3-Benchmark-rtrgsyl.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "armed-jewelry",
   "metadata": {},
   "source": [
    "# About\n",
    "\n",
    "This notebooks aims to compare `rtrgsyl` with scipy's solver against scipy's solver alone. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "desirable-bobby",
   "metadata": {},
   "source": [
    "# Benchmark"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "guided-elements",
   "metadata": {},
   "source": [
    "## Utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "verified-exclusion",
   "metadata": {},
   "outputs": [],
   "source": [
    "from benchmark_utils import benchmark\n",
    "from utils import solve_sylvester_scipy\n",
    "from recursive import rtrgsyl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "organizational-contamination",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "numeric-morrison",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Format the results of the benchmark() function\n",
    "def format_results_bs(res_dic):\n",
    "    df = pd.DataFrame(res_dic)\n",
    "    df.time = df.time.apply(np.array)\n",
    "    df['time_schur'] = df.time.apply(lambda lst: [tpl[0] for tpl in lst])\n",
    "    df['time_solve'] = df.time.apply(lambda lst: [tpl[1] for tpl in lst])\n",
    "    df['time_back'] = df.time.apply(lambda lst: [tpl[2] for tpl in lst])\n",
    "    df.drop(columns='time', inplace=True)\n",
    "\n",
    "    for e in df.columns:\n",
    "        if e.startswith('time_'):\n",
    "            df[f'{e}_mean'] = df[e].apply(np.mean)\n",
    "            df[f'{e}_std'] = df[e].apply(np.std)\n",
    "    \n",
    "    df['m'] = df.dim.apply(lambda e: e[0])\n",
    "    df['n'] = df.dim.apply(lambda e: e[1])\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "major-treatment",
   "metadata": {},
   "source": [
    "## Vary matrix sizes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "prospective-cradle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(100, 100),\n",
       " (127, 127),\n",
       " (163, 163),\n",
       " (209, 209),\n",
       " (268, 268),\n",
       " (343, 343),\n",
       " (439, 439),\n",
       " (562, 562),\n",
       " (719, 719),\n",
       " (921, 921),\n",
       " (1178, 1178),\n",
       " (1508, 1508),\n",
       " (1930, 1930),\n",
       " (2470, 2470),\n",
       " (3162, 3162)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blks = 64\n",
    "nruns_min, nruns_max = (2, 15)\n",
    "dimensions = np.logspace(2, 3.5, 15)\n",
    "dimensions = [(int(e), int(e)) for e in dimensions]\n",
    "dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "explicit-clearing",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=(100, 100) 15 runs\n",
      "dim=(127, 127) 14 runs\n",
      "dim=(163, 163) 13 runs\n",
      "dim=(209, 209) 12 runs\n",
      "dim=(268, 268) 11 runs\n",
      "dim=(343, 343) 10 runs\n",
      "dim=(439, 439) 9 runs\n",
      "dim=(562, 562) 8 runs\n",
      "dim=(719, 719) 7 runs\n",
      "dim=(921, 921) 6 runs\n",
      "dim=(1178, 1178) 5 runs\n",
      "dim=(1508, 1508) 4 runs\n",
      "dim=(1930, 1930) 3 runs\n",
      "dim=(2470, 2470) 2 runs\n",
      "dim=(3162, 3162) 2 runs\n"
     ]
    }
   ],
   "source": [
    "res_rtrgsyl = benchmark(\n",
    "    solve_fun=rtrgsyl,\n",
    "    vary_param=('dim', dimensions),\n",
    "    bartel_stewart=True,\n",
    "    log_context={'solve_fun': 'rtrgsyl', 'std_solver': 'syl_scipy', 'bartel_stewart': True},\n",
    "    blks=blks,\n",
    "    std_solver=solve_sylvester_scipy,\n",
    "    n_runs=(nruns_min, nruns_max)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "informational-theater",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>blks</th>\n",
       "      <th>std_solver</th>\n",
       "      <th>dim</th>\n",
       "      <th>solve_fun</th>\n",
       "      <th>bartel_stewart</th>\n",
       "      <th>time_schur</th>\n",
       "      <th>time_solve</th>\n",
       "      <th>time_back</th>\n",
       "      <th>time_schur_mean</th>\n",
       "      <th>time_schur_std</th>\n",
       "      <th>time_solve_mean</th>\n",
       "      <th>time_solve_std</th>\n",
       "      <th>time_back_mean</th>\n",
       "      <th>time_back_std</th>\n",
       "      <th>m</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>64</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>(100, 100)</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>True</td>\n",
       "      <td>[0.016730546951293945, 0.014522552490234375, 0...</td>\n",
       "      <td>[0.026747703552246094, 0.007695198059082031, 0...</td>\n",
       "      <td>[0.005294084548950195, 0.0067424774169921875, ...</td>\n",
       "      <td>0.021964</td>\n",
       "      <td>0.004994</td>\n",
       "      <td>0.006151</td>\n",
       "      <td>0.005647</td>\n",
       "      <td>0.006246</td>\n",
       "      <td>0.008750</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>64</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>(127, 127)</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>True</td>\n",
       "      <td>[0.040088653564453125, 0.03577613830566406, 0....</td>\n",
       "      <td>[0.012207746505737305, 0.01077890396118164, 0....</td>\n",
       "      <td>[0.0021789073944091797, 0.0039479732513427734,...</td>\n",
       "      <td>0.047641</td>\n",
       "      <td>0.022062</td>\n",
       "      <td>0.009774</td>\n",
       "      <td>0.002046</td>\n",
       "      <td>0.006457</td>\n",
       "      <td>0.005144</td>\n",
       "      <td>127</td>\n",
       "      <td>127</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   blks std_solver         dim solve_fun  bartel_stewart  \\\n",
       "0    64  syl_scipy  (100, 100)   rtrgsyl            True   \n",
       "1    64  syl_scipy  (127, 127)   rtrgsyl            True   \n",
       "\n",
       "                                          time_schur  \\\n",
       "0  [0.016730546951293945, 0.014522552490234375, 0...   \n",
       "1  [0.040088653564453125, 0.03577613830566406, 0....   \n",
       "\n",
       "                                          time_solve  \\\n",
       "0  [0.026747703552246094, 0.007695198059082031, 0...   \n",
       "1  [0.012207746505737305, 0.01077890396118164, 0....   \n",
       "\n",
       "                                           time_back  time_schur_mean  \\\n",
       "0  [0.005294084548950195, 0.0067424774169921875, ...         0.021964   \n",
       "1  [0.0021789073944091797, 0.0039479732513427734,...         0.047641   \n",
       "\n",
       "   time_schur_std  time_solve_mean  time_solve_std  time_back_mean  \\\n",
       "0        0.004994         0.006151        0.005647        0.006246   \n",
       "1        0.022062         0.009774        0.002046        0.006457   \n",
       "\n",
       "   time_back_std    m    n  \n",
       "0       0.008750  100  100  \n",
       "1       0.005144  127  127  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_rtrgsyl = format_results_bs(res_rtrgsyl)\n",
    "df_rtrgsyl.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "rapid-premiere",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim=(100, 100) 15 runs\n",
      "dim=(127, 127) 14 runs\n",
      "dim=(163, 163) 13 runs\n",
      "dim=(209, 209) 12 runs\n",
      "dim=(268, 268) 11 runs\n",
      "dim=(343, 343) 10 runs\n",
      "dim=(439, 439) 9 runs\n",
      "dim=(562, 562) 8 runs\n",
      "dim=(719, 719) 7 runs\n",
      "dim=(921, 921) 6 runs\n",
      "dim=(1178, 1178) 5 runs\n",
      "dim=(1508, 1508) 4 runs\n",
      "dim=(1930, 1930) 3 runs\n",
      "WARNING: incorrect solution, retrying...\n",
      "dim=(2470, 2470) 2 runs\n",
      "dim=(3162, 3162) 2 runs\n"
     ]
    }
   ],
   "source": [
    "res_scipy = benchmark(\n",
    "    solve_fun=solve_sylvester_scipy,\n",
    "    vary_param=('dim', dimensions),\n",
    "    bartel_stewart=True,\n",
    "    log_context={'solve_fun': 'syl_scipy', 'bartel_stewart': True},\n",
    "    n_runs=(nruns_min, nruns_max)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "short-happening",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dim</th>\n",
       "      <th>solve_fun</th>\n",
       "      <th>bartel_stewart</th>\n",
       "      <th>time_schur</th>\n",
       "      <th>time_solve</th>\n",
       "      <th>time_back</th>\n",
       "      <th>time_schur_mean</th>\n",
       "      <th>time_schur_std</th>\n",
       "      <th>time_solve_mean</th>\n",
       "      <th>time_solve_std</th>\n",
       "      <th>time_back_mean</th>\n",
       "      <th>time_back_std</th>\n",
       "      <th>m</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(100, 100)</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>True</td>\n",
       "      <td>[0.018348217010498047, 0.012748003005981445, 0...</td>\n",
       "      <td>[0.0065762996673583984, 0.007719993591308594, ...</td>\n",
       "      <td>[0.00010848045349121094, 0.0001044273376464843...</td>\n",
       "      <td>0.012294</td>\n",
       "      <td>0.001888</td>\n",
       "      <td>0.008063</td>\n",
       "      <td>0.001689</td>\n",
       "      <td>0.000106</td>\n",
       "      <td>0.000008</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(127, 127)</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>True</td>\n",
       "      <td>[0.02109527587890625, 0.02344059944152832, 0.0...</td>\n",
       "      <td>[0.012962579727172852, 0.012353181838989258, 0...</td>\n",
       "      <td>[0.0001888275146484375, 0.00019216537475585938...</td>\n",
       "      <td>0.023765</td>\n",
       "      <td>0.005186</td>\n",
       "      <td>0.014435</td>\n",
       "      <td>0.003145</td>\n",
       "      <td>0.000195</td>\n",
       "      <td>0.000049</td>\n",
       "      <td>127</td>\n",
