examples/notebooks/speed-up-solver.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Speeding up the solvers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains a collection of tips on how to speed up the solvers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARNING: You are using pip version 21.0.1; however, version 21.1 is available.\n",
      "You should consider upgrading via the '/Users/vsulzer/Documents/Energy_storage/PyBaMM/.tox/dev/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
    "import pybamm\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing a solver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since it is very easy to switch which solver is used for the model, we recommend you try different solvers for your particular use case. In general, the `CasadiSolver` is the fastest.\n",
    "\n",
    "Once you have found a good solver, you can further improve performance by trying out different values for the `method`, `rtol`, and `atol` arguments. Further options are sometimes available, but are solver specific. See [solver API docs](https://pybamm.readthedocs.io/en/latest/source/solvers/index.html) for details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing and optimizing CasadiSolver settings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fast mode vs safe mode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `CasadiSolver` comes with a `mode` argument which can be set to \"fast\" or \"safe\" (the third option, \"safe without grid\", is experimental and should not be used for now).\n",
    "The \"fast\" mode is faster but ignores any \"events\" (such as a voltage cut-off point), while the \"safe\" mode is slower but does stop at events (with manually implemented \"step-and-check\" under the hood). Therefore, \"fast\" mode should be used whenever events are not expected to be hit (for example, when simulating a drive cycle or a constant-current discharge where the time interval is such that the simulation will finish before reaching the voltage cut-off). Conversely, \"safe\" mode should be used whenever events are important: in particular, when using the `Experiment` class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To demonstrate the difference between safe mode and fast mode, consider the following example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up model\n",
    "model = pybamm.lithium_ion.DFN()\n",
    "param = model.default_parameter_values\n",
    "cap = param[\"Nominal cell capacity [A.h]\"]\n",
    "param[\"Current function [A]\"] = cap * pybamm.InputParameter(\"Crate\")\n",
    "sim = pybamm.Simulation(model, parameter_values=param)\n",
    "\n",
    "# Set up solvers. Reduce max_num_steps for the fast solver, for faster errors\n",
    "fast_solver = pybamm.CasadiSolver(mode=\"fast\", extra_options_setup={\"max_num_steps\": 1000})\n",
    "safe_solver = pybamm.CasadiSolver(mode=\"safe\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both solvers can solve the model up to 3700 s, but the fast solver ignores the voltage cut-off around 3.1 V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Safe: 392.261 ms\n",
      "Fast: 131.810 ms\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "safe_sol = sim.solve([0,3700], solver=safe_solver, inputs={\"Crate\": 1})\n",
    "fast_sol = sim.solve([0,3700], solver=fast_solver, inputs={\"Crate\": 1})\n",
    "\n",
    "timer = pybamm.Timer()\n",
    "print(\"Safe:\", safe_sol.solve_time)\n",
    "print(\"Fast:\", fast_sol.solve_time)\n",
    "\n",
    "cutoff = param[\"Lower voltage cut-off [V]\"]\n",
    "plt.plot(fast_sol[\"Time [h]\"].data, fast_sol[\"Terminal voltage [V]\"].data, \"b-\", label=\"Fast\")\n",
    "plt.plot(safe_sol[\"Time [h]\"].data, safe_sol[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe\")\n",
    "plt.plot(fast_sol[\"Time [h]\"].data, cutoff * np.ones_like(fast_sol[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we increase the integration interval, the safe solver still stops at the same point, but the fast solver fails"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Safe: 476.941 ms\n",
      "Solving fast mode, error occured: .../casadi/interfaces/sundials/idas_interface.cpp:591: IDASolve returned \"IDA_CONV_FAIL\". Consult IDAS documentation.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "At t = 0.179194 and h = 3.39292e-28, the corrector convergence failed repeatedly or with |h| = hmin.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "safe_sol = sim.solve([0,4500], solver=safe_solver, inputs={\"Crate\": 1})\n",
    "\n",
    "print(\"Safe:\", safe_sol.solve_time)\n",
    "\n",
    "plt.plot(safe_sol[\"Time [h]\"].data, safe_sol[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe\")\n",
    "plt.plot(safe_sol[\"Time [h]\"].data, cutoff * np.ones_like(safe_sol[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
    "plt.legend();\n",
    "\n",
    "try:\n",
    "    sim.solve([0,4500], solver=fast_solver, inputs={\"Crate\": 1})\n",
    "except pybamm.SolverError as e:\n",
    "    print(\"Solving fast mode, error occured:\", e.args[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should be noted here that the time in the warning \"At t = 0.179234, , mxstep steps taken before reaching tout\" is dimensionless time, since this is the time that the casadi solver sees. This can be converted to dimensional time as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Errored at 4050.4391486585114 seconds\n"
     ]
    }
   ],
   "source": [
    "print(f\"Errored at {0.179234 * param.evaluate(model.timescale)} seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can solve with fast mode up to close to this time to understand why the model is failing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f1f9ab302c97445e87a127e80c53b52b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=4049.0, step=40.49), Output()), _dom_classes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fast_sol = sim.solve([0,4049], solver=fast_solver, inputs={\"Crate\": 1})\n",
    "fast_sol.plot([\n",
    "    \"Minimum negative particle surface concentration\",\n",
    "    \"Electrolyte concentration [mol.m-3]\",\n",
    "    \"Maximum positive particle surface concentration\",\n",
    "    \"Terminal voltage [V]\",\n",
    "], time_unit=\"seconds\", figsize=(9,9));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, we can see that the reason the solver is failing is that the concentration at the surface of the particles in the positive electrode hit their maximum (dimensionless) value of 1. Since the exchange current density has a term `sqrt(1-c_s_surf)`, the square root of a negative number is complex, `c_s_surf` going above 1 will cause the solver to fail."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a final note, there are some cases where the \"safe\" mode prints some warnings. This is linked to how the solver looks for events (sometimes stepping too far), and can be safely ignored if the solution looks sensible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "At t = 0.00668001, , mxstep steps taken before reaching tout.\n",
      "At t = 0.00174981, , mxstep steps taken before reaching tout.\n",
      "At t = 0.00174981, , mxstep steps taken before reaching tout.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "safe_sol_160 = sim.solve([0,160], solver=safe_solver, inputs={\"Crate\": 10})\n",
    "plt.plot(safe_sol_160[\"Time [h]\"].data, safe_sol_160[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe\")\n",
    "plt.plot(safe_sol_160[\"Time [h]\"].data, cutoff * np.ones_like(safe_sol_160[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reducing the time interval to [0, 150], we see that the solution is exactly the same, without the warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "safe_sol_150 = sim.solve([0,150], solver=safe_solver, inputs={\"Crate\": 10})\n",
    "plt.plot(safe_sol_150[\"Time [h]\"].data, safe_sol_150[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe [0,150]\")\n",
    "plt.plot(safe_sol_160[\"Time [h]\"].data, safe_sol_160[\"Terminal voltage [V]\"].data, \"b.\", label=\"Safe [0,160]\")\n",
    "plt.plot(safe_sol_150[\"Time [h]\"].data, cutoff * np.ones_like(safe_sol_150[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "safe_solver_2 = pybamm.CasadiSolver(mode=\"safe\", dt_max=30)\n",
    "safe_sol_2 = sim.solve([0,160], solver=safe_solver_2, inputs={\"Crate\": 10})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing dt_max to speed up the safe mode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameter `dt_max` controls how large the steps taken by the `CasadiSolver` with \"safe\" mode are when looking for events."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With dt_max=10, took 1.177 s (integration time: 1.064 s)\n",
      "With dt_max=20, took 1.173 s (integration time: 1.063 s)\n",
      "With dt_max=100, took 733.209 ms (integration time: 639.751 ms)\n",
      "With dt_max=1000, took 160.866 ms (integration time: 109.546 ms)\n",
      "With dt_max=3700, took 137.295 ms (integration time: 84.103 ms)\n",
      "With 'fast' mode, took 98.616 ms (integration time: 78.933 ms)\n"
     ]
    }
   ],
   "source": [
    "for dt_max in [10,20,100,1000,3700]:\n",
    "    safe_sol = sim.solve(\n",
    "        [0,3600], \n",
    "        solver=pybamm.CasadiSolver(mode=\"safe\", dt_max=dt_max),\n",
    "        inputs={\"Crate\": 1}\n",
    "    )\n",
    "    print(f\"With dt_max={dt_max}, took {safe_sol.solve_time} \"+\n",
    "          f\"(integration time: {safe_sol.integration_time})\")\n",
    "\n",
    "fast_sol = sim.solve([0,3600], solver=fast_solver, inputs={\"Crate\": 1})\n",
    "print(f\"With 'fast' mode, took {fast_sol.solve_time} \"+\n",
    "      f\"(integration time: {fast_sol.integration_time})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, a larger value of `dt_max` gives a faster solution, since fewer integrator creations and calls are required.\n",
    "\n",
    "Below the solution time interval of 36s, the value of `dt_max` does not affect the solve time, since steps must be at least 36s large.\n",
    "The discrepancy between the solve time and integration time is due to the extra operations recorded by \"solve time\", such as creating the integrator. The \"fast\" solver does not need to do this (it reuses the first one it had already created), so the solve time is much closer to the integration time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The example above was a case where no events are triggered, so the largest `dt_max` works well. If we step over events, then it is possible to makes `dt_max` too large, so that the solver will attempt (and fail) to take large steps past the event, iteratively reducing the step size until it works. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With dt_max=10, took 1.079 s (integration time: 908.498 ms)\n",
      "With dt_max=20, took 1.012 s (integration time: 840.830 ms)\n",
      "With dt_max=100, took 628.936 ms (integration time: 508.004 ms)\n",
      "With dt_max=1000, took 235.521 ms (integration time: 133.730 ms)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "At t = 0.0202946 and h = 4.01795e-28, the corrector convergence failed repeatedly or with |h| = hmin.\n",
      "At t = 0.0202946 and h = 4.01795e-28, the corrector convergence failed repeatedly or with |h| = hmin.\n",
      "At t = 0.0202946 and h = 3.77863e-28, the corrector convergence failed repeatedly or with |h| = hmin."
