tutorials/robots_and_marbles/robot-marbles-part-4/robot-marbles-part-4.ipynb

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    "# cadCAD Tutorials: The Robot and the Marbles, part 4\n",
    "In parts [1](../robot-marbles-part-1/robot-marbles-part-1.ipynb) and [2](../robot-marbles-part-2/robot-marbles-part-2.ipynb) we introduced the 'language' in which a system must be described in order for it to be interpretable by cadCAD and some of the basic concepts of the library:\n",
    "* State Variables\n",
    "* Timestep\n",
    "* State Update Functions\n",
    "* Partial State Update Blocks\n",
    "* Simulation Configuration Parameters\n",
    "* Policies\n",
    "\n",
    "In [part 3](../robot-marbles-part-3/robot-marbles-part-3.ipynb) we covered how to describe the presence of asynchronous subsystems within the system being modeled in cadCAD.\n",
    "\n",
    "So far, all the examples referred to deterministic systems: no matter how many times you ran one of those simulations, the results would be the same. However, systems are more commonly non-deterministic, and modelling them as deterministic might be an oversimplification sometimes. \n",
    "\n",
    "In this notebook, we'll cover cadCAD's support for modelling non-deterministic systems and Monte Carlo simulations. But first let's copy the base configuration with which we ended Part 3. Here's the description of that system:\n",
    "\n",
    "__The robot and the marbles__  \n",
    "* Picture a box (`box_A`) with ten marbles in it; an empty box (`box_B`) next to the first one; and __two__ robot arms capable of taking a marble from any one of the boxes and dropping it into the other one. \n",
    "* The robots are programmed to take one marble at a time from the box containing the largest number of marbles and drop it in the other box. They repeat that process until the boxes contain an equal number of marbles.\n",
    "* The robots act __asynchronously__; robot 1 acts once every two timesteps, and robot 2 acts once every three timesteps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# List of all the state variables in the system and their initial values\n",
    "genesis_states = {\n",
    "    'box_A': 10, # as per the description of the example, box_A starts out with 10 marbles in it\n",
    "    'box_B': 0 # as per the description of the example, box_B starts out empty\n",
    "}\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# Settings of general simulation parameters, unrelated to the system itself\n",
    "# `T` is a range with the number of discrete units of time the simulation will run for;\n",
    "# `N` is the number of times the simulation will be run (Monte Carlo runs)\n",
    "# In this example, we'll run the simulation once (N=1) and its duration will be of 10 timesteps\n",
    "# We'll cover the `M` key in a future article. For now, let's omit it\n",
    "mc = 1\n",
    "\n",
    "sim_config_dict = {\n",
    "    'T': range(10),\n",
    "    'N': mc,\n",
    "    #'M': {}\n",
    "}\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "\n",
    "# We specify the robot arm's logic in a Policy Function\n",
    "def robot_arm(params, step, sH, s):\n",
    "    add_to_A = 0\n",
    "    if (s['box_A'] > s['box_B']):\n",
    "        add_to_A = -1\n",
    "    elif (s['box_A'] < s['box_B']):\n",
    "        add_to_A = 1\n",
    "    return({'add_to_A': add_to_A, 'add_to_B': -add_to_A})\n",
    "    \n",
    "robots_periods = [2,3] # Robot 1 acts once every 2 timesteps; Robot 2 acts once every 3 timesteps\n",
    "\n",
    "def robot_arm_1(params, step, sH, s):\n",
    "    _robotId = 1\n",
    "    if s['timestep']%robots_periods[_robotId-1]==0: # on timesteps that are multiple of 2, Robot 1 acts\n",
    "        return robot_arm(params, step, sH, s)\n",
    "    else:\n",
    "        return({'add_to_A': 0, 'add_to_B': 0}) # for all other timesteps, Robot 1 doesn't interfere with the system\n",
    "\n",
    "def robot_arm_2(params, step, sH, s):\n",
    "    _robotId = 2\n",
    "    if s['timestep']%robots_periods[_robotId-1]==0: # on timesteps that are multiple of 3, Robot 2 acts\n",
    "        return robot_arm(params, step, sH, s)\n",
    "    else:\n",
    "        return({'add_to_A': 0, 'add_to_B': 0}) # for all other timesteps, Robot 2 doesn't interfere with the system\n",
    "\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# We make the state update functions less \"intelligent\",\n",
    "# ie. they simply add the number of marbles specified in _input \n",
    "# (which, per the policy function definition, may be negative)\n",
    "def increment_A(params, step, sH, s, _input):\n",
    "    y = 'box_A'\n",
    "    x = s['box_A'] + _input['add_to_A']\n",
    "    return (y, x)\n",
    "\n",
    "def increment_B(params, step, sH, s, _input):\n",
    "    y = 'box_B'\n",
    "    x = s['box_B'] + _input['add_to_B']\n",
