tutorials/robot-marbles-part-2/robot-marbles-part-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# cadCAD Tutorials: The Robot and the Marbles, part 2\n",
    "In [Part 1](../robot-marbles-part-1/robot-marbles-part-1.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",
    "\n",
    "This article will introduce the concept of __Policies__. But first let's copy the base configuration from Part 1. As a reminder, here's the description of the simple system we are using for illustration purposes.\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 a robot arm capable of taking a marble from any one of the boxes and dropping it into the other one. \n",
    "* The robot is programmed to take one marble at a time from the box containing the largest number of marbles and drop it in the other box. It repeats that process until the boxes contain an equal number of marbles.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# List of all the state variables in the system and their initial values\n",
    "initial_conditions = {\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",
    "def update_A(params, step, sL, s, _input):\n",
    "    y = 'box_A'\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",
    "    x = s['box_A'] + add_to_A\n",
    "    return (y, x)\n",
    "\n",
    "def update_B(params, step, sL, s, _input):\n",
    "    y = 'box_B'\n",
    "    add_to_B = 0\n",
    "    if (s['box_B'] > s['box_A']):\n",
    "        add_to_B = -1\n",
    "    elif (s['box_B'] < s['box_A']):\n",
    "        add_to_B = 1\n",
    "    x = s['box_B'] + add_to_B\n",
    "    return (y, x)\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# In the Partial State Update Blocks, the user specifies if state update functions will be run in series or in parallel\n",
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { # We'll ignore policies for now\n",
    "        },\n",
    "        'variables': { # The following state variables will be updated simultaneously\n",
    "            'box_A': update_A,\n",
    "            'box_B': update_B\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 leave it empty\n",
    "simulation_parameters = {\n",
    "    'T': range(10),\n",
    "    'N': 1,\n",
    "    'M': {}\n",
    "}\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "\n",
    "from cadCAD.configuration import Configuration\n",
    "\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "config = Configuration(initial_state=initial_conditions, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_config=simulation_parameters #dict containing simulation parameters\n",
    "                      )\n",
    "\n",
    "from cadCAD.engine import ExecutionMode, ExecutionContext, Executor\n",
    "exec_mode = ExecutionMode()\n",
    "exec_context = ExecutionContext(exec_mode.single_proc)\n",
    "executor = Executor(exec_context, [config]) # Pass the configuration object inside an array\n",
    "raw_result, tensor = 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",
    "df = pd.DataFrame(raw_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot('timestep', ['box_A', 'box_B'], grid=True, \n",
    "        colormap = 'RdYlGn',\n",
    "        xticks=list(df['timestep'].drop_duplicates()), \n",
    "        yticks=list(range(1+(df['box_A']+df['box_B']).max())));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Policies\n",
    "In part 1, we ignored the `_input` argument of state update functions. That argument is a signal passed to the state update function by another set of functions: Policy Functions.\n",
    "\n",
    "Policy Functions are most commonly used as representations of the behavior of agents that interact with the components of the system we're simulating in cadCAD. But more generally, they describe the logic of some component or mechanism of the system. It is possible to encode the functionality of a policy function in the state update functions themselves (as we did in part 1, where we had the robot's algorithm reside in the `update_A` and `update_B` functions), but as systems grow more complex this approach makes the code harder to read and maintain, and in some cases more inefficient because of unnecessary repetition of computational steps.\n",
    "\n",
    "The general structure of a policy function is:\n",
    "```python\n",
    "def policy_function(params, step, sL, s):\n",
    "    ...\n",
    "    return {'value1': value1, 'value2': value2, ...}\n",
    "```\n",
    "Just like State Update Functions, policies can read the current state of the system from argument `s`, a Python `dict` where the `dict_keys` are the __names of the variables__ and the `dict_values` are their __current values__. The Policy Function must return a dictionary, which will be passed as an argument (`_input`) to the state update functions.\n",
    "![Policy](policy.png \"Policy\")\n",
    "\n",
    "Let's update our simulation so that the robot arm's logic is encoded in a Policy instead of in the State Update Functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # \n",
    "# We specify the robot arm's logic in a Policy Function\n",
    "def robot_arm(params, step, sL, 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, sL, 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, sL, s, _input):\n",
    "    y = 'box_B'\n",
    "    x = s['box_B'] + _input['add_to_B']\n",
    "    return (y, x)\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': robot_arm\n",
    "        },\n",
    "        'states': { # 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",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "config = Configuration(initial_state=initial_conditions, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_config=simulation_parameters #dict containing simulation parameters\n",
    "                      )\n",
    "\n",
    "exec_mode = ExecutionMode()\n",
    "exec_context = ExecutionContext(exec_mode.single_proc)\n",
    "executor = Executor(exec_context, [config]) # Pass the configuration object inside an array\n",
    "raw_result, tensor = executor.execute() # The `execute()` method returns a tuple; its first elements contains the raw results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": [
    "As expected, the results are the same as when the robot arm logic was encoded within the state update functions.  \n",
    "\n",
    "Several policies may be evaluated within a Partial State Update Block. When that's the case, cadCAD's engine aggregates the outputs of the policies and passes them as a single signal to the state update functions. \n",
    "![Policies](policies.png \"Policies\")\n",
    "\n",
    "Aggregation of policies is defined in cadCAD as __key-wise sum (+) of the elements of the outputted `dict`s__.\n",
    "```python\n",
    ">policy_1_output = {'int': 1, 'str': 'abc', 'list': [1, 2], '1-only': 'Specific to policy 1'}\n",
    ">policy_2_output = {'int': 2, 'str': 'def', 'list': [3, 4], '2-only': 'Specific to policy 2'}\n",
    ">print(aggregate([policy_1_output, policy_2_output]))\n",
    "```\n",
    "```\n",
    "{'int': 3, 'str': 'abcdef', 'list': [1, 2, 3, 4], '1-only': 'Specific to policy 1', '2-only': 'Specific to policy 2'}\n",
    "```\n",
    "\n",
    "To illustrate, let's add to another system another robot arm identical to the first one, that acts in tandem with it. All it takes is to add a policy to the `dict` that describes the partial state update block."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\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",
    "# The configurations above are then packaged into a `Configuration` object\n",
    "config = Configuration(initial_state=initial_conditions, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_config=simulation_parameters #dict containing simulation parameters\n",
    "                      )\n",
    "\n",
    "exec_mode = ExecutionMode()\n",
    "exec_context = ExecutionContext(exec_mode.single_proc)\n",
    "executor = Executor(exec_context, [config]) # Pass the configuration object inside an array\n",
    "raw_result, tensor = executor.execute() # The `execute()` method returns a tuple; its first elements contains the raw results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "df = pd.DataFrame(raw_result)\n",
    "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": [
    "Because we have made it so that both robots read and update the state of the system at the same time, the equilibrium we had before (with 5 marbles in each box) is never reached. Instead, the system oscillates around that point.\n",
    "\n",
    "---\n",
    "\n",
    "_About BlockScience_  \n",
    "[BlockScience](http://bit.ly/github_articles_M_02) is a research and engineering firm specialized in complex adaptive systems and applying practical methodologies from engineering design, development and testing to projects in emerging technologies such as blockchain. Follow us on [Medium](http://bit.ly/bsci-medium) or [Twitter](http://bit.ly/bsci-twitter) to stay in touch."
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}