tutorials/robots_and_marbles/robot-marbles-part-3/robot-marbles-part-3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# cadCAD Tutorials: The Robot and the Marbles, part 3\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 this notebook we'll look at how subsystems within a system can operate in different frequencies. But first let's copy the base configuration with which we ended Part 2. 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 simultaneously; in other words, they assess the state of the system at the exact same time, and decide what their action will be based on that information."
   ]
  },
  {
   "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",
    "sim_config_dict = {\n",
    "    'T': range(10),\n",
    "    'N': 1,\n",
    "    #'M': {}\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",
    "\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,\n",
    "            'robot_arm_2': robot_arm\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",
    "\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",
    "simulation = Executor(local_mode_ctx, configs) # Pass the configuration object inside an array\n",
    "raw_result, tensor, sessions = simulation.execute() # The `execute()` method returns a tuple; its first elements contains the raw results\n",
    "\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "df = pd.DataFrame(raw_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot('timestep', ['box_A', 'box_B'], grid=True, \n",
    "        xticks=list(df['timestep'].drop_duplicates()), \n",
    "        colormap = 'RdYlGn',\n",
    "        yticks=list(range(1+(df['box_A']+df['box_B']).max())));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Asynchronous Subsystems\n",
    "We have defined that the robots operate simultaneously on the boxes of marbles. But it is often the case that agents within a system operate asynchronously, each having their own operation frequencies or conditions.\n",
    "\n",
    "Suppose that instead of acting simultaneously, the robots in our examples operated in the following manner:\n",
    "* Robot 1: acts once every 2 timesteps\n",
    "* Robot 2: acts once every 3 timesteps\n",
    "\n",
    "One way to simulate the system with this change is to introduce a check of the current timestep before the robots act, with the definition of separate policy functions for each robot arm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# We specify each of the robots logic in a Policy Function\n",
    "robots_periods = [2,3] # Robot 1 acts once every 2 timesteps; Robot 2 acts once every 3 timesteps\n",
    "\n",
    "def get_current_timestep(cur_substep, s):\n",
    "    if cur_substep == 1:\n",
    "        return s['timestep']+1\n",
    "    return s['timestep']\n",
    "\n",
    "def robot_arm_1(params, step, sH, s):\n",
    "    _robotId = 1\n",
    "    if get_current_timestep(step, s)%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 get_current_timestep(step, s)%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",
    "# 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",
    "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",
    "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",
    "simulation_result = pd.DataFrame(raw_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fed5534d1c0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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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'], \n",
    "        grid=True, \n",
    "        xticks=list(simulation_result['timestep'].drop_duplicates()), \n",
    "        yticks=list(range(1+max(simulation_result['box_A'].max(),simulation_result['box_B'].max()))),\n",
    "        colormap = 'RdYlGn'\n",
    "       )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a step-by-step look at what the simulation tells us:\n",
    "* Timestep 1: the number of marbles in the boxes does not change, as none of the robots act\n",
    "* Timestep 2: Robot 1 acts, Robot 2 doesn't; resulting in one marble being moved from box A to box B\n",
    "* Timestep 3: Robot 2 acts, Robot 1 doesn't; resulting in one marble being moved from box A to box B\n",
    "* Timestep 4: Robot 1 acts, Robot 2 doesn't; resulting in one marble being moved from box A to box B\n",
    "* Timestep 5: the number of marbles in the boxes does not change, as none of the robots act\n",
    "* Timestep 6: Robots 1 __and__ 2 act, as 6 is a multiple of 2 __and__ 3; resulting in two marbles being moved from box A to box B and an equilibrium being reached."
   ]
  }
 ],
 "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
}