2-Benchmark-blks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "global-trail",
   "metadata": {},
   "source": [
    "# About\n",
    "\n",
    "\n",
    "This notebooks will analyze the  computation time in function of the block size, which is the criterion for which `rtrgsyl` stops the recursion and uses another solver to solve the small system. We will use scipy's solver. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "competitive-reform",
   "metadata": {},
   "source": [
    "# Benchmark"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "norman-governor",
   "metadata": {},
   "source": [
    "## Imports & Utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "neither-rally",
   "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": "computational-burlington",
   "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": "unexpected-acceptance",
   "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": "round-plant",
   "metadata": {},
   "source": [
    "## Vary block size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "tribal-assets",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4,   8,  16,  32,  64, 128, 256, 512])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blks_grid = 2 ** np.arange(2, 10)\n",
    "blks_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "olympic-trouble",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "blks=4 5 runs\n",
      "blks=8 5 runs\n",
      "blks=16 5 runs\n",
      "blks=32 5 runs\n",
      "blks=64 5 runs\n",
      "blks=128 5 runs\n",
      "blks=256 5 runs\n",
      "blks=512 5 runs\n"
     ]
    }
   ],
   "source": [
    "res = benchmark(\n",
    "    solve_fun=rtrgsyl,\n",
    "    vary_param=('blks', blks_grid),\n",
    "    log_context={'algo': 'rtrgsyl', 'std_solver': 'syl_scipy'},\n",
    "    bartel_stewart=True,\n",
    "    dim=(1000, 1000),\n",
    "    std_solver=solve_sylvester_scipy\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "modified-boulder",
   "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>std_solver</th>\n",
       "      <th>blks</th>\n",
       "      <th>algo</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>(1000, 1000)</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>4</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>[1.5868542194366455, 1.441138505935669, 1.4718...</td>\n",
       "      <td>[4.775654554367065, 5.0366129875183105, 4.7833...</td>\n",
       "      <td>[0.018639087677001953, 0.01759028434753418, 0....</td>\n",
       "      <td>1.472846</td>\n",
       "      <td>0.068132</td>\n",
       "      <td>4.794717</td>\n",
