examples/plotting/mcmc-autocorrelation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inference plots - Autocorrelation plot\n",
    "\n",
    "This example builds on [adaptive covariance MCMC](https://pints.readthedocs.io/en/latest/mcmc_samplers/adaptive_covariance_mc.html), and shows you how to plot the autocorrelation of the MCMC samples.\n",
    "\n",
    "Inference plots:\n",
    "* [Predicted time series](mcmc-predicted-time-series.ipynb)\n",
    "* [Trace plots](mcmc-trace-plots.ipynb)\n",
    "* [Pairwise scatterplots](mcmc-pairwise-scatterplots.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up an MCMC routine\n",
    "\n",
    "See the adaptive covariance MCMC example for details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import pints\n",
    "import pints.toy as toy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Load a forward model\n",
    "model = toy.LogisticModel()\n",
    "\n",
    "# Create some toy data\n",
    "real_parameters = [0.015, 500]  # growth rate, carrying capacity\n",
    "times = np.linspace(0, 1000, 100)\n",
    "org_values = model.simulate(real_parameters, times)\n",
    "\n",
    "# Add noise\n",
    "noise = 50\n",
    "values = org_values + np.random.normal(0, noise, org_values.shape)\n",
    "real_parameters = np.array(real_parameters + [noise])\n",
    "\n",
    "# Get properties of the noise sample\n",
    "noise_sample_mean = np.mean(values - org_values)\n",
    "noise_sample_std = np.std(values - org_values)\n",
    "\n",
    "# Create an object with links to the model and time series\n",
    "problem = pints.SingleOutputProblem(model, times, values)\n",
    "\n",
    "# Create a log-likelihood function (adds an extra parameter!)\n",
    "log_likelihood = pints.GaussianLogLikelihood(problem)\n",
    "\n",
    "# Create a uniform log-prior over both the parameters and the new noise variable\n",
    "log_prior = pints.UniformLogPrior(\n",
    "    [0.01, 400, noise*0.1],\n",
    "    [0.02, 600, noise*100]\n",
    "    )\n",
    "\n",
    "# Create a posterior log-likelihood (log(likelihood * prior))\n",
    "log_posterior = pints.LogPosterior(log_likelihood, log_prior)\n",
    "\n",
    "# Perform sampling using MCMC, with a single chain\n",
    "x0 = real_parameters * 1.1\n",
    "mcmc = pints.MCMCController(log_posterior, 1, [x0])\n",
    "mcmc.set_max_iterations(6000)\n",
    "mcmc.set_log_to_screen(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autocorrelation\n",
    "\n",
    "The [autocorrelation](https://en.wikipedia.org/wiki/Autocorrelation) in a Markov chain indicates how much each sample in the chain differs from the next. Checking for (lack of) autocorrelation is an easy way to check if your MCMC routine is converging. It can easily be plotted using pints.plot's autocorrelation method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Running...\nDone!\n"
    }
   ],
   "source": [
    "print('Running...')\n",
    "chains = mcmc.run()\n",
    "print('Done!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Select chain 0 and discard warm-up\n",
    "chain = chains[0]\n",
    "chain = chain[3000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x432 with 3 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"424.15625pt\" version=\"1.1\" viewBox=\"0 0 430.86875 424.15625\" width=\"430.86875pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 424.15625 \nL 430.86875 424.15625 \nL 430.86875 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 50.14375 124.133333 \nL 423.66875 124.133333 \nL 423.66875 7.2 \nL 50.14375 7.2 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_1\">\n    <g id=\"xtick_1\">\n     <g id=\"line2d_1\">\n      <defs>\n       <path d=\"M 0 0 \nL 0 3.5 \n\" id=\"m50856253cc\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"67.122159\" xlink:href=\"#m50856253cc\" y=\"124.133333\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_2\">\n     <g id=\"line2d_2\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"135.035795\" xlink:href=\"#m50856253cc\" y=\"124.133333\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_3\">\n     <g id=\"line2d_3\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"202.949432\" xlink:href=\"#m50856253cc\" y=\"124.133333\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_4\">\n     <g id=\"line2d_4\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"270.863068\" xlink:href=\"#m50856253cc\" y=\"124.133333\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_5\">\n     <g id=\"line2d_5\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"338.776705\" xlink:href=\"#m50856253cc\" y=\"124.133333\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_6\">\n     <g id=\"line2d_6\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"406.690341\" xlink:href=\"#m50856253cc\" y=\"124.133333\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_2\">\n    <g id=\"ytick_1\">\n     <g id=\"line2d_7\">\n      <defs>\n       <path d=\"M 0 0 \nL -3.5 0 \n\" id=\"mb270a424c6\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"118.818182\"/>\n      </g>\n     </g>\n     <g id=\"text_1\">\n      <!