    "    return (y, x)\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# In the Partial State Update Blocks, \n",
    "# the user specifies if state update functions will be run in series or in parallel\n",
    "# and the policy functions that will be evaluated in that block\n",
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { # The following policy functions will be evaluated and their returns will be passed to the state update functions\n",
    "            'robot_arm_1': robot_arm_1,\n",
    "            'robot_arm_2': robot_arm_2\n",
    "        },\n",
    "        'variables': { # The following state variables will be updated simultaneously\n",
    "            'box_A': increment_A,\n",
    "            'box_B': increment_B\n",
    "        }\n",
    "    }\n",
    "]\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "#imported some addition utilities to help with configuration set-up\n",
    "from cadCAD.configuration.utils import config_sim\n",
    "from cadCAD.configuration import Experiment\n",
    "from cadCAD import configs\n",
    "\n",
    "del configs[:] # Clear any prior configs\n",
    "\n",
    "exp = Experiment()\n",
    "c = config_sim(sim_config_dict)\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "exp.append_configs(initial_state=genesis_states, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_configs=c #preprocessed dictionaries containing simulation parameters\n",
    "                      )\n",
    "\n",
    "from cadCAD.engine import ExecutionMode, ExecutionContext, Executor\n",
    "exec_mode = ExecutionMode()\n",
    "local_mode_ctx = ExecutionContext(exec_mode.local_mode)\n",
    "executor = Executor(local_mode_ctx, configs) # Pass the configuration object inside an array\n",
    "raw_result, tensor, sessions = executor.execute() # The `execute()` method returns a tuple; its first elements contains the raw results\n",
    "\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "simulation_result = pd.DataFrame(raw_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulation_result.plot('timestep', ['box_A', 'box_B'], grid=True, \n",
    "        xticks=list(simulation_result['timestep'].drop_duplicates()), \n",
    "        colormap = 'RdYlGn',\n",
    "        yticks=list(range(1+(simulation_result['box_A']+simulation_result['box_B']).max())));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-determinism\n",
    "Non-deterministic systems exhibit different behaviors on different runs for the same input. The order of heads and tails in a series of 3 coin tosses, for example, is non deterministic. \n",
    "\n",
    "Our robots and marbles system is currently modelled as a deterministic system. Meaning that every time we run the simulation: none of the robots act on timestep 1; robot 1 acts on timestep 2; robot 2 acts on timestep 3; an so on. \n",
    "\n",
    "If however we were to define that at every timestep each robot would act with a probability P, then we would have a non-deterministic (probabilistic) system. Let's make the following changes to our system.\n",
    "* Robot 1: instead of acting once every two timesteps, there's a 50% chance it will act in any given timestep\n",
    "* Robot 2: instead of acting once every three timesteps, there's a 33.33% chance it will act in any given timestep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "#from numpy.random import rand\n",
    "from random import random as rand\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# We specify each of the robots logic in a Policy Function\n",
    "robots_probabilities = [0.5,1/3] # Robot 1 acts with a 50% probability; Robot 2, 33.33%\n",
    "\n",
    "def robot_arm_1(params, step, sH, s):\n",
    "    _robotId = 1\n",
    "    if rand()<robots_probabilities[_robotId-1]: # draw a random number between 0 and 1; if it's smaller than the robot's parameter, it acts\n",
    "        return robot_arm(params, step, sH, s)\n",
    "    else:\n",
    "        return({'add_to_A': 0, 'add_to_B': 0}) # otherwise, the robot doesn't interfere with the system\n",
    "\n",
    "def robot_arm_2(params, step, sH, s):\n",
    "    _robotId = 2\n",
    "    if rand()<robots_probabilities[_robotId-1]: # draw a random number between 0 and 1; if it's smaller than the robot's parameter, it acts\n",
    "        return robot_arm(params, step, sH, s)\n",
    "    else:\n",
    "        return({'add_to_A': 0, 'add_to_B': 0}) # otherwise, the robot doesn't interfere with the system\n",
    "\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# In the Partial State Update Blocks, \n",
    "# the user specifies if state update functions will be run in series or in parallel\n",
    "# and the policy functions that will be evaluated in that block\n",
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { # The following policy functions will be evaluated and their returns will be passed to the state update functions\n",
    "            'robot_arm_1': robot_arm_1,\n",
    "            'robot_arm_2': robot_arm_2\n",
