examples/notebooks/Getting Started/Tutorial 3 - Basic plotting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 3 - Basic plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In [Tutorial 2](./Tutorial%202%20-%20Compare%20models.ipynb), we made use of PyBaMM's automatic plotting function when comparing models. This gave a good quick overview of many of the key variables in the model. However, by passing in just a few arguments it is easy to plot any of the many other variables that may be of interest to you. We start by building and solving a model as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pybamm.solvers.solution.Solution at 0x7f0c071f16d0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
    "import pybamm\n",
    "model = pybamm.lithium_ion.DFN()\n",
    "sim = pybamm.Simulation(model)\n",
    "sim.solve([0, 3600])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now want to plot a selection of the model variables. To see a full list of the available variables just type:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Time',\n",
       " 'Time [s]',\n",
       " 'Time [min]',\n",
       " 'Time [h]',\n",
       " 'x',\n",
       " 'x [m]',\n",
       " 'x_n',\n",
       " 'x_n [m]',\n",
       " 'x_s',\n",
       " 'x_s [m]',\n",
       " 'x_p',\n",
       " 'x_p [m]',\n",
       " 'Sum of electrolyte reaction source terms',\n",
       " 'Sum of negative electrode electrolyte reaction source terms',\n",
       " 'Sum of positive electrode electrolyte reaction source terms',\n",
       " 'Sum of x-averaged negative electrode electrolyte reaction source terms',\n",
       " 'Sum of x-averaged positive electrode electrolyte reaction source terms',\n",
       " 'Sum of interfacial current densities',\n",
       " 'Sum of negative electrode interfacial current densities',\n",
       " 'Sum of positive electrode interfacial current densities',\n",
       " 'Sum of x-averaged negative electrode interfacial current densities',\n",
       " 'Sum of x-averaged positive electrode interfacial current densities',\n",
       " 'r_n',\n",
       " 'r_n [m]',\n",
       " 'r_p',\n",
       " 'r_p [m]',\n",
       " 'Total current density',\n",
       " 'Total current density [A.m-2]',\n",
       " 'Current [A]',\n",
       " 'C-rate',\n",
       " 'Discharge capacity [A.h]',\n",
       " 'Porosity',\n",
       " 'Negative electrode porosity',\n",
       " 'Separator porosity',\n",
       " 'Positive electrode porosity',\n",
       " 'X-averaged negative electrode porosity',\n",
       " 'X-averaged separator porosity',\n",
       " 'X-averaged positive electrode porosity',\n",
       " 'Leading-order porosity',\n",
       " 'Leading-order negative electrode porosity',\n",
       " 'Leading-order separator porosity',\n",
       " 'Leading-order positive electrode porosity',\n",
       " 'Leading-order x-averaged negative electrode porosity',\n",
       " 'Leading-order x-averaged separator porosity',\n",
       " 'Leading-order x-averaged positive electrode porosity',\n",
       " 'Porosity change',\n",
       " 'Negative electrode porosity change',\n",
       " 'Separator porosity change',\n",
       " 'Positive electrode porosity change',\n",
       " 'X-averaged negative electrode porosity change',\n",
       " 'X-averaged separator porosity change',\n",
       " 'X-averaged positive electrode porosity change',\n",
       " 'Leading-order x-averaged negative electrode porosity change',\n",
       " 'Leading-order x-averaged separator porosity change',\n",
       " 'Leading-order x-averaged positive electrode porosity change',\n",
       " 'Negative electrode active material volume fraction',\n",
       " 'X-averaged negative electrode active material volume fraction',\n",
       " 'Negative particle radius',\n",
       " 'Negative particle radius [m]',\n",
       " 'Negative electrode surface area to volume ratio',\n",
       " 'Negative electrode surface area to volume ratio [m-1]',\n",
       " 'X-averaged negative electrode surface area to volume ratio',\n",
       " 'X-averaged negative electrode surface area to volume ratio [m-1]',\n",
       " 'Negative electrode active material volume fraction change',\n",
       " 'X-averaged negative electrode active material volume fraction change',\n",
       " 'Positive electrode active material volume fraction',\n",
       " 'X-averaged positive electrode active material volume fraction',\n",
       " 'Positive particle radius',\n",
       " 'Positive particle radius [m]',\n",
       " 'Positive electrode surface area to volume ratio',\n",
       " 'Positive electrode surface area to volume ratio [m-1]',\n",
       " 'X-averaged positive electrode surface area to volume ratio',\n",
       " 'X-averaged positive electrode surface area to volume ratio [m-1]',\n",
       " 'Positive electrode active material volume fraction change',\n",
       " 'X-averaged positive electrode active material volume fraction change',\n",
       " 'Separator pressure',\n",
       " 'X-averaged separator pressure',\n",
       " 'Negative electrode transverse volume-averaged velocity',\n",