-- 0.00 -->\n      <defs>\n       <path d=\"M 31.78125 66.40625 \nQ 24.171875 66.40625 20.328125 58.90625 \nQ 16.5 51.421875 16.5 36.375 \nQ 16.5 21.390625 20.328125 13.890625 \nQ 24.171875 6.390625 31.78125 6.390625 \nQ 39.453125 6.390625 43.28125 13.890625 \nQ 47.125 21.390625 47.125 36.375 \nQ 47.125 51.421875 43.28125 58.90625 \nQ 39.453125 66.40625 31.78125 66.40625 \nz\nM 31.78125 74.21875 \nQ 44.046875 74.21875 50.515625 64.515625 \nQ 56.984375 54.828125 56.984375 36.375 \nQ 56.984375 17.96875 50.515625 8.265625 \nQ 44.046875 -1.421875 31.78125 -1.421875 \nQ 19.53125 -1.421875 13.0625 8.265625 \nQ 6.59375 17.96875 6.59375 36.375 \nQ 6.59375 54.828125 13.0625 64.515625 \nQ 19.53125 74.21875 31.78125 74.21875 \nz\n\" id=\"DejaVuSans-48\"/>\n       <path d=\"M 10.6875 12.40625 \nL 21 12.40625 \nL 21 0 \nL 10.6875 0 \nz\n\" id=\"DejaVuSans-46\"/>\n      </defs>\n      <g transform=\"translate(20.878125 122.617401)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_2\">\n     <g id=\"line2d_8\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"92.242424\"/>\n      </g>\n     </g>\n     <g id=\"text_2\">\n      <!-- 0.25 -->\n      <defs>\n       <path d=\"M 19.1875 8.296875 \nL 53.609375 8.296875 \nL 53.609375 0 \nL 7.328125 0 \nL 7.328125 8.296875 \nQ 12.9375 14.109375 22.625 23.890625 \nQ 32.328125 33.6875 34.8125 36.53125 \nQ 39.546875 41.84375 41.421875 45.53125 \nQ 43.3125 49.21875 43.3125 52.78125 \nQ 43.3125 58.59375 39.234375 62.25 \nQ 35.15625 65.921875 28.609375 65.921875 \nQ 23.96875 65.921875 18.8125 64.3125 \nQ 13.671875 62.703125 7.8125 59.421875 \nL 7.8125 69.390625 \nQ 13.765625 71.78125 18.9375 73 \nQ 24.125 74.21875 28.421875 74.21875 \nQ 39.75 74.21875 46.484375 68.546875 \nQ 53.21875 62.890625 53.21875 53.421875 \nQ 53.21875 48.921875 51.53125 44.890625 \nQ 49.859375 40.875 45.40625 35.40625 \nQ 44.1875 33.984375 37.640625 27.21875 \nQ 31.109375 20.453125 19.1875 8.296875 \nz\n\" id=\"DejaVuSans-50\"/>\n       <path d=\"M 10.796875 72.90625 \nL 49.515625 72.90625 \nL 49.515625 64.59375 \nL 19.828125 64.59375 \nL 19.828125 46.734375 \nQ 21.96875 47.46875 24.109375 47.828125 \nQ 26.265625 48.1875 28.421875 48.1875 \nQ 40.625 48.1875 47.75 41.5 \nQ 54.890625 34.8125 54.890625 23.390625 \nQ 54.890625 11.625 47.5625 5.09375 \nQ 40.234375 -1.421875 26.90625 -1.421875 \nQ 22.3125 -1.421875 17.546875 -0.640625 \nQ 12.796875 0.140625 7.71875 1.703125 \nL 7.71875 11.625 \nQ 12.109375 9.234375 16.796875 8.0625 \nQ 21.484375 6.890625 26.703125 6.890625 \nQ 35.15625 6.890625 40.078125 11.328125 \nQ 45.015625 15.765625 45.015625 23.390625 \nQ 45.015625 31 40.078125 35.4375 \nQ 35.15625 39.890625 26.703125 39.890625 \nQ 22.75 39.890625 18.8125 39.015625 \nQ 14.890625 38.140625 10.796875 36.28125 \nz\n\" id=\"DejaVuSans-53\"/>\n      </defs>\n      <g transform=\"translate(20.878125 96.041643)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_3\">\n     <g id=\"line2d_9\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"65.666667\"/>\n      </g>\n     </g>\n     <g id=\"text_3\">\n      <!-- 0.50 -->\n      <g transform=\"translate(20.878125 69.465885)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_4\">\n     <g id=\"line2d_10\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"39.090909\"/>\n      </g>\n     </g>\n     <g id=\"text_4\">\n      <!-- 0.75 -->\n      <defs>\n       <path d=\"M 8.203125 72.90625 \nL 55.078125 72.90625 \nL 55.078125 68.703125 \nL 28.609375 0 \nL 18.3125 0 \nL 43.21875 64.59375 \nL 8.203125 64.59375 \nz\n\" id=\"DejaVuSans-55\"/>\n      </defs>\n      <g transform=\"translate(20.878125 42.890128)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-55\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_5\">\n     <g id=\"line2d_11\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"12.515152\"/>\n      </g>\n     </g>\n     <g id=\"text_5\">\n      <!-- 1.00 -->\n      <defs>\n       <path d=\"M 12.40625 8.296875 \nL 28.515625 8.296875 \nL 28.515625 63.921875 \nL 10.984375 60.40625 \nL 10.984375 69.390625 \nL 28.421875 72.90625 \nL 38.28125 72.90625 \nL 38.28125 8.296875 \nL 54.390625 8.296875 \nL 54.390625 0 \nL 12.40625 0 \nz\n\" id=\"DejaVuSans-49\"/>\n      </defs>\n      <g transform=\"translate(20.878125 16.31437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-49\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"LineCollection_1\">\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M -0.791477 118.818182 \nL -0.791477 45.629098 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 33.165341 118.818182 \nL 33.165341 30.400597 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 67.122159 118.818182 \nL 67.122159 12.515152 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 101.078977 118.818182 \nL 101.078977 30.400597 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 135.035795 118.818182 \nL 135.035795 45.629098 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 168.992614 118.818182 \nL 168.992614 58.608015 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 202.949432 118.818182 \nL 202.949432 69.562038 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 236.90625 118.818182 \nL 236.90625 78.540751 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 270.863068 118.818182 \nL 270.863068 85.262198 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 304.819886 118.818182 \nL 304.819886 91.29652 