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   "source": [
    "# Differentiating with the LEAN algorithm\n",
    "This example shows how to differentiate cycler data using the LEAN algorithm developed in: Feng X, Merla Y, Weng C, Ouyang M, He X, Liaw BY, et al. A reliable approach of differentiating discrete sampled-data for battery diagnosis. eTransportation. 2020;3: 100051. https://doi.org/10.1016/j.etran.2020.100051.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First import the package and dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyprobe\n",
    "import numpy as np\n",
    "info_dictionary = {'Name': 'Sample cell',\n",
    "                   'Chemistry': 'NMC622',\n",
    "                   'Nominal Capacity [Ah]': 0.04,\n",
    "                   'Cycler number': 1,\n",
    "                   'Channel number': 1,}\n",
    "data_directory = '../../../tests/sample_data/neware'\n",
    "\n",
    "# Create a cell object\n",
    "cell = pyprobe.Cell(info=info_dictionary)\n",
    "cell.add_procedure(procedure_name='Sample',\n",
    "                   folder_path = data_directory,\n",
    "                   filename = 'sample_data_neware.parquet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The break-in cycles of this dataset are at C/10, so can be analysed as pseudo-OCV curves. We're going to look at the last cycle:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_cycle= cell.procedure['Sample'].experiment('Break-in Cycles').cycle(-1)\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(final_cycle, 'Time [hr]', 'Voltage [V]')\n",
    "fig.show_image()\n",
    "# fig.show() # This will show the plot interactively, it is commented out for the sake of the documentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the methods of the `differentiation` module to calculate the gradients of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyprobe.analysis import differentiation\n",
    "discharge_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.discharge(0), \n",
    "                                                    x = 'Capacity [Ah]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "charge_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.charge(0).constant_current(), \n",
    "                                                 x = 'Capacity [Ah]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(discharge_dQdV, 'Capacity [Ah]', 'd(Capacity [Ah])/d(Voltage [V])', label='Discharge', color='blue')\n",
    "fig.add_line(charge_dQdV, 'Capacity [Ah]', 'd(Capacity [Ah])/d(Voltage [V])', label='Charge', color='red')\n",
    "fig.show_image()\n",
    "# fig.show() # This will show the plot interactively, it is commented out for the sake of the documentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On-the-fly unit conversion allows this to be computed in whichever unit you choose:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "discharge_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.discharge(0), x = 'Capacity [mAh]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "charge_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.charge(0).constant_current(), x = 'Capacity [mAh]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(discharge_dQdV, 'Capacity [mAh]', 'd(Capacity [mAh])/d(Voltage [V])', label='Discharge', color='blue')\n",
    "fig.add_line(charge_dQdV, 'Capacity [mAh]', 'd(Capacity [mAh])/d(Voltage [V])', label='Charge', color='red')\n",
    "fig.show_image()\n",
    "# fig.show() # This will show the plot interactively, it is commented out for the sake of the documentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To align the curves, we can instead plot `Cycle Capacity [Ah]` which is set to zero at the beginning of the filtered cycle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "discharge_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.discharge(0), x = 'Cycle Capacity [Ah]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "charge_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.charge(0).constant_current(), x = 'Cycle Capacity [Ah]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(discharge_dQdV, 'Cycle Capacity [Ah]', 'd(Cycle Capacity [Ah])/d(Voltage [V])', label='Discharge', color='blue')\n",
    "fig.add_line(charge_dQdV, 'Cycle Capacity [Ah]', 'd(Cycle Capacity [Ah])/d(Voltage [V])', label='Charge', color='red')\n",
    "fig.show_image()\n",
    "# fig.show() # This will show the plot interactively, it is commented out for the sake of the documentation"
   ]
  }
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