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With dt_max=3600, took 967.320 ms (integration time: 81.977 ms)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "for dt_max in [10,20,100,1000,3600]:\n",
    "    # Reduce max_num_steps to fail faster\n",
    "    safe_sol = sim.solve(\n",
    "        [0,4500], \n",
    "        solver=pybamm.CasadiSolver(mode=\"safe\", dt_max=dt_max, extra_options_setup={\"max_num_steps\": 1000}),\n",
    "        inputs={\"Crate\": 1}\n",
    "    )\n",
    "    print(f\"With dt_max={dt_max}, took {safe_sol.solve_time} \"+\n",
    "          f\"(integration time: {safe_sol.integration_time})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The integration time with `dt_max=3600` remains the fastest, but the solve time is the slowest due to all the failed steps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the period for faster experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"period\" argument of the experiments also affects how long the simulations take, for a similar reason to `dt_max`. Therefore, this argument can be manually tuned to speed up how long an experiment takes to solve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with one cycle of CCCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Took  3.194 s\n"
     ]
    }
   ],
   "source": [
    "experiment = pybamm.Experiment(\n",
    "    [\n",
    "        \"Discharge at C/10 for 10 hours or until 3.3 V\",\n",
    "        \"Rest for 1 hour\",\n",
    "        \"Charge at 1 A until 4.1 V\",\n",
    "        \"Hold at 4.1 V until 50 mA\",\n",
    "        \"Rest for 1 hour\",\n",
    "    ]\n",
    ")\n",
    "solver = pybamm.CasadiSolver(mode=\"safe\", extra_options_setup={\"max_num_steps\": 1000})\n",
    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
    "sol = sim.solve()\n",
    "print(\"Took \", sol.solve_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a nice, smooth voltage curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can speed up the experiment by increasing the period, but tradeoff is that the resolution of the solution becomes worse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Took  1.314 s\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "experiment = pybamm.Experiment(\n",
    "    [\n",
    "        \"Discharge at C/10 for 10 hours or until 3.3 V\",\n",
    "        \"Rest for 1 hour\",\n",
    "        \"Charge at 1 A until 4.1 V\",\n",
    "        \"Hold at 4.1 V until 50 mA\",\n",
    "        \"Rest for 1 hour\",\n",
    "    ],\n",
    "    period=\"10 minutes\",\n",
    ")\n",
    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
    "sol = sim.solve()\n",
    "print(\"Took \", sol.solve_time)\n",
    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we increase the period too much, the experiment becomes slower as the solver takes more failing steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "At t = 0.0556187 and h = 1.41541e-28, the corrector convergence failed repeatedly or with |h| = hmin.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Took  1.145 s\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "experiment = pybamm.Experiment(\n",
    "    [\n",
    "        \"Discharge at C/10 for 10 hours or until 3.3 V\",\n",
    "        \"Rest for 1 hour\",\n",
    "        \"Charge at 1 A until 4.1 V\",\n",
    "        \"Hold at 4.1 V until 50 mA\",\n",
    "        \"Rest for 1 hour\",\n",
    "    ],\n",
    "    period=\"30 minutes\",\n",
    ")\n",
    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
    "sol = sim.solve()\n",
    "print(\"Took \", sol.solve_time)\n",
    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can control the period of individual parts of the experiment to get the fastest solution (again, at the cost of resolution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Took  628.190 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "experiment = pybamm.Experiment(\n",
    "    [\n",
    "        \"Discharge at C/10 for 10 hours or until 3.3 V (5 hour period)\",\n",
    "        \"Rest for 1 hour (30 minute period)\",\n",
    "        \"Charge at 1 C until 4.1 V (10 minute period)\",\n",
    "        \"Hold at 4.1 V until 50 mA (10 minute period)\",\n",
    "        \"Rest for 1 hour (30 minute period)\",\n",
    "    ],\n",
    ")\n",
    "solver = pybamm.CasadiSolver(mode=\"safe\", extra_options_setup={\"max_num_steps\": 1000})\n",
    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
    "sol = sim.solve()\n",
    "print(\"Took \", sol.solve_time)\n",
    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, this kind of optimization requires a lot of manual tuning. We are working on ways to make the experiment class more efficient in general."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Changing the time interval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, in some cases, changing the time interval (either the step size or the final time) may affect whether or not the casadi solver can solve the system. \n",