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 338.776705 118.818182 \nL 338.776705 96.439292 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 372.733523 118.818182 \nL 372.733523 101.402129 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 406.690341 118.818182 \nL 406.690341 104.855755 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"line2d_12\">\n    <path clip-path=\"url(#p7b2b4b3130)\" d=\"M 50.14375 118.818182 \nL 423.66875 118.818182 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"patch_3\">\n    <path d=\"M 50.14375 124.133333 \nL 50.14375 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_4\">\n    <path d=\"M 423.66875 124.133333 \nL 423.66875 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_5\">\n    <path d=\"M 50.14375 124.133333 \nL 423.66875 124.133333 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_6\">\n    <path d=\"M 50.14375 7.2 \nL 423.66875 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"legend_1\">\n    <g id=\"patch_7\">\n     <path d=\"M 326.389062 29.878125 \nL 416.66875 29.878125 \nQ 418.66875 29.878125 418.66875 27.878125 \nL 418.66875 14.2 \nQ 418.66875 12.2 416.66875 12.2 \nL 326.389062 12.2 \nQ 324.389062 12.2 324.389062 14.2 \nL 324.389062 27.878125 \nQ 324.389062 29.878125 326.389062 29.878125 \nz\n\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\n    </g>\n    <g id=\"line2d_13\">\n     <path d=\"M 328.389062 20.298438 \nL 348.389062 20.298438 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n    </g>\n    <g id=\"line2d_14\"/>\n    <g id=\"text_6\">\n     <!-- growth rate -->\n     <defs>\n      <path d=\"M 45.40625 27.984375 \nQ 45.40625 37.75 41.375 43.109375 \nQ 37.359375 48.484375 30.078125 48.484375 \nQ 22.859375 48.484375 18.828125 43.109375 \nQ 14.796875 37.75 14.796875 27.984375 \nQ 14.796875 18.265625 18.828125 12.890625 \nQ 22.859375 7.515625 30.078125 7.515625 \nQ 37.359375 7.515625 41.375 12.890625 \nQ 45.40625 18.265625 45.40625 27.984375 \nz\nM 54.390625 6.78125 \nQ 54.390625 -7.171875 48.1875 -13.984375 \nQ 42 -20.796875 29.203125 -20.796875 \nQ 24.46875 -20.796875 20.265625 -20.09375 \nQ 16.0625 -19.390625 12.109375 -17.921875 \nL 12.109375 -9.1875 \nQ 16.0625 -11.328125 19.921875 -12.34375 \nQ 23.78125 -13.375 27.78125 -13.375 \nQ 36.625 -13.375 41.015625 -8.765625 \nQ 45.40625 -4.15625 45.40625 5.171875 \nL 45.40625 9.625 \nQ 42.625 4.78125 38.28125 2.390625 \nQ 33.9375 0 27.875 0 \nQ 17.828125 0 11.671875 7.65625 \nQ 5.515625 15.328125 5.515625 27.984375 \nQ 5.515625 40.671875 11.671875 48.328125 \nQ 17.828125 56 27.875 56 \nQ 33.9375 56 38.28125 53.609375 \nQ 42.625 51.21875 45.40625 46.390625 \nL 45.40625 54.6875 \nL 54.390625 54.6875 \nz\n\" id=\"DejaVuSans-103\"/>\n      <path d=\"M 41.109375 46.296875 \nQ 39.59375 47.171875 37.8125 47.578125 \nQ 36.03125 48 33.890625 48 \nQ 26.265625 48 22.1875 43.046875 \nQ 18.109375 38.09375 18.109375 28.8125 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.1875 \nQ 20.953125 51.171875 25.484375 53.578125 \nQ 30.03125 56 36.53125 56 \nQ 37.453125 56 38.578125 55.875 \nQ 39.703125 55.765625 41.0625 55.515625 \nz\n\" id=\"DejaVuSans-114\"/>\n      <path d=\"M 30.609375 48.390625 \nQ 23.390625 48.390625 19.1875 42.75 \nQ 14.984375 37.109375 14.984375 27.296875 \nQ 14.984375 17.484375 19.15625 11.84375 \nQ 23.34375 6.203125 30.609375 6.203125 \nQ 37.796875 6.203125 41.984375 11.859375 \nQ 46.1875 17.53125 46.1875 27.296875 \nQ 46.1875 37.015625 41.984375 42.703125 \nQ 37.796875 48.390625 30.609375 48.390625 \nz\nM 30.609375 56 \nQ 42.328125 56 49.015625 48.375 \nQ 55.71875 40.765625 55.71875 27.296875 \nQ 55.71875 13.875 49.015625 6.21875 \nQ 42.328125 -1.421875 30.609375 -1.421875 \nQ 18.84375 -1.421875 12.171875 6.21875 \nQ 5.515625 13.875 5.515625 27.296875 \nQ 5.515625 40.765625 12.171875 48.375 \nQ 18.84375 56 30.609375 56 \nz\n\" id=\"DejaVuSans-111\"/>\n      <path d=\"M 4.203125 54.6875 \nL 13.1875 54.6875 \nL 24.421875 12.015625 \nL 35.59375 54.6875 \nL 46.1875 54.6875 \nL 57.421875 12.015625 \nL 68.609375 54.6875 \nL 77.59375 54.6875 \nL 63.28125 0 \nL 52.6875 0 \nL 40.921875 44.828125 \nL 29.109375 0 \nL 18.5 0 \nz\n\" id=\"DejaVuSans-119\"/>\n      <path d=\"M 18.3125 70.21875 \nL 18.3125 54.6875 \nL 36.8125 54.6875 \nL 36.8125 47.703125 \nL 18.3125 47.703125 \nL 18.3125 18.015625 \nQ 18.3125 11.328125 20.140625 9.421875 \nQ 21.96875 7.515625 27.59375 7.515625 \nL 36.8125 7.515625 \nL 36.8125 0 \nL 27.59375 0 \nQ 17.1875 0 13.234375 3.875 \nQ 9.28125 7.765625 9.28125 18.015625 \nL 9.28125 47.703125 \nL 2.6875 47.703125 \nL 2.6875 54.6875 \nL 9.28125 54.6875 \nL 9.28125 70.21875 \nz\n\" id=\"DejaVuSans-116\"/>\n      <path d=\"M 54.890625 33.015625 \nL 54.890625 0 \nL 45.90625 0 \nL 45.90625 32.71875 \nQ 45.90625 40.484375 42.875 44.328125 \nQ 39.84375 48.1875 33.796875 48.1875 \nQ 26.515625 48.1875 22.3125 43.546875 \nQ 18.109375 38.921875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 75.984375 \nL 18.109375 75.984375 \nL 18.109375 46.1875 \nQ 21.34375 51.125 25.703125 53.5625 \nQ 30.078125 56 35.796875 56 \nQ 45.21875 56 50.046875 50.171875 \nQ 54.890625 44.34375 54.890625 33.015625 \nz\n\" id=\"DejaVuSans-104\"/>\n      <path id=\"DejaVuSans-32\"/>\n      <path d=\"M 34.28125 27.484375 \nQ 