       " 'Separator transverse volume-averaged velocity',\n",
       " 'Positive electrode transverse volume-averaged velocity',\n",
       " 'Negative electrode transverse volume-averaged velocity [m.s-2]',\n",
       " 'Separator transverse volume-averaged velocity [m.s-2]',\n",
       " 'Positive electrode transverse volume-averaged velocity [m.s-2]',\n",
       " 'X-averaged negative electrode transverse volume-averaged velocity',\n",
       " 'X-averaged separator transverse volume-averaged velocity',\n",
       " 'X-averaged positive electrode transverse volume-averaged velocity',\n",
       " 'X-averaged negative electrode transverse volume-averaged velocity [m.s-2]',\n",
       " 'X-averaged separator transverse volume-averaged velocity [m.s-2]',\n",
       " 'X-averaged positive electrode transverse volume-averaged velocity [m.s-2]',\n",
       " 'Transverse volume-averaged velocity',\n",
       " 'Transverse volume-averaged velocity [m.s-2]',\n",
       " 'Negative electrode transverse volume-averaged acceleration',\n",
       " 'Separator transverse volume-averaged acceleration',\n",
       " 'Positive electrode transverse volume-averaged acceleration',\n",
       " 'Negative electrode transverse volume-averaged acceleration [m.s-2]',\n",
       " 'Separator transverse volume-averaged acceleration [m.s-2]',\n",
       " 'Positive electrode transverse volume-averaged acceleration [m.s-2]',\n",
       " 'X-averaged negative electrode transverse volume-averaged acceleration',\n",
       " 'X-averaged separator transverse volume-averaged acceleration',\n",
       " 'X-averaged positive electrode transverse volume-averaged acceleration',\n",
       " 'X-averaged negative electrode transverse volume-averaged acceleration [m.s-2]',\n",
       " 'X-averaged separator transverse volume-averaged acceleration [m.s-2]',\n",
       " 'X-averaged positive electrode transverse volume-averaged acceleration [m.s-2]',\n",
       " 'Transverse volume-averaged acceleration',\n",
       " 'Transverse volume-averaged acceleration [m.s-2]',\n",
       " 'Negative electrode volume-averaged velocity',\n",
       " 'Positive electrode volume-averaged velocity',\n",
       " 'Negative electrode volume-averaged velocity [m.s-1]',\n",
       " 'Positive electrode volume-averaged velocity [m.s-1]',\n",
       " 'Negative electrode volume-averaged acceleration',\n",
       " 'Positive electrode volume-averaged acceleration',\n",
       " 'Negative electrode volume-averaged acceleration [m.s-1]',\n",
       " 'Positive electrode volume-averaged acceleration [m.s-1]',\n",
       " 'X-averaged negative electrode volume-averaged acceleration',\n",
       " 'X-averaged positive electrode volume-averaged acceleration',\n",
       " 'X-averaged negative electrode volume-averaged acceleration [m.s-1]',\n",
       " 'X-averaged positive electrode volume-averaged acceleration [m.s-1]',\n",
       " 'Negative electrode pressure',\n",
       " 'Positive electrode pressure',\n",
       " 'X-averaged negative electrode pressure',\n",
       " 'X-averaged positive electrode pressure',\n",
       " 'Negative particle concentration',\n",
       " 'Negative particle concentration [mol.m-3]',\n",
       " 'X-averaged negative particle concentration',\n",
       " 'X-averaged negative particle concentration [mol.m-3]',\n",
       " 'R-averaged negative particle concentration',\n",
       " 'R-averaged negative particle concentration [mol.m-3]',\n",
       " 'Average negative particle concentration',\n",
       " 'Average negative particle concentration [mol.m-3]',\n",
       " 'Negative particle surface concentration',\n",
       " 'Negative particle surface concentration [mol.m-3]',\n",
       " 'X-averaged negative particle surface concentration',\n",
       " 'X-averaged negative particle surface concentration [mol.m-3]',\n",
       " 'Negative electrode extent of lithiation',\n",
       " 'X-averaged negative electrode extent of lithiation',\n",
       " 'Minimum negative particle concentration',\n",
       " 'Maximum negative particle concentration',\n",
       " 'Minimum negative particle concentration [mol.m-3]',\n",
       " 'Maximum negative particle concentration [mol.m-3]',\n",
       " 'Minimum negative particle surface concentration',\n",
       " 'Maximum negative particle surface concentration',\n",
       " 'Minimum negative particle surface concentration [mol.m-3]',\n",
       " 'Maximum negative particle surface concentration [mol.m-3]',\n",
       " 'Positive particle concentration',\n",
       " 'Positive particle concentration [mol.m-3]',\n",
       " 'X-averaged positive particle concentration',\n",
       " 'X-averaged positive particle concentration [mol.m-3]',\n",
       " 'R-averaged positive particle concentration',\n",
       " 'R-averaged positive particle concentration [mol.m-3]',\n",
       " 'Average positive particle concentration',\n",
       " 'Average positive particle concentration [mol.m-3]',\n",
       " 'Positive particle surface concentration',\n",
       " 'Positive particle surface concentration [mol.m-3]',\n",