       "      <td>127</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          dim  solve_fun  bartel_stewart  \\\n",
       "0  (100, 100)  syl_scipy            True   \n",
       "1  (127, 127)  syl_scipy            True   \n",
       "\n",
       "                                          time_schur  \\\n",
       "0  [0.018348217010498047, 0.012748003005981445, 0...   \n",
       "1  [0.02109527587890625, 0.02344059944152832, 0.0...   \n",
       "\n",
       "                                          time_solve  \\\n",
       "0  [0.0065762996673583984, 0.007719993591308594, ...   \n",
       "1  [0.012962579727172852, 0.012353181838989258, 0...   \n",
       "\n",
       "                                           time_back  time_schur_mean  \\\n",
       "0  [0.00010848045349121094, 0.0001044273376464843...         0.012294   \n",
       "1  [0.0001888275146484375, 0.00019216537475585938...         0.023765   \n",
       "\n",
       "   time_schur_std  time_solve_mean  time_solve_std  time_back_mean  \\\n",
       "0        0.001888         0.008063        0.001689        0.000106   \n",
       "1        0.005186         0.014435        0.003145        0.000195   \n",
       "\n",
       "   time_back_std    m    n  \n",
       "0       0.000008  100  100  \n",
       "1       0.000049  127  127  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scipy = format_results_bs(res_scipy)\n",
    "df_scipy.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "duplicate-kennedy",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(df_rtrgsyl.n, df_rtrgsyl.time_solve_mean, '-o', label='rtrgsyl')\n",
    "plt.loglog(df_scipy.n, df_scipy.time_solve_mean, '-o', label='rtrgsyl')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "corrected-wisconsin",
   "metadata": {},
   "source": [
    "## Save results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "august-gross",
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "\n",
    "res_dump = res_rtrgsyl + res_scipy\n",
    "\n",
    "with open('res/benchmark_rtrgsyl.json', 'w') as f:\n",
    "    json.dump(res_dump, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "contemporary-cologne",
   "metadata": {},
   "source": [
    "# Produce plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "relative-assist",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: Support for setting the 'text.latex.preamble' or 'pgf.preamble' rcParam to a list of strings is deprecated since 3.3 and will be removed two minor releases later; set it to a single string instead.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: \n",
      "The text.latex.preview rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: \n",
      "The mathtext.fallback_to_cm rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: Support for setting the 'mathtext.fallback_to_cm' rcParam is deprecated since 3.3 and will be removed two minor releases later; use 'mathtext.fallback : 'cm' instead.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: \n",
      "The validate_bool_maybe_none function was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: \n",
      "The savefig.jpeg_quality rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: \n",
      "The animation.html_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "  mpl.rcParams[key] = val\n",
      "/home/maousi/miniconda3/envs/ada/lib/python3.9/site-packages/ipypublish/scripts/nb_setup.py:226: MatplotlibDeprecationWarning: \n",
      "The animation.avconv_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "  mpl.rcParams[key] = val\n"
     ]
    }
   ],
   "source": [
    "from ipypublish import nb_setup\n",
    "plt = nb_setup.setup_matplotlib()\n",
    "import seaborn as sns\n",
    "sns.set(style='whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "amazing-valuation",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_multiple_runs(df, x, y, ystd, label, color):\n",
    "    plt.plot(df[x], df[y], '-o', label=label, color=color)\n",
    "    plt.fill_between(df[x], df[y] - df[ystd], df[y] + df[ystd], alpha=.4, color=color)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "worthy-tanzania",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"215.117632pt\" version=\"1.1\" viewBox=\"0 0 396.831756 215.117632\" width=\"396.831756pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2021-06-06T13:29:39.715165</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.4, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 215.117632 \n",
       "L 396.831756 215.117632 \n",
       "L 396.831756 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 54.831756 173.52 \n",
       "L 389.631756 173.52 \n",
       "L 389.631756 7.2 \n",
       "L 54.831756 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 70.049938 173.52 \n",
       "L 70.049938 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- $\\mathdefault{10^{2}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(62.386302 191.159962)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 26.59375 63.40625 \n",
       "C 26.59375 65.5 26.5 65.5 25.09375 65.5 \n",
       "C 21.203125 61.1875 15.296875 59.796875 9.703125 59.796875 \n",
       "C 9.40625 59.796875 8.90625 59.796875 8.796875 59.5 \n",
       "C 8.703125 59.296875 8.703125 59.09375 8.703125 57 \n",
       "C 11.796875 57 17 57.59375 21 59.984375 \n",
       "L 21 7.203125 \n",
       "C 21 3.6875 20.796875 2.5 12.203125 2.5 \n",
       "L 9.203125 2.5 \n",
       "L 9.203125 0 \n",
       "C 14 0 19 0 23.796875 0 \n",
       "C 28.59375 0 33.59375 0 38.40625 0 \n",
       "L 38.40625 2.5 \n",
       "L 35.40625 2.5 \n",
       "C 26.796875 2.5 26.59375 3.59375 26.59375 7.15625 \n",
       "z\n",
       "\" id=\"CMR17-49\"/>\n",
       "        <path d=\"M 42 31.640625 \n",
       "C 42 37.75 41.90625 48.125 37.703125 56.109375 \n",
       "C 34 63.109375 28.09375 65.59375 22.90625 65.59375 \n",
       "C 18.09375 65.59375 12 63.40625 8.203125 56.203125 \n",
       "C 4.203125 48.71875 3.796875 39.4375 3.796875 31.640625 \n",
       "C 3.796875 25.953125 3.90625 17.28125 7 9.671875 \n",
       "C 11.296875 -0.609375 19 -2 22.90625 -2 \n",
       "C 27.5 -2 34.5 -0.109375 38.59375 9.375 \n",
       "C 41.59375 16.28125 42 24.359375 42 31.640625 \n",
       "z\n",
       "M 22.90625 -0.40625 \n",
       "C 16.5 -0.40625 12.703125 5.078125 11.296875 12.6875 \n",
       "C 10.203125 18.5625 10.203125 27.15625 10.203125 32.75 \n",
       "C 10.203125 40.4375 10.203125 46.828125 11.5 52.921875 \n",
       "C 13.40625 61.390625 19 64 22.90625 64 \n",
       "C 27 64 32.296875 61.296875 34.203125 53.125 \n",
       "C 35.5 47.4375 35.59375 40.734375 35.59375 32.75 \n",
       "C 35.59375 26.25 35.59375 18.265625 34.40625 12.375 \n",
       "C 32.296875 1.484375 26.40625 -0.40625 22.90625 -0.40625 \n",
       "z\n",
       "\" id=\"CMR17-48\"/>\n",
       "        <path d=\"M 41.703125 15.453125 \n",
       "L 39.90625 15.453125 \n",
       "C 38.90625 8.375 38.09375 7.171875 37.703125 6.5625 \n",
       "C 37.203125 5.765625 30 5.765625 28.59375 5.765625 \n",
       "L 9.40625 5.765625 \n",
       "C 13 9.671875 20 16.75 28.5 24.953125 \n",
       "C 34.59375 30.734375 41.703125 37.53125 41.703125 47.421875 \n",
       "C 41.703125 59.21875 32.296875 66 21.796875 66 \n",
       "C 10.796875 66 4.09375 56.3125 4.09375 47.34375 \n",
       "C 4.09375 43.4375 7 42.9375 8.203125 42.9375 \n",
       "C 9.203125 42.9375 12.203125 43.546875 12.203125 47.03125 \n",
       "C 12.203125 50.109375 9.59375 51 8.203125 51 \n",
       "C 7.59375 51 7 50.90625 6.59375 50.703125 \n",
       "C 8.5 59.21875 14.296875 63.40625 20.40625 63.40625 \n",
       "C 29.09375 63.40625 34.796875 56.515625 34.796875 47.421875 \n",
       "C 34.796875 38.734375 29.703125 31.25 24 24.75 \n",
       "L 4.09375 2.28125 \n",
       "L 4.09375 0 \n",
       "L 39.296875 0 \n",
       "z\n",
       "\" id=\"CMR17-50\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 272.964188 173.52 \n",
       "L 272.964188 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- $\\mathdefault{10^{3}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(265.300551 191.159962)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 22.09375 33.703125 \n",
       "C 31 33.703125 34.90625 25.96875 34.90625 17.03125 \n",
       "C 34.90625 5 28.5 0.390625 22.703125 0.390625 \n",
       "C 17.40625 0.390625 8.796875 3.03125 6.09375 10.828125 \n",
       "C 6.59375 10.625 7.09375 10.625 7.59375 10.625 \n",
       "C 10 10.625 11.796875 12.21875 11.796875 14.8125 \n",
       "C 11.796875 17.703125 9.59375 19 7.59375 19 \n",
       "C 5.90625 19 3.296875 18.203125 3.296875 14.46875 \n",
       "C 3.296875 5.234375 12.296875 -2 22.90625 -2 \n",
       "C 34 -2 42.5 6.71875 42.5 16.953125 \n",
       "C 42.5 26.671875 34.5 33.703125 25 34.796875 \n",
       "C 32.59375 36.375 39.90625 43.0625 39.90625 52.015625 \n",
       "C 39.90625 59.6875 32 65.296875 23 65.296875 \n",
       "C 13.90625 65.296875 5.90625 59.828125 5.90625 52.015625 \n",
       "C 5.90625 48.59375 8.5 48 9.796875 48 \n",
       "C 11.90625 48 13.703125 49.296875 13.703125 51.890625 \n",
       "C 13.703125 54.46875 11.90625 55.765625 9.796875 55.765625 \n",
       "C 9.40625 55.765625 8.90625 55.765625 8.5 55.578125 \n",
       "C 11.40625 61.859375 19.296875 63 22.796875 63 \n",
       "C 26.296875 63 32.90625 61.328125 32.90625 51.875 \n",
       "C 32.90625 49.109375 32.5 44.1875 29.09375 39.84375 \n",
       "C 26.09375 36 22.703125 36 19.40625 35.6875 \n",
       "C 18.90625 35.6875 16.59375 35.453125 16.203125 35.453125 \n",
       "C 15.5 35.359375 15.09375 35.265625 15.09375 34.5 \n",
       "C 15.09375 33.796875 15.203125 33.703125 17.203125 33.703125 \n",
       "z\n",