       "      <td>0.141195</td>\n",
       "      <td>0.030204</td>\n",
       "      <td>0.023089</td>\n",
       "      <td>1000</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(1000, 1000)</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>8</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>[1.394913673400879, 1.4651854038238525, 1.3487...</td>\n",
       "      <td>[1.796738624572754, 1.8093287944793701, 1.8114...</td>\n",
       "      <td>[0.018682003021240234, 0.018094301223754883, 0...</td>\n",
       "      <td>1.405711</td>\n",
       "      <td>0.037247</td>\n",
       "      <td>1.836198</td>\n",
       "      <td>0.041364</td>\n",
       "      <td>0.018306</td>\n",
       "      <td>0.000496</td>\n",
       "      <td>1000</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            dim std_solver  blks     algo  \\\n",
       "0  (1000, 1000)  syl_scipy     4  rtrgsyl   \n",
       "1  (1000, 1000)  syl_scipy     8  rtrgsyl   \n",
       "\n",
       "                                          time_schur  \\\n",
       "0  [1.5868542194366455, 1.441138505935669, 1.4718...   \n",
       "1  [1.394913673400879, 1.4651854038238525, 1.3487...   \n",
       "\n",
       "                                          time_solve  \\\n",
       "0  [4.775654554367065, 5.0366129875183105, 4.7833...   \n",
       "1  [1.796738624572754, 1.8093287944793701, 1.8114...   \n",
       "\n",
       "                                           time_back  time_schur_mean  \\\n",
       "0  [0.018639087677001953, 0.01759028434753418, 0....         1.472846   \n",
       "1  [0.018682003021240234, 0.018094301223754883, 0...         1.405711   \n",
       "\n",
       "   time_schur_std  time_solve_mean  time_solve_std  time_back_mean  \\\n",
       "0        0.068132         4.794717        0.141195        0.030204   \n",
       "1        0.037247         1.836198        0.041364        0.018306   \n",
       "\n",
       "   time_back_std     m     n  \n",
       "0       0.023089  1000  1000  \n",
       "1       0.000496  1000  1000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = format_results_bs(res)\n",
    "df.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "about-lodging",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe1b19d92e0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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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.blks, df.time_solve_mean, '-o', base=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fixed-metropolitan",
   "metadata": {},
   "source": [
