plots.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3cFbS10sOe3W"
      },
      "source": [
        "Copyright 2021 Google LLC\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "you may not use this file except in compliance with the License.\n",
        "You may obtain a copy of the License at\n",
        "\n",
        "    https://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software\n",
        "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "See the License for the specific language governing permissions and\n",
        "limitations under the License."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GnBhoGI48V6Q"
      },
      "outputs": [],
      "source": [
        "#@title Imports\n",
        "import os\n",
        "import pickle\n",
        "\n",
        "from google.colab import files\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import plotnine as gg\n",
        "from scipy import stats"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "X6DEqKhTtoFr"
      },
      "outputs": [],
      "source": [
        "#@title Utility functions\n",
        "def saveplot(plot, path):\n",
        "  print('Saving figure to {}'.format(path))\n",
        "  plot.save(path)\n",
        "  files.download(path)\n",
        "\n",
        "\n",
        "def chunks(lst, n):\n",
        "  for i in range(0, len(lst), n):\n",
        "    yield lst[i:i + n]\n",
        "\n",
        "\n",
        "def bootstrap_metric(prediction, ground_truth, metric_func, num_repeats=1000):\n",
        "  prediction = np.array(prediction)\n",
        "  ground_truth = np.array(ground_truth)\n",
        "  length = len(ground_truth)\n",
        "  repeats = []\n",
        "  for _ in range(num_repeats):\n",
        "    sample = np.random.choice(range(length), size=length)\n",
        "    prediction_ = prediction[sample]\n",
        "    ground_truth_ = ground_truth[sample]\n",
        "    metric = metric_func(prediction_, ground_truth_)\n",
        "    repeats.append(metric)\n",
        "  return repeats\n",
        "\n",
        "\n",
        "def normalized_regret(prediction, ground_truth, top_k=1):\n",
        "  max_val = np.max(ground_truth)\n",
        "  ind = np.argsort(prediction)\n",
        "  top_k_values = ground_truth[ind][-top_k:]\n",
        "  regret = (max_val - np.max(top_k_values)) / max_val\n",
        "  return regret\n",
        "\n",
        "\n",
        "def absolute_error(prediction, ground_truth):\n",
        "  return np.mean(np.abs(prediction - ground_truth))\n",
        "\n",
        "\n",
        "def rank_correlation(prediction, ground_truth):\n",
        "  return stats.spearmanr(ground_truth, prediction).correlation\n",
        "\n",
        "\n",
        "def make_scatter_data(policy_dict, gt_data, baselines, allowlist=None):\n",
        "  \"\"\"Make dataframe for plotting scatter plots.\"\"\"\n",
        "  data = []\n",
        "  tasks = list(policy_dict.keys())\n",
        "  for task in tasks:\n",
        "    policy_ids = policy_dict[task]\n",
        "    # TODO(tpaine): remove this\n",
        "    if allowlist is not None:\n",
        "      policy_ids = [p for p in policy_ids if p in allowlist]\n",
        "\n",
        "    worst = np.min([gt_data[p][0] for p in policy_ids])\n",
        "    best = np.max([gt_data[p][0] for p in policy_ids])\n",
        "    for baseline_name, baseline in baselines.items():\n",
        "      for policy_id in policy_ids:\n",
        "        gt_value = (gt_data[policy_id][0] - worst) / (best - worst)\n",
        "        baseline_value = np.minimum(\n",
        "            (baseline[policy_id][0] - worst) / (best - worst), 2)\n",
        "\n",
        "        datum = (policy_id, task, baseline_name, gt_value, baseline_value)\n",
        "        data.append(datum)\n",
