=\"translate(142.394481 254.356562)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 10.796875 72.90625 \r\nL 49.515625 72.90625 \r\nL 49.515625 64.59375 \r\nL 19.828125 64.59375 \r\nL 19.828125 46.734375 \r\nQ 21.96875 47.46875 24.109375 47.828125 \r\nQ 26.265625 48.1875 28.421875 48.1875 \r\nQ 40.625 48.1875 47.75 41.5 \r\nQ 54.890625 34.8125 54.890625 23.390625 \r\nQ 54.890625 11.625 47.5625 5.09375 \r\nQ 40.234375 -1.421875 26.90625 -1.421875 \r\nQ 22.3125 -1.421875 17.546875 -0.640625 \r\nQ 12.796875 0.140625 7.71875 1.703125 \r\nL 7.71875 11.625 \r\nQ 12.109375 9.234375 16.796875 8.0625 \r\nQ 21.484375 6.890625 26.703125 6.890625 \r\nQ 35.15625 6.890625 40.078125 11.328125 \r\nQ 45.015625 15.765625 45.015625 23.390625 \r\nQ 45.015625 31 40.078125 35.4375 \r\nQ 35.15625 39.890625 26.703125 39.890625 \r\nQ 22.75 39.890625 18.8125 39.015625 \r\nQ 14.890625 38.140625 10.796875 36.28125 \r\nz\r\n\" id=\"DejaVuSans-53\"/>\r\n       </defs>\r\n       <use transform=\"translate(0 0.684375)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.684375)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_4\">\r\n     <g id=\"line2d_4\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"201.242707\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_4\">\r\n      <!-- $\\mathdefault{10^{-4}}$ -->\r\n      <g transform=\"translate(189.492707 254.356562)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 37.796875 64.3125 \r\nL 12.890625 25.390625 \r\nL 37.796875 25.390625 \r\nz\r\nM 35.203125 72.90625 \r\nL 47.609375 72.90625 \r\nL 47.609375 25.390625 \r\nL 58.015625 25.390625 \r\nL 58.015625 17.1875 \r\nL 47.609375 17.1875 \r\nL 47.609375 0 \r\nL 37.796875 0 \r\nL 37.796875 17.1875 \r\nL 4.890625 17.1875 \r\nL 4.890625 26.703125 \r\nz\r\n\" id=\"DejaVuSans-52\"/>\r\n       </defs>\r\n       <use transform=\"translate(0 0.684375)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.684375)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-52\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_5\">\r\n     <g id=\"line2d_5\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"248.340933\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_5\">\r\n      <!-- $\\mathdefault{10^{-3}}$ -->\r\n      <g transform=\"translate(236.590933 254.356562)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 40.578125 39.3125 \r\nQ 47.65625 37.796875 51.625 33 \r\nQ 55.609375 28.21875 55.609375 21.1875 \r\nQ 55.609375 10.40625 48.1875 4.484375 \r\nQ 40.765625 -1.421875 27.09375 -1.421875 \r\nQ 22.515625 -1.421875 17.65625 -0.515625 \r\nQ 12.796875 0.390625 7.625 2.203125 \r\nL 7.625 11.71875 \r\nQ 11.71875 9.328125 16.59375 8.109375 \r\nQ 21.484375 6.890625 26.8125 6.890625 \r\nQ 36.078125 6.890625 40.9375 10.546875 \r\nQ 45.796875 14.203125 45.796875 21.1875 \r\nQ 45.796875 27.640625 41.28125 31.265625 \r\nQ 36.765625 34.90625 28.71875 34.90625 \r\nL 20.21875 34.90625 \r\nL 20.21875 43.015625 \r\nL 29.109375 43.015625 \r\nQ 36.375 43.015625 40.234375 45.921875 \r\nQ 44.09375 48.828125 44.09375 54.296875 \r\nQ 44.09375 59.90625 40.109375 62.90625 \r\nQ 36.140625 65.921875 28.71875 65.921875 \r\nQ 24.65625 65.921875 20.015625 65.03125 \r\nQ 15.375 64.15625 9.8125 62.3125 \r\nL 9.8125 71.09375 \r\nQ 15.4375 72.65625 20.34375 73.4375 \r\nQ 25.25 74.21875 29.59375 74.21875 \r\nQ 40.828125 74.21875 47.359375 69.109375 \r\nQ 53.90625 64.015625 53.90625 55.328125 \r\nQ 53.90625 49.265625 50.4375 45.09375 \r\nQ 46.96875 40.921875 40.578125 39.3125 \r\nz\r\n\" id=\"DejaVuSans-51\"/>\r\n       </defs>\r\n       <use transform=\"translate(0 0.765625)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.765625)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-51\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_6\">\r\n     <g id=\"line2d_6\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"295.439159\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_6\">\r\n      <!-- $\\mathdefault{10^{-2}}$ -->\r\n      <g transform=\"translate(283.689159 254.356562)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 19.1875 8.296875 \r\nL 53.609375 8.296875 \r\nL 53.609375 0 \r\nL 7.328125 0 \r\nL 7.328125 8.296875 \r\nQ 12.9375 14.109375 22.625 23.890625 \r\nQ 32.328125 33.6875 34.8125 36.53125 \r\nQ 39.546875 41.84375 41.421875 45.53125 \r\nQ 43.3125 49.21875 43.3125 52.78125 \r\nQ 43.3125 58.59375 39.234375 62.25 \r\nQ 35.15625 65.921875 28.609375 65.921875 \r\nQ 23.96875 65.921875 18.8125 64.3125 \r\nQ 13.671875 62.703125 7.8125 59.421875 \r\nL 7.8125 69.390625 \r\nQ 13.765625 71.78125 18.9375 73 \r\nQ 24.125 74.21875 28.421875 74.21875 \r\nQ 39.75 74.21875 46.484375 68.546875 \r\nQ 53.21875 62.890625 53.21875 53.421875 \r\nQ 53.21875 48.921875 51.53125 44.890625 \r\nQ 49.859375 40.875 45.40625 35.40625 \r\nQ 44.1875 33.984375 37.640625 27.21875 \r\nQ 31.109375 20.453125 19.1875 8.296875 \r\nz\r\n\" id=\"DejaVuSans-50\"/>\r\n       </defs>\r\n       <use transform=\"translate(0 0.765625)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.765625)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_7\">\r\n     <g id=\"line2d_7\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"342.537385\" xlink:href=\"#m6f7636d3f5\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_7\">\r\n      <!-- $\\mathdefault{10^{-1}}$ -->\r\n      <g transform=\"translate(330.787385 254.356562)scale(0.1 -0.1)\">\r\n       <use transform=\"translate(0 0.684375)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.684375)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use transform=\"translate(186.855469 38.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-49\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_8\">\r\n     <g id=\"line2d_8\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL 0 2 \r\n\" id=\"m82a746bfb1\" style=\"stroke:#000000;stroke-width:0.6;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.770051\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_9\">\r\n     <g id=\"line2d_9\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"49.499347\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_10\">\r\n     <g id=\"line2d_10\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"52.652422\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_11\">\r\n     <g id=\"line2d_11\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"55.38374\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_12\">\r\n     <g id=\"line2d_12\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"57.792933\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_13\">\r\n     <g id=\"line2d_13\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"74.126008\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_14\">\r\n     <g id=\"line2d_14\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"82.419594\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_15\">\r\n     <g id=\"line2d_15\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"88.303987\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_16\">\r\n     <g id=\"line2d_16\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"92.868277\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_17\">\r\n     <g id=\"line2d_17\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"96.597573\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_18\">\r\n     <g id=\"line2d_18\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"99.750648\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_19\">\r\n     <g id=\"line2d_19\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"102.481966\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_20\">\r\n     <g id=\"line2d_20\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"104.891159\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_21\">\r\n     <g id=\"line2d_21\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"121.224234\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_22\">\r\n     <g id=\"line2d_22\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"129.51782\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_23\">\r\n     <g id=\"line2d_23\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"135.402213\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_24\">\r\n     <g id=\"line2d_24\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"139.966503\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_25\">\r\n     <g id=\"line2d_25\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"143.695799\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_26\">\r\n     <g id=\"line2d_26\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"146.848874\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_27\">\r\n     <g id=\"line2d_27\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"149.580192\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_28\">\r\n     <g id=\"line2d_28\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"151.989385\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_29\">\r\n     <g id=\"line2d_29\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"168.32246\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_30\">\r\n     <g id=\"line2d_30\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"176.616046\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_31\">\r\n     <g id=\"line2d_31\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"182.500439\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_32\">\r\n     <g id=\"line2d_32\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"187.064729\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_33\">\r\n     <g id=\"line2d_33\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"190.794025\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_34\">\r\n     <g id=\"line2d_34\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"193.9471\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_35\">\r\n     <g id=\"line2d_35\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"196.678418\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_36\">\r\n     <g id=\"line2d_36\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"199.087611\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_37\">\r\n     <g id=\"line2d_37\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"215.420686\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_38\">\r\n     <g id=\"line2d_38\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"223.714272\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_39\">\r\n     <g id=\"line2d_39\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"229.598665\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_40\">\r\n     <g id=\"line2d_40\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"234.162955\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_41\">\r\n     <g id=\"line2d_41\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"237.892251\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_42\">\r\n     <g id=\"line2d_42\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"241.045326\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_43\">\r\n     <g id=\"line2d_43\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"243.776644\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_44\">\r\n     <g id=\"line2d_44\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"246.185837\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_45\">\r\n     <g id=\"line2d_45\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"262.518912\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_46\">\r\n     <g