       "\" id=\"CMR17-51\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\"/>\n",
       "    <g id=\"xtick_4\"/>\n",
       "    <g id=\"xtick_5\"/>\n",
       "    <g id=\"xtick_6\"/>\n",
       "    <g id=\"xtick_7\"/>\n",
       "    <g id=\"xtick_8\"/>\n",
       "    <g id=\"xtick_9\"/>\n",
       "    <g id=\"xtick_10\"/>\n",
       "    <g id=\"xtick_11\"/>\n",
       "    <g id=\"xtick_12\"/>\n",
       "    <g id=\"xtick_13\"/>\n",
       "    <g id=\"text_3\">\n",
       "     <!-- $n$ -->\n",
       "     <g style=\"fill:#262626;\" transform=\"translate(218.737953 205.593036)scale(0.12 -0.12)\">\n",
       "      <defs>\n",
       "       <path d=\"M 20.59375 29.234375 \n",
       "C 20.796875 29.84375 23.296875 34.828125 27 38.015625 \n",
       "C 29.59375 40.40625 33 42.015625 36.90625 42.015625 \n",
       "C 40.90625 42.015625 42.296875 39.015625 42.296875 35.03125 \n",
       "C 42.296875 29.34375 38.203125 17.96875 36.203125 12.578125 \n",
       "C 35.296875 10.171875 34.796875 8.875 34.796875 7.078125 \n",
       "C 34.796875 2.59375 37.90625 -1 42.703125 -1 \n",
       "C 52 -1 55.5 13.671875 55.5 14.265625 \n",
       "C 55.5 14.765625 55.09375 15.171875 54.5 15.171875 \n",
       "C 53.59375 15.171875 53.5 14.875 53 13.171875 \n",
       "C 50.703125 4.984375 46.90625 1 43 1 \n",
       "C 42 1 40.40625 1 40.40625 4.203125 \n",
       "C 40.40625 6.703125 41.5 9.703125 42.09375 11.09375 \n",
       "C 44.09375 16.609375 48.296875 27.8125 48.296875 33.515625 \n",
       "C 48.296875 39.5 44.796875 44 37.203125 44 \n",
       "C 28.296875 44 23.59375 37.734375 21.796875 35.234375 \n",
       "C 21.5 40.90625 17.40625 44 13 44 \n",
       "C 9.796875 44 7.59375 42.109375 5.90625 38.71875 \n",
       "C 4.09375 35.125 2.703125 29.140625 2.703125 28.734375 \n",
       "C 2.703125 28.34375 3.09375 27.84375 3.796875 27.84375 \n",
       "C 4.59375 27.84375 4.703125 27.9375 5.296875 30.234375 \n",
       "C 6.90625 36.328125 8.703125 42.015625 12.703125 42.015625 \n",
       "C 15 42.015625 15.796875 40.40625 15.796875 37.421875 \n",
       "C 15.796875 35.21875 14.796875 31.328125 14.09375 28.234375 \n",
       "L 11.296875 17.46875 \n",
       "C 10.90625 15.5625 9.796875 11.078125 9.296875 9.28125 \n",
       "C 8.59375 6.6875 7.5 2 7.5 1.5 \n",
       "C 7.5 0.09375 8.59375 -1 10.09375 -1 \n",
       "C 11.296875 -1 12.703125 -0.40625 13.5 1.09375 \n",
       "C 13.703125 1.59375 14.59375 5.09375 15.09375 7.078125 \n",
       "L 17.296875 16.0625 \n",
       "z\n",
       "\" id=\"CMMI12-110\"/>\n",
       "      </defs>\n",
       "      <use transform=\"scale(0.996264)\" xlink:href=\"#CMMI12-110\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 54.831756 157.368048 \n",
       "L 389.631756 157.368048 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- $\\mathdefault{10^{-3}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(23.155168 161.438029)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 65.90625 23 \n",
       "C 67.59375 23 69.40625 23 69.40625 25 \n",
       "C 69.40625 27 67.59375 27 65.90625 27 \n",
       "L 11.796875 27 \n",
       "C 10.09375 27 8.296875 27 8.296875 25 \n",
       "C 8.296875 23 10.09375 23 11.796875 23 \n",
       "z\n",
       "\" id=\"CMSY10-0\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMSY10-0\"/>\n",
       "       <use transform=\"translate(145.621947 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 54.831756 128.444084 \n",
       "L 389.631756 128.444084 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- $\\mathdefault{10^{-2}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(23.155168 132.514065)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMSY10-0\"/>\n",
       "       <use transform=\"translate(145.621947 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 54.831756 99.52012 \n",
       "L 389.631756 99.52012 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- $\\mathdefault{10^{-1}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(23.155168 103.590101)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMSY10-0\"/>\n",
       "       <use transform=\"translate(145.621947 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 54.831756 70.596157 \n",
       "L 389.631756 70.596157 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- $\\mathdefault{10^{0}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(30.004483 74.666137)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 54.831756 41.672193 \n",
       "L 389.631756 41.672193 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- $\\mathdefault{10^{1}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(30.004483 45.742174)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <path clip-path=\"url(#p021f73b3f4)\" d=\"M 54.831756 12.748229 \n",
       "L 389.631756 12.748229 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- $\\mathdefault{10^{2}}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(30.004483 16.81821)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "       <use transform=\"translate(91.380954 44.560802)scale(0.697382)\" xlink:href=\"#CMR17-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\"/>\n",
       "    <g id=\"ytick_8\"/>\n",
       "    <g id=\"ytick_9\"/>\n",
       "    <g id=\"ytick_10\"/>\n",
       "    <g id=\"ytick_11\"/>\n",
       "    <g id=\"ytick_12\"/>\n",
       "    <g id=\"ytick_13\"/>\n",
       "    <g id=\"ytick_14\"/>\n",
       "    <g id=\"ytick_15\"/>\n",
       "    <g id=\"ytick_16\"/>\n",
       "    <g id=\"ytick_17\"/>\n",
       "    <g id=\"ytick_18\"/>\n",
       "    <g id=\"ytick_19\"/>\n",
       "    <g id=\"ytick_20\"/>\n",
       "    <g id=\"ytick_21\"/>\n",
       "    <g id=\"ytick_22\"/>\n",
       "    <g id=\"ytick_23\"/>\n",
       "    <g id=\"ytick_24\"/>\n",
       "    <g id=\"ytick_25\"/>\n",
       "    <g id=\"ytick_26\"/>\n",
       "    <g id=\"ytick_27\"/>\n",
       "    <g id=\"ytick_28\"/>\n",
       "    <g id=\"ytick_29\"/>\n",
       "    <g id=\"ytick_30\"/>\n",
       "    <g id=\"ytick_31\"/>\n",
       "    <g id=\"ytick_32\"/>\n",
       "    <g id=\"ytick_33\"/>\n",
       "    <g id=\"ytick_34\"/>\n",
       "    <g id=\"ytick_35\"/>\n",
       "    <g id=\"ytick_36\"/>\n",
       "    <g id=\"ytick_37\"/>\n",
       "    <g id=\"ytick_38\"/>\n",
       "    <g id=\"ytick_39\"/>\n",
       "    <g id=\"ytick_40\"/>\n",
       "    <g id=\"ytick_41\"/>\n",
       "    <g id=\"ytick_42\"/>\n",
       "    <g id=\"ytick_43\"/>\n",
       "    <g id=\"ytick_44\"/>\n",
       "    <g id=\"ytick_45\"/>\n",
       "    <g id=\"ytick_46\"/>\n",
       "    <g id=\"ytick_47\"/>\n",
       "    <g id=\"ytick_48\"/>\n",
       "    <g id=\"ytick_49\"/>\n",
       "    <g id=\"ytick_50\"/>\n",
       "    <g id=\"ytick_51\"/>\n",
       "    <g id=\"ytick_52\"/>\n",
       "    <g id=\"ytick_53\"/>\n",
       "    <g id=\"text_10\">\n",
       "     <!-- Time [s] -->\n",
       "     <g style=\"fill:#262626;\" transform=\"translate(16.166376 110.536201)rotate(-90)scale(0.12 -0.12)\">\n",
       "      <defs>\n",
       "       <path d=\"M 36.203125 62 \n",
       "L 44.5 62 \n",
       "C 45.703125 62 46.90625 62 48.09375 62 \n",
       "L 60.59375 62 \n",
       "L 60.59375 68.375 \n",
       "L 3.40625 68.375 \n",
       "L 3.40625 62 \n",
       "L 15.90625 62 \n",
       "C 17.09375 62 18.296875 62 19.5 62 \n",
       "L 27.796875 62 \n",
       "L 27.796875 -0.5 \n",
       "L 36.203125 -0.5 \n",
       "z\n",
       "\" id=\"CMSS17-84\"/>\n",
       "       <path d=\"M 15.296875 65.359375 \n",
       "L 6.90625 65.359375 \n",
       "L 6.90625 57 \n",
       "L 15.296875 57 \n",
       "z\n",
       "M 14.796875 42.796875 \n",
       "L 7.40625 42.796875 \n",
       "L 7.40625 0 \n",
       "L 14.796875 0 \n",
       "z\n",
       "\" id=\"CMSS17-105\"/>\n",
       "       <path d=\"M 67 29.328125 \n",
       "C 67 36.0625 65.296875 44 54.09375 44 \n",
       "C 46.59375 44 42.09375 39.3125 40.09375 36.421875 \n",
       "C 38.296875 41.71875 34.09375 44 28.09375 44 \n",
       "C 21.296875 44 17 40.125 14.703125 37.328125 \n",
       "L 14.703125 43.09375 \n",
       "L 7.40625 43.09375 \n",
       "L 7.40625 0 \n",
       "L 15 0 \n",
       "L 15 24.359375 \n",
       "C 15 30.296875 17.203125 37.9375 24.296875 37.9375 \n",
       "C 33.40625 37.9375 33.40625 31.5 33.40625 28.578125 \n",
       "L 33.40625 0 \n",
       "L 41 0 \n",
       "L 41 24.359375 \n",
       "C 41 30.296875 43.203125 37.9375 50.296875 37.9375 \n",
       "C 59.40625 37.9375 59.40625 31.5 59.40625 28.578125 \n",
       "L 59.40625 0 \n",
       "L 67 0 \n",
       "z\n",
       "\" id=\"CMSS17-109\"/>\n",
       "       <path d=\"M 39.09375 21.515625 \n",
       "C 39.09375 24.84375 38.90625 31.296875 35.703125 36.640625 \n",
       "C 32.203125 42.390625 26.5 44 22.203125 44 \n",
       "C 11.796875 44 3 34.1875 3 21.484375 \n",
       "C 3 9.09375 12.09375 -1 23.59375 -1 \n",
       "C 28.09375 -1 33.59375 0.296875 38.59375 3.875 \n",
       "C 38.59375 4.28125 38.40625 6.46875 38.296875 6.5625 \n",
       "C 38.296875 6.765625 38 9.84375 38 10.25 \n",
       "C 33.203125 6.359375 27.703125 5.078125 23.703125 5.078125 \n",
       "C 17.296875 5.078125 10.40625 10.421875 10.09375 21.515625 \n",
       "z\n",
       "M 10.90625 27 \n",
       "C 12.203125 32.5625 16.59375 37.828125 22.203125 37.828125 \n",
       "C 23.703125 37.828125 30.703125 37.828125 32.5 27 \n",
       "z\n",
       "\" id=\"CMSS17-101\"/>\n",
       "       <path d=\"M 25.203125 -25 \n",
       "L 25.203125 -18.9375 \n",
       "L 16.59375 -18.9375 \n",
       "L 16.59375 68 \n",
       "L 25.203125 68 \n",
       "L 25.203125 74.078125 \n",
       "L 9.296875 74.078125 \n",
       "L 9.296875 -25 \n",
       "z\n",
       "\" id=\"CMSS17-91\"/>\n",