       " 'X-averaged positive particle surface concentration',\n",
       " 'X-averaged positive particle surface concentration [mol.m-3]',\n",
       " 'Positive electrode extent of lithiation',\n",
       " 'X-averaged positive electrode extent of lithiation',\n",
       " 'Minimum positive particle concentration',\n",
       " 'Maximum positive particle concentration',\n",
       " 'Minimum positive particle concentration [mol.m-3]',\n",
       " 'Maximum positive particle concentration [mol.m-3]',\n",
       " 'Minimum positive particle surface concentration',\n",
       " 'Maximum positive particle surface concentration',\n",
       " 'Minimum positive particle surface concentration [mol.m-3]',\n",
       " 'Maximum positive particle surface concentration [mol.m-3]',\n",
       " 'Negative electrode potential',\n",
       " 'Negative electrode potential [V]',\n",
       " 'X-averaged negative electrode potential',\n",
       " 'X-averaged negative electrode potential [V]',\n",
       " 'Negative electrode ohmic losses',\n",
       " 'Negative electrode ohmic losses [V]',\n",
       " 'X-averaged negative electrode ohmic losses',\n",
       " 'X-averaged negative electrode ohmic losses [V]',\n",
       " 'Gradient of negative electrode potential',\n",
       " 'Positive electrode potential',\n",
       " 'Positive electrode potential [V]',\n",
       " 'X-averaged positive electrode potential',\n",
       " 'X-averaged positive electrode potential [V]',\n",
       " 'Positive electrode ohmic losses',\n",
       " 'Positive electrode ohmic losses [V]',\n",
       " 'X-averaged positive electrode ohmic losses',\n",
       " 'X-averaged positive electrode ohmic losses [V]',\n",
       " 'Gradient of positive electrode potential',\n",
       " 'Electrolyte concentration',\n",
       " 'Electrolyte concentration [mol.m-3]',\n",
       " 'Electrolyte concentration [Molar]',\n",
       " 'X-averaged electrolyte concentration',\n",
       " 'X-averaged electrolyte concentration [mol.m-3]',\n",
       " 'X-averaged electrolyte concentration [Molar]',\n",
       " 'Negative electrolyte concentration',\n",
       " 'Negative electrolyte concentration [mol.m-3]',\n",
       " 'Negative electrolyte concentration [Molar]',\n",
       " 'Separator electrolyte concentration',\n",
       " 'Separator electrolyte concentration [mol.m-3]',\n",
       " 'Separator electrolyte concentration [Molar]',\n",
       " 'Positive electrolyte concentration',\n",
       " 'Positive electrolyte concentration [mol.m-3]',\n",
       " 'Positive electrolyte concentration [Molar]',\n",
       " 'X-averaged negative electrolyte concentration',\n",
       " 'X-averaged negative electrolyte concentration [mol.m-3]',\n",
       " 'X-averaged separator electrolyte concentration',\n",
       " 'X-averaged separator electrolyte concentration [mol.m-3]',\n",
       " 'X-averaged positive electrolyte concentration',\n",
       " 'X-averaged positive electrolyte concentration [mol.m-3]',\n",
       " 'Negative electrolyte potential',\n",
       " 'Negative electrolyte potential [V]',\n",
       " 'Separator electrolyte potential',\n",
       " 'Separator electrolyte potential [V]',\n",
       " 'Positive electrolyte potential',\n",
       " 'Positive electrolyte potential [V]',\n",
       " 'Electrolyte potential',\n",
       " 'Electrolyte potential [V]',\n",
       " 'X-averaged electrolyte potential',\n",
       " 'X-averaged electrolyte potential [V]',\n",
       " 'X-averaged negative electrolyte potential',\n",
       " 'X-averaged negative electrolyte potential [V]',\n",
       " 'X-averaged separator electrolyte potential',\n",
       " 'X-averaged separator electrolyte potential [V]',\n",
       " 'X-averaged positive electrolyte potential',\n",
       " 'X-averaged positive electrolyte potential [V]',\n",
       " 'X-averaged electrolyte overpotential',\n",
       " 'X-averaged electrolyte overpotential [V]',\n",
       " 'Gradient of negative electrolyte potential',\n",
       " 'Gradient of separator electrolyte potential',\n",
       " 'Gradient of positive electrolyte potential',\n",
       " 'Gradient of electrolyte potential',\n",
       " 'Negative current collector temperature',\n",
       " 'Negative current collector temperature [K]',\n",
       " 'X-averaged negative electrode temperature',\n",
       " 'X-averaged negative electrode temperature [K]',\n",
       " 'Negative electrode temperature',\n",
       " 'Negative electrode temperature [K]',\n",
       " 'X-averaged separator temperature',\n",
       " 'X-averaged separator temperature [K]',\n",
       " 'Separator temperature',\n",
       " 'Separator temperature [K]',\n",
       " 'X-averaged positive electrode temperature',\n",
       " 'X-averaged positive electrode temperature [K]',\n",
       " 'Positive electrode temperature',\n",
       " 'Positive electrode temperature [K]',\n",
       " 'Positive current collector temperature',\n",
       " 'Positive current collector temperature [K]',\n",
       " 'Cell temperature',\n",
       " 'Cell temperature [K]',\n",