id=\"line2d_46\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"270.812498\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_47\">\r\n     <g id=\"line2d_47\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"276.696891\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_48\">\r\n     <g id=\"line2d_48\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"281.261181\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_49\">\r\n     <g id=\"line2d_49\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"284.990477\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_50\">\r\n     <g id=\"line2d_50\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"288.143552\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_51\">\r\n     <g id=\"line2d_51\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"290.87487\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_52\">\r\n     <g id=\"line2d_52\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"293.284063\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_53\">\r\n     <g id=\"line2d_53\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"309.617138\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_54\">\r\n     <g id=\"line2d_54\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"317.910724\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_55\">\r\n     <g id=\"line2d_55\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"323.795117\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_56\">\r\n     <g id=\"line2d_56\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"328.359406\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_57\">\r\n     <g id=\"line2d_57\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"332.088703\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_58\">\r\n     <g id=\"line2d_58\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"335.241778\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_59\">\r\n     <g id=\"line2d_59\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"337.973095\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_60\">\r\n     <g id=\"line2d_60\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"340.382289\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_61\">\r\n     <g id=\"line2d_61\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"356.715364\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_62\">\r\n     <g id=\"line2d_62\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"365.00895\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_63\">\r\n     <g id=\"line2d_63\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"370.893343\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_64\">\r\n     <g id=\"line2d_64\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"375.457632\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_65\">\r\n     <g id=\"line2d_65\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"379.186929\" xlink:href=\"#m82a746bfb1\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"text_8\">\r\n     <!-- ||error||$_{RMS}$ -->\r\n     <g transform=\"translate(185.978125 268.13625)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 21 76.421875 \r\nL 21 -23.578125 \r\nL 12.703125 -23.578125 \r\nL 12.703125 76.421875 \r\nz\r\n\" id=\"DejaVuSans-124\"/>\r\n       <path d=\"M 56.203125 29.59375 \r\nL 56.203125 25.203125 \r\nL 14.890625 25.203125 \r\nQ 15.484375 15.921875 20.484375 11.0625 \r\nQ 25.484375 6.203125 34.421875 6.203125 \r\nQ 39.59375 6.203125 44.453125 7.46875 \r\nQ 49.3125 8.734375 54.109375 11.28125 \r\nL 54.109375 2.78125 \r\nQ 49.265625 0.734375 44.1875 -0.34375 \r\nQ 39.109375 -1.421875 33.890625 -1.421875 \r\nQ 20.796875 -1.421875 13.15625 6.1875 \r\nQ 5.515625 13.8125 5.515625 26.8125 \r\nQ 5.515625 40.234375 12.765625 48.109375 \r\nQ 20.015625 56 32.328125 56 \r\nQ 43.359375 56 49.78125 48.890625 \r\nQ 56.203125 41.796875 56.203125 29.59375 \r\nz\r\nM 47.21875 32.234375 \r\nQ 47.125 39.59375 43.09375 43.984375 \r\nQ 39.0625 48.390625 32.421875 48.390625 \r\nQ 24.90625 48.390625 20.390625 44.140625 \r\nQ 15.875 39.890625 15.1875 32.171875 \r\nz\r\n\" id=\"DejaVuSans-101\"/>\r\n       <path d=\"M 41.109375 46.296875 \r\nQ 39.59375 47.171875 37.8125 47.578125 \r\nQ 36.03125 48 33.890625 48 \r\nQ 26.265625 48 22.1875 43.046875 \r\nQ 18.109375 38.09375 18.109375 28.8125 \r\nL 18.109375 0 \r\nL 9.078125 0 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.1875 \r\nQ 20.953125 51.171875 25.484375 53.578125 \r\nQ 30.03125 56 36.53125 56 \r\nQ 37.453125 56 38.578125 55.875 \r\nQ 39.703125 55.765625 41.0625 55.515625 \r\nz\r\n\" id=\"DejaVuSans-114\"/>\r\n       <path d=\"M 30.609375 48.390625 \r\nQ 23.390625 48.390625 19.1875 42.75 \r\nQ 14.984375 37.109375 14.984375 27.296875 \r\nQ 14.984375 17.484375 19.15625 11.84375 \r\nQ 23.34375 6.203125 30.609375 6.203125 \r\nQ 37.796875 6.203125 41.984375 11.859375 \r\nQ 46.1875 17.53125 46.1875 27.296875 \r\nQ 46.1875 37.015625 41.984375 42.703125 \r\nQ 37.796875 48.390625 30.609375 48.390625 \r\nz\r\nM 30.609375 56 \r\nQ 42.328125 56 49.015625 48.375 \r\nQ 55.71875 40.765625 55.71875 27.296875 \r\nQ 55.71875 13.875 49.015625 6.21875 \r\nQ 42.328125 -1.421875 30.609375 -1.421875 \r\nQ 18.84375 -1.421875 12.171875 6.21875 \r\nQ 5.515625 13.875 5.515625 27.296875 \r\nQ 5.515625 40.765625 12.171875 48.375 \r\nQ 18.84375 56 30.609375 56 \r\nz\r\n\" id=\"DejaVuSans-111\"/>\r\n       <path d=\"M 25.203125 64.796875 \r\nL 20.21875 38.921875 \r\nL 32.90625 38.921875 \r\nQ 40.375 38.921875 44.984375 43.046875 \r\nQ 49.609375 47.171875 49.609375 53.8125 \r\nQ 49.609375 59.125 46.5 61.953125 \r\nQ 43.40625 64.796875 37.59375 64.796875 \r\nz\r\nM 43.3125 35.015625 \r\nQ 46.4375 34.28125 48.515625 31.390625 \r\nQ 50.59375 28.515625 53.328125 19.921875 \r\nL 59.515625 0 \r\nL 49.125 0 \r\nL 43.40625 18.703125 \r\nQ 41.21875 25.921875 38.328125 28.359375 \r\nQ 35.453125 30.8125 29.5 30.8125 \r\nL 18.609375 30.8125 \r\nL 12.59375 0 \r\nL 2.6875 0 \r\nL 16.890625 72.90625 \r\nL 39.109375 72.90625 \r\nQ 49.21875 72.90625 54.609375 68.328125 \r\nQ 60.015625 63.765625 60.015625 55.171875 \r\nQ 60.015625 47.5625 55.421875 41.984375 \r\nQ 50.828125 36.421875 43.3125 35.015625 \r\nz\r\n\" id=\"DejaVuSans-Oblique-82\"/>\r\n       <path d=\"M 16.890625 72.90625 \r\nL 31.6875 72.90625 \r\nL 40.1875 23.78125 \r\nL 68.40625 72.90625 \r\nL 83.59375 72.90625 \r\nL 69.390625 0 \r\nL 59.8125 0 \r\nL 72.21875 63.921875 \r\nL 43.609375 14.015625 \r\nL 33.984375 14.015625 \r\nL 24.703125 64.109375 \r\nL 12.3125 0 \r\nL 2.6875 0 \r\nz\r\n\" id=\"DejaVuSans-Oblique-77\"/>\r\n       <path d=\"M 60.296875 70.515625 \r\nL 58.40625 60.890625 \r\nQ 53.46875 63.53125 48.609375 64.875 \r\nQ 43.75 66.21875 39.203125 66.21875 \r\nQ 30.375 66.21875 25.140625 62.359375 \r\nQ 19.921875 58.5 19.921875 52.09375 \r\nQ 19.921875 48.578125 21.84375 46.703125 \r\nQ 23.78125 44.828125 31.78125 42.671875 \r\nL 37.703125 41.21875 \r\nQ 47.703125 38.625 51.609375 34.640625 \r\nQ 55.515625 30.671875 55.515625 23.484375 \r\nQ 55.515625 12.453125 46.84375 5.515625 \r\nQ 38.1875 -1.421875 24.03125 -1.421875 \r\nQ 18.21875 -1.421875 12.359375 -0.265625 \r\nQ 6.5 0.875 0.59375 3.21875 \r\nL 2.59375 13.375 \r\nQ 8.015625 10.015625 13.453125 8.296875 \r\nQ 18.890625 6.59375 24.3125 6.59375 \r\nQ 33.546875 6.59375 39.109375 10.6875 \r\nQ 44.671875 14.796875 44.671875 21.390625 \r\nQ 44.671875 25.78125 42.453125 28.046875 \r\nQ 40.234375 30.328125 32.90625 32.171875 \r\nL 27 33.6875 \r\nQ 16.890625 36.328125 13.203125 39.765625 \r\nQ 9.515625 43.21875 9.515625 49.421875 \r\nQ 9.515625 60.296875 17.890625 67.25 \r\nQ 26.265625 74.21875 39.703125 74.21875 \r\nQ 44.921875 74.21875 50.046875 73.28125 \r\nQ 55.171875 72.359375 60.296875 70.515625 \r\nz\r\n\" id=\"DejaVuSans-Oblique-83\"/>\r\n      </defs>\r\n      <use transform=\"translate(0 0.578125)\" xlink:href=\"#DejaVuSans-124\"/>\r\n      <use transform=\"translate(33.691406 0.578125)\" xlink:href=\"#DejaVuSans-124\"/>\r\n      <use transform=\"translate(67.382812 0.578125)\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use transform=\"translate(128.90625 0.578125)\" xlink:href=\"#DejaVuSans-114\"/>\r\n      <use transform=\"translate(170.019531 0.578125)\" xlink:href=\"#DejaVuSans-114\"/>\r\n      <use transform=\"translate(211.132812 0.578125)\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use transform=\"translate(272.314453 0.578125)\" xlink:href=\"#DejaVuSans-114\"/>\r\n      <use transform=\"translate(313.427734 0.578125)\" xlink:href=\"#DejaVuSans-124\"/>\r\n      <use transform=\"translate(347.119141 0.578125)\" xlink:href=\"#DejaVuSans-124\"/>\r\n      <use transform=\"translate(381.767578 -15.828125)scale(0.7)\" xlink:href=\"#DejaVuSans-Oblique-82\"/>\r\n      <use transform=\"translate(430.405273 -15.828125)scale(0.7)\" xlink:href=\"#DejaVuSans-Oblique-77\"/>\r\n      <use transform=\"translate(490.800781 -15.828125)scale(0.7)\" xlink:href=\"#DejaVuSans-Oblique-83\"/>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"matplotlib.axis_2\">\r\n    <g id=\"ytick_1\">\r\n     <g id=\"line2d_66\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL -3.5 0 \r\n\" id=\"m6a0472a225\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"45.478125\" xlink:href=\"#m6a0472a225\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_9\">\r\n      <!-- $\\mathdefault{10^{2}}$ -->\r\n      <g transform=\"translate(20.878125 243.557344)scale(0.1 -0.1)\">\r\n       <use transform=\"translate(0 0.765625)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.765625)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_2\">\r\n     <g id=\"line2d_67\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"45.478125\" xlink:href=\"#m6a0472a225\" y=\"51.518825\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_10\">\r\n      <!-- $\\mathdefault{10^{3}}$ -->\r\n      <g transform=\"translate(20.878125 55.318044)scale(0.1 -0.1)\">\r\n       <use transform=\"translate(0 0.765625)\" xlink:href=\"#DejaVuSans-49\"/>\r\n       <use transform=\"translate(63.623047 0.765625)\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use transform=\"translate(128.203125 39.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-51\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_3\">\r\n     <g id=\"line2d_68\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL -2 0 \r\n\" id=\"m375c028e6b\" style=\"stroke:#000000;stroke-width:0.6;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"183.092449\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_4\">\r\n     <g id=\"line2d_69\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"149.945154\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_5\">\r\n     <g id=\"line2d_70\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"126.426774\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_6\">\r\n     <g id=\"line2d_71\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"108.184501\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_7\">\r\n     <g id=\"line2d_72\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"93.279478\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_8\">\r\n     <g id=\"line2d_73\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"80.677462\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_9\">\r\n     <g id=\"line2d_74\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"69.761098\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_10\">\r\n     <g id=\"line2d_75\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.6;\" x=\"45.478125\" xlink:href=\"#m375c028e6b\" y=\"60.132183\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"text_11\">\r\n     <!