23.390625 27.484375 19.1875 25 \nQ 14.984375 22.515625 14.984375 16.5 \nQ 14.984375 11.71875 18.140625 8.90625 \nQ 21.296875 6.109375 26.703125 6.109375 \nQ 34.1875 6.109375 38.703125 11.40625 \nQ 43.21875 16.703125 43.21875 25.484375 \nL 43.21875 27.484375 \nz\nM 52.203125 31.203125 \nL 52.203125 0 \nL 43.21875 0 \nL 43.21875 8.296875 \nQ 40.140625 3.328125 35.546875 0.953125 \nQ 30.953125 -1.421875 24.3125 -1.421875 \nQ 15.921875 -1.421875 10.953125 3.296875 \nQ 6 8.015625 6 15.921875 \nQ 6 25.140625 12.171875 29.828125 \nQ 18.359375 34.515625 30.609375 34.515625 \nL 43.21875 34.515625 \nL 43.21875 35.40625 \nQ 43.21875 41.609375 39.140625 45 \nQ 35.0625 48.390625 27.6875 48.390625 \nQ 23 48.390625 18.546875 47.265625 \nQ 14.109375 46.140625 10.015625 43.890625 \nL 10.015625 52.203125 \nQ 14.9375 54.109375 19.578125 55.046875 \nQ 24.21875 56 28.609375 56 \nQ 40.484375 56 46.34375 49.84375 \nQ 52.203125 43.703125 52.203125 31.203125 \nz\n\" id=\"DejaVuSans-97\"/>\n      <path d=\"M 56.203125 29.59375 \nL 56.203125 25.203125 \nL 14.890625 25.203125 \nQ 15.484375 15.921875 20.484375 11.0625 \nQ 25.484375 6.203125 34.421875 6.203125 \nQ 39.59375 6.203125 44.453125 7.46875 \nQ 49.3125 8.734375 54.109375 11.28125 \nL 54.109375 2.78125 \nQ 49.265625 0.734375 44.1875 -0.34375 \nQ 39.109375 -1.421875 33.890625 -1.421875 \nQ 20.796875 -1.421875 13.15625 6.1875 \nQ 5.515625 13.8125 5.515625 26.8125 \nQ 5.515625 40.234375 12.765625 48.109375 \nQ 20.015625 56 32.328125 56 \nQ 43.359375 56 49.78125 48.890625 \nQ 56.203125 41.796875 56.203125 29.59375 \nz\nM 47.21875 32.234375 \nQ 47.125 39.59375 43.09375 43.984375 \nQ 39.0625 48.390625 32.421875 48.390625 \nQ 24.90625 48.390625 20.390625 44.140625 \nQ 15.875 39.890625 15.1875 32.171875 \nz\n\" id=\"DejaVuSans-101\"/>\n     </defs>\n     <g transform=\"translate(356.389062 23.798438)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-103\"/>\n      <use x=\"63.476562\" xlink:href=\"#DejaVuSans-114\"/>\n      <use x=\"102.339844\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"163.521484\" xlink:href=\"#DejaVuSans-119\"/>\n      <use x=\"245.308594\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"284.517578\" xlink:href=\"#DejaVuSans-104\"/>\n      <use x=\"347.896484\" xlink:href=\"#DejaVuSans-32\"/>\n      <use x=\"379.683594\" xlink:href=\"#DejaVuSans-114\"/>\n      <use x=\"420.796875\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"482.076172\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"521.285156\" xlink:href=\"#DejaVuSans-101\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n  <g id=\"axes_2\">\n   <g id=\"patch_8\">\n    <path d=\"M 50.14375 255.366667 \nL 423.66875 255.366667 \nL 423.66875 138.433333 \nL 50.14375 138.433333 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_3\">\n    <g id=\"xtick_7\">\n     <g id=\"line2d_15\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"67.122159\" xlink:href=\"#m50856253cc\" y=\"255.366667\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_8\">\n     <g id=\"line2d_16\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"135.035795\" xlink:href=\"#m50856253cc\" y=\"255.366667\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_9\">\n     <g id=\"line2d_17\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"202.949432\" xlink:href=\"#m50856253cc\" y=\"255.366667\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_10\">\n     <g id=\"line2d_18\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"270.863068\" xlink:href=\"#m50856253cc\" y=\"255.366667\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_11\">\n     <g id=\"line2d_19\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"338.776705\" xlink:href=\"#m50856253cc\" y=\"255.366667\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_12\">\n     <g id=\"line2d_20\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"406.690341\" xlink:href=\"#m50856253cc\" y=\"255.366667\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_4\">\n    <g id=\"ytick_6\">\n     <g id=\"line2d_21\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"250.051515\"/>\n      </g>\n     </g>\n     <g id=\"text_7\">\n      <!-- 0.00 -->\n      <g transform=\"translate(20.878125 253.850734)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_7\">\n     <g id=\"line2d_22\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"223.475758\"/>\n      </g>\n     </g>\n     <g id=\"text_8\">\n      <!-- 0.25 -->\n      <g transform=\"translate(20.878125 227.274976)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_8\">\n     <g id=\"line2d_23\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"196.9\"/>\n      </g>\n     </g>\n     <g id=\"text_9\">\n      <!-- 0.50 -->\n      <g transform=\"translate(20.878125 200.699219)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_9\">\n     <g id=\"line2d_24\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"170.324242\"/>\n      </g>\n     </g>\n     <g id=\"text_10\">\n      <!-- 0.75 -->\n      <g transform=\"translate(20.878125 174.123461)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-55\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_10\">\n     <g id=\"line2d_25\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"143.748485\"/>\n      </g>\n     </g>\n     <g id=\"text_11\">\n      <!