       " 'X-averaged cell temperature',\n",
       " 'X-averaged cell temperature [K]',\n",
       " 'Volume-averaged cell temperature',\n",
       " 'Volume-averaged cell temperature [K]',\n",
       " 'Ambient temperature [K]',\n",
       " 'Ambient temperature',\n",
       " 'Inner negative electrode SEI thickness',\n",
       " 'Inner negative electrode SEI thickness [m]',\n",
       " 'X-averaged inner negative electrode SEI thickness',\n",
       " 'X-averaged inner negative electrode SEI thickness [m]',\n",
       " 'Outer negative electrode SEI thickness',\n",
       " 'Outer negative electrode SEI thickness [m]',\n",
       " 'X-averaged outer negative electrode SEI thickness',\n",
       " 'X-averaged outer negative electrode SEI thickness [m]',\n",
       " 'Total negative electrode SEI thickness',\n",
       " 'Total negative electrode SEI thickness [m]',\n",
       " 'X-averaged total negative electrode SEI thickness',\n",
       " 'X-averaged total negative electrode SEI thickness [m]',\n",
       " 'X-averaged negative electrode resistance [Ohm.m2]',\n",
       " 'Inner negative electrode SEI concentration [mol.m-3]',\n",
       " 'X-averaged inner negative electrode SEI concentration [mol.m-3]',\n",
       " 'Outer negative electrode SEI concentration [mol.m-3]',\n",
       " 'X-averaged outer negative electrode SEI concentration [mol.m-3]',\n",
       " 'Negative SEI concentration [mol.m-3]',\n",
       " 'X-averaged negative electrode SEI concentration [mol.m-3]',\n",
       " 'Loss of lithium to negative electrode SEI [mol]',\n",
       " 'Inner negative electrode SEI interfacial current density',\n",
       " 'Inner negative electrode SEI interfacial current density [A.m-2]',\n",
       " 'X-averaged inner negative electrode SEI interfacial current density',\n",
       " 'X-averaged inner negative electrode SEI interfacial current density [A.m-2]',\n",
       " 'Outer negative electrode SEI interfacial current density',\n",
       " 'Outer negative electrode SEI interfacial current density [A.m-2]',\n",
       " 'X-averaged outer negative electrode SEI interfacial current density',\n",
       " 'X-averaged outer negative electrode SEI interfacial current density [A.m-2]',\n",
       " 'Negative electrode SEI interfacial current density',\n",
       " 'Negative electrode SEI interfacial current density [A.m-2]',\n",
       " 'X-averaged negative electrode SEI interfacial current density',\n",
       " 'X-averaged negative electrode SEI interfacial current density [A.m-2]',\n",
       " 'Inner positive electrode SEI thickness',\n",
       " 'Inner positive electrode SEI thickness [m]',\n",
       " 'X-averaged inner positive electrode SEI thickness',\n",
       " 'X-averaged inner positive electrode SEI thickness [m]',\n",
       " 'Outer positive electrode SEI thickness',\n",
       " 'Outer positive electrode SEI thickness [m]',\n",
       " 'X-averaged outer positive electrode SEI thickness',\n",
       " 'X-averaged outer positive electrode SEI thickness [m]',\n",
       " 'Total positive electrode SEI thickness',\n",
       " 'Total positive electrode SEI thickness [m]',\n",
       " 'X-averaged total positive electrode SEI thickness',\n",
       " 'X-averaged total positive electrode SEI thickness [m]',\n",
       " 'X-averaged positive electrode resistance [Ohm.m2]',\n",
       " 'Inner positive electrode SEI concentration [mol.m-3]',\n",
       " 'X-averaged inner positive electrode SEI concentration [mol.m-3]',\n",
       " 'Outer positive electrode SEI concentration [mol.m-3]',\n",
       " 'X-averaged outer positive electrode SEI concentration [mol.m-3]',\n",
       " 'Positive SEI concentration [mol.m-3]',\n",
       " 'X-averaged positive electrode SEI concentration [mol.m-3]',\n",
       " 'Loss of lithium to positive electrode SEI [mol]',\n",
       " 'Inner positive electrode SEI interfacial current density',\n",
       " 'Inner positive electrode SEI interfacial current density [A.m-2]',\n",
       " 'X-averaged inner positive electrode SEI interfacial current density',\n",
       " 'X-averaged inner positive electrode SEI interfacial current density [A.m-2]',\n",
       " 'Outer positive electrode SEI interfacial current density',\n",
       " 'Outer positive electrode SEI interfacial current density [A.m-2]',\n",
       " 'X-averaged outer positive electrode SEI interfacial current density',\n",
       " 'X-averaged outer positive electrode SEI interfacial current density [A.m-2]',\n",
       " 'Positive electrode SEI interfacial current density',\n",
       " 'Positive electrode SEI interfacial current density [A.m-2]',\n",
       " 'X-averaged positive electrode SEI interfacial current density',\n",
       " 'X-averaged positive electrode SEI interfacial current density [A.m-2]',\n",
       " 'Electrolyte tortuosity',\n",
       " 'Negative electrolyte tortuosity',\n",
       " 'Positive electrolyte tortuosity',\n",
       " 'X-averaged negative electrolyte tortuosity',\n",
       " 'X-averaged positive electrolyte tortuosity',\n",
       " 'Separator tortuosity',\n",