-- nr of function evaluations -->\r\n     <g transform=\"translate(14.798438 195.177188)rotate(-90)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 54.890625 33.015625 \r\nL 54.890625 0 \r\nL 45.90625 0 \r\nL 45.90625 32.71875 \r\nQ 45.90625 40.484375 42.875 44.328125 \r\nQ 39.84375 48.1875 33.796875 48.1875 \r\nQ 26.515625 48.1875 22.3125 43.546875 \r\nQ 18.109375 38.921875 18.109375 30.90625 \r\nL 18.109375 0 \r\nL 9.078125 0 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.1875 \r\nQ 21.34375 51.125 25.703125 53.5625 \r\nQ 30.078125 56 35.796875 56 \r\nQ 45.21875 56 50.046875 50.171875 \r\nQ 54.890625 44.34375 54.890625 33.015625 \r\nz\r\n\" id=\"DejaVuSans-110\"/>\r\n       <path id=\"DejaVuSans-32\"/>\r\n       <path d=\"M 37.109375 75.984375 \r\nL 37.109375 68.5 \r\nL 28.515625 68.5 \r\nQ 23.6875 68.5 21.796875 66.546875 \r\nQ 19.921875 64.59375 19.921875 59.515625 \r\nL 19.921875 54.6875 \r\nL 34.71875 54.6875 \r\nL 34.71875 47.703125 \r\nL 19.921875 47.703125 \r\nL 19.921875 0 \r\nL 10.890625 0 \r\nL 10.890625 47.703125 \r\nL 2.296875 47.703125 \r\nL 2.296875 54.6875 \r\nL 10.890625 54.6875 \r\nL 10.890625 58.5 \r\nQ 10.890625 67.625 15.140625 71.796875 \r\nQ 19.390625 75.984375 28.609375 75.984375 \r\nz\r\n\" id=\"DejaVuSans-102\"/>\r\n       <path d=\"M 8.5 21.578125 \r\nL 8.5 54.6875 \r\nL 17.484375 54.6875 \r\nL 17.484375 21.921875 \r\nQ 17.484375 14.15625 20.5 10.265625 \r\nQ 23.53125 6.390625 29.59375 6.390625 \r\nQ 36.859375 6.390625 41.078125 11.03125 \r\nQ 45.3125 15.671875 45.3125 23.6875 \r\nL 45.3125 54.6875 \r\nL 54.296875 54.6875 \r\nL 54.296875 0 \r\nL 45.3125 0 \r\nL 45.3125 8.40625 \r\nQ 42.046875 3.421875 37.71875 1 \r\nQ 33.40625 -1.421875 27.6875 -1.421875 \r\nQ 18.265625 -1.421875 13.375 4.4375 \r\nQ 8.5 10.296875 8.5 21.578125 \r\nz\r\nM 31.109375 56 \r\nz\r\n\" id=\"DejaVuSans-117\"/>\r\n       <path d=\"M 48.78125 52.59375 \r\nL 48.78125 44.1875 \r\nQ 44.96875 46.296875 41.140625 47.34375 \r\nQ 37.3125 48.390625 33.40625 48.390625 \r\nQ 24.65625 48.390625 19.8125 42.84375 \r\nQ 14.984375 37.3125 14.984375 27.296875 \r\nQ 14.984375 17.28125 19.8125 11.734375 \r\nQ 24.65625 6.203125 33.40625 6.203125 \r\nQ 37.3125 6.203125 41.140625 7.25 \r\nQ 44.96875 8.296875 48.78125 10.40625 \r\nL 48.78125 2.09375 \r\nQ 45.015625 0.34375 40.984375 -0.53125 \r\nQ 36.96875 -1.421875 32.421875 -1.421875 \r\nQ 20.0625 -1.421875 12.78125 6.34375 \r\nQ 5.515625 14.109375 5.515625 27.296875 \r\nQ 5.515625 40.671875 12.859375 48.328125 \r\nQ 20.21875 56 33.015625 56 \r\nQ 37.15625 56 41.109375 55.140625 \r\nQ 45.0625 54.296875 48.78125 52.59375 \r\nz\r\n\" id=\"DejaVuSans-99\"/>\r\n       <path d=\"M 18.3125 70.21875 \r\nL 18.3125 54.6875 \r\nL 36.8125 54.6875 \r\nL 36.8125 47.703125 \r\nL 18.3125 47.703125 \r\nL 18.3125 18.015625 \r\nQ 18.3125 11.328125 20.140625 9.421875 \r\nQ 21.96875 7.515625 27.59375 7.515625 \r\nL 36.8125 7.515625 \r\nL 36.8125 0 \r\nL 27.59375 0 \r\nQ 17.1875 0 13.234375 3.875 \r\nQ 9.28125 7.765625 9.28125 18.015625 \r\nL 9.28125 47.703125 \r\nL 2.6875 47.703125 \r\nL 2.6875 54.6875 \r\nL 9.28125 54.6875 \r\nL 9.28125 70.21875 \r\nz\r\n\" id=\"DejaVuSans-116\"/>\r\n       <path d=\"M 9.421875 54.6875 \r\nL 18.40625 54.6875 \r\nL 18.40625 0 \r\nL 9.421875 0 \r\nz\r\nM 9.421875 75.984375 \r\nL 18.40625 75.984375 \r\nL 18.40625 64.59375 \r\nL 9.421875 64.59375 \r\nz\r\n\" id=\"DejaVuSans-105\"/>\r\n       <path d=\"M 2.984375 54.6875 \r\nL 12.5 54.6875 \r\nL 29.59375 8.796875 \r\nL 46.6875 54.6875 \r\nL 56.203125 54.6875 \r\nL 35.6875 0 \r\nL 23.484375 0 \r\nz\r\n\" id=\"DejaVuSans-118\"/>\r\n       <path d=\"M 34.28125 27.484375 \r\nQ 23.390625 27.484375 19.1875 25 \r\nQ 14.984375 22.515625 14.984375 16.5 \r\nQ 14.984375 11.71875 18.140625 8.90625 \r\nQ 21.296875 6.109375 26.703125 6.109375 \r\nQ 34.1875 6.109375 38.703125 11.40625 \r\nQ 43.21875 16.703125 43.21875 25.484375 \r\nL 43.21875 27.484375 \r\nz\r\nM 52.203125 31.203125 \r\nL 52.203125 0 \r\nL 43.21875 0 \r\nL 43.21875 8.296875 \r\nQ 40.140625 3.328125 35.546875 0.953125 \r\nQ 30.953125 -1.421875 24.3125 -1.421875 \r\nQ 15.921875 -1.421875 10.953125 3.296875 \r\nQ 6 8.015625 6 15.921875 \r\nQ 6 25.140625 12.171875 29.828125 \r\nQ 18.359375 34.515625 30.609375 34.515625 \r\nL 43.21875 34.515625 \r\nL 43.21875 35.40625 \r\nQ 43.21875 41.609375 39.140625 45 \r\nQ 35.0625 48.390625 27.6875 48.390625 \r\nQ 23 48.390625 18.546875 47.265625 \r\nQ 14.109375 46.140625 10.015625 43.890625 \r\nL 10.015625 52.203125 \r\nQ 14.9375 54.109375 19.578125 55.046875 \r\nQ 24.21875 56 28.609375 56 \r\nQ 40.484375 56 46.34375 49.84375 \r\nQ 52.203125 43.703125 52.203125 31.203125 \r\nz\r\n\" id=\"DejaVuSans-97\"/>\r\n       <path d=\"M 9.421875 75.984375 \r\nL 18.40625 75.984375 \r\nL 18.40625 0 \r\nL 9.421875 0 \r\nz\r\n\" id=\"DejaVuSans-108\"/>\r\n       <path d=\"M 44.28125 53.078125 \r\nL 44.28125 44.578125 \r\nQ 40.484375 46.53125 36.375 47.5 \r\nQ 32.28125 48.484375 27.875 48.484375 \r\nQ 21.1875 48.484375 17.84375 46.4375 \r\nQ 14.5 44.390625 14.5 40.28125 \r\nQ 14.5 37.15625 16.890625 35.375 \r\nQ 19.28125 33.59375 26.515625 31.984375 \r\nL 29.59375 31.296875 \r\nQ 39.15625 29.25 43.1875 25.515625 \r\nQ 47.21875 21.78125 47.21875 15.09375 \r\nQ 47.21875 7.46875 41.1875 3.015625 \r\nQ 35.15625 -1.421875 24.609375 -1.421875 \r\nQ 20.21875 -1.421875 15.453125 -0.5625 \r\nQ 10.6875 0.296875 5.421875 2 \r\nL 5.421875 11.28125 \r\nQ 10.40625 8.6875 15.234375 7.390625 \r\nQ 20.0625 6.109375 24.8125 6.109375 \r\nQ 31.15625 6.109375 34.5625 8.28125 \r\nQ 37.984375 10.453125 37.984375 14.40625 \r\nQ 37.984375 18.0625 35.515625 20.015625 \r\nQ 33.0625 21.96875 24.703125 23.78125 \r\nL 21.578125 24.515625 \r\nQ 13.234375 26.265625 9.515625 29.90625 \r\nQ 5.8125 33.546875 5.8125 39.890625 \r\nQ 5.8125 47.609375 11.28125 51.796875 \r\nQ 16.75 56 26.8125 56 \r\nQ 31.78125 56 36.171875 55.265625 \r\nQ 40.578125 54.546875 44.28125 53.078125 \r\nz\r\n\" id=\"DejaVuSans-115\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"63.378906\" xlink:href=\"#DejaVuSans-114\"/>\r\n      <use x=\"104.492188\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"136.279297\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use x=\"197.460938\" xlink:href=\"#DejaVuSans-102\"/>\r\n      <use x=\"232.666016\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"264.453125\" xlink:href=\"#DejaVuSans-102\"/>\r\n      <use x=\"299.658203\" xlink:href=\"#DejaVuSans-117\"/>\r\n      <use x=\"363.037109\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"426.416016\" xlink:href=\"#DejaVuSans-99\"/>\r\n      <use x=\"481.396484\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"520.605469\" xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"548.388672\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use x=\"609.570312\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"672.949219\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"704.736328\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"766.259766\" xlink:href=\"#DejaVuSans-118\"/>\r\n      <use x=\"825.439453\" xlink:href=\"#DejaVuSans-97\"/>\r\n      <use x=\"886.71875\" xlink:href=\"#DejaVuSans-108\"/>\r\n      <use x=\"914.501953\" xlink:href=\"#DejaVuSans-117\"/>\r\n      <use x=\"977.880859\" xlink:href=\"#DejaVuSans-97\"/>\r\n      <use x=\"1039.160156\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"1078.369141\" xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"1106.152344\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use x=\"1167.333984\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"1230.712891\" xlink:href=\"#DejaVuSans-115\"/>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_76\">\r\n    <path clip-path=\"url(#p0c53ffec17)\" d=\"M 91.554028 32.885085 \r\nL 145.698087 62.71596 \r\nL 201.349235 93.007427 \r\nL 257.164214 124.408121 \r\nL 326.642884 161.643832 \r\nL 365.059943 188.150843 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    <defs>\r\n     <path d=\"M 0 1.5 \r\nC 0.397805 1.5 0.77937 1.341951 1.06066 1.06066 \r\nC 1.341951 0.77937 1.5 0.397805 1.5 0 \r\nC 1.5 -0.397805 1.341951 -0.77937 1.06066 -1.06066 \r\nC 0.77937 -1.341951 0.397805 -1.5 0 -1.5 \r\nC -0.397805 -1.5 -0.77937 -1.341951 -1.06066 -1.06066 \r\nC -1.341951 -0.77937 -1.5 -0.397805 -1.5 0 \r\nC -1.5 0.397805 -1.341951 0.77937 -1.06066 1.06066 \r\nC -0.77937 1.341951 -0.397805 1.5 0 1.5 \r\nz\r\n\" id=\"m24889e9589\" style=\"stroke:#1f77b4;\"/>\r\n    </defs>\r\n    <g clip-path=\"url(#p0c53ffec17)\">\r\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"91.554028\" xlink:href=\"#m24889e9589\" y=\"32.885085\"/>\r\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"145.698087\" xlink:href=\"#m24889e9589\" y=\"62.71596\"/>\r\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"201.349235\" xlink:href=\"#m24889e9589\" y=\"93.007427\"/>\r\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"257.164214\" xlink:href=\"#m24889e9589\" y=\"124.408121\"/>\r\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"326.642884\" xlink:href=\"#m24889e9589\" y=\"161.643832\"/>\r\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"365.059943\" xlink:href=\"#m24889e9589\" y=\"188.150843\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_77\">\r\n    <path clip-path=\"url(#p0c53ffec17)\" d=\"M 60.696307 32.301376 \r\nL 114.148451 65.772439 \r\nL 170.137798 99.652935 \r\nL 214.43217 132.80023 \r\nL 271.59916 169.90857 \r\nL 325.613109 203.930219 \r\n\" style=\"fill:none;stroke:#ff7f0e;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    <defs>\r\n     <path d=\"M 0 1.5 \r\nC 0.397805 1.5 0.77937 1.341951 1.06066 1.06066 \r\nC 1.341951 0.77937 1.5 0.397805 1.5 0 \r\nC 1.5 -0.397805 1.341951 -0.77937 1.06066 -1.06066 \r\nC 0.77937 -1.341951 0.397805 -1.5 0 -1.5 \r\nC -0.397805 -1.5 -0.77937 -1.341951 -1.06066 -1.06066 \r\nC -1.341951 -0.77937 -1.5 -0.397805 -1.5 0 \r\nC -1.5 0.397805 -1.341951 0.77937 -1.06066 1.06066 \r\nC -0.77937 1.341951 -0.397805 1.5 0 1.5 \r\nz\r\n\" id=\"mebf5a5c357\" style=\"stroke:#ff7f0e;\"/>\r\n    </defs>\r\n    <g clip-path=\"url(#p0c53ffec17)\">\r\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"60.696307\" xlink:href=\"#mebf5a5c357\" y=\"32.301376\"/>\r\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"114.148451\" xlink:href=\"#mebf5a5c357\" y=\"65.772439\"/>\r\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"170.137798\" xlink:href=\"#mebf5a5c357\" y=\"99.652935\"/>\r\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"214.43217\" xlink:href=\"#mebf5a5c357\" y=\"132.80023\"/>\r\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"271.59916\" xlink:href=\"#mebf5a5c357\" y=\"169.90857\"/>\r\n     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"325.613109\" xlink:href=\"#mebf5a5c357\" y=\"203.930219\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_78\">\r\n    <path clip-path=\"url(#p0c53ffec17)\" d=\"M 60.696307 61.321646 \r\nL 114.148451 93.68926 \r\nL 170.137798 126.631408 \r\nL 214.43217 159.166331 \r\nL 271.59916 196.860891 \r\nL 325.613109 231.966395 \r\n\" style=\"fill:none;stroke:#2ca02c;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    <defs>\r\n     <path d=\"M 0 1.5 \r\nC 0.397805 1.5 0.77937 1.341951 1.06066 1.06066 \r\nC 1.341951 0.77937 1.5 0.397805 1.5 0 \r\nC 1.5 -0.397805 1.341951 -0.77937 1.06066 -1.06066 \r\nC 0.77937 -1.341951 0.397805 -1.5 0 -1.5 \r\nC -0.397805 -1.5 -0.77937 -1.341951 -1.06066 -1.06066 \r\nC -1.341951 -0.77937 -1.5 -0.397805 -1.5 0 \r\nC -1.5 0.397805 -1.341951 0.77937 -1.06066 1.06066 \r\nC -0.77937 1.341951 -0.397805 1.5 0 1.5 \r\nz\r\n\" id=\"m5ba74215c1\" style=\"stroke:#2ca02c;\"/>\r\n    </defs>\r\n    <g clip-path=\"url(#p0c53ffec17)\">\r\n     <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"60.696307\" xlink:href=\"#m5ba74215c1\" y=\"61.321646\"/>\r\n     <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"114.148451\" xlink:href=\"#m5ba74215c1\" y=\"93.68926\"/>\r\n     <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"170.137798\" xlink:href=\"#m5ba74215c1\" y=\"126.631408\"/>\r\n     <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"214.43217\" xlink:href=\"#m5ba74215c1\" y=\"159.166331\"/>\r\n     <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"271.59916\" xlink:href=\"#m5ba74215c1\" y=\"196.860891\"/>\r\n     <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"325.613109\" xlink:href=\"#m5ba74215c1\" y=\"231.966395\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"patch_3\">\r\n    <path d=\"M 45.478125 239.758125 \r\nL 45.478125 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_4\">\r\n    <path d=\"M 380.278125 239.758125 \r\nL 380.278125 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_5\">\r\n    <path d=\"M 45.478125 239.758125 \r\nL 380.278125 239.758125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_6\">\r\n    <path d=\"M 45.478125 22.318125 \r\nL 380.278125 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"text_12\">\r\n    <!