    "### Sanity check: rectangular matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "sporting-tackle",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "blks=4 5 runs\n",
      "blks=8 5 runs\n",
      "blks=16 5 runs\n",
      "blks=32 5 runs\n",
      "blks=64 5 runs\n",
      "blks=128 5 runs\n",
      "blks=256 5 runs\n",
      "blks=512 5 runs\n"
     ]
    }
   ],
   "source": [
    "res_wide = benchmark(\n",
    "    solve_fun=rtrgsyl,\n",
    "    vary_param=('blks', blks_grid),\n",
    "    log_context={'algo': 'rtrgsyl', 'std_solver': 'syl_scipy'},\n",
    "    bartel_stewart=True,\n",
    "    dim=(1000, 2000),\n",
    "    std_solver=solve_sylvester_scipy\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "certified-punch",
   "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>std_solver</th>\n",
       "      <th>blks</th>\n",
       "      <th>algo</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>(1000, 2000)</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>4</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>[4.302501201629639, 4.795268297195435, 4.91601...</td>\n",
       "      <td>[9.727572202682495, 9.205167293548584, 9.01951...</td>\n",
       "      <td>[0.04959416389465332, 0.08712315559387207, 0.0...</td>\n",
       "      <td>4.922669</td>\n",
       "      <td>0.502359</td>\n",
       "      <td>9.333014</td>\n",
       "      <td>0.260397</td>\n",
       "      <td>0.069992</td>\n",
       "      <td>0.018452</td>\n",
       "      <td>1000</td>\n",
       "      <td>2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(1000, 2000)</td>\n",
       "      <td>syl_scipy</td>\n",
       "      <td>8</td>\n",
       "      <td>rtrgsyl</td>\n",
       "      <td>[5.002025604248047, 4.373266220092773, 4.39701...</td>\n",
       "      <td>[3.2305185794830322, 3.840277910232544, 3.4738...</td>\n",
       "      <td>[0.05466938018798828, 0.07143402099609375, 0.0...</td>\n",
       "      <td>4.559351</td>\n",
       "      <td>0.246723</td>\n",
       "      <td>3.446779</td>\n",
       "      <td>0.212087</td>\n",
       "      <td>0.062469</td>\n",
       "      <td>0.009959</td>\n",
       "      <td>1000</td>\n",
       "      <td>2000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            dim std_solver  blks     algo  \\\n",
       "0  (1000, 2000)  syl_scipy     4  rtrgsyl   \n",
       "1  (1000, 2000)  syl_scipy     8  rtrgsyl   \n",
       "\n",
       "                                          time_schur  \\\n",
       "0  [4.302501201629639, 4.795268297195435, 4.91601...   \n",
       "1  [5.002025604248047, 4.373266220092773, 4.39701...   \n",