    "Therefore, if the casadi solver is failing, it may be worth changing the time interval (usually, reducing step size or final time) to see if that allows the solver to solve the model.\n",
    "Unfortunately, we have not yet been able to isolate a minimum working example to demonstrate this effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Handling instabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the solver is taking a lot of steps, possibly failing with a `max_steps` error, and the error persists with different solvers and options, this suggests a problem with the model itself. This can be due to a few things:\n",
    "\n",
    "- A singularity in the model (such as division by zero). Solve up to the time where the model fails, and plot some variables to see if they are going to infinity. You can then narrow down the source of the problem.\n",
    "- High model stiffness. The first thing to do to tackle this is to non-dimensionalize your model. If you really don't want to do this, or you do it and the problem persists, plot different variables to identify which variables or parameters may be causing problems. To reduce stiffness, all (dimensionless) parameter values should be as close to 1 as possible.\n",
    "- Non-differentiable functions (see [below](#Smooth-approximations-to-non-differentiable-functions))\n",
    "\n",
    "If none of these fixes work, we are interested in finding out why - please get in touch!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Smooth approximations to non-differentiable functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some functions, such as `minimum`, `maximum`, `heaviside`, and `abs`, are discontinuous and/or non-differentiable (their derivative is discontinuous). Adaptive solvers can deal with this discontinuity, but will take many more steps close to the discontinuity in order to resolve it. Therefore, using smooth approximations instead can reduce the number of steps taken by the solver, and hence the integration time. See [this post](https://discourse.julialang.org/t/handling-instability-when-solving-ode-problems/9019/5) for more details.\n",
    "\n",
    "Here is an example using the `maximum` function. The function `maximum(x,1)` is continuous but non-differentiable at `x=1`, where its derivative jumps from 0 to 1. However, we can approximate it using the [`softplus` function](https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Softplus), which is smooth everywhere and is sometimes used in neural networks as a smooth approximation to the RELU activation function. The `softplus` function is given by\n",
    "$$\n",
    "s(x,y;k) = \\frac{\\log(\\exp(kx)+\\exp(ky))}{k},\n",
    "$$\n",
    "where `k` is a strictly positive smoothing (or sharpness) parameter. The larger the value of `k`, the better the approximation but the stiffer the term (exp blows up quickly!). Usually, a value of `k=10` is a good middle ground.\n",
    "\n",
    "In PyBaMM, you can either call the `softplus` function directly, or change `pybamm.settings.max_smoothing` to automatically replace all your calls to `pybamm.maximum` with `softplus`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact maximum: maximum(x, y)\n",
      "Softplus (k=10): log(exp(10.0 * x) + exp(10.0 * y)) / 10.0\n",
      "Softplus (k=20): log(exp(20.0 * x) + exp(20.0 * y)) / 20.0\n",
      "Softplus (k=30): log(exp(30.0 * x) + exp(30.0 * y)) / 30.0\n",
      "Exact maximum: maximum(x, y)\n"
     ]
    }
   ],
   "source": [
    "x = pybamm.Variable(\"x\")\n",
    "y = pybamm.Variable(\"y\")\n",
    "\n",
    "# Normal maximum\n",
    "print(\"Exact maximum:\", pybamm.maximum(x,y))\n",
    "\n",
    "# Softplus\n",
    "print(\"Softplus (k=10):\", pybamm.softplus(x,y,10))\n",
    "\n",
    "# Changing the setting to call softplus automatically\n",
    "pybamm.settings.max_smoothing = 20\n",
    "print(\"Softplus (k=20):\", pybamm.maximum(x,y))\n",
    "\n",
    "# All smoothing parameters can be changed at once\n",
    "pybamm.settings.set_smoothing_parameters(30)\n",
    "print(\"Softplus (k=30):\", pybamm.maximum(x,y))\n",
    "\n",
    "# Change back\n",
    "pybamm.settings.set_smoothing_parameters(\"exact\")\n",
    "print(\"Exact maximum:\", pybamm.maximum(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that if both sides are constant then pybamm will use the exact value even if the setting is set to smoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact: 1.0\n",
      "Softplus: 1.0341598589863317\n"
     ]
    }
   ],
   "source": [
    "a = pybamm.InputParameter(\"a\")\n",
    "pybamm.settings.max_smoothing = 20\n",
    "# Both inputs are constant so uses exact maximum\n",
    "print(\"Exact:\", pybamm.maximum(0.999,1).evaluate())\n",
    "# One input is not constant (InputParameter) so uses softplus\n",
    "print(\"Softplus:\", pybamm.maximum(a,1).evaluate(inputs={\"a\": 0.999}))\n",