-- 1.00 -->\n      <g transform=\"translate(20.878125 147.547704)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-49\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_12\">\n     <!-- Autocorrelation -->\n     <defs>\n      <path d=\"M 34.1875 63.1875 \nL 20.796875 26.90625 \nL 47.609375 26.90625 \nz\nM 28.609375 72.90625 \nL 39.796875 72.90625 \nL 67.578125 0 \nL 57.328125 0 \nL 50.6875 18.703125 \nL 17.828125 18.703125 \nL 11.1875 0 \nL 0.78125 0 \nz\n\" id=\"DejaVuSans-65\"/>\n      <path d=\"M 8.5 21.578125 \nL 8.5 54.6875 \nL 17.484375 54.6875 \nL 17.484375 21.921875 \nQ 17.484375 14.15625 20.5 10.265625 \nQ 23.53125 6.390625 29.59375 6.390625 \nQ 36.859375 6.390625 41.078125 11.03125 \nQ 45.3125 15.671875 45.3125 23.6875 \nL 45.3125 54.6875 \nL 54.296875 54.6875 \nL 54.296875 0 \nL 45.3125 0 \nL 45.3125 8.40625 \nQ 42.046875 3.421875 37.71875 1 \nQ 33.40625 -1.421875 27.6875 -1.421875 \nQ 18.265625 -1.421875 13.375 4.4375 \nQ 8.5 10.296875 8.5 21.578125 \nz\nM 31.109375 56 \nz\n\" id=\"DejaVuSans-117\"/>\n      <path d=\"M 48.78125 52.59375 \nL 48.78125 44.1875 \nQ 44.96875 46.296875 41.140625 47.34375 \nQ 37.3125 48.390625 33.40625 48.390625 \nQ 24.65625 48.390625 19.8125 42.84375 \nQ 14.984375 37.3125 14.984375 27.296875 \nQ 14.984375 17.28125 19.8125 11.734375 \nQ 24.65625 6.203125 33.40625 6.203125 \nQ 37.3125 6.203125 41.140625 7.25 \nQ 44.96875 8.296875 48.78125 10.40625 \nL 48.78125 2.09375 \nQ 45.015625 0.34375 40.984375 -0.53125 \nQ 36.96875 -1.421875 32.421875 -1.421875 \nQ 20.0625 -1.421875 12.78125 6.34375 \nQ 5.515625 14.109375 5.515625 27.296875 \nQ 5.515625 40.671875 12.859375 48.328125 \nQ 20.21875 56 33.015625 56 \nQ 37.15625 56 41.109375 55.140625 \nQ 45.0625 54.296875 48.78125 52.59375 \nz\n\" id=\"DejaVuSans-99\"/>\n      <path d=\"M 9.421875 75.984375 \nL 18.40625 75.984375 \nL 18.40625 0 \nL 9.421875 0 \nz\n\" id=\"DejaVuSans-108\"/>\n      <path d=\"M 9.421875 54.6875 \nL 18.40625 54.6875 \nL 18.40625 0 \nL 9.421875 0 \nz\nM 9.421875 75.984375 \nL 18.40625 75.984375 \nL 18.40625 64.59375 \nL 9.421875 64.59375 \nz\n\" id=\"DejaVuSans-105\"/>\n      <path d=\"M 54.890625 33.015625 \nL 54.890625 0 \nL 45.90625 0 \nL 45.90625 32.71875 \nQ 45.90625 40.484375 42.875 44.328125 \nQ 39.84375 48.1875 33.796875 48.1875 \nQ 26.515625 48.1875 22.3125 43.546875 \nQ 18.109375 38.921875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.1875 \nQ 21.34375 51.125 25.703125 53.5625 \nQ 30.078125 56 35.796875 56 \nQ 45.21875 56 50.046875 50.171875 \nQ 54.890625 44.34375 54.890625 33.015625 \nz\n\" id=\"DejaVuSans-110\"/>\n     </defs>\n     <g transform=\"translate(14.798438 235.335156)rotate(-90)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-65\"/>\n      <use x=\"68.408203\" xlink:href=\"#DejaVuSans-117\"/>\n      <use x=\"131.787109\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"170.996094\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"232.177734\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"287.158203\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"348.339844\" xlink:href=\"#DejaVuSans-114\"/>\n      <use x=\"387.703125\" xlink:href=\"#DejaVuSans-114\"/>\n      <use x=\"426.566406\" xlink:href=\"#DejaVuSans-101\"/>\n      <use x=\"488.089844\" xlink:href=\"#DejaVuSans-108\"/>\n      <use x=\"515.873047\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"577.152344\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"616.361328\" xlink:href=\"#DejaVuSans-105\"/>\n      <use x=\"644.144531\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"705.326172\" xlink:href=\"#DejaVuSans-110\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"LineCollection_2\">\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M -0.791477 250.051515 \nL -0.791477 177.131776 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 33.165341 250.051515 \nL 33.165341 161.848345 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 67.122159 250.051515 \nL 67.122159 143.748485 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 101.078977 250.051515 \nL 101.078977 161.848345 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 135.035795 250.051515 \nL 135.035795 177.131776 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 168.992614 250.051515 \nL 168.992614 189.846243 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 202.949432 250.051515 \nL 202.949432 200.057526 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 236.90625 250.051515 \nL 236.90625 209.972793 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 270.863068 250.051515 \nL 270.863068 218.552985 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 304.819886 250.051515 \nL 304.819886 226.094344 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 338.776705 250.051515 \nL 338.776705 231.662421 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 372.733523 250.051515 \nL 372.733523 236.299743 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 406.690341 250.051515 \nL 406.690341 239.858035 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"line2d_26\">\n    <path clip-path=\"url(#pf58f251edc)\" d=\"M 50.14375 250.051515 \nL 423.66875 250.051515 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"patch_9\">\n    <path d=\"M 50.14375 255.366667 \nL 50.14375 138.433333 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_10\">\n    <path d=\"M 423.66875 255.366667 \nL 423.66875 138.433333 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_11\">\n    <path d=\"M 50.14375 255.366667 \nL 423.66875 255.366667 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_12\">\n    <path d=\"M 50.14375 138.433333 \nL 423.66875 138.433333 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"legend_2\">\n    <g id=\"patch_13\">\n     <path d=\"M 298.215625 161.111458 \nL 416.66875 161.111458 \nQ 418.66875 161.111458 418.66875 159.111458 \nL 418.66875 145.433333 \nQ 418.66875 143.433333 416.66875 143.433333 \nL 298.215625 143.433333 \nQ 296.215625 143.433333 296.215625 145.433333 \nL 296.215625 159.111458 \nQ 296.215625 161.111458 298.215625 161.111458 \nz\n\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\n    </g>\n    <g id=\"line2d_27\">\n     <path d=\"M 300.215625 151.531771 \nL 320.215625 151.531771 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n    </g>\n    <g id=\"line2d_28\"/>\n    <g id=\"text_13\">\n     <!-- carrying capacity -->\n     <defs>\n      <path d=\"M 32.171875 -5.078125 \nQ 28.375 -14.84375 24.75 -17.8125 \nQ 21.140625 -20.796875 15.09375 -20.796875 \nL 7.90625 -20.796875 \nL 7.90625 -13.28125 \nL 13.1875 -13.28125 \nQ 16.890625 -13.28125 18.9375 -11.515625 \nQ 21 -9.765625 23.484375 -3.21875 \nL 25.09375 0.875 \nL 2.984375 54.6875 \nL 12.5 54.6875 \nL 29.59375 11.921875 \nL 46.6875 54.6875 \nL 56.203125 54.6875 \nz\n\" id=\"DejaVuSans-121\"/>\n      <path d=\"M 18.109375 8.203125 \nL 18.109375 -20.796875 \nL 9.078125 -20.796875 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.390625 \nQ 20.953125 51.265625 25.265625 53.625 \nQ 29.59375 56 35.59375 56 \nQ 45.5625 56 51.78125 48.09375 \nQ 58.015625 40.1875 58.015625 27.296875 \nQ 58.015625 14.40625 51.78125 6.484375 \nQ 45.5625 -1.421875 35.59375 -1.421875 \nQ 29.59375 -1.421875 25.265625 0.953125 \nQ 20.953125 3.328125 18.109375 8.203125 \nz\nM 48.6875 27.296875 \nQ 48.6875 37.203125 44.609375 42.84375 \nQ 40.53125 48.484375 33.40625 48.484375 \nQ 26.265625 48.484375 22.1875 42.84375 \nQ 18.109375 37.203125 18.109375 27.296875 \nQ 18.109375 17.390625 22.1875 11.75 \nQ 26.265625 6.109375 33.40625 6.109375 \nQ 40.53125 6.109375 44.609375 11.75 \nQ 48.6875 17.390625 48.6875 27.296875 \nz\n\" id=\"DejaVuSans-112\"/>\n     </defs>\n     <g transform=\"translate(328.215625 155.031771)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"54.980469\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"116.259766\" xlink:href=\"#DejaVuSans-114\"/>\n      <use x=\"155.623047\" xlink:href=\"#DejaVuSans-114\"/>\n      <use x=\"196.736328\" xlink:href=\"#DejaVuSans-121\"/>\n      <use x=\"255.916016\" xlink:href=\"#DejaVuSans-105\"/>\n      <use x=\"283.699219\" xlink:href=\"#DejaVuSans-110\"/>\n      <use x=\"347.078125\" xlink:href=\"#DejaVuSans-103\"/>\n      <use x=\"410.554688\" xlink:href=\"#DejaVuSans-32\"/>\n      <use x=\"442.341797\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"497.322266\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"558.601562\" xlink:href=\"#DejaVuSans-112\"/>\n      <use x=\"622.078125\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"683.357422\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"738.337891\" xlink:href=\"#DejaVuSans-105\"/>\n      <use x=\"766.121094\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"805.330078\" xlink:href=\"#DejaVuSans-121\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n  <g id=\"axes_3\">\n   <g id=\"patch_14\">\n    <path d=\"M 50.14375 386.6 \nL 423.66875 386.6 \nL 423.66875 269.666667 \nL 50.14375 269.666667 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_5\">\n    <g id=\"xtick_13\">\n     <g id=\"line2d_29\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"67.122159\" xlink:href=\"#m50856253cc\" y=\"386.6\"/>\n      </g>\n     </g>\n     <g id=\"text_14\">\n      <!-- 0 -->\n      <g transform=\"translate(63.940909 401.198437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_14\">\n     <g id=\"line2d_30\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"135.035795\" xlink:href=\"#m50856253cc\" y=\"386.6\"/>\n      </g>\n     </g>\n     <g id=\"text_15\">\n      <!-- 2 -->\n      <g transform=\"translate(131.854545 401.198437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_15\">\n     <g id=\"line2d_31\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"202.949432\" xlink:href=\"#m50856253cc\" y=\"386.6\"/>\n      </g>\n     </g>\n     <g id=\"text_16\">\n      <!-- 4 -->\n      <defs>\n       <path d=\"M 37.796875 64.3125 \nL 12.890625 25.390625 \nL 37.796875 25.390625 \nz\nM 35.203125 72.90625 \nL 47.609375 72.90625 \nL 47.609375 25.390625 \nL 58.015625 25.390625 \nL 58.015625 17.1875 \nL 47.609375 17.1875 \nL 47.609375 0 \nL 37.796875 0 \nL 37.796875 17.1875 \nL 4.890625 17.1875 \nL 4.890625 26.703125 \nz\n\" id=\"DejaVuSans-52\"/>\n      </defs>\n      <g transform=\"translate(199.768182 401.198437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-52\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_16\">\n     <g id=\"line2d_32\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"270.863068\" xlink:href=\"#m50856253cc\" y=\"386.6\"/>\n      </g>\n     </g>\n     <g id=\"text_17\">\n      <!