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   "source": [
    "# Differentiating voltage data\n",
    "\n",
    "Differential Voltage Analysis (DVA) and Incremental Capacity Analysis are popular\n",
    "methods of characterising the degradation state of a cell. PyProBE offers multiple\n",
    "methods to the user which will be explored in this example."
   ]
  },
  {
   "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.discharge(0), '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're going to look at using the finite-difference based differentiation method, first \n",
    "on the raw data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyprobe.analysis import differentiation\n",
    "\n",
    "raw_data_dVdQ = differentiation.gradient(final_cycle.discharge(0),\"Capacity [Ah]\", \"Voltage [V]\")\n",
    "print(raw_data_dVdQ.column_list)\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(raw_data_dVdQ, 'Voltage [V]', 'd(Voltage [V])/d(Capacity [Ah])')\n",
    "fig.show_image()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a clearly poor result. This is due to the noise in the experimental data.\n",
    "We can apply a smoothing function to the voltage prior to differentiating to remove this\n",
    "noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyprobe.analysis import smoothing\n",
    "\n",
    "\n",
    "downsampled_data = smoothing.downsample(input_data = final_cycle.discharge(0),\n",
    "                                            target_column='Voltage [V]',\n",
    "                                                  sampling_interval=0.002,\n",
    "                                                )\n",
    "fig = pyprobe.Plot()\n",
    "# fig.add_line(final_cycle.discharge(0), 'Capacity [Ah]', 'Voltage [V]', label='Raw data', color='red',)\n",
    "fig.add_line(downsampled_data, 'Capacity [Ah]', 'Voltage [V]', label='Level smoothed data', color='blue', dash='dash')\n",
    "fig.show_image()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now differentiate the smoothed data object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "downsampled_data_dVdQ = differentiation.gradient(downsampled_data, \"Voltage [V]\", \"Capacity [Ah]\")\n",
    "\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(downsampled_data_dVdQ, 'Voltage [V]', 'd(Capacity [Ah])/d(Voltage [V])')\n",
    "fig.show_image()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyProBE has multiple smoothing methods, so you can easily compare their effect on the ICA result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "spline_smoothed_data = smoothing.spline_smoothing(input_data = final_cycle.discharge(0),\n",
    "                                                  x='Capacity [Ah]',\n",
    "                                                  target_column='Voltage [V]',\n",
    "                                                  smoothing_lambda=1e-10,\n",
    "                                                  )   \n",
    "spline_smoothed_data_dVdQ = differentiation.gradient(spline_smoothed_data,\"Voltage [V]\",\"Capacity [Ah]\")\n",
    "\n",
    "\n",
    "\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(downsampled_data_dVdQ, 'Voltage [V]', 'd(Capacity [Ah])/d(Voltage [V])', label='Level smoothed data', color='red')\n",
    "fig.add_line(spline_smoothed_data_dVdQ, 'Voltage [V]', 'd(Capacity [Ah])/d(Voltage [V])', label='Spline smoothed data', color='blue')\n",
    "fig.show_image()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also compare to an alternative differentiation method, the LEAN method described 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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LEAN_dQdV = differentiation.differentiate_LEAN(input_data = final_cycle.discharge(0), x = 'Capacity [Ah]', y='Voltage [V]', k = 10, gradient = 'dxdy')\n",
    "\n",
    "fig = pyprobe.Plot()\n",
    "fig.add_line(downsampled_data_dVdQ, 'Voltage [V]', 'd(Capacity [Ah])/d(Voltage [V])', label='Level smoothed data', color='red')\n",
    "fig.add_line(spline_smoothed_data_dVdQ, 'Voltage [V]', 'd(Capacity [Ah])/d(Voltage [V])', label='Spline smoothed data', color='blue')\n",
    "fig.add_line(LEAN_dQdV, 'Voltage [V]', 'd(Capacity [Ah])/d(Voltage [V])', label='LEAN smoothed data', color='green')\n",
    "fig.show_image()"
   ]
  }
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