    "pybamm.settings.set_smoothing_parameters(\"exact\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the plot of softplus with different values of `k`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x150729fa0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xTIpdZfqg3EbDfCIiIpKs8HD4YvxmXh/XhhCXi1WHa1H98x/JV7yMu1PLEtQz9R9MmDCBxo0bM2XKlFQtdPzqq68ya9asNF2zV69eBAUFcfjwYe66667/dO7ff/9NvXr1yJcvH2vXrk2Inz9/no4dO9KsWTOGDBmSMLnpli1baNq0KU2aNGH69OkAnD17lt69e6epDSIikn25XNCy40YG73yf0uZG6hcsSPXlP6mQSkLF1H8wffp01q5dy8CBA1NVTKXV5s2bKVGixHXPMVWqVCl+/vlnunXrdln8zTffpGfPnqxZs4awsDCWL18OwJAhQ5g1axYBAQG8//77BAUFUaxYMfLnz8/27dvT3B4REcmGdmzlRM22UGcGjXrlZelff5GvVCl3Z5WlZOliyow2mNFXLHQ8517MaMPifUkWOt48BTPaMHBxkoWOQ09iRhtKv538Qse7du2icePGtGrVinbt2gGwf/9+WrZsSYsWLejZsycRERGMGzeOw4cP07p1a8aMGcOJEydo2bIl48aNIyAggFatWtGlSxfq1KnD/Pnz/3WdpAsW33XXXRw+fPiq105q3rx5tG/f/l/xDz/8kMcff5y4uLhk2+bv73/VdfdWr15Nx44dAWfh6NWrVxMVFUVYWBiVKlXCx8eHZs2a8ccffwDQvn37q7ZJRERytk0zZjCg0e18N/88Pc6UZeLHK/G/Yrk00T1TLF++nP79+zNw4EBcLhcAw4YNY8yYMTRv3pwxY8bw2WefMXLkSL744gsCAgIAmDFjRsJ2QEAAgYGB/Pzzz4SHh1O/fv1ULctytWsn9eeff/Loo49eFhsxYgR+fn5MnjwZ4LrW5jt//jyFChUCoFChQpw/f55z584lxJLGAapWrcq0adNSbI+IiOQMJ05Av56H2L/+EY7aGG4pVpO5kzaDr6+7U8uSsnQxZV+5ykLHD1xloeN6AxlY74qFjvOXvur5V+rfvz/jxo2jT58+1K5dmxdeeIH9+/fTpEkTAJo0acKCBQtSfJ66devi5eVFgQIFKFGiBIGBgdc89tI9Sle7dnJ27dpFUFAQv/32W0IsubX5rqVw4cKEhIRQqFAhQkJCKFKkCEWKFCE4ODjhmEtxERHJffoOXszKJg9T51Rf7nL9wpA//lAhlYwsPcyXGXx9fXnrrbeYPXs2P//8Mzt37qRq1aqsX78egPXr1/9rAWIALy+vy3qTtm3bRmxsLKGhoZw+fZriV3SDulwuoqKiCA8PZ8+ePde8dlK1atXiwIEDCY9r1qzJiBEj6NGjB1FRUYDTM3VpBvZLX3379k22zS1atGDp0qUALF26lBYtWuDn50fevHk5evQoMTExrF27loYNndW+9+/fT61atVL1/RQRkewt9IcfuDm6N+Q9S82Oa/n8r7/w9vd3d1pZWpbumcoMc+bMYfr06RhjuOGGG6hWrRrjx49n0KBBWGspUaIEM2fO/Nd53bp1o0OHDrRr147atWtTunRpunfvzqFDhxg7diweHpfXqYMHD+b222+nTp06lC1b9prXTqp79+58+eWXtG3b9rLr+vj40K1bN+bNm5dsz9SFCxfo2rUru3fvZteuXbRv357Ro0czbNgw+vbty+TJk6lduzZt2rQB4L333uOBBx7AWsv//d//Jdz4vnTpUh5//PHr+waLiEi2EBgIWz57nT4jR/KNgYaV7uB/7/wCXrm+VEiRuTTk5A7169e3mzZtAiAmJgYAb29vt+VzvQICApg1axZTp05N9+fu2bMnn3zyyXV/oi+tzp49y5AhQ5gzZ85l8ez8eomIyOW2bIFWfQK4+cDT/BG7nWdq1WLS9u3gkesHsC5jjNlsrf3XSs4qN7O4uXPnuvX6xYoV+1chJSIiOctXX0/iQvfhHDp4C5+fbk3/H5erkPoP9J1KBy1btsyQXqmszJ09miIikn5WvfwyfWY8T4Eo6F3W0H/5TxhPT3enla2k2DNljFkO3Aa8Z60de8W+G4HpgAuwwIPW2uPXk4inpydRUVEaNsom4uLi8NUnO0REsq2ffoK9M5/hmVnv0gn40zxK2dc/wKhH6j9LzTDfAOAuoOxV9v0f8Lm19ktjTD9gCJD85/uvwcPDA5fLRUREBJ6enhhjUj5JMp21lri4OFwu179ushcRkexhxQpoP2IqhS8UID+G21q1pNwbH4L+770uKRZT1trjyRQ2u4BC8duFgTNpSSZv3ry4XK4UZ/YW9zHG4Ovrq0JKRCQbi906grhO4wmO8WK96/9o8PqH7k4pW0vrDegrgOXGmAGAL9AwpROMMQOBgeDM1H0lDw8P/UctIiKSQd7v2pUaCxfySAcvqt/RgQbDVUilVVqLqQnAS9baBcaYB4DXgSeSO8FaOwWYAs7UCGm8voiIiKTCpEmwZfYEZm9ZSF7gQJPR3DD8RXenlSOktZgywNn47TOA1h8RERHJYnbvhue/H4OtuYZ7dxSmc+97ueFFFVLpJTWf5vsMaAL4GmPqA68Cd1trJwJjgU+NMbGANzAoA3MVERGR/8i6XBSa+Qz5G0wh1D+KIR88x92PTXR3WjlKam5Af/Qq4W3x+3YBd6RzTiIiIpJGLhecOe1i4r0N2b95M6tuMBwYPYS7B6qQSm+aAV1ERCSHiY2Fhwe4WL56IdFHthIGjBj8Gj0GjnR3ajmSiikREZEcJjwsluURfTnz4Lc8Na8ybXr1oslIFVIZRXMQiIiI5CBx0dH83bcr9138Fl8bS9vRD9J+9Gh3p5WjqWdKREQkB7h4EebMimLl+GosOnKEJT7ePPX4Z9S492F3p5bjqZgSERHJ5lwuuKddFOvNRBqd8Mcb8Jv0jgqpTKJiSkREJJvziInCr0pLqPA7hcsUZHOXuVTp0cPdaeUaumdKREQkG4sICuLVWrV4e8nvVD3vyWsD3lchlcnUMyUiIpINHTwI/R6KpeDeuiw5e4Sjvr7s7rcOz7r13J1arqOeKRERkWzo+ReCWFOpPSeKtKSmpyfPz52rQspN1DMlIiKSzdiQEJqYJiy8aS9BxbzZ8/Am/GrVcXdauZZ6pkRERLKJQ4fg3N8HaVa2LLfM38urWwrw84PLVEi5mXqmREREsoFffoFOPc7S0D7NuosXGertzdZJW/C86SZ3p5brqWdKREQkGzhy8ADhPe9k770HeLF4EZatW6dCKotQz5SIiEgWd2rbNhp82pWiLY9TyM/w5G8bKXlTbXenJfFUTImIiGRRM2ZA+TwbGdCnKdViYljpdRMl5yyiZKVa7k5NklAxJSIikgXNnw8PPXWYwiVW4BETQ2CePJSfvZxClTS0l9WomBIREcmCGlTYiE//e7mQL5DP1laky7RVFKpY0d1pyVXoBnQREZEswlrna/eSJextdw+P7z5Dowt5uf/rX1VIZWHqmRIREckC4uLgscfAO3QH8+d1ItRaAs7U4Y2vlpOnSAl3pyfJUDElIiKSBWzZAl8s3Ya941W6eeXjQgEfbv15BXmKFHV3apICDfOJiIhkAfX4gzJd7sRV4zuqPVSC7w4eJE9RFVLZgYopERERNwkNhQMHYM0nn9C9SVMWfx3EgLPlGfnuFnwKFHB3epJKGuYTERFxg/PnoW1bOHbiOD6nnuSojaVpmdpMnbQJvL3dnZ78ByqmRERE3MDPDyLzf8+Zvv9j5ML8XKA4T/3xhwqpbEjDfCIiIm4QvmQebT0fwOUXyumOxXh31y48fX3dnZZcB/VMiYiIZJI9e5yZzWuEj6D/hPHMAxpUv4v7Jy0DT093pyfXScWUiIhIJoiIgLvvhhM+v9DqxHdcBNbWq8e4d38CY9ydnqSBiikREZFMkCcP9On9OhPzjCL2qOWb4I50/fY7FVI5gO6ZEhERyUAREc6/3z/zDP/7fCQ3hLloVq4xXb/9DuOh/4ZzAr2KIiIiGWTuXKhaFV7v+jid332X58/D1vxDGTdmnQqpHESvpIiISAawFr74Ao6X+pjf9u6nJNCuY0dKvvKmu1OTdKZ7pkRERDKAMfB8i+dYHj2J5XGw0fc5bh35lrvTkgygnikREZF0Yi0sWgQul2XM3XcT/uIkhq2Fdwv2VCGVg6lnSkREJJ089xy8846l6y3jWbBzBf7AoXZvU+LZZ92dmmQg9UyJiIikkztbufC5ewR760/kCR+Y/sQTKqRyAfVMiYiIpANXXBx1Vv4fxWpNZV9+F+9+PIK7B7zu7rQkE6hnSkRE5DqFhEDXrrBzRyyP1q7NQ+9O4cdZhm8rvaBCKhdRz5SIiMh1eu01WLjIxa5907mwezchQOTwN+ncT0N7uYmKKRERkes0+pUYvjvTmb8rLePthV7c9tB4GugeqVxHw3wiIiL/wbFj4HJBVFgYW+9vT48Ty/CNhVteHU+z555zd3riBuqZEhERSaVNm6BdO+jZPZKDCyqz4vQ/LPTzZcALX3Jjm57uTk/cJMWeKWPMcmNMoDHmpWvsf8EYs8IYE2CMuTP9UxQREckagoMhJCySZccep2LQaQoaQ5lPp6iQyuVS0zM1ALgLKHvlDmNMO6Cgtfau9E5MREQkq7mraQTtejfk+3J/crKwF9se+J4y7dq5Oy1xsxR7pqy1x5PZ3QPwM8b8YoyZaYwpmH6piYiIuN/MmbBtGwSfPMlT1aoxbsGf1D3jyehHZquQEiDt90yVBs5Za1sbYwYDI4DhyZ1gjBkIDAQoX758Gi8vIiKScRYvhr59oUSJWOrF3say86cJ8fNj8+MbMbVquTs9ySLS+mm+88CP8ds/ArVTOsFaO8VaW99aW7948eJpvLyIiEjGadMGWt51lvz3V+PuUqdp6u3N6CVLVEjJZdJaTAUA9eO36wMH0vh8IiIibhUX53wBeF4IpFeBhvxd8iAf3ePFih1bqdC6tXsTlCwnxWE+Y8xnQBPA1xhTH3gVuNtaOxGYDnxmjFkFxAB9My5VERGRjBUVBf/7HxQuDKOe2EG72xvxWmQkb0UVodv47/C7uaa7U5QsKMViylr76FXC2+L3RaECSkREcojdu2HJEvAq8A95l97PrshIxvv68ttHW/CoUMHd6UkWpRnQRURE4tWtC1Mn76J476psaHuA8WWKsWyLCilJnoopERHJ1Y4ehc2bne0Da9ZQZ1I74ggltIAv/deuokiNGu5NULI8LScjIiK51tGj0LQpRETAF+NX8Ohjbbk5Lo6l+W6m5NxFFCtXzd0pSjagYkpERHKtUqXg1lvhdOif7Jn2IJ5xcfgUKECl+SvwL1PG3elJNqFiSkREci1vb5g86ncafXsHI/LE8UWByvSYsQ6/EiXcnZpkI7pnSkREcpXZs+Hhh8HlgnUzZ/JHm3t4dGMczUIK0vWrNSqk5D9Tz5SIiOQaZ8/C449DaCg0Kbeap8f0JQpYG1afka/9jE/+Qu5OUbIhFVMiIpJrFCsG334LS5cv4ZujXXjEF4KLlaH+qgA88+Z1d3qSTWmYT0REcrTYWGcyzkta+69jdXhnlleMJV+/qkz76y8VUpImKqZERCTHioyELl2gSRPYuRO+GTOG1i1aMHOOiyHnKvPKu1vxyJPH3WlKNqdhPhERybG8vcHXFzw94eDyJQx79VUOWcu6qg15f9I68NJ/g5J2+ikSEZEcy9MTZs2Crz6fSJ+TwxhTC+J86/PoOhVSkn40zCciIjnKnj0wZAjExTmPT8yYwpn5Iwjzgb/b1mTohg0YFVKSjvTTJCIiOUZsLHTsCAcPQqVKYHb0Y9iXXzIX+KF+J9q9uRA81I8g6Us/USIikmN4ecEXX0CPHlDRbzjH531JLPDPXXfRfuIijAopyQDqmRIRkWzv5EkoXdrZbt4cAv8cTPfTH1G/D6yOe5Dmn38Jxrg3ScmxVKKLiEi2ZS2MHQvVqsGmTWCt5aM+fag+4iPKh0DHcnfSfNoMFVKSodQzJSIi2dr+/RAWBjt2wI+jOzFqyRLuBLbd8CoFh7/i7vQkF1DPlIiIZFvGwNSpsGoVhJy5D79jS7gJeHrAABVSkmlUTImISLZy/jyMGAExMc5jHx/wW/8Ez0Z9x/DOsPidUdw7dap7k5RcRcN8IiKSbVgL990Ha9Y480iNGxtNv/r1uXfnTsY2hxvuf4jqT45xd5qSy6iYEhGRbMMYmDgRnnoKnhziYs4D9/PVzp38CBzs/QkFBw1yd4qSC6mYEhGRLO/8eShSxNlu1AjWr3MxdFRDAoptZqQfdB41ToWUuI3umRIRkSxt5kxnNvP1653HYaGhHP2//nwXtpmdJaHlpy/T4MUX3Zuk5GrqmRIRkSxt3Tq4cAF+/hlq1Qim/c03E3f6NN8X9eLYe6O4q8/L7k5RcjkVUyIikqV9+CG0bQv3dojm20fv4/jp07iAPJM+554+fd2dnoiG+UREJGsJC4NXXoGoKOexlxd07hDDg8Or0qviaobU8+bX2bOp1FeFlGQNKqZERCRL6dMHxoyBp592Hp86coRFzZtTZ8MR8sZAw1cmUbF3b7fmKJKUhvlERCRLefVVOHTIKaZCz56lec2aHAwL4zt/f/aOnUOZlp3cnaLIZVRMiYiI2wUFQeHCznadOrB1K0RdPM+Lw+rT1RXGz56e3P799xRr2dqteYpcjYb5RETErebPhwoVYOXKxJhHRBhPD7uFd0sdYWdPb9atW0ex1iqkJGtSMSUiIm71++8QGgrLljmPd/7+Ox3Ll+fpr07S5JQ3Ex+dT55GjdybpEgyNMwnIiJuNXEi3HGHs+ZezPmzPHL33fxx8SI18uZl7dObMDff7O4URZKlnikREclUFy/C8OEQHu489vCALl0g+J9D3DGmIt2qXGRQvnyM+eMPFVKSLahnSkREMlXfvrBwIQQGwuefO7Eze/aw/IW2/FEvjHOtvPhz/ib8bqrm3kRFUkk9UyIikqnGjoUGDZzeKYAf58zhxlq18Fx8lE82lGDVo+tUSEm2op4pERHJcCdOQJkyznaNGrBhAxgDJ//awm8vDCHM5WJd4cJ89Pk2KFXKrbmK/FfqmRIRkQw1eTLceCMsXZoYMwaO7dlAi09u5/v255hbtRwf7tmjQkqyJRVTIiKSoU6dguho2LYtMfbtxx9z8b6umJgYTJ48tP7lF0zJkm7LUSQtNMwnIiIZavRouPNOaNnSeTzzrbfoO3QoDYHlJWpTaN4iCpeq5M4URdJEPVMiIpKuTpxwPrEXGuo8NiaxkNr7x1LOfj+GG4EHKlak0g9rVEhJtpdiMWWMWW6MCTTGvJTMMaONMQfSNzUREcmO+vaFmTPhhRcujwdtWUfLb+/l2dahTLivBk/v3AkFCrgnSZF0lJqeqQHA0GvtNMaUBKqmW0YiIpKtffqpMwnna685j621DH3oIRY1v4eha1zcHVSE9tNXQ7587k1UJJ2kWExZa4+ncMgo4I30SUdERLIba52pDi6pXBkWLICiRZ3Hv3z8MW/NmMH/hYXRO8+dLBt3BP+CxdyTrEgGSNM9U8aYKkA+a+2OdMpHRESyEWvhkUfg9tudWc2vtH7ZFEZve4qX8sC3t99OqaVL8cyrHinJWdJ6A/qrwGv/5QRjzEBjzCZjzKbAwMA0Xl5ERNzJGKhSBfz9L49HR0dzbvFinln0OGvLxmEfrk77X38FX1/3JCqSgYy1NuWDjOkHlLXWjr0i/hsQEv+wGfC5tfbJ1F68fv36dtOmTanPVkREsgRrnULq0vahQ87EnAARERF0a9mSUxs38lVey/SHazB24ma8fPzcl7BIOjDGbLbW1r8ynppP832GcwN6P2PMImNMHWPMUABrbWNrbVtrbVvg1H8ppEREJHtatswZ1gsOdh4bk1hIAeyZ/zn7N27kmLXE3nUf4yftUCElOVqKk3Zaax+9SnjbVY6rnB4JiYhI1hUXByNHwtatzqf2rpz+YPHMUXT/ayyv3gadbupBjTlzwENTGkrOphnQRUQk1Tw9nU/qzZ0LQ5NMmhMYGMiq8eM5s/5dotrCP3fXocbrXyeOBYrkYCqmREQkWf/8Az/8AAMGOI8rVry8RyoiIoLmdeqw7+RJvgECWvSi+euzVUhJrqFiSkRErikiAho3hsOHoXBh6Nr138cs/WIo3UNOsgho+vTTlHxjkgopyVVUTImIyDXlyQNPPw3z5kHTpv/eP+/9QfQ6P4VafSGg+AiKjH4903MUcTfdFSgiIpeJi4PjSda+ePJJCAiAkiUTY1u2bOHOatWo/eIUqp2FB8u2VyEluZZ6pkREJMGFC9CrF+zdCxs3OkvCGAPe3onHWGsZ3LUrvx05wufA5spv4v/0NZdwFcnxVEyJiEgCb28IDHSKqoMHE9fXS2r8uHa0L3mEhkdg3Acf4DN4cOYnKpKFqJgSEZGEGc3z5HHW2IuJgUqVLj/m4N9/EzTrTV5kOR5tYU//sfg8pkJKRMWUiEgu5nLBmDFw8SK89ZYTK1v238fNnDGDh/v35xOXi/duNxTpO4iqj43M3GRFsigVUyIiudiuXTBunFNUDRgA1av/+xjrcnFyxmfEulwcNYbRT8+Bnj0zP1mRLErFlIhILnbLLc6yMGXKXL2QcsXF8tTI21hZbSc//OFB+y+/gS5dMj9RkSxMxZSISC7z7bdQvjw0aOA8fvjhfx9jreXtt97ivp0bWZV/JweKgN+nr6mQErkKFVMiIrnIokXQrRuUKwc7d0LBglc/bvzrr/PiSy8xH/ipiA/7PnmNVt2HZWaqItmGiikRkVykfXto1sxZFqZAgasfExsVQYV9P1AbeNnXl9LfLKN0q1aZmqdIdqJiSkQkh9u2DWrUAB8f52vVKvD0/PdxsbGxeMbF0Xt4FebfdIKPm/jSYcIKuOOOTM9ZJDvRcjIiIjnYzJnQsCE891xi7GqFVEhICK1bteLj+vVpse4EBSOh7ssfqZASSQX1TImI5GDVqjmTcXp4ONMfeFzjT+iff/iBX9eu5RCwu3Bherw7j+JN7srUXEWyKxVTIiI5zIULifdDNWwIe/bAjTde+/iwoDP8/OtQ3soH3XyKkG/VKvLVrp05yYrkABrmExHJQb76CipUgN9/T4xdq5Das2cPJ/fv57lhtzKl1El+7OVDhTVrQIWUyH+inikRkRxk0yYIDnbmkrr99msft337dlrfeSc3RETwrUcEhx7w5f1Bi5w71UXkP1ExJSKSzV1apBhg/Hho3NiZSyo5xf28KBEeTsXISMqVK8fyEQHJjwWKyDVpmE9EJBubMwfuvBOiopzHPj7QvXticXU1Z4/upcMn9el9ayQLK1XCf80aFVIiaaCeKRGRbCoiAkaOhEOHnKKqX7/kj//ss88IPXGCsr9/zrbGkYQ39ea5J3/Cu0KFTMlXJKdSMSUikk3lyQNz58LmzfDQQ8kfu3v3bgYNGoS1lu3ATFOa1h8uJU+FypmSq0hOpmJKRCSbsBamToXISBgyxIk1aJC4YHFy8hHCmPKFKHYkiNq1a1N7xgooXjxjExbJJVRMiYhkE5s2wcCB4OUFHTqkfJtTdHQ0586dI+rsAVp9eSd+HWMJ2HILLF4JRYtmTtIiuYCKKRGRbKJBA+ceqerVUy6kLl68SLdu3Ti0fz/fE0H+trH4++bFd+FiFVIi6UzFlIhIFhUbCxMmQI8eUKWKExs7NnXnxsXF8c/hwwQdOUKky8WKvQ3xm/stBYqXzbiERXIpTY0gIpJFjRsHL70EDz7o3C/1Xxz7cyU9Sh1nncvFrS1bUuL7X1RIiWQQ9UyJiGRRTz0FP/0EY8YkP2/UJTt27GDlypX0b3Ibd35/P4EtLTeXrE2VaT+Av3/GJyySS6mYEhHJIoKC4NNPYdgw8PCAQoVg7drUFVLBwcG0atWK8+fPU8Hfn7HVLYublaD91NUqpEQymIb5RESyAGuhdWsYMQI+/jgxnppCCqBQoUKMe2QA3by8aBcezsBy9/H9+KP45SuUIfmKSCIVUyIiWYAxMGqUszhx27apPy8oKAiA1d+9x5TQt3nPLxa/Hj1g3jyMr28GZSsiSamYEhFxk02b4LvvEh936QLr1kHlVExK7nK5GDp0KLfddhsnv/6akUueZWtJFx8/XAtmzwZv74xLXEQuo3umRETcYMcOpxcqb17YuRPKl3fiHqn8EzcqKoo1a9Zw/NgxNj34IIt8XHw8sC4j3/rdmdVTRDKN3nEiIm5wyy3QqRNUqHB9q7rkyZOH9wZ2I3zzZlrFxsKjj/Py2x+mvhoTkXSjd52ISCaIiYHx4+H0aeexMTB/PrzzjrNgcWocPnyYt99+G4Bvpz3PHYeHsqVBrDOHwkcfqZAScRP1TImIZIJhw+Ddd2HjRvj2Wyfm6Zn68yMjI2nRogVHjx6l+IEDxP3xKbGd4EyrhjD2ndR/7E9E0p3+jBERyQTPPOMM7Q0efH3n+/n5MXbsWFrXqEGnTz6h/xbLH3EDGP/abyqkRNxMxZSISAb47TdnUeJLypeH7duhVav/9jxnz55N2PY8v5ppx3dTCOC112gwZipGQ3sibqd3oYhIOgsOhjZt4PXX4ccfE+P/pQMpLi6OZ599ltq1a3Ps2DHmTnqYPsGfc3dfCJ8w1lm0T0SyBN0zJSKSzgoVgjfegJMnoWXL63uOuLg4tmzZwtmzZ9nyyivc/fUX1O0LD93YBf9hI1N+AhHJNCn2TBljlhtjAo0x//ozyBgzzBizwRizzhjzgTEauBeR3OfkSejWDZYuTYwNHuz0TPn5Xd9z+vj4sGDBAlb260fnL76gSAT8Xvt9nhq2IH2SFpF0k5phvgHA0GvsW2itbWStbQqUBO5Mt8xERLKJefOcT+gNG+assXe9tm7dyosvvoi1Futy8cH7XVm75zNnfHDaNHz+b0j6JS0i6SbFYT5r7fFrdThZa/9K8jAKiE2nvEREsrSwMGf2cnB6oY4dc6Z7ut7++YsXL9KmTRvOnj1LrZo1qb5rBaN9VmPuhPv6j+fm/v3TL3kRSVfpcs+UMaYFUAr4NRXHDgQGApS/tH6CiEg2ER4Ozz/v3Fi+c6dTUHl5QfxcmtctX758fPTRRyxbtoz7N2zA94PpfFbPkO+xJ7n54WHpk7yIZIg0f5rPGFMbGA/0sjblDm5r7RRrbX1rbf3i17OGgoiIG/n4wO+/Oz1Rv6b452PyIiMj2b17d8Ljbvd3ZWJeg+8HH4C3NwNeWkDPR95N20VEJMOlqZgyxlQGpuEUUmdTOl5EJDvauBEuXHC2vbzgiy9g61Zo1+76nzMoKIhWrVrRokULDh8+jCsulkHDa9HI8wtOFPWBhQvhvvvSJX8RyVip+TTfZzg3oPczxiwyxtQxxly6If1doBDwpTEmwBjTIcMyFRFxgzffhIYNYdy4xNitt0KtWml73gIFClCwYEH8/f0JDQ4mbEBftl7Yx6n88Ncn46CDfp2KZBepuQH90auEt8Xv65jeCYmIZCWtWoGvr/OVHuLi4vD09MTT05M5c+YQEx5Oieefh6+/5qei/uz9fAJNOl/nmjMi4haatFNEJJ61sGAB7NsHL77oxBo0cO6PSustnrGxsQwdOpQzZ84wa9YsjDHk9fPm++fup9vXGyB/fop8t4wmTZumvSEikqlMKu4ZzzD169e3mzZtctv1RUSSOnAAqlVzpjfYtcvZTr/nPkCdOnWIjo5m48aN1K5ala4jKrGo8GneWe3H0+NXO+OJIpJlGWM2W2vrXxlXz5SI5GrnzkHRos525cowfDiULQs33ZS+16lcuTJff/01hQoV4taqVeG+++hy+jRr2xqavzRVhZRINqaeKRHJtUaMgHfegfXr4bbb0ve5rbVMnTqVcuXK0bZt28QdYWFw772wahUUL07Ij4soeFuT9L24iGSIa/VMpXmeKRGR7ComBqKjYeXK9H/uxYsXM3DgQHr37s25c+cACD13kv89V4mjW1bBDTdAQIAKKZEcQMN8IpIrREbClClOD9QddzixESPgwQedqQ7SW8eOHenRowcdO3akaNGiEBzMC8NuY3b5QE709GHVc6uhatX0v7CIZDoVUyKSK0yeDM8+C40awW+/OTeZFy2aeL9Uevj+++9p2bIlBQoUwMPDg7lz5zo7zp+He+7h9T9P888DeXjrqaUqpERyEA3ziUiOFBMDhw4lPn70UWjd2umNyghvv/02nTt35tFHHyXpvahhJw/DnXfCpk0UKn0jC17Zw423tsyYJETELVRMiUiOs3+/M61Bhw4QF+fE8uWDFSugc2enVyq9derUiaJFi9KsWbOE2D8Hd9DorZsZW3C70xP1669QoUL6X1xE3ErFlIjkCEk/mFypklNExcU5E25mlKSfRq5SpQqHDh1i8ODBGGPgxAk2PNqOPfmjmFPPl7AVy6BMmYxLRkTcRsWUiGRrMTHw1lvOTOWRkU7M29v5hN7u3VCxYvpf01pL//79adCgAUuXLk2I58+f39k4ehRatKDzypN880cFAp7eSt5yN6Z/IiKSJaiYEpFszcsLZs+GzZudpWAuuekm8PTMmGsaY6hevTr+/v4EBwdftu/gjtUc7tAE/v4bbruNLrM2U7x89YxJRESyBE3aKSLZyr598N57MHYsFCnixH75BaKioF27jLkfCiAmJoYTJ05QMb6ry+VycfTo0YTHAAe3/kKLr+7BKyaONdvqUHbRKihUKGMSEpFMp+VkRCRHeOYZWLYMSpeGl15yYq1bZ+w1T5w4QadOnQgODmbbtm3kz58fDw+Pywop9uyh2H19KN0mDp+8BSj4zRIVUiK5hIb5RCTLCg+Hzz6DgwcTY88950xz0KNH5uVRvHhxXC4XLpeLI0eO/PuAnTuhRQsKHD3N8sN38OMr+8lfTDebi+QWKqZEJMsaNgwGDoT330+MtW7tzGSe0XNe7t27l8j4O9p9fHxYsGABO3bsoFatWpcdtzVgDm8+dzsEBkKbNhT6bjl5C5fM2OREJEtRMSUiWUJcHHz/PWzfnhh7+GGoXx+STN2UKaZPn06dOnV4+eWXE2KVKlVK/LRevAvrVtJmWR9eaBrO3Afrwnffgb9/5iYrIm6nYkpEsoS33nIm1JwwITF2222wcSPcf3/m5lKjRg1iYmIIDg7mmh/SWb+eAu3u471llvuDS9Pl01/Bzy9zExWRLEHFlIhkuuho+OYbWLUqMdarlzN0d/vtmZ9PcHAwixYtSnjcsGFD9u3bx5QpU5wJOK8QG7AS2rSB0FB61+jJ/AmH8MmTLxMzFpGsRJ/mE5FMN306DBrkLFnXqpUTq1AB9u7NuKkNriUsLIxatWrxzz//sHnzZm699VYAKleufNXjV3zzJkN+Hc6PXpYKDz4I06ZhvPSrVCQ3U8+UiGSokyfhjTdgxozEWI8e0LAhdOly+TIwmV1IAeTNm5fOnTvTqFEjfH19kz3WLl3KGz8MZ29Ry2cP3wpffOHMGioiuZom7RSRdGdtYmH03Xdw331Qqxbs2OGegimpM2fOMHLkSB577DHq1asHQHh4OH5+fnh4JPP35XffQY8ehJhopgy+necmrMHDU4WUSG5yrUk71TMlIulmwwa45x4YPjwx1q4d9Ovn9E5lBZMmTWLq1Kk8//zzCTF/f/9kC6mdM9/GdrsfoqMp+NhTDJ24XoWUiCRQMSUi1+2ffy6fUNNa+OknmDcvcfjOx8cZDevY0T29UrGxsZw4cSLh8YgRI+jduzeffPJJqs7/6pMnqHPgecY0jXMmvnrnHfd3r4lIlqJiSkSuy8yZzpIur7ySGGvUCL78EjZtyhr1xr59+6hduzadOnXC5XIBULBgQWbPnk21atVSfoLp0/H86GMAXC2awfjxWaNhIpKlqJgSkRTt2OEs4zJ/fmLs9tudXqekjIG+faFo0czN71rKlStHSEgIwcHBl/VOpcqUKdC/Pz3/hO1egxk9+lcVUiJyVSqmRORfDh+G06cTH2/aBJMmOVMaXFKlCpw75/RQZQUul4v58+dz7733EhMTAzj3Qv3000/s2bOHcuXKpfq5pr7Vm7+HD3IeTJxIrVEfZETKIpJDqJgSkcu89BJUqgRTpybGOnSAoUNh5MjLj82bN3NzS461llGjRrFkyRK+/vrrhHjNmjXxubILLRlzxv+PR8Pm0PohCHtvIiS5UV1E5GpUTInkYpMnO/M9rVyZGLvtNihQAKKiEmMlS8Kbb0KTJpmf47WcPn2a1157jeDgYAA8PT2ZMGECkydPpnv37tf3pK+/TsdXZtPkKLxYvg95n1QhJSIp02d7RXKJZcvgl1/gxRehSBEndvCgs/bdzz87s5ED3HsvnD0L3t7uyzU1HnroIZYvX07evHl59tlnAejcufN1PZd1uWDMaMzoMeQ3hl+bfobnwwPSM10RycFUTInkMNbCn3/Ctm3w4IOJ8QkTYPVqaN4cOnVyYg8/DK1bwx13JB6XFYuokJAQ5syZQ5s2bbjxxhsBGDx4MH5+fjRu3DhNz21dLoa+0hjf9X8w1sNgZszEs0+f9EhbRHIJzYAuko1ZC0eOOEu2XBqCi4uDwoUhNNSJlyrlxL/4wumJ6tMHbr7ZfTlfj0ceeYTPP/+c4cOH80Z6zv5pLduH9qVe3lkYCzuqTqL6/55Jv+cXkRzlWjOgq2dKJJuIi4MDByA2FmrWdGL79zuFUZkycPy4E/P0dNa8i4qC8PDE8/v3z/ycr8f27duZMWMG999/P03iK8R+/fpx6NChNPdCXcblgiFDuPXjWcy61ZN8z76gQkpErouKKZEs6Nw52L4dKlSAm25yYvPmQe/e0LkzLFrkxKpUgRtvhKpVISIC8uRx4l9+6Za0r0tcXBwulwvv+PHFb775hkmTJhEaGppQTN1xxx388ssv6XbN6JhI/hnSn/Kffg2+vvQa963zkUURkeugT/OJuNmaNfD++xAYmBh74w3nXqY5cxJjdepAuXJQokRizMMD/v7bubn8UiGVnUyaNIlSpUoxb968hFjv3r156qmnGDhwYIZcMzIqjPtHVqGp/9ccLukLixerkBKRNFExJZJJoqKceZr69bs8PmoUPPUUbNmSGGvQwJlhvGTJxFj16nD0qDMxd3a0ceNGxowZw8Eki/l5enoSGBjI+vXrE2LVq1fn3XffpX79f92WkHYxMbj69yPk7HEivOH8Z+/D3Xen/3VEJFfRDegiaRQc7NzLVKwYVKzoxDZuhIcegmrVYOFCJ2Yt5M8PYWHOMN6l6QneeQf27oVBg5w5nnKCixcv8scff3DHHXckTJj5wAMP8PXXX/Phhx/yxBNPABAYGMjp06epWbMmJqOXaomOhgcegAULuFA0Hye/+pSb2/TO2GuKSI5yrRvQ1TMlcg0ulzPfUlIffeT0LCXpXOGdd5yepC++SIz5+8OePc4UBZcYAxMnwuzZ4OubGH/mGfj00+xbSEVFRbFr167LYo0aNaJ169Zs3749IdajRw8GDx5MvXr1EmLFixenVq1aGV5IbTuygZFP1sQuWAAFC1LghxUqpEQk3egGdMlVXC44f94pZvLnd2L79sGsWU6v0oD4eRovXoRChZyFfMPCEte3/e47Z4LLHj2cG7/BuQn81lud6QguqVIFtm5NPOaSxx/PyNZlLJfLxZEjRwgJCaFOnToAREZGUqhQIeLi4rh48SK+8VVi06ZN8ff3JzzJxwm7dOlCly5dMj3viyGB3P1ZM86WiqFG47z0+XBl9q1cRSRL0jCfZHvh4c6wmrXQsmVifNgwZ/jt00+heHEn9thjzuOPP04sbJYvh7Zt4a67nEIJEofk8uRxeqEuFV4LFzq9VffcA+XLZ1oTM91ff/3FmjVrqFy5Ms2bNwfgt99+o0mTJtSpU4etW7cmHFurVi3i4uJYtmwZFePHOa21GT9slxphYXDvvcw/vYoltX2Z8sI6fOvUS/k8EZGr0DCfZAlxcRAS4txnlDS2eLHz0f+kPvjAmRsp6QjS1KnOvUkvvJAYO3HCKaIeeeTy83/4wSl+/vknMVa8OBQsCDExibHq1eHVVyHph8eMcXqwAgMTCylw5m969NHsWUhZazl48OBlN3sDvP766zRv3px169YlxJYvX86AAQOYNWtWQqx69eqUKlWKsmXLXnb+tm3b2LNnT0IhBbi9kNr2zza+3TwL2rWDVavofv4Gvhy1RYWUiGSIFIspY8xyY0ygMealq+zzM8bMNsasif/XL2PSlIwWFORM+ph0cdujR50FcA8cSIwFBsKHHzrDYkkNHeosXZK0SBozxilU5s5NjC1e7AyfXfmJtk6doFcvZxjukuXLYfp056P/l1jr3LyddBqBYsWc5VBuv/3y5xw3zinQkv7fP2aMk+OTTybGypeHV16BK9fGjb9vOkuJi4sjJCSE2NjYhNju3buZPXv2Zfcn7dq1iw4dOjB48ODLzq9VqxZNmzYlNDQ0IbZ3717WrFnDvn37EmL169fnf//7H3ckWWemUKFCnDx5ksWLF1/2nF5eWetugR1HN1L307oM/OYhQjescWY0Xb0aatRwd2oiklNZa5P9AsoC/YCXrrLvMWBU/PbLwGMpPV/Sr3r16ll3iI62Njzc2piYxFhkpLXnzll74UJiLDbW2iNHnK+kDh2ydudOay9eTIydOGHtunXOvksuXLB26VJrV6++/PzvvrN2xgxrQ0MTYwEB1r7zjrVbtiTG/vrL2pEjrf3888vPf+wxa/v1uzz/sWOtbdPG2l9/TYwtXGhtjRrWDh+eGAsMtDZfPmtLl778ORs2tBas/f33xNhrrzmxF19MjG3b5sRuueXy88uXd+JJ2z94sBN7993E2IoV1ubPb223bpef36WLtT17Oq/DJUuXWjt1qrWHDyfGQkOtPX3a2qgo6xaRkZE2KCjIRkREJMTCwsLsvn377OGkiVprV61aZX/88UfrcrkSYj/99JP96KOP7N9//50Q++233+zgwYPtjBkzEmKBgYG2SZMm9u67777sOevUqWMBu3nz5oTYyy+/bAH78ssvJ8S2bNliAXvLFS9U8+bNbaNGjezJkycvO/aXX36xgYGB//Xb4XYul8uuO7rOzt4x27pCQ619+23ruqGkbfM/7DP3YM/fVsPaJN9rEZG0ADbZq9QzqbpnyhjTDyhrrR17RXwO8Ka1dqsxpi4wzFr7QGoLuQy/Z6pvXzwursF6xvFPXGNK+jhDD2VPn+JEsUM8Eng7n93gdM7972Qcs0tuoMLZyhwu6cyKuD/SUM17HR4xPsT5JQ6RFjh3kNBC/zD+fFNeKO58/1qdiCTghi3UOV2TraULAjA3yIteBX7FN6wgkQVqJpzvG7qTaP9Qfrh4B+0LOl0xNU8FsbvEHtqersey0s5NvK+eNowuto5CwaUIKlop4XwTvQE84zgV14Qb4ntPypw+xcliBxlwpjFTSzltevBUHLNK/E75wMocucGZsOhAJFTxXoeJ8cbl1zDhOYsG7SO4wBneDGrKc8Wc8zudOcfy4jtodLYavxYvDcCyi1F0z7eG/JF5OeWXuLRHuZjVXPSN4IeLLWji78we2T1sGwEFj9Mv5CYm5q0OwPyoozyZbyuVI/Kxxqt1wvllPb8nxrj4K7o9BTycRrWNXM2WfEGMCq3BkDxVAZgYsYcJ+fbSKKwoP/g59/Kcio2gps8yfF2enKJzwnPWjvyRI3nCmBbegPvzOONyj4duYkb+w3S8WJq5+ZzZtVdHnKGN32qKRvlw0i/x/EIRCwjxiWFDzF009CsKwF1Bq/ilwBkGht7Ip4UaADAl9G8G+W/ipvC8HMjfMeF8z+i5uDwhxHRJaNOtwT+yI38IY8NqMTL+Z+LF4O28kX8vDUOLsKGQM+fRidhwyprFeMcZon16JDxnxdDFnMgbwZcRjeidt4JzftR2Zhc4SqeLpfnA2xnG2m8v8EjRjZSP9WfWhcTX6cmSWzjjGcl7p2+jZJzTkfxlwUMsy3uKviEVaR/mvM5/+gYztuhuakYXZNTZxJ/dvqV+J9q4+PJUI3ytJwDvFd7Pb3nO8mRQVZpEFAPg1zxn+LjwAZpFFOeJoCoAhJlYBpT6A3/rxbRTiT97rxb7k70+F3jlbC2qRxcAYFG+48wueITOoWX434WKABzyvsiAUhspF+PPl6caJZxfpOpCgjyjOf15EUocOw+ArXMr5qVRzrish+5mEJH0kVFr8xUFguK3g4EiqUhkIDAQoHxG33jyzTfYZyPAGyLHBUJMJABB3YpArfOcmO8Lq50xrNO1b4TWxzi/PRzmngMg2s8fhofjigTGJ441RfTPAxUiODdtLax0FkQ737QU1DpFUEgUzD0DQHixojD4HDGBJ+GjxM/Ixz7pAUVchL+3DIKCnWPbFoRaIVw8nnj9qEqFoGUw0QdPw4w/Ets1EvAGO24+xDjFWFw3b6gVA/OXwK8RAHjV9oE7o7HbT8HcOCfmBwwHGwmMP5SYU39wVQDfafMhftWO2KYQXQMi152B+KG62GIQNhhiAs/BR0cTzv/nSYgtApHvfZ/wE3GgLZytAgd+3AFLdgBwuBL88xBEHYyEGYnjfyfi2xQ9biHE38+0qxsEVoED87fCLueG579rw7musHv7qYTxw2g/CBoORMbA+MTnPNIfLlSAU9N+g6O/ObGmEN4QDq07lnB+aDGIHgznAiPho8Tzw54EikDoeysS2hTcFqgF5348CMsPxr9OwEMQdjDssjZdep1ikrTJu5tzvpn/J+xyfiYK1gYaQ/7t5xNy8ot/nXwj7WVtKtcfjlSActN+h6O/A1CoKRytA3nWHYCfnZ/nuGKwZjDcHAjMTXydfngSDhaEcdOPUTK+TVvbwtzb4fbfjtHeeUpOV4K5D8GdB48xam7iz+43IyHCG6Z9eCyhTeu7wbxa0OWnYxB/f9uR2jC3K3gfPsYTC53ZSGP8YO5wKBgJ0+Ym/uz90h/WFocnvj0G8anuawrf3A2Vdh6HnzcAEFkMViW06XDC+R26QJQXRIWch4YNYdQoTIcOiR/BFBHJYGntmfoaGG+t3WaMqQO8kKV6pubP55kN04m1cUys2xs/L6d3YPK+n9kTeoIHyjWhcUmnx2PtP3uZd/x3auUvx8BqTo/JxZhIXtz+Nb4eXky87X8JT/vmn99zPPI8j990N9ULlwFgybEt/HR6B02LVKXnjU6Px7GLZ3lr3w8U8crLK7d2Szj/le3zCY4N54Wb76V0Xqf+/OrvtWwI/pu2JW+lXdk6AOw8d4SphwOomKc4z9Ron3D+c1tmEmtdTLj1gYQ2fbpvBXsunqBXuSbcXqJKQpu+ObGBWgXK8UiVOxPaNGrnPHw8vJhQJ3Genbd3L+F45HkGVWrNzfFtWnZ8GysCd9K4SFW6VXB6Ao6HneOd/Usp4p2PkbUSP+Y+9s8FBMeG83zVDtzg78wRMP/Ib2wMPsg9JWrTutQtAOwOPs6MY79S3q8Y/1elTcL5L++aT6yN45Xq9+Pr6azRNvPwGv6KOMV9JRtwWxGnZ27Tub/54exWbvYvQ89yTo9LRFw07xz8AR8PL56/6d6E55x5/Ff+iQmhe4lGVMzr9DZuCP6L30MPUCdvBVoUce6hORcdyjfnN1DYKy89iiX24iwM2UgE0XTMV5cCnv4AbIk8xP7oU9T1q0g1H6cX55/YYALCd1PSqyCt/BN7ceaH/k6cddEtfyO8jNOLsy58H8diz9EkT1XKezu9OIdjAvk94i8qeBejcXwPXLSNZUHoH3gbT+7Pn9gLsyJsJ2fjQmntX4viXk4vzp6oE2yPOsLNPqWp41cRgJC4cJaFbaOARx7a56ubcP6Si1u46IqkQ7665PfIk2XbtDfqBDujj1HNuxS1/ZweuHBXFL9H/EUBzzzU97uJfylXDpo0URElIhnmWj1TaS2mHgcKW2tfN8a8CJy31n6S2qQ0NYKIiIhkF9c9NYIx5jNgKNDPGLPIGFPHGDM0fvd04BZjzBrglvjHIiIiIrlGivdMWWsfvUp4W/y+CCDVw3oiIiIiOY0+5iIiIiKSBiqmRERERNJAxZSIiIhIGqiYEhEREUkDFVMiIiIiaaBiSkRERCQNVEyJiIiIpIGKKREREZE0SNVyMhl2cWMCgSMZfJliwNkMvkZWlZvbDrm7/bm57ZC726+25165uf2Z1fYK1triVwbdWkxlBmPMpquto5Mb5Oa2Q+5uf25uO+Tu9qvtubPtkLvb7+62a5hPREREJA1UTImIiIikQW4opqa4OwE3ys1th9zd/tzcdsjd7Vfbc6/c3H63tj3H3zMlIiIikpFyQ8+UiIiISIZRMSUiIiKSBiqmRERERNIg2xdTxph+xpj1xph1xpjbrtjnZ4yZbYxZE/+vX3y8ojFmZfw5L7on87RLoe3DjDEb4vd9YIwx8fEAY8xv8f9+4J7M0y6FtvczxhyKb2OAMaZMfDxHvO6QYvufTdL2Q8aYt+Pj040xW+Pj892TedoZY5YbYwKNMS9dZV9Of88n1/ac/p5Pru254T2fXPtz+nu+bvxr+Gv863njFfuLGGOWxL/vk/7s3xZ/3npjTL8MTdJam22/gMLAFsAHqASsvWL/Y8Co+O2Xgcfit78GmsVvrwBudndbMqDtVZJszwNax28HAGXdnX8Gt70f8NJVzsv2r3tq2n/FsUuB2+O3pwN3uDv/dGh/2WRe4xz7nk9F23Psez4Vbc/R7/mU2n/