        "  df = pd.DataFrame(\n",
        "      data,\n",
        "      columns=[\n",
        "          'policy_id', 'task_name', 'baseline', 'ground_truth', 'prediction'\n",
        "      ])\n",
        "  return df\n",
        "\n",
        "\n",
        "def make_results(policy_dict, gt_data, baselines, metric_func, allowlist=None):\n",
        "  \"\"\"Make dataframe containing metric results for each bootstrap 'trial'.\"\"\"\n",
        "  results = []\n",
        "  tasks = list(policy_dict.keys())\n",
        "  for task in tasks:\n",
        "    policy_ids = policy_dict[task]\n",
        "    if allowlist is not None:\n",
        "      policy_ids = [p for p in policy_ids if p in allowlist]\n",
        "\n",
        "    worst = np.min([gt_data[p][0] for p in policy_ids])\n",
        "    best = np.max([gt_data[p][0] for p in policy_ids])\n",
        "    for baseline_name, baseline in baselines.items():\n",
        "      gt_values = np.array([gt_data[pid][0] for pid in policy_ids])\n",
        "      baseline_values = np.array([baseline[pid][0] for pid in policy_ids])\n",
        "      gt_values = (gt_values - worst) / (best - worst)\n",
        "      baseline_values = (baseline_values - worst) / (best - worst)\n",
        "      baseline_values = np.minimum(baseline_values, 2)\n",
        "      repeats = bootstrap_metric(\n",
        "          prediction=baseline_values,\n",
        "          ground_truth=gt_values,\n",
        "          metric_func=metric_func)\n",
        "      for i, repeat in enumerate(repeats):\n",
        "        row = (baseline_name, task, i, repeat)\n",
        "        results.append(row)\n",
        "  result_df = pd.DataFrame(\n",
        "      results, columns=['baseline', 'task_name', 'trial', 'metric'])\n",
        "  return result_df\n",
        "\n",
        "\n",
        "def make_per_task(results):\n",
        "  \"\"\"Make dataframe containing per task performance per baseline.\"\"\"\n",
        "  per_task = results.groupby(['baseline', 'task_name'],\n",
        "                             as_index=False)['metric'].mean()\n",
        "  temp = results.groupby(['baseline', 'task_name'],\n",
        "                         as_index=False)['metric'].std()\n",
        "  per_task['metric_dn'] = per_task['metric'] - temp['metric']\n",
        "  per_task['metric_up'] = per_task['metric'] + temp['metric']\n",
        "  return per_task\n",
        "\n",
        "\n",
        "def make_d4rl_per_domain(results):\n",
        "  results['task_domain'] = [t.split('-')[0] for t in results['task_name']]\n",
        "  per_domain = results.groupby(['baseline', 'task_domain'],\n",
        "                               as_index=False)['metric'].mean()\n",
        "  temp = results.groupby(['baseline', 'task_domain', 'trial'],\n",
        "                         as_index=False)['metric'].mean()\n",
        "  temp = temp.groupby(['baseline', 'task_domain'],\n",
        "                      as_index=False)['metric'].std()\n",
        "  per_domain['metric_dn'] = per_domain['metric'] - temp['metric']\n",
        "  per_domain['metric_up'] = per_domain['metric'] + temp['metric']\n",
        "  return per_domain\n",
        "\n",
        "\n",
        "def make_overall(results):\n",
        "  \"\"\"Make dataframe containing aggregate performance per baseline.\"\"\"\n",
        "  overall = results.groupby(['baseline'], as_index=False)['metric'].mean()\n",
        "  temp = results.groupby(['baseline', 'trial'], as_index=False)['metric'].mean()\n",
        "  temp = temp.groupby(['baseline'], as_index=False)['metric'].std()\n",
        "  overall['metric_dn'] = overall['metric'] - temp['metric']\n",
        "  overall['metric_up'] = overall['metric'] + temp['metric']\n",
        "  return overall\n",
        "\n",
        "\n",