       "       <path d=\"M 32.203125 41.046875 \n",
       "C 26.296875 43.859375 21.703125 43.859375 18.703125 43.859375 \n",
       "C 11.59375 43.859375 3.09375 41.375 3.09375 31.296875 \n",
       "C 3.09375 21.234375 14.09375 19.03125 17.09375 18.421875 \n",
       "C 21.703125 17.53125 26.796875 16.53125 26.796875 11.5625 \n",
       "C 26.796875 5.265625 19.59375 5.265625 18.296875 5.265625 \n",
       "C 14.296875 5.265625 8.796875 6.359375 3.796875 9.96875 \n",
       "L 2.59375 3.28125 \n",
       "C 8.296875 0 13.796875 -1 18.40625 -1 \n",
       "C 30.703125 -1 33.796875 6.5 33.796875 12.203125 \n",
       "C 33.796875 17.09375 31 20.390625 29.09375 21.890625 \n",
       "C 25.796875 24.5 24.59375 24.796875 16.40625 26.5 \n",
       "C 15 26.703125 10.09375 27.796875 10.09375 32.28125 \n",
       "C 10.09375 38 16.40625 38 17.796875 38 \n",
       "C 24.296875 38 28.296875 35.984375 31 34.5 \n",
       "z\n",
       "\" id=\"CMSS17-115\"/>\n",
       "       <path d=\"M 17.90625 74.078125 \n",
       "L 2 74.078125 \n",
       "L 2 68 \n",
       "L 10.59375 68 \n",
       "L 10.59375 -18.9375 \n",
       "L 2 -18.9375 \n",
       "L 2 -25 \n",
       "L 17.90625 -25 \n",
       "z\n",
       "\" id=\"CMSS17-93\"/>\n",
       "      </defs>\n",
       "      <use transform=\"scale(0.996264)\" xlink:href=\"#CMSS17-84\"/>\n",
       "      <use transform=\"translate(63.819454 0)scale(0.996264)\" xlink:href=\"#CMSS17-105\"/>\n",
       "      <use transform=\"translate(86.000177 0)scale(0.996264)\" xlink:href=\"#CMSS17-109\"/>\n",
       "      <use transform=\"translate(160.229431 0)scale(0.996264)\" xlink:href=\"#CMSS17-101\"/>\n",
       "      <use transform=\"translate(233.097366 0)scale(0.996264)\" xlink:href=\"#CMSS17-91\"/>\n",
       "      <use transform=\"translate(260.282805 0)scale(0.996264)\" xlink:href=\"#CMSS17-115\"/>\n",
       "      <use transform=\"translate(296.196347 0)scale(0.996264)\" xlink:href=\"#CMSS17-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_1\">\n",
       "    <defs>\n",
       "     <path d=\"M 70.049938 -88.750622 \n",
       "L 70.049938 -49.157632 \n",
       "L 91.113192 -83.437075 \n",
       "L 113.105827 -75.973593 \n",
       "L 135.012182 -98.586697 \n",
       "L 156.924589 -101.963305 \n",
       "L 178.668743 -106.546156 \n",
       "L 200.415144 -115.280639 \n",
       "L 222.18212 -120.648529 \n",
       "L 243.892438 -128.542983 \n",
       "L 265.711957 -132.06557 \n",
       "L 287.400581 -139.726812 \n",
       "L 309.164362 -144.973412 \n",
       "L 330.907835 -152.414271 \n",
       "L 352.647995 -158.498561 \n",
       "L 374.413574 -163.936819 \n",
       "L 374.413574 -164.138508 \n",
       "L 374.413574 -164.138508 \n",
       "L 352.647995 -159.260395 \n",
       "L 330.907835 -153.023549 \n",
       "L 309.164362 -146.40284 \n",
       "L 287.400581 -142.866888 \n",
       "L 265.711957 -137.363782 \n",
       "L 243.892438 -129.333182 \n",
       "L 222.18212 -123.35666 \n",
       "L 200.415144 -120.598607 \n",
       "L 178.668743 -111.889204 \n",
       "L 156.924589 -110.870778 \n",
       "L 135.012182 -107.850064 \n",
       "L 113.105827 -103.17345 \n",
       "L 91.113192 -88.774038 \n",
       "L 70.049938 -88.750622 \n",
       "z\n",
       "\" id=\"m7d99bfbed1\" style=\"stroke:#4c72b0;stroke-opacity:0.4;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p021f73b3f4)\">\n",
       "     <use style=\"fill:#4c72b0;fill-opacity:0.4;stroke:#4c72b0;stroke-opacity:0.4;\" x=\"0\" xlink:href=\"#m7d99bfbed1\" y=\"215.117632\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_2\">\n",
       "    <defs>\n",
       "     <path d=\"M 70.049938 -86.358356 \n",
       "L 70.049938 -81.016151 \n",
       "L 91.113192 -88.197502 \n",
       "L 113.105827 -97.593217 \n",
       "L 135.012182 -111.288009 \n",
       "L 156.924589 -112.179404 \n",
       "L 178.668743 -118.069219 \n",
       "L 200.415144 -127.101412 \n",
       "L 222.18212 -133.310322 \n",
       "L 243.892438 -146.4826 \n",
       "L 265.711957 -150.865581 \n",
       "L 287.400581 -159.587473 \n",
       "L 309.164362 -168.619501 \n",
       "L 330.907835 -178.816615 \n",
       "L 352.647995 -188.724766 \n",
       "L 374.413574 -199.950223 \n",
       "L 374.413574 -200.357632 \n",
       "L 374.413574 -200.357632 \n",
       "L 352.647995 -188.97739 \n",
       "L 330.907835 -179.395339 \n",
       "L 309.164362 -171.341357 \n",
       "L 287.400581 -161.34026 \n",
       "L 265.711957 -152.492161 \n",
       "L 243.892438 -150.033216 \n",
       "L 222.18212 -136.630249 \n",
       "L 200.415144 -130.378367 \n",
       "L 178.668743 -122.118278 \n",
       "L 156.924589 -119.264331 \n",
       "L 135.012182 -116.152687 \n",
       "L 113.105827 -104.04273 \n",
       "L 91.113192 -93.760159 \n",
       "L 70.049938 -86.358356 \n",
       "z\n",
       "\" id=\"md6ae58abac\" style=\"stroke:#dd8452;stroke-opacity:0.4;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p021f73b3f4)\">\n",
       "     <use style=\"fill:#dd8452;fill-opacity:0.4;stroke:#dd8452;stroke-opacity:0.4;\" x=\"0\" xlink:href=\"#md6ae58abac\" y=\"215.117632\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_9\">\n",
       "    <path clip-path=\"url(#p021f73b3f4)\" d=\"M 70.049938 134.547911 \n",
       "L 91.113192 128.730745 \n",
       "L 113.105827 119.287033 \n",
       "L 135.012182 111.064029 \n",
       "L 156.924589 107.927053 \n",
       "L 178.668743 105.617985 \n",
       "L 200.415144 96.898663 \n",
       "L 222.18212 93.042198 \n",
       "L 243.892438 86.173337 \n",
       "L 265.711957 80.125667 \n",
       "L 287.400581 73.722918 \n",
       "L 309.164362 69.409184 \n",
       "L 330.907835 62.395028 \n",
       "L 352.647995 56.232379 \n",
       "L 374.413574 51.079563 \n",
       "\" style=\"fill:none;stroke:#4c72b0;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"mbfad4b4d6b\" style=\"stroke:#4c72b0;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p021f73b3f4)\">\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"70.049938\" xlink:href=\"#mbfad4b4d6b\" y=\"134.547911\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"91.113192\" xlink:href=\"#mbfad4b4d6b\" y=\"128.730745\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"113.105827\" xlink:href=\"#mbfad4b4d6b\" y=\"119.287033\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"135.012182\" xlink:href=\"#mbfad4b4d6b\" y=\"111.064029\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"156.924589\" xlink:href=\"#mbfad4b4d6b\" y=\"107.927053\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"178.668743\" xlink:href=\"#mbfad4b4d6b\" y=\"105.617985\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"200.415144\" xlink:href=\"#mbfad4b4d6b\" y=\"96.898663\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"222.18212\" xlink:href=\"#mbfad4b4d6b\" y=\"93.042198\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"243.892438\" xlink:href=\"#mbfad4b4d6b\" y=\"86.173337\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"265.711957\" xlink:href=\"#mbfad4b4d6b\" y=\"80.125667\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"287.400581\" xlink:href=\"#mbfad4b4d6b\" y=\"73.722918\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"309.164362\" xlink:href=\"#mbfad4b4d6b\" y=\"69.409184\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"330.907835\" xlink:href=\"#mbfad4b4d6b\" y=\"62.395028\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"352.647995\" xlink:href=\"#mbfad4b4d6b\" y=\"56.232379\"/>\n",
       "     <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"374.413574\" xlink:href=\"#mbfad4b4d6b\" y=\"51.079563\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_10\">\n",
       "    <path clip-path=\"url(#p021f73b3f4)\" d=\"M 70.049938 131.148499 \n",
       "L 91.113192 123.833369 \n",
       "L 113.105827 113.890202 \n",
       "L 135.012182 101.163249 \n",
       "L 156.924589 98.902744 \n",
       "L 178.668743 94.861439 \n",
       "L 200.415144 86.271185 \n",
       "L 222.18212 80.037984 \n",
       "L 243.892438 66.734688 \n",
       "L 265.711957 63.412451 \n",
       "L 287.400581 54.623218 \n",
       "L 309.164362 45.063625 \n",
       "L 330.907835 36.008322 \n",
       "L 352.647995 26.265919 \n",
       "L 374.413574 14.962053 \n",
       "\" style=\"fill:none;stroke:#dd8452;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m6d75e0a010\" style=\"stroke:#dd8452;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p021f73b3f4)\">\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"70.049938\" xlink:href=\"#m6d75e0a010\" y=\"131.148499\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"91.113192\" xlink:href=\"#m6d75e0a010\" y=\"123.833369\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"113.105827\" xlink:href=\"#m6d75e0a010\" y=\"113.890202\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"135.012182\" xlink:href=\"#m6d75e0a010\" y=\"101.163249\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"156.924589\" xlink:href=\"#m6d75e0a010\" y=\"98.902744\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"178.668743\" xlink:href=\"#m6d75e0a010\" y=\"94.861439\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"200.415144\" xlink:href=\"#m6d75e0a010\" y=\"86.271185\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"222.18212\" xlink:href=\"#m6d75e0a010\" y=\"80.037984\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"243.892438\" xlink:href=\"#m6d75e0a010\" y=\"66.734688\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"265.711957\" xlink:href=\"#m6d75e0a010\" y=\"63.412451\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"287.400581\" xlink:href=\"#m6d75e0a010\" y=\"54.623218\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"309.164362\" xlink:href=\"#m6d75e0a010\" y=\"45.063625\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"330.907835\" xlink:href=\"#m6d75e0a010\" y=\"36.008322\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"352.647995\" xlink:href=\"#m6d75e0a010\" y=\"26.265919\"/>\n",