       " 'X-averaged separator tortuosity',\n",
       " 'Electrode tortuosity',\n",
       " 'Negative electrode tortuosity',\n",
       " 'Positive electrode tortuosity',\n",
       " 'X-averaged negative electrode tortuosity',\n",
       " 'X-averaged positive electrode tortuosity',\n",
       " 'Separator volume-averaged velocity',\n",
       " 'Separator volume-averaged velocity [m.s-1]',\n",
       " 'Separator volume-averaged acceleration',\n",
       " 'Separator volume-averaged acceleration [m.s-1]',\n",
       " 'X-averaged separator volume-averaged acceleration',\n",
       " 'X-averaged separator volume-averaged acceleration [m.s-1]',\n",
       " 'Volume-averaged velocity',\n",
       " 'Volume-averaged velocity [m.s-1]',\n",
       " 'Volume-averaged acceleration',\n",
       " 'X-averaged volume-averaged acceleration',\n",
       " 'Volume-averaged acceleration [m.s-1]',\n",
       " 'X-averaged volume-averaged acceleration [m.s-1]',\n",
       " 'Pressure',\n",
       " 'Negative electrode surface potential difference',\n",
       " 'X-averaged negative electrode surface potential difference',\n",
       " 'Negative electrode surface potential difference [V]',\n",
       " 'X-averaged negative electrode surface potential difference [V]',\n",
       " 'Positive electrode surface potential difference',\n",
       " 'X-averaged positive electrode surface potential difference',\n",
       " 'Positive electrode surface potential difference [V]',\n",
       " 'X-averaged positive electrode surface potential difference [V]',\n",
       " 'Negative particle flux',\n",
       " 'X-averaged negative particle flux',\n",
       " 'Negative electrode volume-averaged concentration',\n",
       " 'Negative electrode volume-averaged concentration [mol.m-3]',\n",
       " 'Total lithium in negative electrode [mol]',\n",
       " 'Positive particle flux',\n",
       " 'X-averaged positive particle flux',\n",
       " 'Positive electrode volume-averaged concentration',\n",
       " 'Positive electrode volume-averaged concentration [mol.m-3]',\n",
       " 'Total lithium in positive electrode [mol]',\n",
       " 'Negative electrode effective conductivity',\n",
       " 'Negative electrode current density',\n",
       " 'Negative electrode current density [A.m-2]',\n",
       " 'Positive electrode effective conductivity',\n",
       " 'Positive electrode current density',\n",
       " 'Positive electrode current density [A.m-2]',\n",
       " 'Electrode current density',\n",
       " 'Electrolyte current density',\n",
       " 'Electrolyte current density [A.m-2]',\n",
       " 'Ohmic heating',\n",
       " 'Ohmic heating [W.m-3]',\n",
       " 'X-averaged Ohmic heating',\n",
       " 'X-averaged Ohmic heating [W.m-3]',\n",
       " 'Volume-averaged Ohmic heating',\n",
       " 'Volume-averaged Ohmic heating [W.m-3]',\n",
       " 'Irreversible electrochemical heating',\n",
       " 'Irreversible electrochemical heating [W.m-3]',\n",
       " 'X-averaged irreversible electrochemical heating',\n",
       " 'X-averaged irreversible electrochemical heating [W.m-3]',\n",
       " 'Volume-averaged irreversible electrochemical heating',\n",
       " 'Volume-averaged irreversible electrochemical heating[W.m-3]',\n",
       " 'Reversible heating',\n",
       " 'Reversible heating [W.m-3]',\n",
       " 'X-averaged reversible heating',\n",
       " 'X-averaged reversible heating [W.m-3]',\n",
       " 'Volume-averaged reversible heating',\n",
       " 'Volume-averaged reversible heating [W.m-3]',\n",
       " 'Total heating',\n",
       " 'Total heating [W.m-3]',\n",
       " 'X-averaged total heating',\n",
       " 'X-averaged total heating [W.m-3]',\n",
       " 'Volume-averaged total heating',\n",
       " 'Volume-averaged total heating [W.m-3]',\n",
       " 'Negative current collector potential',\n",
       " 'Negative current collector potential [V]',\n",
       " 'Current collector current density',\n",
       " 'Current collector current density [A.m-2]',\n",
       " 'Leading-order current collector current density',\n",
       " 'SEI interfacial current density',\n",
       " 'SEI interfacial current density [A.m-2]',\n",
       " 'SEI interfacial current density per volume [A.m-3]',\n",
       " 'Negative electrode interfacial current density',\n",
       " 'X-averaged negative electrode interfacial current density',\n",
       " 'Negative electrode interfacial current density [A.m-2]',\n",
       " 'X-averaged negative electrode interfacial current density [A.m-2]',\n",
       " 'Negative electrode interfacial current density per volume [A.m-3]',\n",
       " 'X-averaged negative electrode interfacial current density per volume [A.m-3]',\n",
       " 'X-averaged negative electrode total interfacial current density',\n",
       " 'X-averaged negative electrode total interfacial current density [A.m-2]',\n",
       " 'X-averaged negative electrode total interfacial current density per volume [A.m-3]',\n",
       " 'Negative electrode exchange current density',\n",
       " 'X-averaged negative electrode exchange current density',\n",