    "        },\n",
    "        'variables': { # The following state variables will be updated simultaneously\n",
    "            'box_A': increment_A,\n",
    "            'box_B': increment_B\n",
    "        }\n",
    "    }\n",
    "]\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run the simulation with those configurations, the system is unlikely to exhibit the same behavior as it did in its deterministic version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "del configs[:] # Clear any prior configs\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "exp.append_configs(initial_state=genesis_states, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_configs=c #preprocessed dictionaries containing simulation parameters\n",
    "                      )\n",
    "\n",
    "raw_result, tensor, sessions = executor.execute() # The `execute()` method returns a tuple; its first elements contains the raw results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "simulation_result = pd.DataFrame(raw_result)\n",
    "\n",
    "simulation_result.plot('timestep', ['box_A', 'box_B'], grid=True, \n",
    "        xticks=list(simulation_result['timestep'].drop_duplicates()), \n",
    "        colormap = 'RdYlGn',\n",
    "        yticks=list(range(1+(simulation_result['box_A']+simulation_result['box_B']).max())));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And if we run it again, it returns yet another result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "del configs[:] # Clear any prior configs\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "exp.append_configs(initial_state=genesis_states, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_configs=c #preprocessed dictionaries containing simulation parameters\n",
    "                      )\n",
    "\n",
    "raw_result, tensor, sessions = executor.execute() # The `execute()` method returns a tuple; its first elements contains the raw results\n",
    "\n",
    "simulation_result = pd.DataFrame(raw_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "simulation_result.plot('timestep', ['box_A', 'box_B'], grid=True, \n",
    "        xticks=list(simulation_result['timestep'].drop_duplicates()), \n",
    "        colormap = 'RdYlGn',\n",
    "        yticks=list(range(1+(simulation_result['box_A']+simulation_result['box_B']).max())));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to take advantage of cadCAD's Monte Carlo simulation features, we should modify the configuration file so as to define the number of times we want the same simulation to be run. This is done in the `N` key of the `sim_config_dict` dict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# Settings of general simulation parameters, unrelated to the system itself\n",
    "# `T` is a range with the number of discrete units of time the simulation will run for;\n",
    "# `N` is the number of times the simulation will be run (Monte Carlo runs)\n",
    "# In this example, we'll run the simulation once (N=1) and its duration will be of 10 timesteps\n",
    "# We'll cover the `M` key in a future article. For now, let's omit it\n",
    "mc = 50\n",
    "sim_config_dict = {\n",
    "    'T': range(10),\n",
    "    'N': mc, # We'll run the same simulation 50 times; the random events in each simulation are independent\n",
    "    #'M': {}\n",
    "}\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "del configs[:] # Clear any prior configs\n",
    "\n",
    "c = config_sim(sim_config_dict)\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "exp.append_configs(initial_state=genesis_states, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_configs=c #preprocessed dictionaries containing simulation parameters\n",
    "                      )\n",
    "\n",
    "raw_result, tensor, sessions = executor.execute() # The `execute()` method returns a tuple; its first elements contains the raw results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>box_A</th>\n",
       "      <th>box_B</th>\n",
       "      <th>subset</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>simulation</th>\n",
       "      <th>run</th>\n",
       "      <th>timestep</th>\n",
       "      <th>substep</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"11\" valign=\"top\">0</th>\n",
       "      <th rowspan=\"5\" valign=\"top\">1</th>\n",
       "      <th>0</th>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>1</th>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">50</th>\n",
       "      <th>6</th>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>550 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 box_A  box_B  subset\n",
       "simulation run timestep substep                      \n",
       "0          1   0        0           10      0       0\n",
       "               1        1            8      2       0\n",
       "               2        1            6      4       0\n",
