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   "cell_type": "markdown",
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   "source": [
    "# Basic usage of tidynamics\n",
    "\n",
    "This notebook demonstrates the use of the library [tidynamics](http://lab.pdebuyl.be/tidynamics).\n",
    "\n",
    "tidynamics is open-source and developed for research purposes. Consider citing\n",
    "the corresponding article if you use it in research or teaching material:\n",
    "[![status](http://joss.theoj.org/papers/c4784e48e7514c207d95f440c2a07874/status.svg)](http://joss.theoj.org/papers/c4784e48e7514c207d95f440c2a07874)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tidynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the autocorrelation function\n",
    "\n",
    "We generate random numbers uniformly in the range -1..1 and compute\n",
    "their autocorrelation function using tidynamics's acf routine.\n",
    "\n",
    "*Note:* the numerical results for large lags contain fewer samples than\n",
    "for short lags and are not accurate. This is intrinsic to the computation\n",
    "and not a limitation of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = -1+2*np.random.random(size=1000)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(data)\n",
    "plt.xlabel('time')\n",
    "plt.title('data')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(tidynamics.acf(data))\n",
    "plt.xlabel('lag')\n",
    "plt.title('autocorrelation function of data')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the mean-square displacement\n",
    "\n",
    "We generate a random walk using +1/-1 random steps and compute\n",
    "the corresponding mean-square displacement using tidynamics' msd\n",
    "routine.\n",
    "\n",
    "*Note:* the numerical results for large lags contain fewer samples than\n",
    "for short lags and are not accurate. This is intrinsic to the computation\n",
    "and not a limitation of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate random numbers of +1 or -1\n",
    "steps = -1 + 2*np.random.randint(0, 2, size=1000)\n",
    "# Add the steps to obtain the position\n",
    "position = np.cumsum(steps)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(position)\n",
    "plt.xlabel('time')\n",
    "plt.title('Position as a function of time for a random walk')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(tidynamics.msd(position))\n",
    "plt.xlabel('lag')\n",
    "plt.title('Mean-square displacement for the random walk')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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