       " 'Negative electrode exchange current density [A.m-2]',\n",
       " 'X-averaged negative electrode exchange current density [A.m-2]',\n",
       " 'Negative electrode exchange current density per volume [A.m-3]',\n",
       " 'X-averaged negative electrode exchange current density per volume [A.m-3]',\n",
       " 'Negative electrode reaction overpotential',\n",
       " 'X-averaged negative electrode reaction overpotential',\n",
       " 'Negative electrode reaction overpotential [V]',\n",
       " 'X-averaged negative electrode reaction overpotential [V]',\n",
       " 'Negative electrode open circuit potential',\n",
       " 'Negative electrode open circuit potential [V]',\n",
       " 'X-averaged negative electrode open circuit potential',\n",
       " 'X-averaged negative electrode open circuit potential [V]',\n",
       " 'Negative electrode entropic change',\n",
       " 'X-averaged negative electrode entropic change',\n",
       " 'Negative electrode SEI film overpotential',\n",
       " 'X-averaged negative electrode SEI film overpotential',\n",
       " 'Negative electrode SEI film overpotential [V]',\n",
       " 'X-averaged negative electrode SEI film overpotential [V]',\n",
       " 'Positive electrode interfacial current density',\n",
       " 'X-averaged positive electrode interfacial current density',\n",
       " 'Positive electrode interfacial current density [A.m-2]',\n",
       " 'X-averaged positive electrode interfacial current density [A.m-2]',\n",
       " 'Positive electrode interfacial current density per volume [A.m-3]',\n",
       " 'X-averaged positive electrode interfacial current density per volume [A.m-3]',\n",
       " 'X-averaged positive electrode total interfacial current density',\n",
       " 'X-averaged positive electrode total interfacial current density [A.m-2]',\n",
       " 'X-averaged positive electrode total interfacial current density per volume [A.m-3]',\n",
       " 'Positive electrode exchange current density',\n",
       " 'X-averaged positive electrode exchange current density',\n",
       " 'Positive electrode exchange current density [A.m-2]',\n",
       " 'X-averaged positive electrode exchange current density [A.m-2]',\n",
       " 'Positive electrode exchange current density per volume [A.m-3]',\n",
       " 'X-averaged positive electrode exchange current density per volume [A.m-3]',\n",
       " 'Positive electrode reaction overpotential',\n",
       " 'X-averaged positive electrode reaction overpotential',\n",
       " 'Positive electrode reaction overpotential [V]',\n",
       " 'X-averaged positive electrode reaction overpotential [V]',\n",
       " 'Positive electrode open circuit potential',\n",
       " 'Positive electrode open circuit potential [V]',\n",
       " 'X-averaged positive electrode open circuit potential',\n",
       " 'X-averaged positive electrode open circuit potential [V]',\n",
       " 'Positive electrode entropic change',\n",
       " 'X-averaged positive electrode entropic change',\n",
       " 'Positive electrode SEI film overpotential',\n",
       " 'X-averaged positive electrode SEI film overpotential',\n",
       " 'Positive electrode SEI film overpotential [V]',\n",
       " 'X-averaged positive electrode SEI film overpotential [V]',\n",
       " 'Interfacial current density',\n",
       " 'Interfacial current density [A.m-2]',\n",
       " 'Interfacial current density per volume [A.m-3]',\n",
       " 'Exchange current density',\n",
       " 'Exchange current density [A.m-2]',\n",
       " 'Exchange current density per volume [A.m-3]',\n",
       " 'Negative electrode oxygen interfacial current density',\n",
       " 'X-averaged negative electrode oxygen interfacial current density',\n",
       " 'Negative electrode oxygen interfacial current density [A.m-2]',\n",
       " 'X-averaged negative electrode oxygen interfacial current density [A.m-2]',\n",
       " 'Negative electrode oxygen interfacial current density per volume [A.m-3]',\n",
       " 'X-averaged negative electrode oxygen interfacial current density per volume [A.m-3]',\n",
       " 'Negative electrode oxygen exchange current density',\n",
       " 'X-averaged negative electrode oxygen exchange current density',\n",
       " 'Negative electrode oxygen exchange current density [A.m-2]',\n",
       " 'X-averaged negative electrode oxygen exchange current density [A.m-2]',\n",
       " 'Negative electrode oxygen exchange current density per volume [A.m-3]',\n",
       " 'X-averaged negative electrode oxygen exchange current density per volume [A.m-3]',\n",
       " 'Negative electrode oxygen reaction overpotential',\n",
       " 'X-averaged negative electrode oxygen reaction overpotential',\n",
       " 'Negative electrode oxygen reaction overpotential [V]',\n",
       " 'X-averaged negative electrode oxygen reaction overpotential [V]',\n",
       " 'Negative electrode oxygen open circuit potential',\n",
       " 'Negative electrode oxygen open circuit potential [V]',\n",
       " 'X-averaged negative electrode oxygen open circuit potential',\n",