        "def plot_per_task(per_task, y_axis_name, figure_size=(20, 5), order=None):\n",
        "  baseline_sorted = pd.Categorical(per_task['baseline'], categories=order)\n",
        "  per_task['baseline_sorted'] = baseline_sorted\n",
        "  x_axis_name = 'Tasks'\n",
        "  tasks = list(np.unique(per_task['task_name']))[::-1]\n",
        "  p = (\n",
        "      gg.ggplot(per_task) + gg.aes('task_name', y='metric') + gg.geom_bar(\n",
        "          gg.aes(fill='baseline'),\n",
        "          stat='identity',\n",
        "          position=gg.position_dodge()) + gg.geom_errorbar(\n",
        "              gg.aes(\n",
        "                  x='task_name',\n",
        "                  group='baseline',\n",
        "                  ymin='metric_dn',\n",
        "                  ymax='metric_up'),\n",
        "              width=.2,\n",
        "              position=gg.position_dodge(0.9)) +\n",
        "      gg.labs(y=y_axis_name, x=x_axis_name) + gg.theme_minimal() +\n",
        "      gg.facet_wrap(['baseline_sorted'], ncol=8) + gg.theme(\n",
        "          legend_position='none',\n",
        "          figure_size=figure_size,\n",
        "          panel_spacing=.2,\n",
        "          text=gg.element_text(size=16),\n",
        "          axis_text=gg.element_text(size=14),\n",
        "          axis_title=gg.element_text(size=16)) +\n",
        "      gg.scale_x_discrete(limits=tasks) + gg.coord_flip())\n",
        "  return p\n",
        "\n",
        "\n",
        "def plot_overall(overall, y_axis_name, ascending=True, order=None):\n",
        "  baseline_sorted = pd.Categorical(overall['baseline'], categories=order)\n",
        "  overall['baseline_sorted'] = baseline_sorted\n",
        "  p = (\n",
        "      gg.ggplot(overall) + gg.aes('baseline_sorted', y='metric') + gg.geom_bar(\n",
        "          gg.aes(fill='baseline'),\n",
        "          stat='identity',\n",
        "          position=gg.position_dodge()) + gg.geom_errorbar(\n",
        "              gg.aes(x='baseline_sorted', ymin='metric_dn', ymax='metric_up'),\n",
        "              width=.2,\n",
        "              position=gg.position_dodge(0.9)) +\n",
        "      gg.labs(y=y_axis_name, x='Baselines') + gg.theme_minimal() + gg.theme(\n",
        "          legend_position='none',\n",
        "          figure_size=(9, 3),\n",
        "          panel_spacing=.5,\n",
        "          text=gg.element_text(size=16),\n",
        "          axis_text=gg.element_text(size=14),\n",
        "          axis_title=gg.element_text(size=16)))\n",
        "  return p\n",
        "\n",
        "\n",
        "def plot_scatter(scatter_data, order=None):\n",
        "  y_axis_name = 'Estimate'\n",
        "  x_axis_name = 'Return (d=0.995)'\n",
        "  scatter_data['task_name'] = [\n",
        "      t.replace('_', '\\n') for t in scatter_data['task_name']\n",
        "  ]\n",
        "  scatter_data['task_name'] = [\n",
        "      t.replace('-', '\\n') for t in scatter_data['task_name']\n",
        "  ]\n",
        "  if order is None:\n",
        "    scatter_data['baseline_sorted'] = scatter_data['baseline']\n",
        "  else:\n",
        "    baseline_sorted = pd.Categorical(scatter_data['baseline'], categories=order)\n",
        "    scatter_data['baseline_sorted'] = baseline_sorted\n",
        "  p = (\n",
        "      gg.ggplot(scatter_data) + gg.geom_abline(color='grey', alpha=0.8) +\n",
        "      gg.aes(y='prediction', x='ground_truth', color='baseline') +\n",
        "      gg.geom_point(alpha=0.8) +\n",
        "      gg.facet_grid(['task_name', 'baseline_sorted']) + gg.coord_fixed() +\n",
        "      gg.labs(y=y_axis_name, x=x_axis_name) + gg.theme_minimal() +\n",
        "      gg.xlim(0, 2) + gg.ylim(0, 2) + gg.theme(\n",
