notebooks/paper_graphs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "652fc3e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#   Copyright 2023 Phasecraft Ltd.\n",
    "#\n",
    "#   Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "#   you may not use this file except in compliance with the License.\n",
    "#   You may obtain a copy of the License at\n",
    "#\n",
    "#       http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "#   Unless required by applicable law or agreed to in writing, software\n",
    "#   distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "#   See the License for the specific language governing permissions and\n",
    "#   limitations under the Licensefrom pathlib import Path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2b15e12",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(str(Path(\"..\", \"lib\").resolve()))\n",
    "\n",
    "import json\n",
    "import logging\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import linregress, median_abs_deviation\n",
    "from time import time\n",
    "from functools import reduce\n",
    "\n",
    "import analysis_helpers\n",
    "import generalized_binomial_sum\n",
    "from importlib import reload\n",
    "generalized_binomial_sum = reload(generalized_binomial_sum)\n",
    "from optimal_angles import optimal_angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a73bc895",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up directories\n",
    "\n",
    "logger = logging.getLogger()\n",
    "logger.setLevel(logging.INFO)\n",
    "\n",
    "DATA_DIRECTORY_QAOA = Path(\"..\", \"data\", \"data_save_analytic_compare\")\n",
    "DATA_DIRECTORY = Path(\"..\", \"data\", \"data_save_analytic_compare_8sat_other_solvers\")\n",
    "SAVE_ANALYTIC_EXPONENTS_DIRECTORY = Path(\"..\", \"data\", \"analytic_exponents\")\n",
    "DATA_SUMMARY_FILENAME = Path(\"..\", \"data\", \"data_save_analytic_compare\", \"summary.json\")\n",
    "FIGURES_DIRECTORY = Path(\"..\", \"figures\")\n",
    "\n",
    "FIGURES_DIRECTORY.mkdir(exist_ok=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bd059392",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up figures\n",
    "\n",
    "def figsize_revtex(scale=1., ratio=3/4):\n",
    "    \"\"\"\n",
    "    Standard figsize for a one-column figure in a revtex document. The standard\n",
    "    aspect ratio chosen here is the golden ratio.\n",
    "    \"\"\"\n",
    "    fig_width_pt = 246               # Get this from LaTeX using \\the\\textwidth\n",
    "    inches_per_pt = 1.0/72.27        # Convert pt to inch\n",
    "    fig_width = fig_width_pt * inches_per_pt * scale    # width in inches\n",
    "    fig_height = fig_width * ratio              # height in inches\n",
    "    fig_size = (fig_width, fig_height)\n",
    "    return fig_size\n",
    "\n",
    "def pt2inch(length):\n",
    "    inches_per_pt = 1.0/72.27        # Convert pt to inch\n",
    "    return length * inches_per_pt\n",
    "\n",
    "pgf_with_latex = {               # setup matplotlib to use latex for output\n",
    "#     \"pgf.texsystem\": \"pdflatex\",   # change this if using xetex or lautex\n",
    "#     \"text.usetex\": False,            # use LaTeX to write all text\n",
    "#    \"font.family\": \"sans-serif\",\n",
    "#    \"font.serif\": [],               # should cause plots to inherit fonts from the document\n",
    "    \"font.sans-serif\" : \"Arial\",\n",
    "    \"mathtext.fontset\": \"custom\",\n",
    "    \"mathtext.rm\": \"sans\",\n",
    "    \"mathtext.it\": \"sans:italic\",\n",
    "    \"mathtext.default\": \"it\",\n",
    "    \"font.monospace\" : [],\n",
    "    \"axes.labelsize\" : 8,      # LaTeX default is 10pt font.\n",
    "    \"font.size\" : 8,\n",
    "    \"xtick.labelsize\" : 8,\n",
    "    \"ytick.labelsize\" : 8,\n",
    "    \"legend.fontsize\" : 6,\n",
    "#    \"pgf.rcfonts\" : false,\n",
    "    \"lines.linewidth\" : 0.75,\n",
    "    \"axes.linewidth\" : 0.5,      # nature physics insists on 1pt lines\n",
    "    \"lines.markersize\": 3,\n",
    "    \"axes.grid\"           : False,\n",
    "    \"legend.frameon\" : True,\n",
    "    \"patch.linewidth\" : 0.5,\n",
    "}\n",
    "plt.matplotlib.rcParams.update(pgf_with_latex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8e98f2b3",
   "metadata": {
    "scrolled": true
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    {
     "name": "stderr",
     "output_type": "stream",
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      "INFO:root:result 0\n",
      "INFO:root:result 1000\n"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading QAOA benchmarks...\n"
     ]
    },
    {
     "name": "stderr",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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      "INFO:root:result 0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Schoning+QAOA benchmarks...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading WalkSATlm benchmarks...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading PySAT benchmarks...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading analytic exponents...\n",
      "Getting summary results...\n"