-- efficiency -->\r\n    <g transform=\"translate(183.984375 16.318125)scale(0.12 -0.12)\">\r\n     <defs>\r\n      <path d=\"M 32.171875 -5.078125 \r\nQ 28.375 -14.84375 24.75 -17.8125 \r\nQ 21.140625 -20.796875 15.09375 -20.796875 \r\nL 7.90625 -20.796875 \r\nL 7.90625 -13.28125 \r\nL 13.1875 -13.28125 \r\nQ 16.890625 -13.28125 18.9375 -11.515625 \r\nQ 21 -9.765625 23.484375 -3.21875 \r\nL 25.09375 0.875 \r\nL 2.984375 54.6875 \r\nL 12.5 54.6875 \r\nL 29.59375 11.921875 \r\nL 46.6875 54.6875 \r\nL 56.203125 54.6875 \r\nz\r\n\" id=\"DejaVuSans-121\"/>\r\n     </defs>\r\n     <use xlink:href=\"#DejaVuSans-101\"/>\r\n     <use x=\"61.523438\" xlink:href=\"#DejaVuSans-102\"/>\r\n     <use x=\"96.728516\" xlink:href=\"#DejaVuSans-102\"/>\r\n     <use x=\"131.933594\" xlink:href=\"#DejaVuSans-105\"/>\r\n     <use x=\"159.716797\" xlink:href=\"#DejaVuSans-99\"/>\r\n     <use x=\"214.697266\" xlink:href=\"#DejaVuSans-105\"/>\r\n     <use x=\"242.480469\" xlink:href=\"#DejaVuSans-101\"/>\r\n     <use x=\"304.003906\" xlink:href=\"#DejaVuSans-110\"/>\r\n     <use x=\"367.382812\" xlink:href=\"#DejaVuSans-99\"/>\r\n     <use x=\"422.363281\" xlink:href=\"#DejaVuSans-121\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"legend_1\">\r\n    <g id=\"patch_7\">\r\n     <path d=\"M 307.740625 74.630625 \r\nL 373.278125 74.630625 \r\nQ 375.278125 74.630625 375.278125 72.630625 \r\nL 375.278125 29.318125 \r\nQ 375.278125 27.318125 373.278125 27.318125 \r\nL 307.740625 27.318125 \r\nQ 305.740625 27.318125 305.740625 29.318125 \r\nL 305.740625 72.630625 \r\nQ 305.740625 74.630625 307.740625 74.630625 \r\nz\r\n\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\r\n    </g>\r\n    <g id=\"line2d_79\">\r\n     <path d=\"M 309.740625 35.416562 \r\nL 329.740625 35.416562 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_80\">\r\n     <g>\r\n      <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"319.740625\" xlink:href=\"#m24889e9589\" y=\"35.416562\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"text_13\">\r\n     <!-- RK45 -->\r\n     <g transform=\"translate(337.740625 38.916562)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 44.390625 34.1875 \r\nQ 47.5625 33.109375 50.5625 29.59375 \r\nQ 53.5625 26.078125 56.59375 19.921875 \r\nL 66.609375 0 \r\nL 56 0 \r\nL 46.6875 18.703125 \r\nQ 43.0625 26.03125 39.671875 28.421875 \r\nQ 36.28125 30.8125 30.421875 30.8125 \r\nL 19.671875 30.8125 \r\nL 19.671875 0 \r\nL 9.8125 0 \r\nL 9.8125 72.90625 \r\nL 32.078125 72.90625 \r\nQ 44.578125 72.90625 50.734375 67.671875 \r\nQ 56.890625 62.453125 56.890625 51.90625 \r\nQ 56.890625 45.015625 53.6875 40.46875 \r\nQ 50.484375 35.9375 44.390625 34.1875 \r\nz\r\nM 19.671875 64.796875 \r\nL 19.671875 38.921875 \r\nL 32.078125 38.921875 \r\nQ 39.203125 38.921875 42.84375 42.21875 \r\nQ 46.484375 45.515625 46.484375 51.90625 \r\nQ 46.484375 58.296875 42.84375 61.546875 \r\nQ 39.203125 64.796875 32.078125 64.796875 \r\nz\r\n\" id=\"DejaVuSans-82\"/>\r\n       <path d=\"M 9.8125 72.90625 \r\nL 19.671875 72.90625 \r\nL 19.671875 42.09375 \r\nL 52.390625 72.90625 \r\nL 65.09375 72.90625 \r\nL 28.90625 38.921875 \r\nL 67.671875 0 \r\nL 54.6875 0 \r\nL 19.671875 35.109375 \r\nL 19.671875 0 \r\nL 9.8125 0 \r\nz\r\n\" id=\"DejaVuSans-75\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-82\"/>\r\n      <use x=\"69.482422\" xlink:href=\"#DejaVuSans-75\"/>\r\n      <use x=\"135.058594\" xlink:href=\"#DejaVuSans-52\"/>\r\n      <use x=\"198.681641\" xlink:href=\"#DejaVuSans-53\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_81\">\r\n     <path d=\"M 309.740625 50.094687 \r\nL 329.740625 50.094687 \r\n\" style=\"fill:none;stroke:#ff7f0e;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_82\">\r\n     <g>\r\n      <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"319.740625\" xlink:href=\"#mebf5a5c357\" y=\"50.094687\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"text_14\">\r\n     <!-- BS45 -->\r\n     <g transform=\"translate(337.740625 53.594687)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 19.671875 34.8125 \r\nL 19.671875 8.109375 \r\nL 35.5 8.109375 \r\nQ 43.453125 8.109375 47.28125 11.40625 \r\nQ 51.125 14.703125 51.125 21.484375 \r\nQ 51.125 28.328125 47.28125 31.5625 \r\nQ 43.453125 34.8125 35.5 34.8125 \r\nz\r\nM 19.671875 64.796875 \r\nL 19.671875 42.828125 \r\nL 34.28125 42.828125 \r\nQ 41.5 42.828125 45.03125 45.53125 \r\nQ 48.578125 48.25 48.578125 53.8125 \r\nQ 48.578125 59.328125 45.03125 62.0625 \r\nQ 41.5 64.796875 34.28125 64.796875 \r\nz\r\nM 9.8125 72.90625 \r\nL 35.015625 72.90625 \r\nQ 46.296875 72.90625 52.390625 68.21875 \r\nQ 58.5 63.53125 58.5 54.890625 \r\nQ 58.5 48.1875 55.375 44.234375 \r\nQ 52.25 40.28125 46.1875 39.3125 \r\nQ 53.46875 37.75 57.5 32.78125 \r\nQ 61.53125 27.828125 61.53125 20.40625 \r\nQ 61.53125 10.640625 54.890625 5.3125 \r\nQ 48.25 0 35.984375 0 \r\nL 9.8125 0 \r\nz\r\n\" id=\"DejaVuSans-66\"/>\r\n       <path d=\"M 53.515625 70.515625 \r\nL 53.515625 60.890625 \r\nQ 47.90625 63.578125 42.921875 64.890625 \r\nQ 37.9375 66.21875 33.296875 66.21875 \r\nQ 25.25 66.21875 20.875 63.09375 \r\nQ 16.5 59.96875 16.5 54.203125 \r\nQ 16.5 49.359375 19.40625 46.890625 \r\nQ 22.3125 44.4375 30.421875 42.921875 \r\nL 36.375 41.703125 \r\nQ 47.40625 39.59375 52.65625 34.296875 \r\nQ 57.90625 29 57.90625 20.125 \r\nQ 57.90625 9.515625 50.796875 4.046875 \r\nQ 43.703125 -1.421875 29.984375 -1.421875 \r\nQ 24.8125 -1.421875 18.96875 -0.25 \r\nQ 13.140625 0.921875 6.890625 3.21875 \r\nL 6.890625 13.375 \r\nQ 12.890625 10.015625 18.65625 8.296875 \r\nQ 24.421875 6.59375 29.984375 6.59375 \r\nQ 38.421875 6.59375 43.015625 9.90625 \r\nQ 47.609375 13.234375 47.609375 19.390625 \r\nQ 47.609375 24.75 44.3125 27.78125 \r\nQ 41.015625 30.8125 33.5 32.328125 \r\nL 27.484375 33.5 \r\nQ 16.453125 35.6875 11.515625 40.375 \r\nQ 6.59375 45.0625 6.59375 53.421875 \r\nQ 6.59375 63.09375 13.40625 68.65625 \r\nQ 20.21875 74.21875 32.171875 74.21875 \r\nQ 37.3125 74.21875 42.625 73.28125 \r\nQ 47.953125 72.359375 53.515625 70.515625 \r\nz\r\n\" id=\"DejaVuSans-83\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-66\"/>\r\n      <use x=\"66.853516\" xlink:href=\"#DejaVuSans-83\"/>\r\n      <use x=\"130.330078\" xlink:href=\"#DejaVuSans-52\"/>\r\n      <use x=\"193.953125\" xlink:href=\"#DejaVuSans-53\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_83\">\r\n     <path d=\"M 309.740625 64.772812 \r\nL 329.740625 64.772812 \r\n\" style=\"fill:none;stroke:#2ca02c;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_84\">\r\n     <g>\r\n      <use style=\"fill:#2ca02c;stroke:#2ca02c;\" x=\"319.740625\" xlink:href=\"#m5ba74215c1\" y=\"64.772812\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"text_15\">\r\n     <!-- BS45_i -->\r\n     <g transform=\"translate(337.740625 68.272812)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 50.984375 -16.609375 \r\nL 50.984375 -23.578125 \r\nL -0.984375 -23.578125 \r\nL -0.984375 -16.609375 \r\nz\r\n\" id=\"DejaVuSans-95\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-66\"/>\r\n      <use x=\"66.853516\" xlink:href=\"#DejaVuSans-83\"/>\r\n      <use x=\"130.330078\" xlink:href=\"#DejaVuSans-52\"/>\r\n      <use x=\"193.953125\" xlink:href=\"#DejaVuSans-53\"/>\r\n      <use x=\"257.576172\" xlink:href=\"#DejaVuSans-95\"/>\r\n      <use x=\"307.576172\" xlink:href=\"#DejaVuSans-105\"/>\r\n     </g>\r\n    </g>\r\n   </g>\r\n  </g>\r\n </g>\r\n <defs>\r\n  <clipPath id=\"p0c53ffec17\">\r\n   <rect height=\"217.44\" width=\"334.8\" x=\"45.478125\" y=\"22.318125\"/>\r\n  </clipPath>\r\n </defs>\r\n</svg>\r\n",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "from extensisq import BS45, BS45_i\n",
    "\n",
    "methods = ['RK45', BS45, BS45_i]\n",
    "tolerances = np.logspace(-7, -2, 6)\n",
    "\n",
    "plt.figure()\n",
    "solutions = []\n",
    "for method in methods:\n",
    "    name = method if isinstance(method, str) else method.__name__\n",
    "    e = []\n",
    "    n = []\n",
    "    for tol in tolerances:\n",
    "        sol = solve_ivp(**problem, rtol=1e-13, atol=tol, method=method,\n",
    "                dense_output=True)       # this triggers the extra function calls in BS45\n",
    "        err = rms_err_norm(sol, reference)\n",
    "        e.append(err)\n",
    "        n.append(sol.nfev)\n",
    "    solutions.append(sol)                # save only high tol solution\n",
    "    plt.loglog(e, n, '.:', label=name)\n",
    "plt.legend()\n",
    "plt.xlabel(r'||error||$_{RMS}$')\n",
    "plt.ylabel('nr of function evaluations')\n",
    "plt.title('efficiency')\n",
    "plt.ylim(ymin=1e2)\n",
    "plt.show()     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows that `BS45_i` is roughly twice (!) as efficient as `RK45`, scipy's default method. This graph also shows that `BS45` needs more function evaluations (for the accurate fifth order interpolant), but is still more efficient than `RK45`.\n",
    "\n",
    "## Interpolation\n",
    "\n",