       "     <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"374.413574\" xlink:href=\"#m6d75e0a010\" y=\"14.962053\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_11\">\n",
       "    <path clip-path=\"url(#p021f73b3f4)\" d=\"M 70.049938 129.641325 \n",
       "L 374.413574 42.871639 \n",
       "\" style=\"fill:none;stroke:#1a1a1a;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 54.831756 173.52 \n",
       "L 54.831756 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 389.631756 173.52 \n",
       "L 389.631756 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 54.831756 173.52 \n",
       "L 389.631756 173.52 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 54.831756 7.2 \n",
       "L 389.631756 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"M 62.531756 64.281051 \n",
       "L 164.459418 64.281051 \n",
       "Q 166.659418 64.281051 166.659418 62.081051 \n",
       "L 166.659418 14.9 \n",
       "Q 166.659418 12.7 164.459418 12.7 \n",
       "L 62.531756 12.7 \n",
       "Q 60.331756 12.7 60.331756 14.9 \n",
       "L 60.331756 62.081051 \n",
       "Q 60.331756 64.281051 62.531756 64.281051 \n",
       "z\n",
       "\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_12\">\n",
       "     <path d=\"M 64.731756 21.608281 \n",
       "L 86.731756 21.608281 \n",
       "\" style=\"fill:none;stroke:#4c72b0;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_13\">\n",
       "     <g>\n",
       "      <use style=\"fill:#4c72b0;stroke:#4c72b0;\" x=\"75.731756\" xlink:href=\"#mbfad4b4d6b\" y=\"21.608281\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_11\">\n",
       "     <!-- rtrgsyl + scipy -->\n",
       "     <g style=\"fill:#262626;\" transform=\"translate(95.531756 25.458281)scale(0.11 -0.11)\">\n",
       "      <defs>\n",
       "       <path d=\"M 14.90625 21.296875 \n",
       "C 14.90625 30.703125 21.796875 37 30.59375 37 \n",
       "L 30.59375 43.578125 \n",
       "C 24.203125 43.578125 18.203125 40.390625 14.59375 35.203125 \n",
       "L 14.59375 43.09375 \n",
       "L 7.5 43.09375 \n",
       "L 7.5 0 \n",
       "L 14.90625 0 \n",
       "z\n",
       "\" id=\"CMSS17-114\"/>\n",
       "       <path d=\"M 16.703125 37 \n",
       "L 29.703125 37 \n",
       "L 29.703125 42.765625 \n",
       "L 16.703125 42.765625 \n",
       "L 16.703125 55 \n",
       "L 9.59375 55 \n",
       "L 9.59375 42.765625 \n",
       "L 1.703125 42.765625 \n",
       "L 1.703125 37 \n",
       "L 9.40625 37 \n",
       "L 9.40625 11.703125 \n",
       "C 9.40625 6 10.703125 -1 17.296875 -1 \n",
       "C 22.296875 -1 26.90625 0.390625 31.296875 2.6875 \n",
       "L 29.703125 8.5625 \n",
       "C 27.296875 6.46875 24.40625 5.265625 21.296875 5.265625 \n",
       "C 16.90625 5.265625 16.703125 10.875 16.703125 13.375 \n",
       "z\n",
       "\" id=\"CMSS17-116\"/>\n",
       "       <path d=\"M 44.5 43.875 \n",
       "C 38.796875 43.875 33.90625 42.78125 29.90625 40.890625 \n",
       "C 26.59375 43.390625 23.203125 43.875 20.90625 43.875 \n",
       "C 12.203125 43.875 5.59375 36.703125 5.59375 28.34375 \n",
       "C 5.59375 22.9375 8.59375 18.859375 8.796875 18.671875 \n",
       "C 7 16.171875 6 13.484375 6 10.5 \n",
       "C 6 7 7.40625 4.515625 8.5 3.125 \n",
       "C 3.296875 -0.046875 2.59375 -4.90625 2.59375 -6.796875 \n",
       "C 2.59375 -14.03125 11.703125 -20 23.40625 -20 \n",
       "C 35.203125 -20 44.296875 -14.03125 44.296875 -6.6875 \n",
       "C 44.296875 7 29 7 24.796875 7 \n",
       "L 16.703125 7 \n",
       "C 15.203125 7 11.203125 7 11.203125 12.359375 \n",
       "C 11.203125 14.390625 12.09375 15.6875 12.203125 15.78125 \n",
       "C 13.703125 14.6875 16.796875 13 20.90625 13 \n",
       "C 29.203125 13 36.09375 19.96875 36.09375 28.546875 \n",
       "C 36.09375 33.3125 33.90625 36.796875 33 38 \n",
       "L 33.296875 38 \n",
       "C 33.59375 38 37.796875 38 39.296875 38 \n",
       "C 42.5 38 42.796875 37.953125 45.59375 37.796875 \n",
       "z\n",
       "M 20.90625 18.46875 \n",
       "C 17.5 18.46875 12.703125 20.546875 12.703125 28.484375 \n",
       "C 12.703125 37.109375 18.203125 38.5 20.796875 38.5 \n",
       "C 24.203125 38.5 29 36.421875 29 28.484375 \n",
       "C 29 19.859375 23.5 18.46875 20.90625 18.46875 \n",
       "z\n",
       "M 24.703125 -0.15625 \n",
       "C 27.09375 -0.15625 37.203125 -0.15625 37.203125 -6.90625 \n",
       "C 37.203125 -11.15625 31 -14.515625 23.5 -14.515625 \n",
       "C 15.90625 -14.515625 9.703125 -11.25 9.703125 -6.796875 \n",
       "C 9.703125 -6.296875 9.703125 -0.15625 16.59375 -0.15625 \n",
       "z\n",
       "\" id=\"CMSS17-103\"/>\n",
       "       <path d=\"M 41.796875 43 \n",
       "L 34 43 \n",
       "C 25.5 20.21875 22.59375 10.96875 22.40625 5.984375 \n",
       "L 22.296875 5.984375 \n",
       "C 22 10.875 17.59375 22.8125 14.09375 31.359375 \n",
       "L 9.40625 43 \n",
       "L 1.296875 43 \n",
       "L 19 0.203125 \n",
       "C 17.90625 -2.78125 16.296875 -7.265625 15.796875 -8.265625 \n",
       "C 13.59375 -13.828125 12.09375 -13.828125 10.5 -13.828125 \n",
       "C 10.09375 -13.828125 6.90625 -13.828125 3.296875 -12.640625 \n",
       "L 3.90625 -19.203125 \n",
       "C 6.40625 -19.703125 8.90625 -20 10.703125 -20 \n",
       "C 13.203125 -20 18.203125 -20 22.796875 -7.765625 \n",
       "z\n",
       "\" id=\"CMSS17-121\"/>\n",
       "       <path d=\"M 14.796875 69 \n",
       "L 7.40625 69 \n",
       "L 7.40625 0 \n",
       "L 14.796875 0 \n",
       "z\n",
       "\" id=\"CMSS17-108\"/>\n",
       "       <path d=\"M 38.296875 23.515625 \n",
       "L 64.703125 23.515625 \n",
       "C 66.09375 23.515625 67.796875 23.515625 67.796875 25.203125 \n",
       "C 67.796875 27 66.203125 27 64.703125 27 \n",
       "L 38.296875 27 \n",
       "L 38.296875 53.328125 \n",
       "C 38.296875 54.71875 38.296875 56.421875 36.59375 56.421875 \n",
       "C 34.796875 56.421875 34.796875 54.828125 34.796875 53.328125 \n",
       "L 34.796875 27 \n",
       "L 8.296875 27 \n",
       "C 6.90625 27 5.203125 27 5.203125 25.3125 \n",
       "C 5.203125 23.515625 6.796875 23.515625 8.296875 23.515625 \n",
       "L 34.796875 23.515625 \n",
       "L 34.796875 -2.90625 \n",
       "C 34.796875 -4.296875 34.796875 -6 36.5 -6 \n",
       "C 38.296875 -6 38.296875 -4.40625 38.296875 -2.90625 \n",
       "z\n",
       "\" id=\"CMSS17-43\"/>\n",
       "       <path d=\"M 38.5 39.703125 \n",
       "C 38.5 40.390625 33.90625 42.40625 32.703125 42.796875 \n",
       "C 29.40625 44 25.203125 44 24.09375 44 \n",
       "C 11.09375 44 3.296875 32.703125 3.296875 21.296875 \n",
       "C 3.296875 9.296875 12 -1 23.703125 -1 \n",
       "C 30.40625 -1 35.203125 1.1875 39.09375 3.78125 \n",
       "L 38.5 10.375 \n",
       "C 34.203125 7.078125 29.203125 5.265625 23.796875 5.265625 \n",
       "C 16 5.265625 10.90625 12.09375 10.90625 21.390625 \n",
       "C 10.90625 28.609375 14.203125 37.71875 24.203125 37.71875 \n",
       "C 29.703125 37.71875 32.796875 36.609375 37.40625 33.515625 \n",
       "z\n",
       "\" id=\"CMSS17-99\"/>\n",
       "       <path d=\"M 15.09375 5.203125 \n",
       "C 18.40625 2.015625 22.90625 -0.078125 27.703125 -0.078125 \n",
       "C 37 -0.078125 45 9.421875 45 22.0625 \n",
       "C 45 33.734375 39 44 30.40625 44 \n",
       "C 25.40625 44 19.40625 42.21875 14.90625 38.625 \n",
       "L 14.90625 43.203125 \n",
       "L 7.5 43.203125 \n",
       "L 7.5 -19 \n",
       "L 15.09375 -19 \n",
       "z\n",
       "M 15.09375 32.8125 \n",
       "C 15.90625 34 19.296875 37.734375 24.796875 37.734375 \n",
       "C 31.796875 37.734375 37.40625 30.625 37.40625 22.0625 \n",
       "C 37.40625 12.296875 30.59375 6 23.90625 6 \n",
       "C 21.90625 6 19.796875 6.484375 17.796875 8.171875 \n",
       "C 15.09375 10.53125 15.09375 12 15.09375 13.390625 \n",
       "z\n",
       "\" id=\"CMSS17-112\"/>\n",
       "      </defs>\n",
       "      <use transform=\"scale(0.996264)\" xlink:href=\"#CMSS17-114\"/>\n",
       "      <use transform=\"translate(31.909773 0)scale(0.996264)\" xlink:href=\"#CMSS17-116\"/>\n",
       "      <use transform=\"translate(65.741339 0)scale(0.996264)\" xlink:href=\"#CMSS17-114\"/>\n",
       "      <use transform=\"translate(97.651112 0)scale(0.996264)\" xlink:href=\"#CMSS17-103\"/>\n",
       "      <use transform=\"translate(144.494735 0)scale(0.996264)\" xlink:href=\"#CMSS17-115\"/>\n",
       "      <use transform=\"translate(180.408277 0)scale(0.996264)\" xlink:href=\"#CMSS17-121\"/>\n",
       "      <use transform=\"translate(223.408419 0)scale(0.996264)\" xlink:href=\"#CMSS17-108\"/>\n",
       "      <use transform=\"translate(276.818255 0)scale(0.996264)\" xlink:href=\"#CMSS17-43\"/>\n",
       "      <use transform=\"translate(380.915302 0)scale(0.996264)\" xlink:href=\"#CMSS17-115\"/>\n",
       "      <use transform=\"translate(416.828844 0)scale(0.996264)\" xlink:href=\"#CMSS17-99\"/>\n",
       "      <use transform=\"translate(458.467666 0)scale(0.996264)\" xlink:href=\"#CMSS17-105\"/>\n",
       "      <use transform=\"translate(480.648389 0)scale(0.996264)\" xlink:href=\"#CMSS17-112\"/>\n",
       "      <use transform=\"translate(526.250879 0)scale(0.996264)\" xlink:href=\"#CMSS17-121\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_14\">\n",
       "     <path d=\"M 64.731756 37.754219 \n",
       "L 86.731756 37.754219 \n",
       "\" style=\"fill:none;stroke:#dd8452;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_15\">\n",
       "     <g>\n",