-- 6 -->\n      <defs>\n       <path d=\"M 33.015625 40.375 \nQ 26.375 40.375 22.484375 35.828125 \nQ 18.609375 31.296875 18.609375 23.390625 \nQ 18.609375 15.53125 22.484375 10.953125 \nQ 26.375 6.390625 33.015625 6.390625 \nQ 39.65625 6.390625 43.53125 10.953125 \nQ 47.40625 15.53125 47.40625 23.390625 \nQ 47.40625 31.296875 43.53125 35.828125 \nQ 39.65625 40.375 33.015625 40.375 \nz\nM 52.59375 71.296875 \nL 52.59375 62.3125 \nQ 48.875 64.0625 45.09375 64.984375 \nQ 41.3125 65.921875 37.59375 65.921875 \nQ 27.828125 65.921875 22.671875 59.328125 \nQ 17.53125 52.734375 16.796875 39.40625 \nQ 19.671875 43.65625 24.015625 45.921875 \nQ 28.375 48.1875 33.59375 48.1875 \nQ 44.578125 48.1875 50.953125 41.515625 \nQ 57.328125 34.859375 57.328125 23.390625 \nQ 57.328125 12.15625 50.6875 5.359375 \nQ 44.046875 -1.421875 33.015625 -1.421875 \nQ 20.359375 -1.421875 13.671875 8.265625 \nQ 6.984375 17.96875 6.984375 36.375 \nQ 6.984375 53.65625 15.1875 63.9375 \nQ 23.390625 74.21875 37.203125 74.21875 \nQ 40.921875 74.21875 44.703125 73.484375 \nQ 48.484375 72.75 52.59375 71.296875 \nz\n\" id=\"DejaVuSans-54\"/>\n      </defs>\n      <g transform=\"translate(267.681818 401.198437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_17\">\n     <g id=\"line2d_33\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"338.776705\" xlink:href=\"#m50856253cc\" y=\"386.6\"/>\n      </g>\n     </g>\n     <g id=\"text_18\">\n      <!-- 8 -->\n      <defs>\n       <path d=\"M 31.78125 34.625 \nQ 24.75 34.625 20.71875 30.859375 \nQ 16.703125 27.09375 16.703125 20.515625 \nQ 16.703125 13.921875 20.71875 10.15625 \nQ 24.75 6.390625 31.78125 6.390625 \nQ 38.8125 6.390625 42.859375 10.171875 \nQ 46.921875 13.96875 46.921875 20.515625 \nQ 46.921875 27.09375 42.890625 30.859375 \nQ 38.875 34.625 31.78125 34.625 \nz\nM 21.921875 38.8125 \nQ 15.578125 40.375 12.03125 44.71875 \nQ 8.5 49.078125 8.5 55.328125 \nQ 8.5 64.0625 14.71875 69.140625 \nQ 20.953125 74.21875 31.78125 74.21875 \nQ 42.671875 74.21875 48.875 69.140625 \nQ 55.078125 64.0625 55.078125 55.328125 \nQ 55.078125 49.078125 51.53125 44.71875 \nQ 48 40.375 41.703125 38.8125 \nQ 48.828125 37.15625 52.796875 32.3125 \nQ 56.78125 27.484375 56.78125 20.515625 \nQ 56.78125 9.90625 50.3125 4.234375 \nQ 43.84375 -1.421875 31.78125 -1.421875 \nQ 19.734375 -1.421875 13.25 4.234375 \nQ 6.78125 9.90625 6.78125 20.515625 \nQ 6.78125 27.484375 10.78125 32.3125 \nQ 14.796875 37.15625 21.921875 38.8125 \nz\nM 18.3125 54.390625 \nQ 18.3125 48.734375 21.84375 45.5625 \nQ 25.390625 42.390625 31.78125 42.390625 \nQ 38.140625 42.390625 41.71875 45.5625 \nQ 45.3125 48.734375 45.3125 54.390625 \nQ 45.3125 60.0625 41.71875 63.234375 \nQ 38.140625 66.40625 31.78125 66.40625 \nQ 25.390625 66.40625 21.84375 63.234375 \nQ 18.3125 60.0625 18.3125 54.390625 \nz\n\" id=\"DejaVuSans-56\"/>\n      </defs>\n      <g transform=\"translate(335.595455 401.198437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-56\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_18\">\n     <g id=\"line2d_34\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"406.690341\" xlink:href=\"#m50856253cc\" y=\"386.6\"/>\n      </g>\n     </g>\n     <g id=\"text_19\">\n      <!-- 10 -->\n      <g transform=\"translate(400.327841 401.198437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-49\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_20\">\n     <!-- Lag -->\n     <defs>\n      <path d=\"M 9.8125 72.90625 \nL 19.671875 72.90625 \nL 19.671875 8.296875 \nL 55.171875 8.296875 \nL 55.171875 0 \nL 9.8125 0 \nz\n\" id=\"DejaVuSans-76\"/>\n     </defs>\n     <g transform=\"translate(227.882031 414.876562)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-76\"/>\n      <use x=\"55.712891\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"116.992188\" xlink:href=\"#DejaVuSans-103\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_6\">\n    <g id=\"ytick_11\">\n     <g id=\"line2d_35\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"381.284848\"/>\n      </g>\n     </g>\n     <g id=\"text_21\">\n      <!-- 0.00 -->\n      <g transform=\"translate(20.878125 385.084067)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_12\">\n     <g id=\"line2d_36\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"354.709091\"/>\n      </g>\n     </g>\n     <g id=\"text_22\">\n      <!-- 0.25 -->\n      <g transform=\"translate(20.878125 358.50831)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_13\">\n     <g id=\"line2d_37\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"328.133333\"/>\n      </g>\n     </g>\n     <g id=\"text_23\">\n      <!-- 0.50 -->\n      <g transform=\"translate(20.878125 331.932552)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_14\">\n     <g id=\"line2d_38\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"301.557576\"/>\n      </g>\n     </g>\n     <g id=\"text_24\">\n      <!-- 0.75 -->\n      <g transform=\"translate(20.878125 305.356795)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-55\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_15\">\n     <g id=\"line2d_39\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mb270a424c6\" y=\"274.981818\"/>\n      </g>\n     </g>\n     <g id=\"text_25\">\n      <!