    "Notice in the plot how the errors of `BS45` and `BS45_i` are exactly the same for a given tolerance value. This is expected, since the only diference between the two methods is the interpolant. Let's take a closer look at the interpolation accuracy *in-between* the solution points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<!-- Created with matplotlib (https://matplotlib.org/) -->\r\n<svg height=\"263.63625pt\" version=\"1.1\" viewBox=\"0 0 394.796875 263.63625\" width=\"394.796875pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-02-10T08:19:13.346829</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.3.2, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n </defs>\r\n <g id=\"figure_1\">\r\n  <g id=\"patch_1\">\r\n   <path d=\"M -0 263.63625 \r\nL 394.796875 263.63625 \r\nL 394.796875 0 \r\nL -0 0 \r\nz\r\n\" style=\"fill:none;\"/>\r\n  </g>\r\n  <g id=\"axes_1\">\r\n   <g id=\"patch_2\">\r\n    <path d=\"M 38.482813 239.758125 \r\nL 373.282813 239.758125 \r\nL 373.282813 22.318125 \r\nL 38.482813 22.318125 \r\nz\r\n\" style=\"fill:#ffffff;\"/>\r\n   </g>\r\n   <g id=\"matplotlib.axis_1\">\r\n    <g id=\"xtick_1\">\r\n     <g id=\"line2d_1\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL 0 3.5 \r\n\" id=\"mbb30dc4bdb\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_1\">\r\n      <!-- 12.00 -->\r\n      <g transform=\"translate(24.16875 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 12.40625 8.296875 \r\nL 28.515625 8.296875 \r\nL 28.515625 63.921875 \r\nL 10.984375 60.40625 \r\nL 10.984375 69.390625 \r\nL 28.421875 72.90625 \r\nL 38.28125 72.90625 \r\nL 38.28125 8.296875 \r\nL 54.390625 8.296875 \r\nL 54.390625 0 \r\nL 12.40625 0 \r\nz\r\n\" id=\"DejaVuSans-49\"/>\r\n        <path d=\"M 19.1875 8.296875 \r\nL 53.609375 8.296875 \r\nL 53.609375 0 \r\nL 7.328125 0 \r\nL 7.328125 8.296875 \r\nQ 12.9375 14.109375 22.625 23.890625 \r\nQ 32.328125 33.6875 34.8125 36.53125 \r\nQ 39.546875 41.84375 41.421875 45.53125 \r\nQ 43.3125 49.21875 43.3125 52.78125 \r\nQ 43.3125 58.59375 39.234375 62.25 \r\nQ 35.15625 65.921875 28.609375 65.921875 \r\nQ 23.96875 65.921875 18.8125 64.3125 \r\nQ 13.671875 62.703125 7.8125 59.421875 \r\nL 7.8125 69.390625 \r\nQ 13.765625 71.78125 18.9375 73 \r\nQ 24.125 74.21875 28.421875 74.21875 \r\nQ 39.75 74.21875 46.484375 68.546875 \r\nQ 53.21875 62.890625 53.21875 53.421875 \r\nQ 53.21875 48.921875 51.53125 44.890625 \r\nQ 49.859375 40.875 45.40625 35.40625 \r\nQ 44.1875 33.984375 37.640625 27.21875 \r\nQ 31.109375 20.453125 19.1875 8.296875 \r\nz\r\n\" id=\"DejaVuSans-50\"/>\r\n        <path d=\"M 10.6875 12.40625 \r\nL 21 12.40625 \r\nL 21 0 \r\nL 10.6875 0 \r\nz\r\n\" id=\"DejaVuSans-46\"/>\r\n        <path d=\"M 31.78125 66.40625 \r\nQ 24.171875 66.40625 20.328125 58.90625 \r\nQ 16.5 51.421875 16.5 36.375 \r\nQ 16.5 21.390625 20.328125 13.890625 \r\nQ 24.171875 6.390625 31.78125 6.390625 \r\nQ 39.453125 6.390625 43.28125 13.890625 \r\nQ 47.125 21.390625 47.125 36.375 \r\nQ 47.125 51.421875 43.28125 58.90625 \r\nQ 39.453125 66.40625 31.78125 66.40625 \r\nz\r\nM 31.78125 74.21875 \r\nQ 44.046875 74.21875 50.515625 64.515625 \r\nQ 56.984375 54.828125 56.984375 36.375 \r\nQ 56.984375 17.96875 50.515625 8.265625 \r\nQ 44.046875 -1.421875 31.78125 -1.421875 \r\nQ 19.53125 -1.421875 13.0625 8.265625 \r\nQ 6.59375 17.96875 6.59375 36.375 \r\nQ 6.59375 54.828125 13.0625 64.515625 \r\nQ 19.53125 74.21875 31.78125 74.21875 \r\nz\r\n\" id=\"DejaVuSans-48\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_2\">\r\n     <g id=\"line2d_2\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"80.332812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_2\">\r\n      <!-- 12.25 -->\r\n      <g transform=\"translate(66.01875 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 10.796875 72.90625 \r\nL 49.515625 72.90625 \r\nL 49.515625 64.59375 \r\nL 19.828125 64.59375 \r\nL 19.828125 46.734375 \r\nQ 21.96875 47.46875 24.109375 47.828125 \r\nQ 26.265625 48.1875 28.421875 48.1875 \r\nQ 40.625 48.1875 47.75 41.5 \r\nQ 54.890625 34.8125 54.890625 23.390625 \r\nQ 54.890625 11.625 47.5625 5.09375 \r\nQ 40.234375 -1.421875 26.90625 -1.421875 \r\nQ 22.3125 -1.421875 17.546875 -0.640625 \r\nQ 12.796875 0.140625 7.71875 1.703125 \r\nL 7.71875 11.625 \r\nQ 12.109375 9.234375 16.796875 8.0625 \r\nQ 21.484375 6.890625 26.703125 6.890625 \r\nQ 35.15625 6.890625 40.078125 11.328125 \r\nQ 45.015625 15.765625 45.015625 23.390625 \r\nQ 45.015625 31 40.078125 35.4375 \r\nQ 35.15625 39.890625 26.703125 39.890625 \r\nQ 22.75 39.890625 18.8125 39.015625 \r\nQ 14.890625 38.140625 10.796875 36.28125 \r\nz\r\n\" id=\"DejaVuSans-53\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_3\">\r\n     <g id=\"line2d_3\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"122.182812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_3\">\r\n      <!-- 12.50 -->\r\n      <g transform=\"translate(107.86875 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_4\">\r\n     <g id=\"line2d_4\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"164.032812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_4\">\r\n      <!-- 12.75 -->\r\n      <g transform=\"translate(149.71875 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 8.203125 72.90625 \r\nL 55.078125 72.90625 \r\nL 55.078125 68.703125 \r\nL 28.609375 0 \r\nL 18.3125 0 \r\nL 43.21875 64.59375 \r\nL 8.203125 64.59375 \r\nz\r\n\" id=\"DejaVuSans-55\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-55\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_5\">\r\n     <g id=\"line2d_5\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"205.882812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_5\">\r\n      <!-- 13.00 -->\r\n      <g transform=\"translate(191.56875 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 40.578125 39.3125 \r\nQ 47.65625 37.796875 51.625 33 \r\nQ 55.609375 28.21875 55.609375 21.1875 \r\nQ 55.609375 10.40625 48.1875 4.484375 \r\nQ 40.765625 -1.421875 27.09375 -1.421875 \r\nQ 22.515625 -1.421875 17.65625 -0.515625 \r\nQ 12.796875 0.390625 7.625 2.203125 \r\nL 7.625 11.71875 \r\nQ 11.71875 9.328125 16.59375 8.109375 \r\nQ 21.484375 6.890625 26.8125 6.890625 \r\nQ 36.078125 6.890625 40.9375 10.546875 \r\nQ 45.796875 14.203125 45.796875 21.1875 \r\nQ 45.796875 27.640625 41.28125 31.265625 \r\nQ 36.765625 34.90625 28.71875 34.90625 \r\nL 20.21875 34.90625 \r\nL 20.21875 43.015625 \r\nL 29.109375 43.015625 \r\nQ 36.375 43.015625 40.234375 45.921875 \r\nQ 44.09375 48.828125 44.09375 54.296875 \r\nQ 44.09375 59.90625 40.109375 62.90625 \r\nQ 36.140625 65.921875 28.71875 65.921875 \r\nQ 24.65625 65.921875 20.015625 65.03125 \r\nQ 15.375 64.15625 9.8125 62.3125 \r\nL 9.8125 71.09375 \r\nQ 15.4375 72.65625 20.34375 73.4375 \r\nQ 25.25 74.21875 29.59375 74.21875 \r\nQ 40.828125 74.21875 47.359375 69.109375 \r\nQ 53.90625 64.015625 53.90625 55.328125 \r\nQ 53.90625 49.265625 50.4375 45.09375 \r\nQ 46.96875 40.921875 40.578125 39.3125 \r\nz\r\n\" id=\"DejaVuSans-51\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_6\">\r\n     <g id=\"line2d_6\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"247.732812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_6\">\r\n      <!-- 13.25 -->\r\n      <g transform=\"translate(233.41875 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-50\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_7\">\r\n     <g id=\"line2d_7\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"289.582812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_7\">\r\n      <!-- 13.50 -->\r\n      <g transform=\"translate(275.26875 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_8\">\r\n     <g id=\"line2d_8\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"331.432812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_8\">\r\n      <!-- 13.75 -->\r\n      <g transform=\"translate(317.11875 254.356563)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-51\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-55\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-53\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_9\">\r\n     <g id=\"line2d_9\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"373.282812\" xlink:href=\"#mbb30dc4bdb\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_9\">\r\n      <!-- 14.00 -->\r\n      <g transform=\"translate(358.96875 254.356563)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 37.796875 64.3125 \r\nL 12.890625 25.390625 \r\nL 37.796875 25.390625 \r\nz\r\nM 35.203125 72.90625 \r\nL 47.609375 72.90625 \r\nL 47.609375 25.390625 \r\nL 58.015625 25.390625 \r\nL 58.015625 17.1875 \r\nL 47.609375 17.1875 \r\nL 47.609375 0 \r\nL 37.796875 0 \r\nL 37.796875 17.1875 \r\nL 4.890625 17.1875 \r\nL 4.890625 26.703125 \r\nz\r\n\" id=\"DejaVuSans-52\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-52\"/>\r\n       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"222.65625\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"matplotlib.axis_2\">\r\n    <g id=\"ytick_1\">\r\n     <g id=\"line2d_10\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL -3.5 0 \r\n\" id=\"ma336a4ec0e\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"239.758125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_10\">\r\n      <!-- −0.2 -->\r\n      <g transform=\"translate(7.2 243.557344)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 10.59375 35.5 \r\nL 73.1875 35.5 \r\nL 73.1875 27.203125 \r\nL 10.59375 27.203125 \r\nz\r\n\" id=\"DejaVuSans-8722\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-8722\"/>\r\n       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_2\">\r\n     <g id=\"line2d_11\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"215.598125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_11\">\r\n      <!-- 0.0 -->\r\n      <g transform=\"translate(15.579688 219.397344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_3\">\r\n     <g id=\"line2d_12\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"191.438125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_12\">\r\n      <!-- 0.2 -->\r\n      <g transform=\"translate(15.579688 195.237344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_4\">\r\n     <g id=\"line2d_13\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"167.278125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_13\">\r\n      <!-- 0.4 -->\r\n      <g transform=\"translate(15.579688 171.077344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_5\">\r\n     <g id=\"line2d_14\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"143.118125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_14\">\r\n      <!-- 0.6 -->\r\n      <g transform=\"translate(15.579688 146.917344)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 33.015625 40.375 \r\nQ 26.375 40.375 22.484375 35.828125 \r\nQ 18.609375 31.296875 18.609375 23.390625 \r\nQ 18.609375 15.53125 22.484375 10.953125 \r\nQ 26.375 6.390625 33.015625 6.390625 \r\nQ 39.65625 6.390625 43.53125 10.953125 \r\nQ 47.40625 15.53125 47.40625 23.390625 \r\nQ 47.40625 31.296875 43.53125 35.828125 \r\nQ 39.65625 40.375 33.015625 40.375 \r\nz\r\nM 52.59375 71.296875 \r\nL 52.59375 62.3125 \r\nQ 48.875 64.0625 45.09375 64.984375 \r\nQ 41.3125 65.921875 37.59375 65.921875 \r\nQ 27.828125 65.921875 22.671875 59.328125 \r\nQ 17.53125 52.734375 16.796875 39.40625 \r\nQ 19.671875 43.65625 24.015625 45.921875 \r\nQ 28.375 48.1875 33.59375 48.1875 \r\nQ 44.578125 48.1875 50.953125 41.515625 \r\nQ 57.328125 34.859375 57.328125 23.390625 \r\nQ 57.328125 12.15625 50.6875 5.359375 \r\nQ 44.046875 -1.421875 33.015625 -1.421875 \r\nQ 20.359375 -1.421875 13.671875 8.265625 \r\nQ 6.984375 17.96875 6.984375 36.375 \r\nQ 6.984375 53.65625 15.1875 63.9375 \r\nQ 23.390625 74.21875 37.203125 74.21875 \r\nQ 40.921875 74.21875 44.703125 73.484375 \r\nQ 48.484375 72.75 52.59375 71.296875 \r\nz\r\n\" id=\"DejaVuSans-54\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_6\">\r\n     <g id=\"line2d_15\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"118.958125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_15\">\r\n      <!