        "          legend_position='none',\n",
        "          figure_size=(15, 25),\n",
        "          panel_spacing=.2,\n",
        "          text=gg.element_text(size=16),\n",
        "          axis_text=gg.element_text(size=14),\n",
        "          axis_title=gg.element_text(size=16)))\n",
        "\n",
        "  return p\n",
        "\n",
        "\n",
        "def plot_per_domain(per_domain, y_axis_name, order=None):\n",
        "  x_axis_name = 'Domains'\n",
        "  baseline_sorted = pd.Categorical(per_domain['baseline'], categories=order)\n",
        "  per_domain['baseline_sorted'] = baseline_sorted\n",
        "  domains = list(np.unique(per_domain['task_domain']))[::-1]\n",
        "  p = (\n",
        "      gg.ggplot(per_domain) + gg.aes('task_domain', y='metric') + gg.geom_bar(\n",
        "          gg.aes(fill='baseline'),\n",
        "          stat='identity',\n",
        "          position=gg.position_dodge()) + gg.geom_errorbar(\n",
        "              gg.aes(\n",
        "                  x='task_domain',\n",
        "                  group='baseline',\n",
        "                  ymin='metric_dn',\n",
        "                  ymax='metric_up'),\n",
        "              width=.2,\n",
        "              position=gg.position_dodge(0.9)) +\n",
        "      gg.labs(y=y_axis_name, x=x_axis_name) + gg.theme_minimal() +\n",
        "      gg.facet_wrap(['baseline_sorted'], ncol=8) + gg.theme(\n",
        "          legend_position='none',\n",
        "          figure_size=(20, 5),\n",
        "          panel_spacing=.1,\n",
        "          text=gg.element_text(size=16),\n",
        "          axis_text=gg.element_text(size=14),\n",
        "          axis_title=gg.element_text(size=16)) +\n",
        "      gg.scale_x_discrete(limits=domains) + gg.coord_flip())\n",
        "  return p\n",
        "\n",
        "\n",
        "def make_all_metric_plots(benchmark,\n",
        "                          metric_type,\n",
        "                          policy_dict,\n",
        "                          gt_data,\n",
        "                          baselines,\n",
        "                          allowlist=None):\n",
        "  \"\"\"Utility function to make and save all metric plots.\"\"\"\n",
        "  # setup\n",
        "  if benchmark == 'rlunplugged':\n",
        "    per_task_figure_size = (25, 5)\n",
        "  elif benchmark == 'd4rl':\n",
        "    per_task_figure_size = (25, 15)\n",
        "  else:\n",
        "    ValueError('Unknown benchmark')\n",
        "\n",
        "  if metric_type == 'absolute_error':\n",
        "    y_axis_name = '\u003c Absolute Error'\n",
        "    metric_func = absolute_error\n",
        "    ascending = True\n",
        "  elif metric_type == 'rank_correlation':\n",
        "    y_axis_name = '\u003e Rank Correlation'\n",
        "    metric_func = rank_correlation\n",
        "    ascending = False\n",
        "  elif metric_type == 'normalized_regret':\n",
        "    y_axis_name = '\u003c Regret@1'\n",
        "    metric_func = normalized_regret\n",
        "    ascending = True\n",
        "  else:\n",
        "    ValueError('Unknown metric_type')\n",
        "\n",
        "  # Prepare data for plots\n",
        "  results = make_results(\n",
        "      policy_dict,\n",
        "      gt_data,\n",
        "      baselines,\n",
        "      metric_func=metric_func,\n",
        "      allowlist=allowlist)\n",
        "  per_task = make_per_task(results)\n",
        "  overall = make_overall(results)\n",
        "  if benchmark == 'd4rl':\n",
        "    per_domain = make_d4rl_per_domain(results)\n",
        "\n",
        "  # Order baselines by overall performance\n",
        "  overall.sort_values('metric', inplace=True, ascending=ascending)\n",
