test3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "from src.utils import *\n",
    "from src.contracts import *"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Battery charging & discharging behavior contracts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1: PolyhedralContract = charging(s=1, generation=[0.5, 0.8])\n",
    "c2: PolyhedralContract = discharging(s=2, consumption=[0.6, 1.2])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sequence of such behaviors is modeled as contract composition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c12:\n",
      "InVars: [t1_entry, t1_var, duration1, soc1_entry, t2_var, duration2]\n",
      "OutVars:[soc1_var, soc2_var, output_t1, output_soc1, output_t2, output_soc2]\n",
      "A: [\n",
      "  -duration2 <= 0\n",
      "  duration1 + t1_entry - t2_var <= 0\n",
      "  -duration1 <= 0\n",
      "  -t1_entry <= 0\n",
      "  t1_entry - t1_var <= 0\n",
      "  -soc1_entry <= 0\n",
      "  soc1_entry <= 100\n",
      "]\n",
      "G: [\n",
      "  0.8 duration1 + soc1_entry <= 100\n",
      "  duration1 - output_t1 + t1_entry = 0\n",
      "  0.5 duration1 - output_soc1 + soc1_entry <= 0\n",
      "  -0.8 duration1 + output_soc1 - soc1_entry <= 0\n",
      "  soc1_entry - soc1_var - 0.5 t1_entry + 0.5 t1_var <= 0\n",
      "  -soc1_entry + soc1_var + 0.8 t1_entry - 0.8 t1_var <= 0\n",
      "  -output_t1 + t1_var <= 0\n",
      "  -output_soc1 + soc1_var <= 0\n",
      "  1.2 duration2 - output_soc1 <= 0\n",
      "  duration2 + output_t1 - output_t2 = 0\n",
      "  0.6 duration2 - output_soc1 + output_soc2 <= 0\n",
      "  -1.2 duration2 + output_soc1 - output_soc2 <= 0\n",
      "  -output_soc1 - 0.6 output_t1 + soc2_var + 0.6 t2_var <= 0\n",
      "  output_soc1 + 1.2 output_t1 - soc2_var - 1.2 t2_var <= 0\n",
      "  -output_t2 + t2_var <= 0\n",
      "  output_soc2 - soc2_var <= 0\n",
      "]\n"
     ]
    }
   ],
   "source": [
    "c12 = scenario_sequence(\n",
    "    c1=c1, \n",
    "    c2=c2, \n",
    "    variables=[\"t\", \"soc\"], c1index=1\n",
    ").rename_variables([\n",
    "    (\"t2_exit\", \"output_t2\"), \n",
    "    (\"soc2_exit\", \"output_soc2\")\n",
    "])\n",
    "print(f\"c12:\\n{c12}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To use a contract for simulation purposes, we need to extract its `PolyhedralTermList`: the list of all assumptions and guarantees constraints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "constraints:\n",
      "[\n",
      "  -duration2 <= 0\n",
      "  duration1 + t1_entry - t2_var <= 0\n",
      "  -duration1 <= 0\n",
      "  -t1_entry <= 0\n",
      "  t1_entry - t1_var <= 0\n",
      "  -soc1_entry <= 0\n",
      "  soc1_entry <= 100\n",
      "  0.8 duration1 + soc1_entry <= 100\n",
      "  duration1 - output_t1 + t1_entry = 0\n",
      "  0.5 duration1 - output_soc1 + soc1_entry <= 0\n",
      "  -0.8 duration1 + output_soc1 - soc1_entry <= 0\n",
      "  soc1_entry - soc1_var - 0.5 t1_entry + 0.5 t1_var <= 0\n",
      "  -soc1_entry + soc1_var + 0.8 t1_entry - 0.8 t1_var <= 0\n",
      "  -output_t1 + t1_var <= 0\n",
      "  -output_soc1 + soc1_var <= 0\n",
      "  1.2 duration2 - output_soc1 <= 0\n",
      "  duration2 + output_t1 - output_t2 = 0\n",
      "  0.6 duration2 - output_soc1 + output_soc2 <= 0\n",
      "  -1.2 duration2 + output_soc1 - output_soc2 <= 0\n",
      "  -output_soc1 - 0.6 output_t1 + soc2_var + 0.6 t2_var <= 0\n",
      "  output_soc1 + 1.2 output_t1 - soc2_var - 1.2 t2_var <= 0\n",
      "  -output_t2 + t2_var <= 0\n",
      "  output_soc2 - soc2_var <= 0\n",
      "]\n"
     ]
    }
   ],
   "source": [
    "constraints: PolyhedralTermList = c12.a | c12.g\n",
    "print(f\"constraints:\\n{constraints}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "duration1 bounds: (0.0, 125.0)\n",
      "duration2 bounds: (0.0, 83.33333333333334)\n",
      "soc1_var bounds: (0.0, 100.0)\n"
     ]
    }
   ],
   "source": [