       "\n",
       "                                          time_solve  \\\n",
       "0  [9.727572202682495, 9.205167293548584, 9.01951...   \n",
       "1  [3.2305185794830322, 3.840277910232544, 3.4738...   \n",
       "\n",
       "                                           time_back  time_schur_mean  \\\n",
       "0  [0.04959416389465332, 0.08712315559387207, 0.0...         4.922669   \n",
       "1  [0.05466938018798828, 0.07143402099609375, 0.0...         4.559351   \n",
       "\n",
       "   time_schur_std  time_solve_mean  time_solve_std  time_back_mean  \\\n",
       "0        0.502359         9.333014        0.260397        0.069992   \n",
       "1        0.246723         3.446779        0.212087        0.062469   \n",
       "\n",
       "   time_back_std     m     n  \n",
       "0       0.018452  1000  2000  \n",
       "1       0.009959  1000  2000  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_wide = format_results_bs(res_wide)\n",
    "df_wide.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "streaming-program",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe1af8fd730>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bp0CzJ+ClzdDjaynqdiSFPR9PtapFTI1yvDV7J6cSUwr/BlspWxUe/hmSTsHkx+VYPeF8tIbDq+GnHvD13XBgmdE7H7wdOn0M5WpYndDlSWHPh6eH4qPejcjI1Lw+bRumDllFNINu4+DIKlgwTGbKCOegNexZCN91gB86Gr31NiOMudlt34ZAk7bsEPLmaUFqVijD8Afr8tbsnfz61zEevr26eY1H94HTu4xZMmH14fZnzWtbiOLIzMheVPQJnN4JwdWh40fGXi6yLsMSUtgL0b9FDRbuOMW782JpdVsFIsqZuPrt/hFwejcseN3Ye6L2vea1LURh0lNgyyRYMxYuHIYKkdD9K2PvI08T9lwS+ZKhmEJ4eCg+7BWN1pphU7eRlWXisIiHB/T8xliFN/kJY7tSIayWmmSsEP0sGua9auzj0ncS/H0dNH5EiroDkMJeBNXKB/DPTlGsOXCOSeuPmNu4b5AxU0Z5GDNlUhLNbV+4r9wHRP81EZa9aywqWjLCmNXy+Gx4ZqmxyM6VFxU5GZnHXkRaa574/i/+OnSehYNbUyO0jLkBDq8ydoOsfS/0mwwenua2L9zL1QOic58lClC3s7GoKLyZ+bnENTKP3QaUUnzQsyFenoqhU0wekgGo2Qo6job9vxm9JSHsKa8DogECK8PDk6SoOzgp7MVQJdift7rU58/D5/lu9SHzA8Q8ZexHvXYcbJ5kfvvCfeR3QPSleHNziBKRwl5MPZuG07ZeJUYv2sOBM5fMD/DASKh1D8wdDEfXm9++cA/5nQ1gwx0Ihf1IYS8mpRTv92iIv48nQyZvJSMzy9wAnt7Q+wfjH9ivj0LCMXPbF65Pa2PIJTcb70Ao7EcKewlUCvLjnW4N2HIsgQkrD5ofIKA8PPI/43CC/z0CaZfNzyBc145pxpGNUT2y9w5XxudiHt0mrCMLlEqoS3QVFu44yadL9tGmbhiRlYPMDVAxEnp9Bz/3gRkDoPePMt1MlN7FkzBvCEQ0h17fyuwrJyWVoISUUvy7WwOC/Lx4dfIW0s0ekgG4rR20ewdiZ8PvH5jfvnAtWsPsQcYrwYe+lqLuxKSwl0JooC/vPdSQnScuMn75fmtC3PkiNH4Ufh9l7NchRElt+hH2LzE6C6G3WJ1GlIIU9lJ6oEFlujeuyrhl+9kRZ8GqUKWg8ycQcTvMeMHYUU+I4rpwGBb905hx1fwZq9OIUpLCbgP/17UB5cv4MGTyVlIzMs0P4OVrLBoJCIVfHoEkmWssiiErC2b+3di2ott4ea/GBcj/QRsIDvDmg57R7IlP4rPf9lkTIrASPPIzJF+AXx8zxkmFKIr1X8KR1fDAKAipZnUaYQNS2G3kvrqV6BMTwVe/H2Dz0QvWhKjSCLp/Ccf/hDkvywEdonBn9sBv/weRHaFxP6vTCBuxeWFXStVWSk1USk219XM7ujc7R1G5rB9DpmwlJd2CIRmA+t3h3jdg6y+w5nNrMgjnkJkOM54HnzLQ+VPj/RrhEkpc2JVS1ZRSy5VSu5RSO5VSLwNorQ9qrZ+2XUTnUdbPmw97NeLgmct8tGiPdUHuHgZR3YzNwvYuti6HcGyrPoETm40334PCrE4jbKg0PfYMYIjWOgpoAQxUSkXZJpbzanVbBR69ozoTVx/ir8PnrQnh4WEMyVRuANOeNk5hEiKnE1uMtQ8Nexuv8oRLKXFh11qf1Fpvyv46CYgFwm0VzJn9o2M9Isr589qUrVxJy7AmhE8ZePgX8PIzDui4YtEfGeF40lOM1cplKhpbQQuXY5MxdqVUTaAJsF4pFaqU+gpoopR6I5/HP6eU2qCU2nDmzBlbRHAoZXy9GN2rEUfOXeGDBRb2lkOqGdMgL8bBlCeMMVUhVrwPZ2Kh6+fgX87qNMIOSl3YlVKBwDRgsNb6otb6nNZ6gNb6Fq31yLy+R2s9QWsdo7WOqVixYmkjOKQWtUN5smVNflx7hDX7z1oXpNrt0OUzOPQHLMzz76xwJ0fXweqx0OxvxpYUwiWVahMwpZQ3RlGfpLWebptIrmNYh7qs2HOGv0/ahL+PJ6cSU6ga4s/QDpF0b2LiqFXjfhC/0zigo1I9aO6W722L1EvGEExIdWj/rtVphB2VZlaMAiYCsVrrMbaL5Dr8fTzp2qgqCcnpnExMQQNxCcm8MX07MzfHmRum3TtwaztYMAwOrTS3beEYlowwtg7o/qVxSLpwWaUZimkJ9AfuV0ptyf7oaKNcLmPqxpuPGEtOz2S02dMhPTyh10QofwtM7g/nLTjaT1hn/1LYMBHuHAg1W1qdRthZaWbFrNJaK611tNa6cfbHfFuGcwUnEvI4ELiA63blFwyP/GKsSP3lEUi5aH4GYb7kBJj1IlSIhPv/ZXUaYQLZUsDOqob4F+u63YXeAn1+hLN7YfqzkGXRCllhngWvG4dQP/QVePtZnUaYQAq7nQ3tEIm/940HFnh6KIZ2iLQoEVD7XnjwA9i7EJa+Y10OYX+xc2Db/+Du1yC8qdVphEnkaDw7uzr7ZfSiPZxISCbA15PLqZl4eVq8L0fzZ4yZMqs/hUpR0KivtXmE7V06A3MGG5vD3T3U6jTCRFLYTdC9Sfi1Ap+WkcUj36xj2NRtRIYFcVuYRbMTlDJWHZ7bbxyHFnoLRMRYk0XYntYwdzCkXoSH5oKnt9WJhIlkKMZkPl4ejO/XlAAfTwb8dyOXUi3acgCMf+y9f4SgyvC/fpBo8hRMYT/bfoXdc+H+N421C8KtSGG3QOVgPz5/pCmHz11h2NStaCv3TS8TCv1+hbTLRnFPu2JdFmEbiXEwfxhUv9M4E1e4HSnsFrnzllBefyCS+dtPMXGVxXPKK9WDnt8a56XOGigHdDgzrWH2i5CVDt2/MNYvCLcjY+wWerZ1bTYfTWDkgt00DA/mjtqh1oWJfBDavgW/vW2cgXliIyQeh+AIaDMCovtYl00U3YaJcGAZdPoYyte2Oo1pZm6OuzZBwZJtOxyM9NgtpJTiw17R1AgNYODPm4m/mGJtoJaDoVoLiJ0JiccAbXye8xJsm2xtNlG48wdh8b/glvshxn32A5q5OY43pm8nLiHZ2m07HIgUdosF+Xnz1WPNuJyawcBJm0jPzLIujFJGLz239GSZ7+7osjJhxgvg4Q1dx7nVMXejF+0hOddRlMa2He57wIwUdgdQJyyID3pFs+HIBUbOt/iX8WI+vZy8Cr5wHGvHwbF10PFDCHaPIYi0jCxW7jtDXD7bc8QlpNDji9UMn7aNiasOsXLfGeIvplg7WcEkMsbuILo2qsqmIxf4bvUhmlQPoUujqtYECY7IHobJpaxFeUThTsfCsnehbmeIdu2FZhdT0lmx5wxLdsWzYs9pklLyny5cxscTb08PFu+K539/Xf+dDvb3pk5YILeFBVGnUiB1steTVAj0QbnIKx0p7A7kHx3rsSMukdenbaNuZYsWL7UZYYypp+fqBWVmGGenVqprfiaRv8x0mPE8+JY1DlRxkcKU04mEZH6LjWfJrnjWHTxHeqamQqAPHRtUoV1UGBeupDFi1s4bhmP8vT1576GG195APXsplb3xSew9lcTe05fYF5/EvG0n+Tn5+qli5QK8jWIfll3sKxlfhwb6mv7fXFrK6pclMTExesOGDZZmcCTxF1PoNHYVZf29mDWwJUF+FqwY3DbZGFO/Oismui9s+tEo9t3Gy+HHjmT5+8ah1H0nQb3OVqexCa01sSeTWLIrniWxp9gRZ+xCWrtiGdpFhdE+KozG1crh6XH9j1hJZsVorTmTlMre+EvsjU9i3+mka1/nfCUQWsaHOtkF3yj8xtchAT72+QEUkVJqo9Y6z+XiUtgd0LqD53j02/W0jwrji0ebOsbLw4snYPLjcPwvuOslaPMWeMoLPkvFbYRv20HD3tDja6vTlEp6ZhZ/HTrP4l3x/BYbz/ELySgFTauXo11UGO2iwrilYqApWbTWnLqYwt54o2e/N94o+PtPX7phpXjFIF+j2FcKuqHwB/ub0xmTwu6EJvxxgPfn7+afHevx7N0OMh85