       "      <use style=\"fill:#dd8452;stroke:#dd8452;\" x=\"75.731756\" xlink:href=\"#m6d75e0a010\" y=\"37.754219\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_12\">\n",
       "     <!-- scipy alone -->\n",
       "     <g style=\"fill:#262626;\" transform=\"translate(95.531756 41.604219)scale(0.11 -0.11)\">\n",
       "      <defs>\n",
       "       <path d=\"M 37.59375 27.984375 \n",
       "C 37.59375 37.375 30.90625 43.875 21.90625 43.875 \n",
       "C 17.5 43.875 12.703125 43.078125 7.203125 39.890625 \n",
       "L 7.796875 33.359375 \n",
       "C 10.296875 35.125 14.59375 38 21.796875 38 \n",
       "C 26.90625 38 30 34.0625 30 27.84375 \n",
       "L 30 24 \n",
       "C 14 24 4 19.34375 4 11.34375 \n",
       "C 4 7.203125 6.5 -1 14.796875 -1 \n",
       "C 16.296875 -1 24.40625 -1 30.203125 3.390625 \n",
       "L 30.203125 -0.296875 \n",
       "L 37.59375 -0.296875 \n",
       "z\n",
       "M 30 12.75 \n",
       "C 30 10.953125 30 8.5625 27 6.78125 \n",
       "C 24.40625 5.078125 21.09375 5.078125 19.703125 5.078125 \n",
       "C 14.703125 5.078125 11.296875 7.984375 11.296875 11.625 \n",
       "C 11.296875 18.921875 26.90625 18.921875 30 18.921875 \n",
       "z\n",
       "\" id=\"CMSS17-97\"/>\n",
       "       <path d=\"M 44.203125 21.1875 \n",
       "C 44.203125 34 34.703125 44 23.5 44 \n",
       "C 12 44 2.703125 33.703125 2.703125 21.1875 \n",
       "C 2.703125 8.5 12.296875 -1 23.40625 -1 \n",
       "C 34.796875 -1 44.203125 8.796875 44.203125 21.1875 \n",
       "z\n",
       "M 23.5 5.265625 \n",
       "C 16.40625 5.265625 10.296875 11.078125 10.296875 22 \n",
       "C 10.296875 33.609375 17.40625 37.921875 23.40625 37.921875 \n",
       "C 29.90625 37.921875 36.59375 33.21875 36.59375 22 \n",
       "C 36.59375 10.671875 30.09375 5.265625 23.5 5.265625 \n",
       "z\n",
       "\" id=\"CMSS17-111\"/>\n",
       "       <path d=\"M 40.90625 29.328125 \n",
       "C 40.90625 35.671875 39.40625 44 28.09375 44 \n",
       "C 21.703125 44 17.5 40.71875 14.703125 37.328125 \n",
       "L 14.703125 43.09375 \n",
       "L 7.40625 43.09375 \n",
       "L 7.40625 0 \n",
       "L 15 0 \n",
       "L 15 24.359375 \n",
       "C 15 30.6875 17.40625 37.9375 24.203125 37.9375 \n",
       "C 33 37.9375 33.296875 32 33.296875 28.578125 \n",
       "L 33.296875 0 \n",
       "L 40.90625 0 \n",
       "z\n",
       "\" id=\"CMSS17-110\"/>\n",
       "      </defs>\n",
       "      <use transform=\"scale(0.996264)\" xlink:href=\"#CMSS17-115\"/>\n",
       "      <use transform=\"translate(35.913542 0)scale(0.996264)\" xlink:href=\"#CMSS17-99\"/>\n",
       "      <use transform=\"translate(77.552364 0)scale(0.996264)\" xlink:href=\"#CMSS17-105\"/>\n",
       "      <use transform=\"translate(99.733087 0)scale(0.996264)\" xlink:href=\"#CMSS17-112\"/>\n",
       "      <use transform=\"translate(145.335576 0)scale(0.996264)\" xlink:href=\"#CMSS17-121\"/>\n",
       "      <use transform=\"translate(219.564831 0)scale(0.996264)\" xlink:href=\"#CMSS17-97\"/>\n",
       "      <use transform=\"translate(264.486751 0)scale(0.996264)\" xlink:href=\"#CMSS17-108\"/>\n",
       "      <use transform=\"translate(286.667474 0)scale(0.996264)\" xlink:href=\"#CMSS17-111\"/>\n",
       "      <use transform=\"translate(333.511098 0)scale(0.996264)\" xlink:href=\"#CMSS17-110\"/>\n",
       "      <use transform=\"translate(381.716041 0)scale(0.996264)\" xlink:href=\"#CMSS17-101\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_16\">\n",
       "     <path d=\"M 64.731756 53.900156 \n",
       "L 86.731756 53.900156 \n",
       "\" style=\"fill:none;stroke:#1a1a1a;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_17\"/>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- quadratic -->\n",
       "     <g style=\"fill:#262626;\" transform=\"translate(95.531756 57.750156)scale(0.11 -0.11)\">\n",
       "      <defs>\n",
       "       <path d=\"M 40.796875 44 \n",
       "L 33.40625 44 \n",
       "L 33.40625 37.9375 \n",
       "C 33 38.4375 28.40625 44 20.59375 44 \n",
       "C 11.5 44 3.296875 34.8125 3.296875 21.859375 \n",
       "C 3.296875 9.890625 10.203125 -0.078125 19.203125 -0.078125 \n",
       "C 23.40625 -0.078125 28.703125 1.421875 33.203125 5.703125 \n",
       "L 33.203125 -19 \n",
       "L 40.796875 -19 \n",
       "z\n",
       "M 33.40625 14.28125 \n",
       "C 33.40625 13 33.40625 11.21875 30.296875 8.65625 \n",
       "C 29.5 7.96875 27.296875 6 23.5 6 \n",
       "C 16.40625 6 10.90625 13.28125 10.90625 21.859375 \n",
       "C 10.90625 31.421875 17.59375 37.734375 24.40625 37.734375 \n",
       "C 30.09375 37.734375 33.40625 32.203125 33.40625 28.078125 \n",
       "z\n",
       "\" id=\"CMSS17-113\"/>\n",
       "       <path d=\"M 40.90625 42.796875 \n",
       "L 33.296875 42.796875 \n",
       "L 33.296875 15.1875 \n",
       "C 33.296875 7.78125 27.90625 4.78125 22.203125 4.78125 \n",
       "C 15.59375 4.78125 15 6.984375 15 11.078125 \n",
       "L 15 42.796875 \n",
       "L 7.40625 42.796875 \n",
       "L 7.40625 10.59375 \n",
       "C 7.40625 2.796875 10.09375 -1 17 -1 \n",
       "C 20.40625 -1 28.09375 -0.203125 33.5 4.78125 \n",
       "L 33.5 0 \n",
       "L 40.90625 0 \n",
       "z\n",
       "\" id=\"CMSS17-117\"/>\n",
       "       <path d=\"M 40.796875 69 \n",
       "L 33.40625 69 \n",
       "L 33.40625 38.09375 \n",
       "C 30.296875 40.671875 25.203125 43.0625 19.59375 43.0625 \n",
       "C 10.5 43.0625 3.296875 33.296875 3.296875 21.046875 \n",
       "C 3.296875 8.78125 10.40625 -1 19.296875 -1 \n",
       "C 26.203125 -1 30.796875 2.6875 33.203125 4.78125 \n",
       "L 33.203125 -0.203125 \n",
       "L 40.796875 -0.203125 \n",
       "z\n",
       "M 33.203125 13.0625 \n",
       "C 33.203125 11.671875 33.203125 10.203125 30.09375 7.53125 \n",
       "C 28.09375 5.859375 25.703125 5.078125 23.40625 5.078125 \n",
       "C 18 5.078125 10.90625 9 10.90625 20.9375 \n",
       "C 10.90625 33.34375 18.90625 37 24.40625 37 \n",
       "C 28.09375 37 31.09375 35.21875 33.203125 32.265625 \n",
       "z\n",
       "\" id=\"CMSS17-100\"/>\n",
       "      </defs>\n",
       "      <use transform=\"scale(0.996264)\" xlink:href=\"#CMSS17-113\"/>\n",
       "      <use transform=\"translate(48.204943 0)scale(0.996264)\" xlink:href=\"#CMSS17-117\"/>\n",
       "      <use transform=\"translate(96.409886 0)scale(0.996264)\" xlink:href=\"#CMSS17-97\"/>\n",
       "      <use transform=\"translate(141.331807 0)scale(0.996264)\" xlink:href=\"#CMSS17-100\"/>\n",
       "      <use transform=\"translate(189.53675 0)scale(0.996264)\" xlink:href=\"#CMSS17-114\"/>\n",
       "      <use transform=\"translate(221.446523 0)scale(0.996264)\" xlink:href=\"#CMSS17-97\"/>\n",
       "      <use transform=\"translate(266.368443 0)scale(0.996264)\" xlink:href=\"#CMSS17-116\"/>\n",
       "      <use transform=\"translate(300.20001 0)scale(0.996264)\" xlink:href=\"#CMSS17-105\"/>\n",
       "      <use transform=\"translate(322.380733 0)scale(0.996264)\" xlink:href=\"#CMSS17-99\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p021f73b3f4\">\n",
       "   <rect height=\"166.32\" width=\"334.8\" x=\"54.831756\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cols = sns.color_palette()\n",
    "\n",
    "plt.figure(figsize=(6, 3))\n",
    "\n",
    "plot_multiple_runs(df_rtrgsyl, 'n', 'time_solve_mean', 'time_solve_std', 'rtrgsyl + scipy', cols[0])\n",
    "plot_multiple_runs(df_scipy, 'n', 'time_solve_mean', 'time_solve_std', 'scipy alone', cols[1])\n",
    "\n",
    "point = np.array([df_rtrgsyl.n.min(), df_rtrgsyl.n.max()])\n",
    "plt.loglog(point, point**2 / 1100000, '--k', label='quadratic')\n",
    "\n",
    "plt.xlabel('$n$'); plt.ylabel('Time [s]')\n",
    "plt.legend();\n",
    "from matplotlib.ticker import (MultipleLocator, AutoMinorLocator, LogLocator)\n",
    "plt.gca().set_xscale('log')\n",
    "plt.gca().set_yscale('log')\n",
    "\n",
    "plt.savefig('res/benchmark_retrgsyl_vs_scipy.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "earlier-cornell",
   "metadata": {},
   "source": [
    "# Determine slopes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "quick-video",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>time_solve_mean</th>\n",
       "      <th>fun</th>\n",
       "      <th>logn</th>\n",
       "      <th>logtime</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1178</td>\n",
       "      <td>0.779646</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>7.071573</td>\n",
       "      <td>-0.248916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1508</td>\n",
       "      <td>1.099101</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>7.318540</td>\n",
       "      <td>0.094493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1930</td>\n",
       "      <td>1.921060</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>7.565275</td>\n",
       "      <td>0.652877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2470</td>\n",
       "      <td>3.137652</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>7.811973</td>\n",
       "      <td>1.143475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3162</td>\n",
       "      <td>4.728846</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>8.058960</td>\n",
       "      <td>1.553681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1178</td>\n",
       "      <td>3.566473</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>7.071573</td>\n",
       "      <td>1.271577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1508</td>\n",
       "      <td>7.633903</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>7.318540</td>\n",
       "      <td>2.032599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1930</td>\n",
       "      <td>15.697096</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>7.565275</td>\n",