    "duration1_bounds=get_bounds(constraints, \"duration1\")\n",
    "print(f\"duration1 bounds: {duration1_bounds}\")\n",
    "duration2_bounds=get_bounds(constraints, \"duration2\")\n",
    "print(f\"duration2 bounds: {duration2_bounds}\")\n",
    "soc1_var_bounds=get_bounds(constraints, \"soc1_var\")\n",
    "print(f\"soc1_var bounds: {soc1_var_bounds}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot the 1st contract, we need to provide values for the allocation variables, `duration1` and `duration2`, as well as for the 1st contract initial conditions, `t1_entry`, `soc1_entry`.\n",
    "\n",
    "We also need to eliminate the `output_*` variables that represent the bounds on all contracts: `output_t1`, `output_t2`, `output_soc1`, and `output_soc2`.\n",
    "\n",
    "Since we are focusing the plot on the 1st component, we also need to eliminate the 2nd component's `*_var` variables: `soc2_var` and `t2_var`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ce1:\n",
      "[\n",
      "  -soc1_var + 0.5 t1_var <= -50\n",
      "  soc1_var - 0.8 t1_var <= 50\n",
      "  t1_var <= 10\n",
      "]\n"
     ]
    }
   ],
   "source": [
    "ce1: PolyhedralTermList = constraints \\\n",
    ".evaluate({\n",
    "    Var(\"duration1\"): 10.0,\n",
    "    Var(\"duration2\"): 10.0,\n",
    "    Var(\"t1_entry\"): 0,\n",
    "    Var(\"soc1_entry\"): 50.0,\n",
    "}) \\\n",
    ".simplify() \\\n",
    ".elim_vars_by_relaxing(context=PolyhedralTermList([]),\n",
    "    vars_to_elim=[\n",
    "        Var(\"output_t1\"), \n",
    "        Var(\"output_t2\"), \n",
    "        Var(\"output_soc1\"), \n",
    "        Var(\"output_soc2\"), \n",
    "        Var(\"soc2_var\"), \n",
    "        Var(\"t2_var\")\n",
    "    ]) \n",
    "print(f\"ce1:\\n{ce1}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8c79804ec14542d2947e7060c194d030",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plot_input_output_polyhedral_term_list(ce1, Var(\"t1_var\"), Var(\"soc1_var\"))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot the 2nd contract, we need to provide values for the allocation variables, `duration1` and `duration2`, as well as for the 1st contract initial conditions, `t1_entry`, `soc1_entry` and the 2nd contract initial conditions, `t1_var` and `soc1_var`.\n",
    "\n",
    "\n",
    "We also need to eliminate the `output_*` variables that represent the bounds on all contracts: `output_t1`, `output_t2`, `output_soc1`, and `output_soc2`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ce2:\n",
      "[\n",
      "  t2_var <= 20\n",
      "  soc2_var + 0.6 t2_var <= 64\n",
      "  -soc2_var - 1.2 t2_var <= -69\n",
      "]\n"
     ]
    }
   ],
   "source": [
    "ce2: PolyhedralTermList = constraints \\\n",
    ".evaluate({\n",
    "    Var(\"duration1\"): 10.0,\n",
    "    Var(\"duration2\"): 10.0,\n",
    "    Var(\"t1_entry\"): 0,\n",
    "    Var(\"soc1_entry\"): 50.0,\n",
    "    Var(\"soc1_var\"):57.0,\n",
    "    Var(\"t1_var\"):10.0,\n",
    "}) \\\n",
    ".simplify() \\\n",
    ".elim_vars_by_relaxing(context=PolyhedralTermList([]),\n",
    "    vars_to_elim=[\n",
    "        Var(\"output_t1\"), \n",
    "        Var(\"output_t2\"), \n",
    "        Var(\"output_soc1\"), \n",
    "        Var(\"output_soc2\"), \n",
    "    ])\n",
    "print(f\"ce2:\\n{ce2}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t2_var bounds: (8.333333333333334, 20.0)\n",
      "soc2_var bounds: (45.0, 59.0)\n"
     ]
    }
   ],
   "source": [
    "t2_bounds=get_bounds(ce2, \"t2_var\")\n",
    "print(f\"t2_var bounds: {t2_bounds}\")\n",
    "soc2_bounds=get_bounds(ce2, \"soc2_var\")\n",
    "print(f\"soc2_var bounds: {soc2_bounds}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ca56ca56e55041319a3f640dbd946bca",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = plot_input_output_polyhedral_term_list(ce2, Var(\"t2_var\"), Var(\"soc2_var\"))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.11.2"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}