Iw0WvQF/fQu17oZe30OZClanck/pyfD1PZB2CV5YA/4hVicqtkupGfy+5wxLdp1i2e7TXEzJwNfLg9a3VaBdVBj31w2jYpDjDINorTmRmGL07rOL/dXPOYeBwsr6Zhf668X+tkqBN7z6tsW8eynsTkhrzd8nbWLxrnh+fuYOaxcv5bblZ5j7CgRUgL7/gfBmVidyP4v+acyEeWw63NrG6jRFFn8xxRhi2RXP2gPnSMvMolyAN23qGb3y1rdVIMDHuV4JZmVp4hKSr/Xs98Unsfd0EvtPXyIl/fr05arBftwWFoSH0qzab7xXcJW/tycjezQsVnGXwu6kklLS6TZ+NReTM5j3UivCyjrQIQknt8Kvj0HSKWOXyGZ/szqR+zi8Cn7oDDFPQWfHPm5Ya83e+Ess2XWKJbvi2Xo8EYCaoQHZQyyVaVbjxvFyV5GZpTl+4cr1Mfzswr/rZN4nl4WH+LN6+P1Ffn4p7E5sX3wS3cavJqpKWX55rgXeng609ODKeZj2tLGEvenj8OBoOaHH3lKT4MuWoDzghdXgU8bqRDfJyMxiw5EL13rmR88bG8s1rhZy7c3PWysFOsZ7RxaoNXweeVVdBRwa1anIz1NQYXeu1zxu6LawID7oGc2gXzbz/vxY3upS3+pI1wWUh0enwvL3YOXHcGoH9P3JmEkj7GPxm5BwFJ5a6FBF/UpaBn/sPcPiXfEs332aC1fS8fHyoOUtoQy45xba1qtEJUd6xWmhqiH+eS6qsuVxmVLYnUCXRlXZdPQC368+TJPq5ehq1eKlvHh4GnPfw5vB9Ofh6+w3VWvfY3Uy17NvCWz8wZiVVL2F1Wk4nZTC0tjTLNkVz6r9Z0nLyCLY35s2dSvRLiqMu+tUpIyvlJjchnaI5I3p22+ad2/L4zJlKMZJpGdm8ciEdew6eZFZA1tad/JSQc7uM8bdz+6Ftm8bBchNX27b3JXz8MWd4F8OnlthypBX7pkbr7WvQ8OIYBZnD7FsOZaA1lCtvD/t6lWmXVQYzWuWw8uRhgsdlMyKEdc4xOKlwqReMvZ03zUToroZC5p8HfCPkLOZ9gzsnAHPLjPOMLWzqzsm5uxVKrg2NhwdEUy7emG0qx9GZFiQ246XW6mgwi5/Wp1IWFk/xvVrwpFzVxg2dZtjbmbkGwi9f4D270LsXPimDZzZa3Uq57ZzJmyfAve8bkpRh7x3TNQY+6ysfeN+Zr/YikFtbqNu5bJS1B2QFHYn06J2KMMfqMuCHaf4ZuVBq+PkTSm4axA8PhOunINv7ofYOVanck5J8caagapNoNUrpjV7Ip8dEy8mp1Ml2HZv8gn7kMLuhJ5pXYuODSvzwcI9rDt4zuo4+at1Nzz/O1SsY4y9//a2sW+4KBqtYe5g4zzah742Dh83SYV8Nr6y5cwNYT9S2J2QcfJSI2qEBvCiI5y8VJDgCHhyATR7ElZ9Av/tCZcd+I+RI9nyM+yZbxxZWNF2MyYKcyUtA40m9wCLrWduCPuRwu6kAn29+PqxZlxJc4CTlwrj5QtdPjVO9jmyBibcAyc2W53KsSUcg4XDoUZLuOMFU5seOX83Zy+l8cJ9txAe4o/CWBVZ3CXvwjoyK8bJzdl6gkG/bObJljUda/FSfuI2GbtEXjptHLjctL/ViRxPVhb81M34Wb2wGsrVNK3pFXtO87fv/+KZVrV4s3OUae2K4pNZMS6sS6OqPNWyFt+vPsysLU5weG94U3jud6hxJ8x+EeYMhoxUq1M5lr++hUN/QIf3TC3qFy6nMWzqNuqEBfKaDLk4NSnsLuCNjnVpXrMcw6dtZ298ktVxClcm1NiVsNUrsPF7+L4jJDrBHyUznN0PS0bAre2g6ROmNau15s1ZO7hwJY0xfRrj5+1pWtvC9qSwuwBvTw/G92tKGV8vBvy0kaSU9MK/yWoensbq1D4/wZndxlYEh1ZancpamRkwc4DxnkTXz01dtTt76wnmbTvJ4LZ1aBAebFq7wj6ksLuISmX9GN+vCUfOX2HoFAddvJSXqK7w7HJjQ7H/dIM1nxvT/NzRmrHGCVWdPoayVUxr9kRCMm/O3EGzGuUYcM8tprUr7EcKuwu5I3vx0sKdDrx4KS8V6xhL5et2MnYvnPqksTWBOzm1wzi/NKo7NOhpWrNZWZqhU7eSmaUZ06eRS+6L7o6ksLuYnIuX1h5wovnivkHQ5z/Q9v9g1yz4tq0x3uwOMtJgxgBjg69OY0wdgvlx7WFW7z/HvzpHUSPUcbYBFqUjhd3FXF28VDM0gEG/bOJUogMvXspNKWg1GPrPgMun4Zv7YPc8q1PZ3+8fQPx26DrWeGPZJPtPJzFqwW7a1K3Ew82rmdausD8p7C4o0NeLr/s340paJgN/3kRahgMvXspL7XuNKZGht8D/+sHSf7vuVgTHN8CqMdD4MYh80LRm0zOzeOXXrQT4eDKyZ0PZyMvF2LywK6XKKKV+VEp9o5R61NbPL4rm1kpBfNgrmo1HLvD+/Fir4xRfSDV4cqFx5N7Kj2BSb2NPcleSdgVmPA9lw+GB901t+vOl+9gel8jIHg2pFCQnG7maEhd2pVQ1pdRypdQupdROpdTL2Xf1AKZqrZ8FutokpSiRztHG4qUf1jjJ4