       " 'X-averaged negative electrode oxygen open circuit potential [V]',\n",
       " 'Positive electrode oxygen interfacial current density',\n",
       " 'X-averaged positive electrode oxygen interfacial current density',\n",
       " 'Positive electrode oxygen interfacial current density [A.m-2]',\n",
       " 'X-averaged positive electrode oxygen interfacial current density [A.m-2]',\n",
       " 'Positive electrode oxygen interfacial current density per volume [A.m-3]',\n",
       " 'X-averaged positive electrode oxygen interfacial current density per volume [A.m-3]',\n",
       " 'Positive electrode oxygen exchange current density',\n",
       " 'X-averaged positive electrode oxygen exchange current density',\n",
       " 'Positive electrode oxygen exchange current density [A.m-2]',\n",
       " 'X-averaged positive electrode oxygen exchange current density [A.m-2]',\n",
       " 'Positive electrode oxygen exchange current density per volume [A.m-3]',\n",
       " 'X-averaged positive electrode oxygen exchange current density per volume [A.m-3]',\n",
       " 'Positive electrode oxygen reaction overpotential',\n",
       " 'X-averaged positive electrode oxygen reaction overpotential',\n",
       " 'Positive electrode oxygen reaction overpotential [V]',\n",
       " 'X-averaged positive electrode oxygen reaction overpotential [V]',\n",
       " 'Positive electrode oxygen open circuit potential',\n",
       " 'Positive electrode oxygen open circuit potential [V]',\n",
       " 'X-averaged positive electrode oxygen open circuit potential',\n",
       " 'X-averaged positive electrode oxygen open circuit potential [V]',\n",
       " 'Oxygen interfacial current density',\n",
       " 'Oxygen interfacial current density [A.m-2]',\n",
       " 'Oxygen interfacial current density per volume [A.m-3]',\n",
       " 'Oxygen exchange current density',\n",
       " 'Oxygen exchange current density [A.m-2]',\n",
       " 'Oxygen exchange current density per volume [A.m-3]',\n",
       " 'Positive current collector potential',\n",
       " 'Positive current collector potential [V]',\n",
       " 'Local voltage',\n",
       " 'Local voltage [V]',\n",
       " 'Terminal voltage',\n",
       " 'Terminal voltage [V]',\n",
       " 'Electrolyte flux',\n",
       " 'Electrolyte flux [mol.m-2.s-1]',\n",
       " 'Total concentration in electrolyte [mol]',\n",
       " 'X-averaged open circuit voltage',\n",
       " 'Measured open circuit voltage',\n",
       " 'X-averaged open circuit voltage [V]',\n",
       " 'Measured open circuit voltage [V]',\n",
       " 'X-averaged reaction overpotential',\n",
       " 'X-averaged reaction overpotential [V]',\n",
       " 'X-averaged SEI film overpotential',\n",
       " 'X-averaged SEI film overpotential [V]',\n",
       " 'X-averaged solid phase ohmic losses',\n",
       " 'X-averaged solid phase ohmic losses [V]',\n",
       " 'X-averaged battery open circuit voltage [V]',\n",
       " 'Measured battery open circuit voltage [V]',\n",
       " 'X-averaged battery reaction overpotential [V]',\n",
       " 'X-averaged battery solid phase ohmic losses [V]',\n",
       " 'X-averaged battery electrolyte ohmic losses [V]',\n",
       " 'X-averaged battery concentration overpotential [V]',\n",
       " 'Battery voltage [V]',\n",
       " 'Change in measured open circuit voltage',\n",
       " 'Change in measured open circuit voltage [V]',\n",
       " 'Local ECM resistance',\n",
       " 'Local ECM resistance [Ohm]',\n",
       " 'Terminal power [W]']"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.variable_names()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a _lot_ of variables. You can also search the list of variables for a particular string (e.g. \"electrolyte\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Electrolyte concentration\n",
      "Electrolyte concentration [Molar]\n",
      "Electrolyte concentration [mol.m-3]\n",
      "Electrolyte current density\n",
      "Electrolyte current density [A.m-2]\n",
      "Electrolyte flux\n",
      "Electrolyte flux [mol.m-2.s-1]\n",
      "Electrolyte potential\n",
      "Electrolyte potential [V]\n",
      "Electrolyte tortuosity\n",
      "Gradient of electrolyte potential\n",
      "Gradient of negative electrolyte potential\n",
      "Gradient of positive electrolyte potential\n",
      "Gradient of separator electrolyte potential\n",
      "Negative electrolyte concentration\n",
      "Negative electrolyte concentration [Molar]\n",
      "Negative electrolyte concentration [mol.m-3]\n",
      "Negative electrolyte potential\n",
      "Negative electrolyte potential [V]\n",
      "Negative electrolyte tortuosity\n",
      "Positive electrolyte concentration\n",
      "Positive electrolyte concentration [Molar]\n",
      "Positive electrolyte concentration [mol.m-3]\n",
      "Positive electrolyte potential\n",
      "Positive electrolyte potential [V]\n",
      "Positive electrolyte tortuosity\n",
      "Separator electrolyte concentration\n",
      "Separator electrolyte concentration [Molar]\n",