-- 0.8 -->\r\n      <g transform=\"translate(15.579688 122.757344)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 31.78125 34.625 \r\nQ 24.75 34.625 20.71875 30.859375 \r\nQ 16.703125 27.09375 16.703125 20.515625 \r\nQ 16.703125 13.921875 20.71875 10.15625 \r\nQ 24.75 6.390625 31.78125 6.390625 \r\nQ 38.8125 6.390625 42.859375 10.171875 \r\nQ 46.921875 13.96875 46.921875 20.515625 \r\nQ 46.921875 27.09375 42.890625 30.859375 \r\nQ 38.875 34.625 31.78125 34.625 \r\nz\r\nM 21.921875 38.8125 \r\nQ 15.578125 40.375 12.03125 44.71875 \r\nQ 8.5 49.078125 8.5 55.328125 \r\nQ 8.5 64.0625 14.71875 69.140625 \r\nQ 20.953125 74.21875 31.78125 74.21875 \r\nQ 42.671875 74.21875 48.875 69.140625 \r\nQ 55.078125 64.0625 55.078125 55.328125 \r\nQ 55.078125 49.078125 51.53125 44.71875 \r\nQ 48 40.375 41.703125 38.8125 \r\nQ 48.828125 37.15625 52.796875 32.3125 \r\nQ 56.78125 27.484375 56.78125 20.515625 \r\nQ 56.78125 9.90625 50.3125 4.234375 \r\nQ 43.84375 -1.421875 31.78125 -1.421875 \r\nQ 19.734375 -1.421875 13.25 4.234375 \r\nQ 6.78125 9.90625 6.78125 20.515625 \r\nQ 6.78125 27.484375 10.78125 32.3125 \r\nQ 14.796875 37.15625 21.921875 38.8125 \r\nz\r\nM 18.3125 54.390625 \r\nQ 18.3125 48.734375 21.84375 45.5625 \r\nQ 25.390625 42.390625 31.78125 42.390625 \r\nQ 38.140625 42.390625 41.71875 45.5625 \r\nQ 45.3125 48.734375 45.3125 54.390625 \r\nQ 45.3125 60.0625 41.71875 63.234375 \r\nQ 38.140625 66.40625 31.78125 66.40625 \r\nQ 25.390625 66.40625 21.84375 63.234375 \r\nQ 18.3125 60.0625 18.3125 54.390625 \r\nz\r\n\" id=\"DejaVuSans-56\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-48\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_7\">\r\n     <g id=\"line2d_16\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"94.798125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_16\">\r\n      <!-- 1.0 -->\r\n      <g transform=\"translate(15.579688 98.597344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_8\">\r\n     <g id=\"line2d_17\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"70.638125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_17\">\r\n      <!-- 1.2 -->\r\n      <g transform=\"translate(15.579688 74.437344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_9\">\r\n     <g id=\"line2d_18\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"46.478125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_18\">\r\n      <!-- 1.4 -->\r\n      <g transform=\"translate(15.579688 50.277344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_10\">\r\n     <g id=\"line2d_19\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"38.482813\" xlink:href=\"#ma336a4ec0e\" y=\"22.318125\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_19\">\r\n      <!-- 1.6 -->\r\n      <g transform=\"translate(15.579688 26.117344)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-49\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-54\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_20\">\r\n    <path clip-path=\"url(#p32e130995f)\" d=\"M 159.260996 264.63625 \r\nL 161.470568 262.910977 \r\nL 168.303221 257.817281 \r\nL 175.135874 252.998669 \r\nL 181.968527 248.484116 \r\nL 188.80118 244.297489 \r\nL 195.633833 240.457267 \r\nL 202.466486 236.976341 \r\nL 209.299139 233.861883 \r\nL 216.131792 231.115304 \r\nL 222.964445 228.732286 \r\nL 229.797098 226.702896 \r\nL 236.629751 225.011775 \r\nL 243.462404 223.638401 \r\nL 250.295057 222.557423 \r\nL 257.12771 221.73906 \r\nL 263.960364 221.14955 \r\nL 270.793017 220.751668 \r\nL 277.62567 220.505276 \r\nL 284.458323 220.367914 \r\nL 291.290976 220.295433 \r\nL 298.123629 220.242631 \r\nL 304.956282 220.163921 \r\nL 311.788935 220.013992 \r\nL 318.621588 219.748474 \r\nL 325.454241 219.324586 \r\nL 332.286894 218.701767 \r\nL 339.119547 217.842276 \r\nL 345.9522 216.711754 \r\nL 352.784853 215.279745 \r\nL 359.617506 213.520164 \r\nL 366.450159 211.411707 \r\nL 373.282812 208.938201 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_21\">\r\n    <path clip-path=\"url(#p32e130995f)\" d=\"M 38.482812 165.50266 \r\nL 45.315466 152.474214 \r\nL 52.148119 140.073646 \r\nL 58.980772 128.416737 \r\nL 65.813425 117.611387 \r\nL 72.646078 107.756305 \r\nL 79.478731 98.939734 \r\nL 86.311384 91.23824 \r\nL 93.144037 84.715583 \r\nL 99.97669 79.421703 \r\nL 106.809343 75.391858 \r\nL 113.641996 72.645933 \r\nL 120.474649 71.187946 \r\nL 127.307302 71.005795 \r\nL 134.139955 72.07123 \r\nL 140.972608 74.340089 \r\nL 147.805261 77.75279 \r\nL 154.637915 82.235069 \r\nL 161.470568 87.698965 \r\nL 168.303221 94.044028 \r\nL 175.135874 101.158721 \r\nL 181.968527 108.922001 \r\nL 188.80118 117.205035 \r\nL 195.633833 125.873031 \r\nL 202.466486 134.787145 \r\nL 209.299139 143.806426 \r\nL 216.131792 152.789786 \r\nL 222.964445 161.597948 \r\nL 229.797098 170.095354 \r\nL 236.629751 178.15201 \r\nL 243.462404 185.64524 \r\nL 250.295057 192.461329 \r\nL 257.12771 198.497044 \r\nL 263.960364 203.661005 \r\nL 270.793017 207.874892 \r\nL 277.62567 211.074486 \r\nL 284.458323 213.210516 \r\nL 291.290976 214.249306 \r\nL 298.123629 214.173227 \r\nL 304.956282 212.980927 \r\nL 311.788935 210.687353 \r\nL 318.621588 207.323563 \r\nL 325.454241 202.936318 \r\nL 332.286894 197.587479 \r\nL 339.119547 191.353194 \r\nL 345.9522 184.322913 \r\nL 352.784853 176.598207 \r\nL 359.617506 168.291441 \r\nL 366.450159 159.524291 \r\nL 373.282812 150.426122 \r\n\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_22\">\r\n    <path clip-path=\"url(#p32e130995f)\" d=\"M 152.979383 264.63625 \r\nL 154.637915 263.273605 \r\nL 161.470568 257.86948 \r\nL 168.303221 252.712628 \r\nL 175.135874 247.836341 \r\nL 181.968527 243.269217 \r\nL 188.80118 239.034927 \r\nL 195.633833 235.152029 \r\nL 202.466486 231.633832 \r\nL 209.299139 228.488307 \r\nL 216.131792 225.718041 \r\nL 222.964445 223.320247 \r\nL 229.797098 221.28681 \r\nL 236.629751 219.604385 \r\nL 243.462404 218.254549 \r\nL 250.295057 217.213985 \r\nL 257.12771 216.454728 \r\nL 263.960364 215.944451 \r\nL 270.793017 215.646796 \r\nL 277.62567 215.521757 \r\nL 284.458323 215.526109 \r\nL 291.290976 215.613882 \r\nL 298.123629 215.736884 \r\nL 304.956282 215.84527 \r\nL 311.788935 215.888159 \r\nL 318.621588 215.814297 \r\nL 325.454241 215.57277 \r\nL 332.286894 215.131721 \r\nL 339.119547 214.488778 \r\nL 345.9522 213.594727 \r\nL 352.784853 212.406158 \r\nL 359.617506 210.888376 \r\nL 366.450159 209.014994 \r\nL 373.282812 206.767514 \r\n\" style=\"fill:none;stroke:#000000;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_23\">\r\n    <path clip-path=\"url(#p32e130995f)\" d=\"M 157.428855 264.63625 \r\nL 161.470568 261.448178 \r\nL 168.303221 256.201104 \r\nL 175.135874 251.133088 \r\nL 181.968527 246.27977 \r\nL 188.80118 241.675248 \r\nL 195.633833 237.351488 \r\nL 202.466486 233.337735 \r\nL 209.299139 229.659917 \r\nL 216.131792 226.340056 \r\nL 222.964445 223.395675 \r\nL 229.797098 220.839211 \r\nL 236.629751 218.677416 \r\nL 243.462404 216.910772 \r\nL 250.295057 215.532897 \r\nL 257.12771 214.529952 \r\nL 263.960364 213.880053 \r\nL 270.793017 213.552676 \r\nL 277.62567 213.508068 \r\nL 284.458323 213.696654 \r\nL 291.290976 214.058446 \r\nL 298.123629 214.522451 \r\nL 304.956282 215.006082 \r\nL 311.788935 215.414561 \r\nL 318.621588 215.640335 \r\nL 325.454241 215.562478 \r\nL 332.286894 215.107747 \r\nL 339.119547 214.364423 \r\nL 345.9522 213.318343 \r\nL 352.784853 211.95108 \r\nL 359.617506 210.248758 \r\nL 366.450159 208.201906 \r\nL 373.282812 205.805314 \r\n\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_24\">\r\n    <defs>\r\n     <path d=\"M 0 3 \r\nC 0.795609 3 1.55874 2.683901 2.12132 2.12132 \r\nC 2.683901 1.55874 3 0.795609 3 0 \r\nC 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \r\nC 1.55874 -2.683901 0.795609 -3 0 -3 \r\nC -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \r\nC -2.683901 -1.55874 -3 -0.795609 -3 0 \r\nC -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \r\nC -1.55874 2.683901 -0.795609 3 0 3 \r\nz\r\n\" id=\"m1e8e074354\" style=\"stroke:#000000;\"/>\r\n    </defs>\r\n    <g clip-path=\"url(#p32e130995f)\">\r\n     <use style=\"stroke:#000000;\" x=\"-1\" xlink:href=\"#m1e8e074354\" y=\"296.367597\"/>\r\n     <use style=\"stroke:#000000;\" x=\"79.613404\" xlink:href=\"#m1e8e074354\" y=\"325.793823\"/>\r\n     <use style=\"stroke:#000000;\" x=\"327.462662\" xlink:href=\"#m1e8e074354\" y=\"215.462603\"/>\r\n     <use style=\"stroke:#000000;\" x=\"568.120189\" xlink:href=\"#m1e8e074354\" y=\"79.57279\"/>\r\n     <use style=\"stroke:#000000;\" x=\"824.186501\" xlink:href=\"#m1e8e074354\" y=\"218.118319\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1068.112947\" xlink:href=\"#m1e8e074354\" y=\"317.004209\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1314.980604\" xlink:href=\"#m1e8e074354\" y=\"237.230169\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1377.682812\" xlink:href=\"#m1e8e074354\" y=\"212.584607\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_25\">\r\n    <g clip-path=\"url(#p32e130995f)\">\r\n     <use style=\"stroke:#000000;\" x=\"-1\" xlink:href=\"#m1e8e074354\" y=\"172.722213\"/>\r\n     <use style=\"stroke:#000000;\" x=\"79.613404\" xlink:href=\"#m1e8e074354\" y=\"98.295837\"/>\r\n     <use style=\"stroke:#000000;\" x=\"327.462662\" xlink:href=\"#m1e8e074354\" y=\"205.597634\"/>\r\n     <use style=\"stroke:#000000;\" x=\"568.120189\" xlink:href=\"#m1e8e074354\" y=\"193.368905\"/>\r\n     <use style=\"stroke:#000000;\" x=\"824.186501\" xlink:href=\"#m1e8e074354\" y=\"230.755347\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1068.112947\" xlink:href=\"#m1e8e074354\" y=\"341.743497\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1314.980604\" xlink:href=\"#m1e8e074354\" y=\"107.942219\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1377.682812\" xlink:href=\"#m1e8e074354\" y=\"190.034394\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_26\">\r\n    <path clip-path=\"url(#p32e130995f)\" d=\"M 38.482812 164.253507 \r\nL 45.315466 151.307304 \r\nL 52.148119 139.019913 \r\nL 58.980772 127.50258 \r\nL 65.813425 116.852576 \r\nL 72.646078 107.150386 \r\nL 79.478731 98.456757 \r\nL 86.311384 90.830534 \r\nL 93.144037 84.363606 \r\nL 99.97669 79.129802 \r\nL 106.809343 75.178701 \r\nL 113.641996 72.537054 \r\nL 120.474649 71.210205 \r\nL 127.307302 71.183522 \r\nL 134.139955 72.423849 \r\nL 140.972608 74.880956 \r\nL 147.805261 78.489008 \r\nL 154.637915 83.168043 \r\nL 161.470568 88.82546 \r\nL 168.303221 95.357521 \r\nL 175.135874 102.650857 \r\nL 181.968527 110.583993 \r\nL 188.80118 119.02888 \r\nL 195.633833 127.852436 \r\nL 202.466486 136.918102 \r\nL 209.299139 146.087406 \r\nL 216.131792 155.221539 \r\nL 222.964445 164.182943 \r\nL 229.797098 172.836905 \r\nL 236.629751 181.05317 \r\nL 243.462404 188.707558 \r\nL 250.295057 195.683594 \r\nL 257.12771 201.87415 \r\nL 263.960364 207.183098 \r\nL 270.793017 211.526971 \r\nL 277.62567 214.836636 \r\nL 284.458323 217.058983 \r\nL 291.290976 218.158618 \r\nL 298.123629 218.119568 \r\nL 304.956282 216.947002 \r\nL 311.788935 214.668955 \r\nL 318.621588 211.338072 \r\nL 325.454241 207.033355 \r\nL 332.286894 201.839033 \r\nL 339.119547 195.777726 \r\nL 345.9522 188.909714 \r\nL 352.784853 181.320683 \r\nL 359.617506 173.115317 \r\nL 366.450159 164.413624 \r\nL 373.282812 155.347455 \r\n\" style=\"fill:none;stroke:#000000;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_27\">\r\n    <path clip-path=\"url(#p32e130995f)\" d=\"M 38.482812 168.072066 \r\nL 45.315466 154.437452 \r\nL 52.148119 141.366351 \r\nL 58.980772 129.039078 \r\nL 65.813425 117.644851 \r\nL 72.646078 107.381778 \r\nL 79.478731 98.456856 \r\nL 86.311384 91.027127 \r\nL 93.144037 85.070651 \r\nL 99.97669 80.531294 \r\nL 106.809343 77.349012 \r\nL 113.641996 75.460049 \r\nL 120.474649 74.79715 \r\nL 127.307302 75.289772 \r\nL 134.139955 76.864298 \r\nL 140.972608 79.444241 \r\nL 147.805261 82.950464 \r\nL 154.637915 87.301384 \r\nL 161.470568 92.413186 \r\nL 168.303221 98.200034 \r\nL 175.135874 104.574281 \r\nL 181.968527 111.446681 \r\nL 188.80118 118.726601 \r\nL 195.633833 126.32223 \r\nL 202.466486 134.14079 \r\nL 209.299139 142.08875 \r\nL 216.131792 150.072035 \r\nL 222.964445 157.996234 \r\nL 229.797098 165.766819 \r\nL 236.629751 173.289347 \r\nL 243.462404 180.469679 \r\nL 250.295057 187.214183 \r\nL 