-- 1.00 -->\n      <g transform=\"translate(20.878125 278.781037)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-49\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"LineCollection_3\">\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M -0.791477 381.284848 \nL -0.791477 309.094242 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 33.165341 381.284848 \nL 33.165341 293.270519 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 67.122159 381.284848 \nL 67.122159 274.981818 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 101.078977 381.284848 \nL 101.078977 293.270519 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 135.035795 381.284848 \nL 135.035795 309.094242 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 168.992614 381.284848 \nL 168.992614 322.571155 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 202.949432 381.284848 \nL 202.949432 333.154342 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 236.90625 381.284848 \nL 236.90625 341.026411 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 270.863068 381.284848 \nL 270.863068 348.320275 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 304.819886 381.284848 \nL 304.819886 354.717589 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 338.776705 381.284848 \nL 338.776705 358.375453 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 372.733523 381.284848 \nL 372.733523 361.175541 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 406.690341 381.284848 \nL 406.690341 363.298099 \n\" style=\"fill:none;stroke:#000000;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"line2d_40\">\n    <path clip-path=\"url(#p10382c9033)\" d=\"M 50.14375 381.284848 \nL 423.66875 381.284848 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"patch_15\">\n    <path d=\"M 50.14375 386.6 \nL 50.14375 269.666667 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_16\">\n    <path d=\"M 423.66875 386.6 \nL 423.66875 269.666667 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_17\">\n    <path d=\"M 50.14375 386.6 \nL 423.66875 386.6 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_18\">\n    <path d=\"M 50.14375 269.666667 \nL 423.66875 269.666667 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"legend_3\">\n    <g id=\"patch_19\">\n     <path d=\"M 358.071875 292.344792 \nL 416.66875 292.344792 \nQ 418.66875 292.344792 418.66875 290.344792 \nL 418.66875 276.666667 \nQ 418.66875 274.666667 416.66875 274.666667 \nL 358.071875 274.666667 \nQ 356.071875 274.666667 356.071875 276.666667 \nL 356.071875 290.344792 \nQ 356.071875 292.344792 358.071875 292.344792 \nz\n\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\n    </g>\n    <g id=\"line2d_41\">\n     <path d=\"M 360.071875 282.765104 \nL 380.071875 282.765104 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n    </g>\n    <g id=\"line2d_42\"/>\n    <g id=\"text_26\">\n     <!-- noise -->\n     <defs>\n      <path d=\"M 44.28125 53.078125 \nL 44.28125 44.578125 \nQ 40.484375 46.53125 36.375 47.5 \nQ 32.28125 48.484375 27.875 48.484375 \nQ 21.1875 48.484375 17.84375 46.4375 \nQ 14.5 44.390625 14.5 40.28125 \nQ 14.5 37.15625 16.890625 35.375 \nQ 19.28125 33.59375 26.515625 31.984375 \nL 29.59375 31.296875 \nQ 39.15625 29.25 43.1875 25.515625 \nQ 47.21875 21.78125 47.21875 15.09375 \nQ 47.21875 7.46875 41.1875 3.015625 \nQ 35.15625 -1.421875 24.609375 -1.421875 \nQ 20.21875 -1.421875 15.453125 -0.5625 \nQ 10.6875 0.296875 5.421875 2 \nL 5.421875 11.28125 \nQ 10.40625 8.6875 15.234375 7.390625 \nQ 20.0625 6.109375 24.8125 6.109375 \nQ 31.15625 6.109375 34.5625 8.28125 \nQ 37.984375 10.453125 37.984375 14.40625 \nQ 37.984375 18.0625 35.515625 20.015625 \nQ 33.0625 21.96875 24.703125 23.78125 \nL 21.578125 24.515625 \nQ 13.234375 26.265625 9.515625 29.90625 \nQ 5.8125 33.546875 5.8125 39.890625 \nQ 5.8125 47.609375 11.28125 51.796875 \nQ 16.75 56 26.8125 56 \nQ 31.78125 56 36.171875 55.265625 \nQ 40.578125 54.546875 44.28125 53.078125 \nz\n\" id=\"DejaVuSans-115\"/>\n     </defs>\n     <g transform=\"translate(388.071875 286.265104)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-110\"/>\n      <use x=\"63.378906\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"124.560547\" xlink:href=\"#DejaVuSans-105\"/>\n      <use x=\"152.34375\" xlink:href=\"#DejaVuSans-115\"/>\n      <use x=\"204.443359\" xlink:href=\"#DejaVuSans-101\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"p7b2b4b3130\">\n   <rect height=\"116.933333\" width=\"373.525\" x=\"50.14375\" y=\"7.2\"/>\n  </clipPath>\n  <clipPath id=\"pf58f251edc\">\n   <rect height=\"116.933333\" width=\"373.525\" x=\"50.14375\" y=\"138.433333\"/>\n  </clipPath>\n  <clipPath id=\"p10382c9033\">\n   <rect height=\"116.933333\" width=\"373.525\" x=\"50.14375\" y=\"269.666667\"/>\n  </clipPath>\n </defs>\n</svg>\n",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import pints.plot\n",
    "pints.plot.autocorrelation(chain, parameter_names=['growth rate', 'carrying capacity', 'noise'], max_lags=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.5-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}