        "  order = list(overall['baseline'])\n",
        "\n",
        "  # Make plots\n",
        "  p = plot_per_task(\n",
        "      per_task,\n",
        "      y_axis_name=y_axis_name,\n",
        "      figure_size=per_task_figure_size,\n",
        "      order=order)\n",
        "  print(p)\n",
        "  output_path = output_pattern.format(benchmark,\n",
        "                                      'per_task_{}'.format(metric_type))\n",
        "  saveplot(p, output_path)\n",
        "\n",
        "  overall = make_overall(results)\n",
        "  p = plot_overall(\n",
        "      overall, y_axis_name=y_axis_name, ascending=ascending, order=order)\n",
        "  print(p)\n",
        "  output_path = output_pattern.format(benchmark,\n",
        "                                      'overall_{}'.format(metric_type))\n",
        "  saveplot(p, output_path)\n",
        "\n",
        "  if benchmark == 'd4rl':\n",
        "    p = plot_per_domain(per_domain, y_axis_name, order=order)\n",
        "    print(p)\n",
        "    output_path = output_pattern.format(benchmark,\n",
        "                                        'per_domain_{}'.format(metric_type))\n",
        "    saveplot(p, output_path)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6ZjPAeHyOqfH"
      },
      "outputs": [],
      "source": [
        "#@title Download benchmark data\n",
        "!gsutil cp -r gs://gresearch/deep-ope/benchmark.zip /tmp/\n",
        "!unzip /tmp/benchmark.zip -d /tmp/"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mmHaXXhSRZ88"
      },
      "outputs": [],
      "source": [
        "#@title Read benchmark data\n",
        "BENCHMARK_ROOT = '/tmp/dope/'\n",
        "# BENCHMARK = 'rlunplugged'\n",
        "BENCHMARK = 'd4rl'\n",
        "\n",
        "if BENCHMARK == 'rlunplugged':\n",
        "  gt_path = os.path.join(BENCHMARK_ROOT, 'rlunplugged_gt.pkl')\n",
        "  policy_path = os.path.join(BENCHMARK_ROOT, 'rlunplugged_policys.pkl')\n",
        "  baseline_paths = {}\n",
        "  baseline_paths['FQE-D'] = os.path.join(BENCHMARK_ROOT, 'rlunplugged_fqed.pkl')\n",
        "  baseline_paths['FQE-L2'] = os.path.join(BENCHMARK_ROOT,\n",
        "                                          'rlunplugged_fqel2.pkl')\n",
        "  baseline_paths['VPM'] = os.path.join(BENCHMARK_ROOT, 'rlunplugged_vpm.pkl')\n",
        "  baseline_paths['DICE'] = os.path.join(BENCHMARK_ROOT, 'rlunplugged_dice.pkl')\n",
        "  baseline_paths['MB-FF'] = os.path.join(BENCHMARK_ROOT,\n",
        "                                         'rlunplugged_mb_ff.pkl')\n",
        "  baseline_paths['MB-AR'] = os.path.join(BENCHMARK_ROOT,\n",
        "                                         'rlunplugged_mb_ar.pkl')\n",
        "  baseline_paths['DR'] = os.path.join(BENCHMARK_ROOT, 'rlunplugged_dr.pkl')\n",
        "  baseline_paths['IS'] = os.path.join(BENCHMARK_ROOT, 'rlunplugged_is.pkl')\n",
        "elif BENCHMARK == 'd4rl':\n",
        "  gt_path = os.path.join(BENCHMARK_ROOT, 'd4rl_gt.pkl')\n",
        "  policy_path = os.path.join(BENCHMARK_ROOT, 'd4rl_policys.pkl')\n",
        "  baseline_paths = {}\n",
        "  baseline_paths['FQE-L2'] = os.path.join(BENCHMARK_ROOT, 'd4rl_fqel2.pkl')\n",
        "  baseline_paths['DICE'] = os.path.join(BENCHMARK_ROOT, 'd4rl_dice.pkl')\n",
        "  baseline_paths['DR'] = os.path.join(BENCHMARK_ROOT, 'd4rl_dr.pkl')\n",
        "  baseline_paths['IS'] = os.path.join(BENCHMARK_ROOT, 'd4rl_is.pkl')\n",
        "  baseline_paths['VPM'] = os.path.join(BENCHMARK_ROOT, 'd4rl_vpm.pkl')\n",
        "\n",
        "# Ground truth AND baseline pickle files are simple dicts with the format\n",
        "# key: policy_id\n",
        "# value: (Return average, Return standard deviation)\n",
        "with open(gt_path, 'rb') as f:\n",
        "  gt_data = pickle.load(f)\n",
        "\n",