      "Separator electrolyte concentration [mol.m-3]\n",
      "Separator electrolyte potential\n",
      "Separator electrolyte potential [V]\n",
      "Sum of electrolyte reaction source terms\n",
      "Sum of negative electrode electrolyte reaction source terms\n",
      "Sum of positive electrode electrolyte reaction source terms\n",
      "Sum of x-averaged negative electrode electrolyte reaction source terms\n",
      "Sum of x-averaged positive electrode electrolyte reaction source terms\n",
      "Total concentration in electrolyte [mol]\n",
      "X-averaged battery electrolyte ohmic losses [V]\n",
      "X-averaged electrolyte concentration\n",
      "X-averaged electrolyte concentration [Molar]\n",
      "X-averaged electrolyte concentration [mol.m-3]\n",
      "X-averaged electrolyte overpotential\n",
      "X-averaged electrolyte overpotential [V]\n",
      "X-averaged electrolyte potential\n",
      "X-averaged electrolyte potential [V]\n",
      "X-averaged negative electrolyte concentration\n",
      "X-averaged negative electrolyte concentration [mol.m-3]\n",
      "X-averaged negative electrolyte potential\n",
      "X-averaged negative electrolyte potential [V]\n",
      "X-averaged negative electrolyte tortuosity\n",
      "X-averaged positive electrolyte concentration\n",
      "X-averaged positive electrolyte concentration [mol.m-3]\n",
      "X-averaged positive electrolyte potential\n",
      "X-averaged positive electrolyte potential [V]\n",
      "X-averaged positive electrolyte tortuosity\n",
      "X-averaged separator electrolyte concentration\n",
      "X-averaged separator electrolyte concentration [mol.m-3]\n",
      "X-averaged separator electrolyte potential\n",
      "X-averaged separator electrolyte potential [V]\n"
     ]
    }
   ],
   "source": [
    "model.variables.search(\"electrolyte\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have tried to make variables names fairly self explanatory. However, there are two variables for most quantities. This is because PyBaMM utilises both dimensionless and dimensional variables for these quantities. As a rule, the dimensionless variables have no units in their name and the dimensional variables have units in their name. If in doubt, we recommend using the dimensional variable with units."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a first example, we choose to plot the terminal voltage. We add this to a list and then pass this list to the `plot` method of our simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5649a5caf2494529b7ada432fca82e0e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_variables = [\"Terminal voltage [V]\"]\n",
    "sim.plot(output_variables=output_variables)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we may be interested in plotting both the electrolyte concentration and the terminal voltage. In which case, we would do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ebbb366d7cc249efacabd469553bea2e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_variables = [\"Electrolyte concentration [mol.m-3]\", \"Terminal voltage [V]\"]\n",
    "sim.plot(output_variables=output_variables)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also plot multiple variables on the same plot by nesting lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "df723b100e0c4aa8aea66d253048872b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim.plot([[\"Electrode current density\", \"Electrolyte current density\"], \"Terminal voltage [V]\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "07222c0fb3684209907a10dc4aabd9bb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we have seen how to use the plotting functionality in PyBaMM.\n",
    "\n",
    "In [Tutorial 4](./Tutorial%204%20-%20Setting%20parameter%20values.ipynb) we show how to change parameter values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "The relevant papers for this notebook are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] Joel A. E. Andersson, Joris Gillis, Greg Horn, James B. Rawlings, and Moritz Diehl. CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1–36, 2019. doi:10.1007/s12532-018-0139-4.\n",
      "[2] Marc Doyle, Thomas F. Fuller, and John Newman. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6):1526–1533, 1993. doi:10.1149/1.2221597.\n",
      "[3] Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, and others. Array programming with NumPy. Nature, 585(7825):357–362, 2020. doi:10.1038/s41586-020-2649-2.\n",
      "[4] Scott G. Marquis, Valentin Sulzer, Robert Timms, Colin P. Please, and S. Jon Chapman. An asymptotic derivation of a single particle model with electrolyte. Journal of The Electrochemical Society, 166(15):A3693–A3706, 2019. doi:10.1149/2.0341915jes.\n",
      "[5] Valentin Sulzer, Scott G. Marquis, Robert Timms, Martin Robinson, and S. Jon Chapman. Python Battery Mathematical Modelling (PyBaMM). ECSarXiv. February, 2020. doi:10.1149/osf.io/67ckj.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pybamm.print_citations()"
   ]
  }
 ],
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