257.12771 193.429955 \r\nL 263.960364 199.02502 \r\nL 270.793017 203.908549 \r\nL 277.62567 207.991069 \r\nL 284.458323 211.184675 \r\nL 291.290976 213.403236 \r\nL 298.123629 214.562614 \r\nL 304.956282 214.580869 \r\nL 311.788935 213.378472 \r\nL 318.621588 210.878515 \r\nL 325.454241 207.006926 \r\nL 332.286894 201.769478 \r\nL 339.119547 195.433508 \r\nL 345.9522 188.18189 \r\nL 352.784853 180.184326 \r\nL 359.617506 171.606685 \r\nL 366.450159 162.610561 \r\nL 373.282812 153.352825 \r\n\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"line2d_28\">\r\n    <g clip-path=\"url(#p32e130995f)\">\r\n     <use style=\"stroke:#000000;\" x=\"-1\" xlink:href=\"#m1e8e074354\" y=\"296.367597\"/>\r\n     <use style=\"stroke:#000000;\" x=\"79.613404\" xlink:href=\"#m1e8e074354\" y=\"325.793823\"/>\r\n     <use style=\"stroke:#000000;\" x=\"327.462662\" xlink:href=\"#m1e8e074354\" y=\"215.462603\"/>\r\n     <use style=\"stroke:#000000;\" x=\"568.120189\" xlink:href=\"#m1e8e074354\" y=\"79.57279\"/>\r\n     <use style=\"stroke:#000000;\" x=\"824.186501\" xlink:href=\"#m1e8e074354\" y=\"218.118319\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1068.112947\" xlink:href=\"#m1e8e074354\" y=\"317.004209\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1314.980604\" xlink:href=\"#m1e8e074354\" y=\"237.230169\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1377.682812\" xlink:href=\"#m1e8e074354\" y=\"212.584607\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_29\">\r\n    <g clip-path=\"url(#p32e130995f)\">\r\n     <use style=\"stroke:#000000;\" x=\"-1\" xlink:href=\"#m1e8e074354\" y=\"172.722213\"/>\r\n     <use style=\"stroke:#000000;\" x=\"79.613404\" xlink:href=\"#m1e8e074354\" y=\"98.295837\"/>\r\n     <use style=\"stroke:#000000;\" x=\"327.462662\" xlink:href=\"#m1e8e074354\" y=\"205.597634\"/>\r\n     <use style=\"stroke:#000000;\" x=\"568.120189\" xlink:href=\"#m1e8e074354\" y=\"193.368905\"/>\r\n     <use style=\"stroke:#000000;\" x=\"824.186501\" xlink:href=\"#m1e8e074354\" y=\"230.755347\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1068.112947\" xlink:href=\"#m1e8e074354\" y=\"341.743497\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1314.980604\" xlink:href=\"#m1e8e074354\" y=\"107.942219\"/>\r\n     <use style=\"stroke:#000000;\" x=\"1377.682812\" xlink:href=\"#m1e8e074354\" y=\"190.034394\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"patch_3\">\r\n    <path d=\"M 38.482813 239.758125 \r\nL 38.482813 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_4\">\r\n    <path d=\"M 373.282813 239.758125 \r\nL 373.282813 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_5\">\r\n    <path d=\"M 38.482812 239.758125 \r\nL 373.282812 239.758125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_6\">\r\n    <path d=\"M 38.482812 22.318125 \r\nL 373.282812 22.318125 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"text_20\">\r\n    <!-- interpolants -->\r\n    <g transform=\"translate(169.798438 16.318125)scale(0.12 -0.12)\">\r\n     <defs>\r\n      <path d=\"M 9.421875 54.6875 \r\nL 18.40625 54.6875 \r\nL 18.40625 0 \r\nL 9.421875 0 \r\nz\r\nM 9.421875 75.984375 \r\nL 18.40625 75.984375 \r\nL 18.40625 64.59375 \r\nL 9.421875 64.59375 \r\nz\r\n\" id=\"DejaVuSans-105\"/>\r\n      <path d=\"M 54.890625 33.015625 \r\nL 54.890625 0 \r\nL 45.90625 0 \r\nL 45.90625 32.71875 \r\nQ 45.90625 40.484375 42.875 44.328125 \r\nQ 39.84375 48.1875 33.796875 48.1875 \r\nQ 26.515625 48.1875 22.3125 43.546875 \r\nQ 18.109375 38.921875 18.109375 30.90625 \r\nL 18.109375 0 \r\nL 9.078125 0 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.1875 \r\nQ 21.34375 51.125 25.703125 53.5625 \r\nQ 30.078125 56 35.796875 56 \r\nQ 45.21875 56 50.046875 50.171875 \r\nQ 54.890625 44.34375 54.890625 33.015625 \r\nz\r\n\" id=\"DejaVuSans-110\"/>\r\n      <path d=\"M 18.3125 70.21875 \r\nL 18.3125 54.6875 \r\nL 36.8125 54.6875 \r\nL 36.8125 47.703125 \r\nL 18.3125 47.703125 \r\nL 18.3125 18.015625 \r\nQ 18.3125 11.328125 20.140625 9.421875 \r\nQ 21.96875 7.515625 27.59375 7.515625 \r\nL 36.8125 7.515625 \r\nL 36.8125 0 \r\nL 27.59375 0 \r\nQ 17.1875 0 13.234375 3.875 \r\nQ 9.28125 7.765625 9.28125 18.015625 \r\nL 9.28125 47.703125 \r\nL 2.6875 47.703125 \r\nL 2.6875 54.6875 \r\nL 9.28125 54.6875 \r\nL 9.28125 70.21875 \r\nz\r\n\" id=\"DejaVuSans-116\"/>\r\n      <path d=\"M 56.203125 29.59375 \r\nL 56.203125 25.203125 \r\nL 14.890625 25.203125 \r\nQ 15.484375 15.921875 20.484375 11.0625 \r\nQ 25.484375 6.203125 34.421875 6.203125 \r\nQ 39.59375 6.203125 44.453125 7.46875 \r\nQ 49.3125 8.734375 54.109375 11.28125 \r\nL 54.109375 2.78125 \r\nQ 49.265625 0.734375 44.1875 -0.34375 \r\nQ 39.109375 -1.421875 33.890625 -1.421875 \r\nQ 20.796875 -1.421875 13.15625 6.1875 \r\nQ 5.515625 13.8125 5.515625 26.8125 \r\nQ 5.515625 40.234375 12.765625 48.109375 \r\nQ 20.015625 56 32.328125 56 \r\nQ 43.359375 56 49.78125 48.890625 \r\nQ 56.203125 41.796875 56.203125 29.59375 \r\nz\r\nM 47.21875 32.234375 \r\nQ 47.125 39.59375 43.09375 43.984375 \r\nQ 39.0625 48.390625 32.421875 48.390625 \r\nQ 24.90625 48.390625 20.390625 44.140625 \r\nQ 15.875 39.890625 15.1875 32.171875 \r\nz\r\n\" id=\"DejaVuSans-101\"/>\r\n      <path d=\"M 41.109375 46.296875 \r\nQ 39.59375 47.171875 37.8125 47.578125 \r\nQ 36.03125 48 33.890625 48 \r\nQ 26.265625 48 22.1875 43.046875 \r\nQ 18.109375 38.09375 18.109375 28.8125 \r\nL 18.109375 0 \r\nL 9.078125 0 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.1875 \r\nQ 20.953125 51.171875 25.484375 53.578125 \r\nQ 30.03125 56 36.53125 56 \r\nQ 37.453125 56 38.578125 55.875 \r\nQ 39.703125 55.765625 41.0625 55.515625 \r\nz\r\n\" id=\"DejaVuSans-114\"/>\r\n      <path d=\"M 18.109375 8.203125 \r\nL 18.109375 -20.796875 \r\nL 9.078125 -20.796875 \r\nL 9.078125 54.6875 \r\nL 18.109375 54.6875 \r\nL 18.109375 46.390625 \r\nQ 20.953125 51.265625 25.265625 53.625 \r\nQ 29.59375 56 35.59375 56 \r\nQ 45.5625 56 51.78125 48.09375 \r\nQ 58.015625 40.1875 58.015625 27.296875 \r\nQ 58.015625 14.40625 51.78125 6.484375 \r\nQ 45.5625 -1.421875 35.59375 -1.421875 \r\nQ 29.59375 -1.421875 25.265625 0.953125 \r\nQ 20.953125 3.328125 18.109375 8.203125 \r\nz\r\nM 48.6875 27.296875 \r\nQ 48.6875 37.203125 44.609375 42.84375 \r\nQ 40.53125 48.484375 33.40625 48.484375 \r\nQ 26.265625 48.484375 22.1875 42.84375 \r\nQ 18.109375 37.203125 18.109375 27.296875 \r\nQ 18.109375 17.390625 22.1875 11.75 \r\nQ 26.265625 6.109375 33.40625 6.109375 \r\nQ 40.53125 6.109375 44.609375 11.75 \r\nQ 48.6875 17.390625 48.6875 27.296875 \r\nz\r\n\" id=\"DejaVuSans-112\"/>\r\n      <path d=\"M 30.609375 48.390625 \r\nQ 23.390625 48.390625 19.1875 42.75 \r\nQ 14.984375 37.109375 14.984375 27.296875 \r\nQ 14.984375 17.484375 19.15625 11.84375 \r\nQ 23.34375 6.203125 30.609375 6.203125 \r\nQ 37.796875 6.203125 41.984375 11.859375 \r\nQ 46.1875 17.53125 46.1875 27.296875 \r\nQ 46.1875 37.015625 41.984375 42.703125 \r\nQ 37.796875 48.390625 30.609375 48.390625 \r\nz\r\nM 30.609375 56 \r\nQ 42.328125 56 49.015625 48.375 \r\nQ 55.71875 40.765625 55.71875 27.296875 \r\nQ 55.71875 13.875 49.015625 6.21875 \r\nQ 42.328125 -1.421875 30.609375 -1.421875 \r\nQ 18.84375 -1.421875 12.171875 6.21875 \r\nQ 5.515625 13.875 5.515625 27.296875 \r\nQ 5.515625 40.765625 12.171875 48.375 \r\nQ 18.84375 56 30.609375 56 \r\nz\r\n\" id=\"DejaVuSans-111\"/>\r\n      <path d=\"M 9.421875 75.984375 \r\nL 18.40625 75.984375 \r\nL 18.40625 0 \r\nL 9.421875 0 \r\nz\r\n\" id=\"DejaVuSans-108\"/>\r\n      <path d=\"M 34.28125 27.484375 \r\nQ 23.390625 27.484375 19.1875 25 \r\nQ 14.984375 22.515625 14.984375 16.5 \r\nQ 14.984375 11.71875 18.140625 8.90625 \r\nQ 21.296875 6.109375 26.703125 6.109375 \r\nQ 34.1875 6.109375 38.703125 11.40625 \r\nQ 43.21875 16.703125 43.21875 25.484375 \r\nL 43.21875 27.484375 \r\nz\r\nM 52.203125 31.203125 \r\nL 52.203125 0 \r\nL 43.21875 0 \r\nL 43.21875 8.296875 \r\nQ 40.140625 3.328125 35.546875 0.953125 \r\nQ 30.953125 -1.421875 24.3125 -1.421875 \r\nQ 15.921875 -1.421875 10.953125 3.296875 \r\nQ 6 8.015625 6 15.921875 \r\nQ 6 25.140625 12.171875 29.828125 \r\nQ 18.359375 34.515625 30.609375 34.515625 \r\nL 43.21875 34.515625 \r\nL 43.21875 35.40625 \r\nQ 43.21875 41.609375 39.140625 45 \r\nQ 35.0625 48.390625 27.6875 48.390625 \r\nQ 23 48.390625 18.546875 47.265625 \r\nQ 14.109375 46.140625 10.015625 43.890625 \r\nL 10.015625 52.203125 \r\nQ 14.9375 54.109375 19.578125 55.046875 \r\nQ 24.21875 56 28.609375 56 \r\nQ 40.484375 56 46.34375 49.84375 \r\nQ 52.203125 43.703125 52.203125 31.203125 \r\nz\r\n\" id=\"DejaVuSans-97\"/>\r\n      <path d=\"M 44.28125 53.078125 \r\nL 44.28125 44.578125 \r\nQ 40.484375 46.53125 36.375 47.5 \r\nQ 32.28125 48.484375 27.875 48.484375 \r\nQ 21.1875 48.484375 17.84375 46.4375 \r\nQ 14.5 44.390625 14.5 40.28125 \r\nQ 14.5 37.15625 16.890625 35.375 \r\nQ 19.28125 33.59375 26.515625 31.984375 \r\nL 29.59375 31.296875 \r\nQ 39.15625 29.25 43.1875 25.515625 \r\nQ 47.21875 21.78125 47.21875 15.09375 \r\nQ 47.21875 7.46875 41.1875 3.015625 \r\nQ 35.15625 -1.421875 24.609375 -1.421875 \r\nQ 20.21875 -1.421875 15.453125 -0.5625 \r\nQ 10.6875 0.296875 5.421875 2 \r\nL 5.421875 11.28125 \r\nQ 10.40625 8.6875 15.234375 7.390625 \r\nQ 20.0625 6.109375 24.8125 6.109375 \r\nQ 31.15625 6.109375 34.5625 8.28125 \r\nQ 37.984375 10.453125 37.984375 14.40625 \r\nQ 37.984375 18.0625 35.515625 20.015625 \r\nQ 33.0625 21.96875 24.703125 23.78125 \r\nL 21.578125 24.515625 \r\nQ 13.234375 26.265625 9.515625 29.90625 \r\nQ 5.8125 33.546875 5.8125 39.890625 \r\nQ 5.8125 47.609375 11.28125 51.796875 \r\nQ 16.75 56 26.8125 56 \r\nQ 31.78125 56 36.171875 55.265625 \r\nQ 40.578125 54.546875 44.28125 53.078125 \r\nz\r\n\" id=\"DejaVuSans-115\"/>\r\n     </defs>\r\n     <use xlink:href=\"#DejaVuSans-105\"/>\r\n     <use x=\"27.783203\" xlink:href=\"#DejaVuSans-110\"/>\r\n     <use x=\"91.162109\" xlink:href=\"#DejaVuSans-116\"/>\r\n     <use x=\"130.371094\" xlink:href=\"#DejaVuSans-101\"/>\r\n     <use x=\"191.894531\" xlink:href=\"#DejaVuSans-114\"/>\r\n     <use x=\"233.007812\" xlink:href=\"#DejaVuSans-112\"/>\r\n     <use x=\"296.484375\" xlink:href=\"#DejaVuSans-111\"/>\r\n     <use x=\"357.666016\" xlink:href=\"#DejaVuSans-108\"/>\r\n     <use x=\"385.449219\" xlink:href=\"#DejaVuSans-97\"/>\r\n     <use x=\"446.728516\" xlink:href=\"#DejaVuSans-110\"/>\r\n     <use x=\"510.107422\" xlink:href=\"#DejaVuSans-116\"/>\r\n     <use x=\"549.316406\" xlink:href=\"#DejaVuSans-115\"/>\r\n    </g>\r\n   </g>\r\n   <g id=\"legend_1\">\r\n    <g id=\"patch_7\">\r\n     <path d=\"M 56.304688 59.9525 \r\nL 355.460938 59.9525 \r\nQ 357.460938 59.9525 357.460938 57.9525 \r\nL 357.460938 29.318125 \r\nQ 357.460938 27.318125 355.460938 27.318125 \r\nL 56.304688 27.318125 \r\nQ 54.304688 27.318125 54.304688 29.318125 \r\nL 54.304688 57.9525 \r\nQ 54.304688 59.9525 56.304688 59.9525 \r\nz\r\n\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\r\n    </g>\r\n    <g id=\"line2d_30\">\r\n     <path d=\"M 58.304688 35.416562 \r\nL 78.304688 35.416562 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_31\"/>\r\n    <g id=\"text_21\">\r\n     <!