        "with open(policy_path, 'rb') as f:\n",
        "  policy_dict = pickle.load(f)\n",
        "\n",
        "baselines = {}\n",
        "for baseline, path in baseline_paths.items():\n",
        "  with open(path, 'rb') as f:\n",
        "    baseline_data = pickle.load(f)\n",
        "  baselines[baseline] = baseline_data\n",
        "\n",
        "# Allowlist of policy ids.\n",
        "# Used to analyze results on a subset of the policies.\n",
        "# If None, analysis will be over all policies in policy_dict.\n",
        "allowlist = None\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9WWpgAOdZYHs"
      },
      "source": [
        "## Make plots"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6lsm0ehwO3c7"
      },
      "outputs": [],
      "source": [
        "OUTPUT_ROOT = '/tmp/figures'\n",
        "!mkdir {OUTPUT_ROOT}\n",
        "output_pattern = os.path.join(OUTPUT_ROOT, '{}_{}.pdf')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "i0c2oeVpOTzH"
      },
      "outputs": [],
      "source": [
        "#@title Scatterplots\n",
        "# setup\n",
        "if BENCHMARK == 'rlunplugged':\n",
        "  order = ['MB-AR', 'FQE-D', 'FQE-L2', 'MB-FF', 'DR', 'VPM', 'IS', 'DICE']\n",
        "  tasks_per_page = 9\n",
        "elif BENCHMARK == 'd4rl':\n",
        "  order = ['IS', 'DR', 'FQE-L2', 'VPM', 'DICE']\n",
        "  tasks_per_page = 7\n",
        "\n",
        "scatter_data = make_scatter_data(policy_dict,\n",
        "                                 gt_data,\n",
        "                                 baselines,\n",
        "                                 allowlist=allowlist)\n",
        "\n",
        "# Make scatter plot with pagination\n",
        "tasks = list(np.unique(scatter_data['task_name']))\n",
        "task_pages = list(chunks(tasks, tasks_per_page))\n",
        "for page_i, page in enumerate(task_pages):\n",
        "  mask = [t in page for t in scatter_data['task_name']]\n",
        "  scatter_copy = scatter_data[mask].copy()\n",
        "  p = plot_scatter(scatter_copy, order=order)\n",
        "  print(p)\n",
        "  output_path = output_pattern.format(BENCHMARK, 'scatter_{:02}'.format(page_i))\n",
        "  saveplot(p, output_path)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fHAfTlfB0_Q3"
      },
      "outputs": [],
      "source": [
        "#@title Absolute Error\n",
        "make_all_metric_plots(benchmark=BENCHMARK,\n",
        "                      metric_type='absolute_error',\n",
        "                      policy_dict=policy_dict,\n",
        "                      gt_data=gt_data,\n",
        "                      baselines=baselines,\n",
        "                      allowlist=allowlist)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qsqov36w1K7E"
      },
      "outputs": [],
      "source": [
        "#@title Rank Correlation\n",
        "make_all_metric_plots(benchmark=BENCHMARK,\n",
        "                      metric_type='rank_correlation',\n",
        "                      policy_dict=policy_dict,\n",
        "                      gt_data=gt_data,\n",
        "                      baselines=baselines,\n",
        "                      allowlist=allowlist)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UsQmc5XT1QcS"
      },
      "outputs": [],
      "source": [
        "#@title Normalized Regret\n",
        "make_all_metric_plots(benchmark=BENCHMARK,\n",
        "                      metric_type='normalized_regret',\n",
        "                      policy_dict=policy_dict,\n",
        "                      gt_data=gt_data,\n",
        "                      baselines=baselines,\n",
        "                      allowlist=allowlist)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "plots.ipynb"
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}