qXcvP2MaX9dPoPDK42tCE5utTqV7Sx9B87tN/as9zNviuGmoxcYv+IAPZtG8EAD82bfCPOUpseeAQzRWkcBLYCBSqkoIAI4lv0YF3397DycbvFSXpr9zei9Z2XCxPbG5ljO7tAfsP5LuP15U48RvJKWwau/bqFyWT/e6ipbBriqEhd2rfVJrfWm7K+TgFggHDiOUdzzfX6l1HNKqQ1KqQ1nzpwpaQRRBE65eCkvEc2McfeI5jDzBZg3xJhN4ky2TYZPGsDbIfCf7lCmkrFIy0Tvz4/lyPkrfNS7EWUd8QQuYRM2GWNXStUEmgDrgelAT6XUl0CepytorSdorWO01jEVK1a0RQRRAKddvJRbYEXoP9M4S/Wvb+GHTrD+6+vF8pMGRvF0RNsmw5yXIPEYoEFnQkoi7J5rWoTle07z33VHeaZVLe68xbzZN8J8pd7dUSkVCPwOvKe1nl7c75fdHc3z7cqDvDsvljcerMvzzr7CcOcMmPYcZOXqtXv7Q5exEN0n/+/NyoKMlFwfqcbn9Fy3C7w/OcfjUiE91+2c918+y/UTQ3MIrgav7LDpjyYvFy6n0f7TPygf4MOsF1vKXjAuoKDdHb1K+cTewDRgUkmKujDX061qsenoBT5YuJvoiBDn7rXVfwgWDIdLp268np4Ms140evL5FefMUg7heHiBl7+xp4uXn/HZO8dtv7I337/x+7yfK/F46bIUgdaaN2fuIOFKGj882VyKuhsocWFXxsTXiUCs1nqM7SIJe7m6eGnPqSQG/bKJuYNaUznYiae6XYrP+3pmat7F1TvX7Zz3e/vluO6X4+Pq/dmP9fQFzxL8s9n/W/YwTC7BETdfs7FZW04wb/tJhj0QSf2qssGXOyhNj70l0B/YrpTakn3tH1rr+aVOJezm6uKlruNWM/DnTfzybAt8vJx0nVpwRD7FspqxetWRtBlhjLGn5zgk2tvfuG5HJxKS+desHcTUKMfzdzv58JsostLMilmltVZa62itdePsDynqTsDpFy9d1WaEURxzMqFYlkh0H2PsP7gaoIzPhb0XUEpZWZrXphgbfH0sG3y5lVKNsQvn1Tm6KpuPJjBx1SGaVA+hW2MnPMvyalFc+o4xVh0cYRR1OxbLUonuY2q2H9YcZs2Bc4zq0VA2+HIzUtjd2PAH67LteALDp22nbuWyRFYOsjpS8ZlcLJ3FvvgkPli4m7b1KtFXNvhyO046uCps4eripUA/L174rxMvXhI3SMvI4pXJWyjj68XIHtGywZcbksLu5ozFS02df/GSuObzZfvYEXeR9x9qSMUgX6vjCAtIYRfcXqs8bzxonLw04Q8nOnlJ3GTT0QuMX76fXs0ieKBBZavjCIvIGLsAjMVLm48m8MHC3SSmpDNr8wlOJCRTNcSfoR0i6d7ECd9cdTNXN/iqEuzPW11kgy93Jj12ARiLlz7oFU2FQB++WH6AuIRkNBCXkMwb07czc7MTbvvrZt6bZ2zw9XGfRgTJBl9uTQq7uCbQ1wu4+Y225PRMRi/aY34gUWTL95xm0vqjPNu6Ni1qO/FWEcImpLCLG5xJSs3z+omE5DyvC+udv5zGsKnbiAwL4tV2dayOIxyAFHZxg6oh/sW6LqxlbPC1nYQraXzSt7Fs8CUAKewil6EdIvHPozjUqhBAaoYciOVoZm6JY/72U7zaLpKoqmWtjiMchBR2cYPuTcIZ2aMh4SH+KKBqsB/31qnAqv3n6PXlWo6eu2J1RJEtLiGZETN30rxmOZ67u7bVcYQDkemO4ibdm4TfNL1x8c5TvDZlK50+X8noXtFyCLLFsrI0r03eSpbWfNy7sWzwJW4gPXZRJO3rV2beS62pXaEMA/67ibdn7yQtI8vqWG7r+zWHWXvwHCO6RFE9NMDqOMLBSGEXRVatfABTBtzFky1r8sOaw/T+ag3HzsvQjNlybvDVJ0Y2+BI3k8IuisXHy4O3utTnq8eacvDsZTqNXcninacK/0ZhE2kZWQz+dQtBssGXKIAUdlEiDzSowrxBrakeGsBzP23k3bm7SM+UoRl7G7t0HztPXOT9HrLBl8ifFHZRYtVDA5j2wl08fmcNvl11iD5fryVOFjLZzcYjF/hixX56N4ugQ33Z4EvkTwq7KBVfL0/e6daAcf2asC/+Ep3GrmTZ7nwOmRYldjk1g1cnb6FqiD8jZIMvUQgp7MImOkdXZc6gVlQN9uepHzYwckGsDM3Y0HvzYzl6/gof95YNvkThpLALm6lVoQzT/34Xj95Rna9/P8gjE9ZxMlGGZkpr+e7T/Lz+KM+1rs0dssGXKAIp7MKm/Lw9ee+hhnz2cGNiT16k42crWb7ntNWxnNb5y2kMnbqNupWDeLW9bPAlikYKu7CLbo3DmT2oFWFl/Xjy+7/4cOFuMmRopli01vxzxnYSk9MY06cxvl6ywZcoGinswm5uqRjIzIEtebh5Nb5YcYB+364n/mKK1bGcxozNcSzYcYoh7WWDL1E8UtiFXfl5ezKqZzSf9G3E9uOJdPxsJSv3nbE6lsOLS0jmrVk7ub1meZ5tLRt8ieKRwi5M8VCTCOYMaklooA+Pf/cnYxbvITNLWx3LId2wwVefRrLBlyg2KezCNLdWCmLWwFb0ahrB2GX7efTbdZyWoZmbfLf6EGsPnuOtLvWpVl42+BLFJ4VdmMrfx5PRvRsxulc0W44l0HHsKtbsP2t1LIexNz6JDxftoW29MHrHRFgdRzgpKezCEr1jqjH7xVaEBHjz6MT1fPrbXrcfmknLyGLw/4wNvkb1bCgbfIkSk8IuLFMnLIhZA1vyUONwPv1tH09892e+h2m7g8+W7mXXyYuM7NGQCoGywZcoOSnswlJlfL34uE8jPujZkL8On6fj2JWsPXDO6lim23jkPF+uOECfmAjaywZfopSksAvLKaXo27w6Mwe2JMjXi0e/XcfnS/eR5SZDM5dTM3jl161UDfHnX51lgy9RelLYhcOoV6Usswe1onN0VT5espcnvv+Tc5dcf2jm3XmxHLtwhTF9GssGX8ImpLALhxLo68VnDzfm/Ycasv6QMTTz56HzVseym2W74/nlz6M8d3dtbq9V3uo4wkVIYRcORylFvzuqM+Pvd+Hv7ckj36zjixX7XW5o5tylVIZN3W5s8NVONvgStiOFXTis+lWDmTOoFQ80qMyHC/fw9I9/cf5ymtWxbMLY4GsHF5PT+aSvbPAlbMvmhV0pVVspNVEpNdXWzy3cT5CfN+MeacK/u9Vn9f5zdBq7ko1HnH9oZvqmOBbuPMWQ9nWoV0U2+BK2VWhhV0pVU0otV0rtUkrtVEq9XNDjtdYHtdZP2y6icHdKKfrfWZNpL9y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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(df.blks, df.time_solve_mean, '-o', base=2)\n",
    "plt.loglog(df_wide.blks, df_wide.time_solve_mean, '-o', base=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prime-pleasure",
   "metadata": {},
   "source": [
    "## Save results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aboriginal-helicopter",
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "\n",
    "res_dump = res + res_wide\n",
    "for e in res_dump:\n",
    "    e['dim'] = (int(e['dim'][0]), int(e['dim'][1]))\n",
    "    e['blks'] = int(e['blks'])\n",
    "\n",
    "with open('res/benchmark_blks.json', 'w') as f:\n",
    "    json.dump(res_dump, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "authorized-bibliography",
   "metadata": {},
   "source": [
    "# Generate plots for report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cordless-catalyst",
   "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": 15,
   "id": "marine-repeat",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_multiple_runs(df, x, y, ystd, label, base=2):\n",
    "    plt.semilogx(df[x], df[y], '-o', label=label, base=base)\n",
    "    plt.fill_between(df[x], df[y] - df[ystd], df[y] + df[ystd], alpha=.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "lovely-degree",
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "plt.figure(figsize=(6, 3))\n",
    "\n",
    "plot_multiple_runs(df, 'blks', 'time_solve_mean', 'time_solve_std', label='$m=1000,\\; n=1000$')\n",
    "plot_multiple_runs(df_wide, 'blks', 'time_solve_mean', 'time_solve_std', label='$m=1000,\\; n=2000$')\n",
    "\n",
    "plt.xlabel('Block size'); plt.ylabel('Time [s]')\n",
    "plt.legend()\n",
    "plt.savefig('res/benchmark_blks.pdf', bbox_inches='tight')"
   ]
  }
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