-- ref displ -->\r\n     <g transform=\"translate(86.304688 38.916562)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 37.109375 75.984375 \r\nL 37.109375 68.5 \r\nL 28.515625 68.5 \r\nQ 23.6875 68.5 21.796875 66.546875 \r\nQ 19.921875 64.59375 19.921875 59.515625 \r\nL 19.921875 54.6875 \r\nL 34.71875 54.6875 \r\nL 34.71875 47.703125 \r\nL 19.921875 47.703125 \r\nL 19.921875 0 \r\nL 10.890625 0 \r\nL 10.890625 47.703125 \r\nL 2.296875 47.703125 \r\nL 2.296875 54.6875 \r\nL 10.890625 54.6875 \r\nL 10.890625 58.5 \r\nQ 10.890625 67.625 15.140625 71.796875 \r\nQ 19.390625 75.984375 28.609375 75.984375 \r\nz\r\n\" id=\"DejaVuSans-102\"/>\r\n       <path id=\"DejaVuSans-32\"/>\r\n       <path d=\"M 45.40625 46.390625 \r\nL 45.40625 75.984375 \r\nL 54.390625 75.984375 \r\nL 54.390625 0 \r\nL 45.40625 0 \r\nL 45.40625 8.203125 \r\nQ 42.578125 3.328125 38.25 0.953125 \r\nQ 33.9375 -1.421875 27.875 -1.421875 \r\nQ 17.96875 -1.421875 11.734375 6.484375 \r\nQ 5.515625 14.40625 5.515625 27.296875 \r\nQ 5.515625 40.1875 11.734375 48.09375 \r\nQ 17.96875 56 27.875 56 \r\nQ 33.9375 56 38.25 53.625 \r\nQ 42.578125 51.265625 45.40625 46.390625 \r\nz\r\nM 14.796875 27.296875 \r\nQ 14.796875 17.390625 18.875 11.75 \r\nQ 22.953125 6.109375 30.078125 6.109375 \r\nQ 37.203125 6.109375 41.296875 11.75 \r\nQ 45.40625 17.390625 45.40625 27.296875 \r\nQ 45.40625 37.203125 41.296875 42.84375 \r\nQ 37.203125 48.484375 30.078125 48.484375 \r\nQ 22.953125 48.484375 18.875 42.84375 \r\nQ 14.796875 37.203125 14.796875 27.296875 \r\nz\r\n\" id=\"DejaVuSans-100\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-114\"/>\r\n      <use x=\"38.863281\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"100.386719\" xlink:href=\"#DejaVuSans-102\"/>\r\n      <use x=\"135.591797\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"167.378906\" xlink:href=\"#DejaVuSans-100\"/>\r\n      <use x=\"230.855469\" xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"258.638672\" xlink:href=\"#DejaVuSans-115\"/>\r\n      <use x=\"310.738281\" xlink:href=\"#DejaVuSans-112\"/>\r\n      <use x=\"374.214844\" xlink:href=\"#DejaVuSans-108\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_32\">\r\n     <path d=\"M 58.304688 50.094687 \r\nL 78.304688 50.094687 \r\n\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_33\"/>\r\n    <g id=\"text_22\">\r\n     <!-- ref vel -->\r\n     <g transform=\"translate(86.304688 53.594687)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 2.984375 54.6875 \r\nL 12.5 54.6875 \r\nL 29.59375 8.796875 \r\nL 46.6875 54.6875 \r\nL 56.203125 54.6875 \r\nL 35.6875 0 \r\nL 23.484375 0 \r\nz\r\n\" id=\"DejaVuSans-118\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-114\"/>\r\n      <use x=\"38.863281\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"100.386719\" xlink:href=\"#DejaVuSans-102\"/>\r\n      <use x=\"135.591797\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"167.378906\" xlink:href=\"#DejaVuSans-118\"/>\r\n      <use x=\"226.558594\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"288.082031\" xlink:href=\"#DejaVuSans-108\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_34\">\r\n     <path d=\"M 146.504688 35.416562 \r\nL 166.504688 35.416562 \r\n\" style=\"fill:none;stroke:#000000;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_35\"/>\r\n    <g id=\"text_23\">\r\n     <!-- interp BS45 -->\r\n     <g transform=\"translate(174.504688 38.916562)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 19.671875 34.8125 \r\nL 19.671875 8.109375 \r\nL 35.5 8.109375 \r\nQ 43.453125 8.109375 47.28125 11.40625 \r\nQ 51.125 14.703125 51.125 21.484375 \r\nQ 51.125 28.328125 47.28125 31.5625 \r\nQ 43.453125 34.8125 35.5 34.8125 \r\nz\r\nM 19.671875 64.796875 \r\nL 19.671875 42.828125 \r\nL 34.28125 42.828125 \r\nQ 41.5 42.828125 45.03125 45.53125 \r\nQ 48.578125 48.25 48.578125 53.8125 \r\nQ 48.578125 59.328125 45.03125 62.0625 \r\nQ 41.5 64.796875 34.28125 64.796875 \r\nz\r\nM 9.8125 72.90625 \r\nL 35.015625 72.90625 \r\nQ 46.296875 72.90625 52.390625 68.21875 \r\nQ 58.5 63.53125 58.5 54.890625 \r\nQ 58.5 48.1875 55.375 44.234375 \r\nQ 52.25 40.28125 46.1875 39.3125 \r\nQ 53.46875 37.75 57.5 32.78125 \r\nQ 61.53125 27.828125 61.53125 20.40625 \r\nQ 61.53125 10.640625 54.890625 5.3125 \r\nQ 48.25 0 35.984375 0 \r\nL 9.8125 0 \r\nz\r\n\" id=\"DejaVuSans-66\"/>\r\n       <path d=\"M 53.515625 70.515625 \r\nL 53.515625 60.890625 \r\nQ 47.90625 63.578125 42.921875 64.890625 \r\nQ 37.9375 66.21875 33.296875 66.21875 \r\nQ 25.25 66.21875 20.875 63.09375 \r\nQ 16.5 59.96875 16.5 54.203125 \r\nQ 16.5 49.359375 19.40625 46.890625 \r\nQ 22.3125 44.4375 30.421875 42.921875 \r\nL 36.375 41.703125 \r\nQ 47.40625 39.59375 52.65625 34.296875 \r\nQ 57.90625 29 57.90625 20.125 \r\nQ 57.90625 9.515625 50.796875 4.046875 \r\nQ 43.703125 -1.421875 29.984375 -1.421875 \r\nQ 24.8125 -1.421875 18.96875 -0.25 \r\nQ 13.140625 0.921875 6.890625 3.21875 \r\nL 6.890625 13.375 \r\nQ 12.890625 10.015625 18.65625 8.296875 \r\nQ 24.421875 6.59375 29.984375 6.59375 \r\nQ 38.421875 6.59375 43.015625 9.90625 \r\nQ 47.609375 13.234375 47.609375 19.390625 \r\nQ 47.609375 24.75 44.3125 27.78125 \r\nQ 41.015625 30.8125 33.5 32.328125 \r\nL 27.484375 33.5 \r\nQ 16.453125 35.6875 11.515625 40.375 \r\nQ 6.59375 45.0625 6.59375 53.421875 \r\nQ 6.59375 63.09375 13.40625 68.65625 \r\nQ 20.21875 74.21875 32.171875 74.21875 \r\nQ 37.3125 74.21875 42.625 73.28125 \r\nQ 47.953125 72.359375 53.515625 70.515625 \r\nz\r\n\" id=\"DejaVuSans-83\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"27.783203\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"91.162109\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"130.371094\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"191.894531\" xlink:href=\"#DejaVuSans-114\"/>\r\n      <use x=\"233.007812\" xlink:href=\"#DejaVuSans-112\"/>\r\n      <use x=\"296.484375\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"328.271484\" xlink:href=\"#DejaVuSans-66\"/>\r\n      <use x=\"395.125\" xlink:href=\"#DejaVuSans-83\"/>\r\n      <use x=\"458.601562\" xlink:href=\"#DejaVuSans-52\"/>\r\n      <use x=\"522.224609\" xlink:href=\"#DejaVuSans-53\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_36\">\r\n     <path d=\"M 146.504688 50.094687 \r\nL 166.504688 50.094687 \r\n\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\r\n    </g>\r\n    <g id=\"line2d_37\"/>\r\n    <g id=\"text_24\">\r\n     <!-- interp BS45_i -->\r\n     <g transform=\"translate(174.504688 53.594687)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 50.984375 -16.609375 \r\nL 50.984375 -23.578125 \r\nL -0.984375 -23.578125 \r\nL -0.984375 -16.609375 \r\nz\r\n\" id=\"DejaVuSans-95\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"27.783203\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"91.162109\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"130.371094\" xlink:href=\"#DejaVuSans-101\"/>\r\n      <use x=\"191.894531\" xlink:href=\"#DejaVuSans-114\"/>\r\n      <use x=\"233.007812\" xlink:href=\"#DejaVuSans-112\"/>\r\n      <use x=\"296.484375\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"328.271484\" xlink:href=\"#DejaVuSans-66\"/>\r\n      <use x=\"395.125\" xlink:href=\"#DejaVuSans-83\"/>\r\n      <use x=\"458.601562\" xlink:href=\"#DejaVuSans-52\"/>\r\n      <use x=\"522.224609\" xlink:href=\"#DejaVuSans-53\"/>\r\n      <use x=\"585.847656\" xlink:href=\"#DejaVuSans-95\"/>\r\n      <use x=\"635.847656\" xlink:href=\"#DejaVuSans-105\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"line2d_38\"/>\r\n    <g id=\"line2d_39\">\r\n     <g>\r\n      <use style=\"stroke:#000000;\" x=\"270.86875\" xlink:href=\"#m1e8e074354\" y=\"35.416562\"/>\r\n     </g>\r\n    </g>\r\n    <g id=\"text_25\">\r\n     <!-- solution pnts -->\r\n     <g transform=\"translate(288.86875 38.916562)scale(0.1 -0.1)\">\r\n      <defs>\r\n       <path d=\"M 8.5 21.578125 \r\nL 8.5 54.6875 \r\nL 17.484375 54.6875 \r\nL 17.484375 21.921875 \r\nQ 17.484375 14.15625 20.5 10.265625 \r\nQ 23.53125 6.390625 29.59375 6.390625 \r\nQ 36.859375 6.390625 41.078125 11.03125 \r\nQ 45.3125 15.671875 45.3125 23.6875 \r\nL 45.3125 54.6875 \r\nL 54.296875 54.6875 \r\nL 54.296875 0 \r\nL 45.3125 0 \r\nL 45.3125 8.40625 \r\nQ 42.046875 3.421875 37.71875 1 \r\nQ 33.40625 -1.421875 27.6875 -1.421875 \r\nQ 18.265625 -1.421875 13.375 4.4375 \r\nQ 8.5 10.296875 8.5 21.578125 \r\nz\r\nM 31.109375 56 \r\nz\r\n\" id=\"DejaVuSans-117\"/>\r\n      </defs>\r\n      <use xlink:href=\"#DejaVuSans-115\"/>\r\n      <use x=\"52.099609\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use x=\"113.28125\" xlink:href=\"#DejaVuSans-108\"/>\r\n      <use x=\"141.064453\" xlink:href=\"#DejaVuSans-117\"/>\r\n      <use x=\"204.443359\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"243.652344\" xlink:href=\"#DejaVuSans-105\"/>\r\n      <use x=\"271.435547\" xlink:href=\"#DejaVuSans-111\"/>\r\n      <use x=\"332.617188\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"395.996094\" xlink:href=\"#DejaVuSans-32\"/>\r\n      <use x=\"427.783203\" xlink:href=\"#DejaVuSans-112\"/>\r\n      <use x=\"491.259766\" xlink:href=\"#DejaVuSans-110\"/>\r\n      <use x=\"554.638672\" xlink:href=\"#DejaVuSans-116\"/>\r\n      <use x=\"593.847656\" xlink:href=\"#DejaVuSans-115\"/>\r\n     </g>\r\n    </g>\r\n   </g>\r\n  </g>\r\n </g>\r\n <defs>\r\n  <clipPath id=\"p32e130995f\">\r\n   <rect height=\"217.44\" width=\"334.8\" x=\"38.482813\" y=\"22.318125\"/>\r\n  </clipPath>\r\n </defs>\r\n</svg>\r\n",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "x_plot = np.linspace(12, 14)\n",
    "styles = ['--k', ':k']\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x_plot, reference.sol(x_plot).T, label='ref solution')\n",
    "for i in range(2):\n",
    "    for sol, style in zip(solutions[1:], styles):\n",
    "        plt.plot(x_plot, sol.sol(x_plot)[i], style)\n",
    "    plt.plot(solutions[i+1].t, solutions[i+1].y.T, 'ko')\n",
    "plt.xlim((x_plot.min(), x_plot.max()))\n",
    "plt.ylim((-0.2, 1.6))\n",
    "plt.legend(('ref displ', 'ref vel', 'interp BS45', 'interp BS45_i', 'solution pnts' ), \n",
    "           ncol=3, loc='upper center')\n",
    "plt.title('interpolants')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a solution with a very high tolerance value. The method takes very large steps. The interpolation between the solution points is different for the two methods and the accurate interpolant of `BS45` better resembles the reference solution than the free interpolant of `BS45_i`. On the other hand, the global error (of the solution points) is of similat magnitude as the difference between the interpolants. Therefore, the extra evaluations seem better spent at solving the problem with lower tolerance. This yields almost an order of magnitude of improvement in the error according to the efficiency plot.\n",
    "\n",
    "Dense interpolation is triggered by:\n",
    "* `dense_output`: extra evaluations for all successful steps.\n",
    "* `t_eval`: extra evaluations only for steps where output is requested.\n",
    "* `events`: extra evaluations only at steps in which an event is detected. \n",
    "\n",
    "The two methods `BS45` and `BS45_i` are the identical if none of these are used.\n",
    "\n",
    "Bogacki and Shampine have develloped the accurate interpolant in `BS45` for use on a small fraction of the steps, not for all steps. It is very useful with `events`, and maybe in some cases with `t_eval`. However, `BS45_i` seems more efficient  in combination with `dense_output=True`, at least for this problem.\n",
    "\n",
    "\n",
    "## Discussion\n",
    "The Bogacki Shampine method solves this Duffing's equation much more efficiently than scipy's default method `RK45`. Of course, the problem was selected for this reason. Nevertheless, `BS45` and `BS45_i` will be more efficient for many other problems as well. For some problems (not this Duffing problem) it may need somewhat more stringent tolerances than the default values of `solve_ivp` to really shine."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}