       "               3        1            5      5       0\n",
       "               4        1            5      5       0\n",
       "...                                ...    ...     ...\n",
       "           50  6        1            6      4       0\n",
       "               7        1            6      4       0\n",
       "               8        1            5      5       0\n",
       "               9        1            5      5       0\n",
       "               10       1            5      5       0\n",
       "\n",
       "[550 rows x 3 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulation_result = pd.DataFrame(raw_result)\n",
    "df = simulation_result\n",
    "df.set_index(['simulation', 'run', 'timestep', 'substep'])\n",
    "\n",
    "from IPython.display import display\n",
    "tmp_rows = pd.options.display.max_rows\n",
    "pd.options.display.max_rows = 10\n",
    "display(df.set_index(['simulation', 'run', 'timestep', 'substep']))\n",
    "pd.options.display.max_rows = tmp_rows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting two of those runs allows us to see the different behaviors over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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"
    },
    {
     "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": [
    "df[df['run']==1].plot('timestep', ['box_A', 'box_B'], grid=True,\n",
    "                          xticks=list(df['timestep'].drop_duplicates()), \n",
    "                          yticks=list(range(11)),\n",
    "                          colormap = 'RdYlGn');\n",
    "\n",
    "df[df['run']==9].plot('timestep', ['box_A', 'box_B'], grid=True,\n",
    "                            xticks=list(df['timestep'].drop_duplicates()), \n",
    "                            yticks=list(range(11)),\n",
    "                            colormap = 'RdYlGn');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot all those runs onto a single chart, we can see every possible trajectory for the number of marbles in each box."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "ax = None\n",
    "for i in range(0,mc):\n",
    "    ax = df[df['run']==i+1].plot('timestep', ['box_A', 'box_B'],\n",
    "                                     grid=True,\n",
    "                                     xticks=list(df['timestep'].drop_duplicates()), \n",
    "                                     yticks=list(range(1+max(df['box_A'].max(),df['box_B'].max()))),\n",
    "                                     legend = (ax == None),\n",
    "                                     colormap = 'RdYlGn',\n",
    "                                     ax = ax\n",
    "                                  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For some analyses, it might make sense to look at the data in aggregate. Take the median for example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fdb26f10>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "dfmc_median = df.groupby(['timestep', 'substep']).median().reset_index()\n",
    "dfmc_median.plot('timestep', ['box_A', 'box_B'], \n",
    "                 grid=True,\n",
    "                 xticks=list(dfmc_median['timestep'].drop_duplicates()), \n",
    "                 yticks=list(range(int(1+max(dfmc_median['box_A'].max(),dfmc_median['box_B'].max())))),\n",
    "                 colormap = 'RdYlGn'\n",
    "                )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or look at edge cases"
   ]
  },
  {
   "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": [
    "max_final_A = df[df['timestep']==df['timestep'].max()]['box_A'].max()\n",
    "# max_final_A\n",
    "slow_runs = df[(df['timestep']==df['timestep'].max()) & \n",
    "         (df['box_A']==max_final_A)]['run']\n",
    "slow_runs = list(slow_runs)\n",
    "slow_runs\n",
    "\n",
    "ax = None\n",
    "for i in slow_runs:\n",
    "    ax = df[df['run']==i].plot('timestep', ['box_A', 'box_B'],\n",
    "                                     grid=True,\n",
    "                                     xticks=list(df['timestep'].drop_duplicates()), \n",
    "                                     yticks=list(range(1+max(df['box_A'].max(),df['box_B'].max()))),\n",
    "                                     legend = (ax == None),\n",
    "                                     colormap = 'RdYlGn',\n",
    "                                     ax = ax\n",
    "                                  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We invite the reader to fork this code and come up with answers for their other questions that might be interesting to look at. For example:\n",
    "* How often does box B momentarily contain more marbles than box A?\n",
    "* What's the frequency distribution of the time to reach equilibrium?\n",
    "* What's the probability distribution of the waiting times of each one of the robots?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}