       "      <td>2.753476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2470</td>\n",
       "      <td>34.091600</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>7.811973</td>\n",
       "      <td>3.529051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>3162</td>\n",
       "      <td>83.841794</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>8.058960</td>\n",
       "      <td>4.428932</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       n  time_solve_mean        fun      logn   logtime\n",
       "10  1178         0.779646    rtrgsyl  7.071573 -0.248916\n",
       "11  1508         1.099101    rtrgsyl  7.318540  0.094493\n",
       "12  1930         1.921060    rtrgsyl  7.565275  0.652877\n",
       "13  2470         3.137652    rtrgsyl  7.811973  1.143475\n",
       "14  3162         4.728846    rtrgsyl  8.058960  1.553681\n",
       "25  1178         3.566473  syl_scipy  7.071573  1.271577\n",
       "26  1508         7.633903  syl_scipy  7.318540  2.032599\n",
       "27  1930        15.697096  syl_scipy  7.565275  2.753476\n",
       "28  2470        34.091600  syl_scipy  7.811973  3.529051\n",
       "29  3162        83.841794  syl_scipy  8.058960  4.428932"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.concat((df_rtrgsyl, df_scipy)).reset_index(drop=True)[['n', 'time_solve_mean', 'solve_fun']]\n",
    "df['logn'] = np.log(df.n)\n",
    "df['logtime'] = np.log(df.time_solve_mean)\n",
    "df.rename(columns={'solve_fun': 'fun'}, inplace=True)\n",
    "\n",
    "df = df[df.n > 1000]\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "organic-grade",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "boxed-uncertainty",
   "metadata": {},
   "outputs": [],
   "source": [
    "regline_rtrgsyl = LinearRegression().fit(df.loc[df.fun == 'rtrgsyl', 'logn'].values.reshape(-1, 1), \n",
    "                                         df.loc[df.fun == 'rtrgsyl', 'logtime'].values.reshape(-1, 1))\n",
    "regline_scipy   = LinearRegression().fit(df.loc[df.fun == 'syl_scipy', 'logn'].values.reshape(-1, 1), \n",
    "                                         df.loc[df.fun == 'syl_scipy', 'logtime'].values.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "governmental-cincinnati",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.8856260511995822, 3.1647242198074976)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope_rtrgsyl = regline_rtrgsyl.coef_[0, 0]\n",
    "slope_scipy = regline_scipy.coef_[0, 0]\n",
    "\n",
    "slope_rtrgsyl, slope_scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "smart-comfort",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.88562605]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regline_rtrgsyl.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "decimal-matrix",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-13.62613755])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regline_rtrgsyl.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "second-prior",
   "metadata": {},
   "source": [
    "Sanity check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ordered-glucose",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f914c7194f0>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"299.753241pt\" version=\"1.1\" viewBox=\"0 0 386.499467 299.753241\" width=\"386.499467pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2021-06-06T13:29:42.007076</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.4, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 299.753241 \n",
       "L 386.499467 299.753241 \n",
       "L 386.499467 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 22.179467 273.312 \n",
       "L 379.299467 273.312 \n",
       "L 379.299467 7.2 \n",
       "L 22.179467 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 80.639108 273.312 \n",
       "L 80.639108 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- $\\mathdefault{7.2}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(73.63757 290.422347)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 45.09375 61.578125 \n",
       "L 45.09375 63.765625 \n",
       "L 21.59375 63.765625 \n",
       "C 9.90625 63.765625 9.703125 65.078125 9.296875 67 \n",
       "L 7.5 67 \n",
       "L 4.59375 48.34375 \n",
       "L 6.40625 48.34375 \n",
       "C 6.703125 50.234375 7.40625 55.3125 8.59375 57.203125 \n",
       "C 9.203125 58 16.59375 58 18.296875 58 \n",
       "L 40.296875 58 \n",
       "L 29.203125 41.578125 \n",
       "C 21.796875 30.53125 16.703125 15.609375 16.703125 2.578125 \n",
       "C 16.703125 1.390625 16.703125 -2 20.296875 -2 \n",
       "C 23.90625 -2 23.90625 1.390625 23.90625 2.671875 \n",
       "L 23.90625 7.265625 \n",
       "C 23.90625 23.5625 26.703125 34.3125 31.296875 41.1875 \n",
       "z\n",
       "\" id=\"CMR17-55\"/>\n",
       "        <path d=\"M 18.40625 4.796875 \n",
       "C 18.40625 7.6875 16 9.671875 13.59375 9.671875 \n",
       "C 10.703125 9.671875 8.703125 7.28125 8.703125 4.890625 \n",
       "C 8.703125 2 11.09375 0 13.5 0 \n",
       "C 16.40625 0 18.40625 2.390625 18.40625 4.796875 \n",
       "z\n",
       "\" id=\"CMMI12-58\"/>\n",
       "        <path d=\"M 41.703125 15.453125 \n",
       "L 39.90625 15.453125 \n",
       "C 38.90625 8.375 38.09375 7.171875 37.703125 6.5625 \n",
       "C 37.203125 5.765625 30 5.765625 28.59375 5.765625 \n",
       "L 9.40625 5.765625 \n",
       "C 13 9.671875 20 16.75 28.5 24.953125 \n",
       "C 34.59375 30.734375 41.703125 37.53125 41.703125 47.421875 \n",
       "C 41.703125 59.21875 32.296875 66 21.796875 66 \n",
       "C 10.796875 66 4.09375 56.3125 4.09375 47.34375 \n",
       "C 4.09375 43.4375 7 42.9375 8.203125 42.9375 \n",
       "C 9.203125 42.9375 12.203125 43.546875 12.203125 47.03125 \n",
       "C 12.203125 50.109375 9.59375 51 8.203125 51 \n",
       "C 7.59375 51 7 50.90625 6.59375 50.703125 \n",
       "C 8.5 59.21875 14.296875 63.40625 20.40625 63.40625 \n",
       "C 29.09375 63.40625 34.796875 56.515625 34.796875 47.421875 \n",
       "C 34.796875 38.734375 29.703125 31.25 24 24.75 \n",
       "L 4.09375 2.28125 \n",
       "L 4.09375 0 \n",
       "L 39.296875 0 \n",
       "z\n",
       "\" id=\"CMR17-50\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-55\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMMI12-58\"/>\n",
       "       <use transform=\"translate(72.787654 0)scale(0.996264)\" xlink:href=\"#CMR17-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 146.399476 273.312 \n",
       "L 146.399476 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- $\\mathdefault{7.4}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(139.397938 290.422347)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 33.59375 64.40625 \n",
       "C 33.59375 66.5 33.5 66.5 31.703125 66.5 \n",
       "L 2 19.59375 \n",
       "L 2 17 \n",
       "L 27.796875 17 \n",
       "L 27.796875 7.140625 \n",
       "C 27.796875 3.5 27.59375 2.5 20.59375 2.5 \n",
       "L 18.703125 2.5 \n",
       "L 18.703125 0 \n",
       "C 21.90625 0 27.296875 0 30.703125 0 \n",
       "C 34.09375 0 39.5 0 42.703125 0 \n",
       "L 42.703125 2.5 \n",
       "L 40.796875 2.5 \n",
       "C 33.796875 2.5 33.59375 3.5 33.59375 7.140625 \n",
       "L 33.59375 17 \n",
       "L 43.796875 17 \n",
       "L 43.796875 19.59375 \n",
       "L 33.59375 19.59375 \n",
       "z\n",
       "M 28.09375 57.859375 \n",
       "L 28.09375 19.59375 \n",
       "L 4 19.59375 \n",
       "z\n",
       "\" id=\"CMR17-52\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-55\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMMI12-58\"/>\n",
       "       <use transform=\"translate(72.787654 0)scale(0.996264)\" xlink:href=\"#CMR17-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 212.159843 273.312 \n",
       "L 212.159843 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- $\\mathdefault{7.6}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(205.158305 290.422347)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.59375 34 \n",
       "C 10.59375 57.65625 21.796875 63 28.296875 63 \n",
       "C 30.40625 63 35.5 62.640625 37.5 59 \n",
       "C 35.90625 59 32.90625 59 32.90625 55.515625 \n",
       "C 32.90625 52.828125 35.09375 51.921875 36.5 51.921875 \n",
       "C 37.40625 51.921875 40.09375 52.3125 40.09375 55.625 \n",
       "C 40.09375 61.78125 35.09375 65.296875 28.203125 65.296875 \n",
       "C 16.296875 65.296875 3.796875 52.96875 3.796875 31 \n",
       "C 3.796875 3.953125 15.09375 -2 23.09375 -2 \n",
       "C 32.796875 -2 42 6.671875 42 20.046875 \n",
       "C 42 32.515625 33.90625 41.59375 23.703125 41.59375 \n",
       "C 17.59375 41.59375 13.09375 37.609375 10.59375 30.625 \n",
       "z\n",
       "M 23.09375 0.390625 \n",
       "C 10.796875 0.390625 10.796875 18.75 10.796875 22.4375 \n",
       "C 10.796875 29.625 14.203125 40 23.5 40 \n",
       "C 25.203125 40 30.09375 40 33.40625 33.125 \n",
       "C 35.203125 29.21875 35.203125 25.140625 35.203125 20.140625 \n",
       "C 35.203125 14.75 35.203125 10.78125 33.09375 6.78125 \n",
       "C 30.90625 2.671875 27.703125 0.390625 23.09375 0.390625 \n",
       "z\n",
       "\" id=\"CMR17-54\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-55\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMMI12-58\"/>\n",
       "       <use transform=\"translate(72.787654 0)scale(0.996264)\" xlink:href=\"#CMR17-54\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 277.92021 273.312 \n",
       "L 277.92021 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- $\\mathdefault{7.8}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(270.918672 290.422347)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 27.203125 35.375 \n",
       "C 33.5 38.546875 39.90625 43.328125 39.90625 50.984375 \n",
