scalability-statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "be7b679795754b579d471434f7f88830",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found 547 successful system designs from exploring 1001 contracts.\n",
      "Total time 7.311911582946777 running on AMD Ryzen Threadripper PRO 3955WX 16-Cores @ 3.8927 GHz with up to 32 threads.\n",
      "Pacti compose,quotient,merge statistics:\n",
      "compose invocation counts: (min: 4, max: 172, avg: 83.45854145854146, total: 83542)\n",
      "min/max compose contract size: (constraints: 2, variables: 2)/(constraints: 6, variables: 6)\n",
      "no quotient operations\n",
      "no merge operations\n",
      "Pacti PolyhedralTermList statistics:\n",
      "no contains_behavior operations\n",
      "Pacti PolyhedralCompoundContract statistics:\n",
      "no compound_merge operations\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from scalability import *\n",
    "from pacti_instrumentation.pacti_counters import PactiInstrumentationData, summarize_instrumentation_data\n",
    "from p_tqdm import p_umap\n",
    "from pacti_instrumentation.cpu_usage_plot import cpu_usage_plot\n",
    "\n",
    "from cpuinfo import get_cpu_info\n",
    "cpu_info = get_cpu_info()\n",
    "cpu_info_message = f\"{cpu_info['brand_raw']} @ {cpu_info['hz_advertised_friendly']} with up to {cpu_info['count']} threads.\"\n",
    "\n",
    "def explore_combination_params(params) -> Tuple[PactiInstrumentationData, Optional[PolyhedralIoContract]]:\n",
    "    return explore_combination(*params)\n",
    "\n",
    "# Get all possible combinations of sensors from the library\n",
    "number_of_sensors = 4\n",
    "all_combinations = list(itertools.combinations(sensor_library.keys(), number_of_sensors))\n",
    "num_contracts = len(all_combinations)\n",
    "\n",
    "with cpu_usage_plot(finally_clear_output=True):\n",
    "    t0 = time.time()\n",
    "    results = p_umap(explore_combination_params, list(enumerate(all_combinations)))\n",
    "    tf = time.time()\n",
    "\n",
    "stats = summarize_instrumentation_data([result[0] for result in results])\n",
    "filtered_results = [result[1] for result in results if result[1]]\n",
    "\n",
    "print(\n",
    "    f\"Found {len(filtered_results)} successful system designs from exploring {num_contracts} contracts.\\n\"\n",
    "    f\"Total time {tf-t0} running on {cpu_info_message}\\n\"\n",
    "    f\"{stats.stats()}\"\n",
    ")\n"
   ]
  }
 ],
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    "name": "ipython",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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