FcTnxPX8DkD9+uz0w84r944EH47enAW3jt9fF/470if+dWTijcszuPVMNgTXW2mhr7SEgvzHGN8n+FsCS+O3F8Y8B6lhr18Rv/5Aknp0k23Zr7V9Jjo0CYi/tAr6Or+7vzLx001VKrztAX2PMWmPMa8aYSz/nOeF1h9S1H2NMCaCStfb3JOFJ8X+99cysZNObtfZ4Mrtz8ns+2bbn8Pd8Sq875Oz3fGran5Pf8/9Ya0PjHyb92b7kX+/7+N+Jea21h6y10cAanN+dGSK7F1NFgaAkj4OBItfYn3Rf0nZfeU52kVLbATDGtABKAb/Gh7pba+8AHgImG2PyZ3CeGSGltn8HVMd5g1UA+sTHc8LrDql87YFeOD0UlzxvrW0IdAaGX9lVnkPk5Pd8quTQ93xKcvp7PrVy9HveGJMXGAtMvGJXEZzXFxJf56JJYknjGSK7F1PngUJJHheMj11tf9J9rmTOyS5SajvGmNo43Z+9bHyfp7X2bPy/x4DtQOXMSDadJdt2a22QtTbOWhuH081/ab2mnPC6Qype+3h9gFmXHiR57c8DPwO3ZlyKbpOT3/MpysHv+WTlgvd8auXY97wxxhuYC0yw1u6+YncQzusLia9zan9PpovsXkxtAO4wxngbY8oDF621UUn2r8YZXyX+39Xx29uNMU3it9uR+BdcdpJs240xlXHGjntdekMZR4H47fzALcCRzE89zVJqe6Ekx94J7IvfzgmvO6T8c48xpipgkw79XPq+GGN8gKbA/sxLOdPk5Pd8snL4ez5ZueA9n6Kc/J6PH7adBSyy1i66yiH/et9bayOBMGNM+fhC7A7gjwzLMf6Pl2zLGPMw8AjOfQFP4Yyl3m2tnWiMyYPzy6UscBzob62NjO/q/BznprRl1tqx7sk+bVJo+xLgZpx2g9Mt+hPwOxABeAOTrLVzMz3xdJBC28cBd8XH9gGDrLUxOeV1h+TbH79/DBBorf0gyTnLgXw4r/0sa+37mZ54OjDGfAY0AXyBP4FXyT3v+eTantPf88m1PTe856/Z/vj9Ofk93w3nZvpN8aGdOPfAFbfWzjTGFAVmAAWAHcAQa63LGFMfeA8wwFRr7bQMyzG7F1MiIiIi7pTdh/lERERE3ErFlIiIiEgaqJgSERERSQMVUyIiIiJpoGJKREREJA1UTImIiIikgYopERERkTRQMSUiIiKSBv8PdV3kPvTE8dcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pts = pybamm.linspace(0, 2, 100)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "ax.plot(pts.evaluate(), pybamm.maximum(pts,1).evaluate(), lw=2, label=\"exact\")\n",
    "ax.plot(pts.evaluate(), pybamm.softplus(pts,1,5).evaluate(), \":\", lw=2, label=\"softplus (k=5)\")\n",
    "ax.plot(pts.evaluate(), pybamm.softplus(pts,1,10).evaluate(), \":\", lw=2, label=\"softplus (k=10)\")\n",
    "ax.plot(pts.evaluate(), pybamm.softplus(pts,1,100).evaluate(), \":\", lw=2, label=\"softplus (k=100)\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solving a model with the exact maximum, and smooth approximations, demonstrates a clear speed-up even for a very simple model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact: 366.813 us\n",
      "Smooth, k=5: 348.585 us\n",
      "Smooth, k=10: 279.639 us\n",
      "Smooth, k=100: 325.853 us\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1b459eb21aec4a1d87d63e17e4e1db20",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='t', max=2.0, step=0.02), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_exact = pybamm.BaseModel()\n",
    "model_exact.rhs = {x: pybamm.maximum(x, 1)}\n",
    "model_exact.initial_conditions = {x: 0.5}\n",
    "model_exact.variables = {\"x\": x, \"max(x,1)\": pybamm.maximum(x, 1)}\n",
    "\n",
    "model_smooth = pybamm.BaseModel()\n",
    "k = pybamm.InputParameter(\"k\")\n",
    "model_smooth.rhs = {x: pybamm.softplus(x, 1, k)}\n",
    "model_smooth.initial_conditions = {x: 0.5}\n",
    "model_smooth.variables = {\"x\": x, \"max(x,1)\": pybamm.softplus(x, 1, k)}\n",
    "\n",
    "solver = pybamm.CasadiSolver(mode=\"fast\")\n",
    "\n",
    "# Exact solution\n",
    "timer = pybamm.Timer()\n",
    "time = 0\n",
    "for _ in range(100):\n",
    "    exact_sol = solver.solve(model_exact, [0, 2])\n",
    "    # Report integration time, which is the time spent actually doing the integration\n",
    "    time += exact_sol.integration_time\n",
    "print(\"Exact:\", time/100)\n",
    "sols = [exact_sol]\n",
    "\n",
    "ks = [5, 10, 100]\n",
    "for k in ks:\n",
    "    time = 0\n",
    "    for _ in range(100):\n",
    "        sol = solver.solve(model_smooth, [0, 2], inputs={\"k\": k})\n",
    "        time += sol.integration_time\n",
    "    print(f\"Smooth, k={k}:\", time/100)\n",
    "    sols.append(sol)\n",
    "\n",
    "pybamm.dynamic_plot(sols, [\"x\", \"max(x,1)\"], labels=[\"exact\"] + [f\"smooth (k={k})\" for k in ks]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Other smooth approximations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the other smooth approximations for the other non-smooth functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Smooth minimum (softminus):\t log(exp(-10.0 * x) + exp(-10.0 * y)) / -10.0\n",
      "Smooth heaviside (sigmoid):\t (1.0 + tanh(10.0 * (y - x))) / 2.0\n",
      "Smooth absolute value: \t\t x * (exp(10.0 * x) - exp(-10.0 * x)) / (exp(10.0 * x) + exp(-10.0 * x))\n"
     ]
    }
   ],
   "source": [
    "pybamm.settings.set_smoothing_parameters(10)\n",
    "print(\"Smooth minimum (softminus):\\t {!s}\".format(pybamm.minimum(x,y)))\n",
    "print(\"Smooth heaviside (sigmoid):\\t {!s}\".format(x < y))\n",
    "print(\"Smooth absolute value: \\t\\t {!s}\".format(abs(x)))\n",
    "pybamm.settings.set_smoothing_parameters(\"exact\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "The relevant papers for this notebook are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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",
      "[6] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, and others. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods, 17(3):261–272, 2020. doi:10.1038/s41592-019-0686-2.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pybamm.print_citations()"
   ]
  }
 ],
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