       "C 39.90625 60.015625 31.09375 65.296875 23 65.296875 \n",
       "C 13.90625 65.296875 5.90625 58.734375 5.90625 49.6875 \n",
       "C 5.90625 47.203125 6.5 42.921875 10.40625 39.140625 \n",
       "C 11.40625 38.15625 15.59375 35.171875 18.296875 33.28125 \n",
       "C 13.796875 30.984375 3.296875 25.53125 3.296875 14.59375 \n",
       "C 3.296875 4.359375 13.09375 -2 22.796875 -2 \n",
       "C 33.5 -2 42.5 5.65625 42.5 15.78125 \n",
       "C 42.5 24.84375 36.40625 29.015625 32.40625 31.703125 \n",
       "z\n",
       "M 14.09375 44.09375 \n",
       "C 13.296875 44.59375 9.296875 47.671875 9.296875 52.359375 \n",
       "C 9.296875 58.421875 15.59375 63 22.796875 63 \n",
       "C 30.703125 63 36.5 57.4375 36.5 50.96875 \n",
       "C 36.5 41.703125 26.09375 36.421875 25.59375 36.421875 \n",
       "C 25.5 36.421875 25.40625 36.421875 24.59375 37.03125 \n",
       "z\n",
       "M 32.5 23.734375 \n",
       "C 34 22.640625 38.796875 19.375 38.796875 13.296875 \n",
       "C 38.796875 5.953125 31.40625 0.390625 23 0.390625 \n",
       "C 13.90625 0.390625 7 6.84375 7 14.6875 \n",
       "C 7 22.546875 13.09375 29.09375 20 32.1875 \n",
       "z\n",
       "\" id=\"CMR17-56\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-55\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMMI12-58\"/>\n",
       "       <use transform=\"translate(72.787654 0)scale(0.996264)\" xlink:href=\"#CMR17-56\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 343.680578 273.312 \n",
       "L 343.680578 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- $\\mathdefault{8.0}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(336.67904 290.422347)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 42 31.640625 \n",
       "C 42 37.75 41.90625 48.125 37.703125 56.109375 \n",
       "C 34 63.109375 28.09375 65.59375 22.90625 65.59375 \n",
       "C 18.09375 65.59375 12 63.40625 8.203125 56.203125 \n",
       "C 4.203125 48.71875 3.796875 39.4375 3.796875 31.640625 \n",
       "C 3.796875 25.953125 3.90625 17.28125 7 9.671875 \n",
       "C 11.296875 -0.609375 19 -2 22.90625 -2 \n",
       "C 27.5 -2 34.5 -0.109375 38.59375 9.375 \n",
       "C 41.59375 16.28125 42 24.359375 42 31.640625 \n",
       "z\n",
       "M 22.90625 -0.40625 \n",
       "C 16.5 -0.40625 12.703125 5.078125 11.296875 12.6875 \n",
       "C 10.203125 18.5625 10.203125 27.15625 10.203125 32.75 \n",
       "C 10.203125 40.4375 10.203125 46.828125 11.5 52.921875 \n",
       "C 13.40625 61.390625 19 64 22.90625 64 \n",
       "C 27 64 32.296875 61.296875 34.203125 53.125 \n",
       "C 35.5 47.4375 35.59375 40.734375 35.59375 32.75 \n",
       "C 35.59375 26.25 35.59375 18.265625 34.40625 12.375 \n",
       "C 32.296875 1.484375 26.40625 -0.40625 22.90625 -0.40625 \n",
       "z\n",
       "\" id=\"CMR17-48\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-56\"/>\n",
       "       <use transform=\"translate(45.690477 0)scale(0.996264)\" xlink:href=\"#CMMI12-58\"/>\n",
       "       <use transform=\"translate(72.787654 0)scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 22.179467 246.262591 \n",
       "L 379.299467 246.262591 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- $\\mathdefault{0}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(7.2 250.067765)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 22.179467 195.016239 \n",
       "L 379.299467 195.016239 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- $\\mathdefault{1}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(7.2 198.821412)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 26.59375 63.40625 \n",
       "C 26.59375 65.5 26.5 65.5 25.09375 65.5 \n",
       "C 21.203125 61.1875 15.296875 59.796875 9.703125 59.796875 \n",
       "C 9.40625 59.796875 8.90625 59.796875 8.796875 59.5 \n",
       "C 8.703125 59.296875 8.703125 59.09375 8.703125 57 \n",
       "C 11.796875 57 17 57.59375 21 59.984375 \n",
       "L 21 7.203125 \n",
       "C 21 3.6875 20.796875 2.5 12.203125 2.5 \n",
       "L 9.203125 2.5 \n",
       "L 9.203125 0 \n",
       "C 14 0 19 0 23.796875 0 \n",
       "C 28.59375 0 33.59375 0 38.40625 0 \n",
       "L 38.40625 2.5 \n",
       "L 35.40625 2.5 \n",
       "C 26.796875 2.5 26.59375 3.59375 26.59375 7.15625 \n",
       "z\n",
       "\" id=\"CMR17-49\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 22.179467 143.769886 \n",
       "L 379.299467 143.769886 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- $\\mathdefault{2}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(7.2 147.575059)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 22.179467 92.523533 \n",
       "L 379.299467 92.523533 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- $\\mathdefault{3}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(7.2 96.328707)scale(0.11 -0.11)\">\n",
       "       <defs>\n",
       "        <path d=\"M 22.09375 33.703125 \n",
       "C 31 33.703125 34.90625 25.96875 34.90625 17.03125 \n",
       "C 34.90625 5 28.5 0.390625 22.703125 0.390625 \n",
       "C 17.40625 0.390625 8.796875 3.03125 6.09375 10.828125 \n",
       "C 6.59375 10.625 7.09375 10.625 7.59375 10.625 \n",
       "C 10 10.625 11.796875 12.21875 11.796875 14.8125 \n",
       "C 11.796875 17.703125 9.59375 19 7.59375 19 \n",
       "C 5.90625 19 3.296875 18.203125 3.296875 14.46875 \n",
       "C 3.296875 5.234375 12.296875 -2 22.90625 -2 \n",
       "C 34 -2 42.5 6.71875 42.5 16.953125 \n",
       "C 42.5 26.671875 34.5 33.703125 25 34.796875 \n",
       "C 32.59375 36.375 39.90625 43.0625 39.90625 52.015625 \n",
       "C 39.90625 59.6875 32 65.296875 23 65.296875 \n",
       "C 13.90625 65.296875 5.90625 59.828125 5.90625 52.015625 \n",
       "C 5.90625 48.59375 8.5 48 9.796875 48 \n",
       "C 11.90625 48 13.703125 49.296875 13.703125 51.890625 \n",
       "C 13.703125 54.46875 11.90625 55.765625 9.796875 55.765625 \n",
       "C 9.40625 55.765625 8.90625 55.765625 8.5 55.578125 \n",
       "C 11.40625 61.859375 19.296875 63 22.796875 63 \n",
       "C 26.296875 63 32.90625 61.328125 32.90625 51.875 \n",
       "C 32.90625 49.109375 32.5 44.1875 29.09375 39.84375 \n",
       "C 26.09375 36 22.703125 36 19.40625 35.6875 \n",
       "C 18.90625 35.6875 16.59375 35.453125 16.203125 35.453125 \n",
       "C 15.5 35.359375 15.09375 35.265625 15.09375 34.5 \n",
       "C 15.09375 33.796875 15.203125 33.703125 17.203125 33.703125 \n",
       "z\n",
       "\" id=\"CMR17-51\"/>\n",
       "       </defs>\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <path clip-path=\"url(#p9c3fb01391)\" d=\"M 22.179467 41.277181 \n",
       "L 379.299467 41.277181 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:round;\"/>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- $\\mathdefault{4}$ -->\n",
       "      <g style=\"fill:#262626;\" transform=\"translate(7.2 45.082354)scale(0.11 -0.11)\">\n",
       "       <use transform=\"scale(0.996264)\" xlink:href=\"#CMR17-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_11\">\n",
       "    <path clip-path=\"url(#p9c3fb01391)\" d=\"M 38.412195 259.018624 \n",
       "L 119.61513 241.420183 \n",
       "L 200.742292 212.805018 \n",
       "L 281.857096 187.663686 \n",
       "L 363.06674 166.642101 \n",
       "\" style=\"fill:none;stroke:#4c72b0;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path clip-path=\"url(#p9c3fb01391)\" d=\"M 38.412195 261.216 \n",
       "L 74.484922 250.614599 \n",
       "L 110.557649 240.013197 \n",
       "L 146.630376 229.411796 \n",
       "L 182.703104 218.810395 \n",
       "L 218.775831 208.208994 \n",
       "L 254.848558 197.607592 \n",
       "L 290.921285 187.006191 \n",
       "L 326.994013 176.40479 \n",
       "L 363.06674 165.803388 \n",
       "\" style=\"fill:none;stroke:#dd8452;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#p9c3fb01391)\" d=\"M 38.412195 181.098902 \n",
       "L 119.61513 142.099293 \n",
       "L 200.742292 105.157004 \n",
       "L 281.857096 65.411599 \n",
       "L 363.06674 19.296 \n",
       "\" style=\"fill:none;stroke:#55a868;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path clip-path=\"url(#p9c3fb01391)\" d=\"M 38.412195 182.679643 \n",
       "L 74.484922 164.886873 \n",
       "L 110.557649 147.094102 \n",
       "L 146.630376 129.301332 \n",
       "L 182.703104 111.508561 \n",
       "L 218.775831 93.715791 \n",
       "L 254.848558 75.923021 \n",
       "L 290.921285 58.13025 \n",
       "L 326.994013 40.33748 \n",
       "L 363.06674 22.544709 \n",
       "\" style=\"fill:none;stroke:#c44e52;stroke-linecap:round;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 22.179467 273.312 \n",
       "L 22.179467 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 379.299467 273.312 \n",
       "L 379.299467 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 22.179467 273.312 \n",
       "L 379.299467 273.312 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 22.179467 7.2 \n",
       "L 379.299467 7.2 \n",
       "\" style=\"fill:none;stroke:#cccccc;stroke-linecap:square;stroke-linejoin:miter;stroke-width:1.25;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p9c3fb01391\">\n",
       "   <rect height=\"266.112\" width=\"357.12\" x=\"22.179467\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = np.linspace(min(df.logn), max(df.logn), 10)\n",
    "\n",
    "plt.plot(df.loc[df.fun == 'rtrgsyl', 'logn'], df.loc[df.fun == 'rtrgsyl', 'logtime'])\n",
    "plt.plot(grid, grid * slope_rtrgsyl + regline_rtrgsyl.intercept_)\n",
    "\n",
    "plt.plot(df.loc[df.fun == 'syl_scipy', 'logn'], df.loc[df.fun == 'syl_scipy', 'logtime'])\n",
    "plt.plot(grid, grid * slope_scipy + regline_scipy.intercept_)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:ada]",
   "language": "python",
   "name": "conda-env-ada-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}