     ]
    }
   ],
   "source": [
    "# Get QAOA benchmarks\n",
    "print(\"Loading QAOA benchmarks...\")\n",
    "qaoa_benchmarks_df = analysis_helpers.load_qaoa_benchmarks(DATA_DIRECTORY_QAOA)\n",
    "\n",
    "print(\"Loading Schoning+QAOA benchmarks...\")\n",
    "schoning_qaoa_benchmarks_df = analysis_helpers.load_schoning_qaoa_benchmarks(DATA_DIRECTORY)\n",
    "\n",
    "# Get other benchmarks\n",
    "print(\"Loading WalkSATlm benchmarks...\")\n",
    "walksatlm_df = analysis_helpers.load_walksatlm_benchmarks(DATA_DIRECTORY)\n",
    "\n",
    "print(\"Loading PySAT benchmarks...\")\n",
    "pysat_benchmarks_df = analysis_helpers.load_pysat_benchmarks(DATA_DIRECTORY)\n",
    "\n",
    "# Get saved analytic exponents\n",
    "print(\"Loading analytic exponents...\")\n",
    "saved_analytic_exponents = []\n",
    "for saved_analytic_exponent_file in SAVE_ANALYTIC_EXPONENTS_DIRECTORY.glob(\"analytic_exponent*json\"):\n",
    "    with saved_analytic_exponent_file.open(\"r\") as f:\n",
    "        saved_analytic_exponents.append(json.load(f))\n",
    "saved_analytic_exponents_df = pd.DataFrame(saved_analytic_exponents)\n",
    "\n",
    "# Get summary results\n",
    "print(\"Getting summary results...\")\n",
    "with DATA_SUMMARY_FILENAME.open(\"r\") as f:\n",
    "    summary_results = json.load(f)\n",
    "summary_results_df = pd.DataFrame(summary_results)\n",
    "summary_results_df[\"empirical_excess_exponent\"] = summary_results_df[\"empirical_exponent\"] + summary_results_df[\"r\"] * 2.0 ** (-summary_results_df[\"k\"]) / np.log(2)\n",
    "summary_results_df[\"empirical_exponent_relative_error\"] = summary_results_df[\"empirical_exponent_error\"] / summary_results_df[\"empirical_exponent\"]\n",
    "summary_results_df[\"empirical_excess_exponent_relative_error\"] = summary_results_df[\"empirical_exponent_error\"] / summary_results_df[\"empirical_excess_exponent\"]\n",
    "summary_results_df[\"empirical_exponent_runtime_relative_error\"] = summary_results_df[\"empirical_exponent_runtime_error\"] / summary_results_df[\"empirical_exponent_runtime\"]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7a443f34",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans-serif' not found because none of the following families were found: Arial\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['cursive'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'cursive' not found because none of the following families were found: Apple Chancery, Textile, Zapf Chancery, Sand, Script MT, Felipa, Comic Neue, Comic Sans MS, cursive\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans' not found because none of the following families were found: Arial\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['monospace'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'monospace' not found because none of the following families were found: \n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans' not found because none of the following families were found: Arial\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans' not found because none of the following families were found: Arial\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans-serif' not found because none of the following families were found: Arial\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# p=1 relative errors in the exponent\n",
    "\n",
    "n_min, n_max, n_step = 10, 71, 4\n",
    "n_values = np.arange(n_min, n_max + 1, n_step)\n",
    "q_r_values = [(1, 1.0), (2, 9.93), (3, 176.54), (4, 45425.2)]\n",
    "landscape_n, landscape_fit_points, landscape_resolution, landscape_rescalings = 20, 10, 4, [1.0, 0.5, 0.25]\n",
    "colors = [\"b\", \"g\", \"r\", \"k\"]\n",
    "\n",
    "plot_data = []\n",
    "for idx, (q, r) in enumerate(q_r_values):\n",
    "    k = 2 ** q\n",
    "    betas, gammas = optimal_angles[(k, r)][1][\"betas\"], optimal_angles[(k, r)][1][\"gammas\"]\n",
    "    A, b, c = generalized_binomial_sum.generalized_binomial_sum_random_pow2_sat_data(r, betas, gammas)\n",
    "    sum_values = np.array([generalized_binomial_sum.generalized_flip_symmetric_multinomial_sum_p1(q, A, b, c, n) for n in n_values])\n",
    "    sum_ratios = (sum_values[1:] / sum_values[:-1]) ** (1 / (n_values[1:] - n_values[:-1]))# * np.exp(-2 ** (-k) * r)\n",
    "    num_iter, zstar, dz, exponent = generalized_binomial_sum.generalized_binomial_sum_scaling_exponent_ksat(q, r, betas, gammas, num_iter=300, dz_threshold=1e-10, damping=0.9)\n",
    "    #ax.plot(n_values[1:], np.log(sum_ratios.real) / (exponent.real - r * 2 ** (-k)) - 1, \"-o\", color=colors[idx], label=f\"$k$ = {k}\")\n",
    "    #ax.plot(n_values[1:], np.log(sum_ratios.real) / exponent.real - 1, \"-o\", color=colors[idx], label=f\"$k$ = {k}\")\n",
    "    plot_data.append((n_values[1:], np.abs(np.log(sum_ratios.real) / exponent.real - 1)))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "for idx, (q, r) in enumerate(q_r_values):\n",
    "    k = 2 ** q\n",
    "    ax.semilogy(*plot_data[idx], \"-o\", color=colors[idx], label=f\"$k$ = {k}\")\n",
    "ax.set_xlabel(\"$n$\")\n",
    "ax.set_ylabel(\"Relative exponent error\")\n",
    "#plt.legend(loc=\"upper center\", ncol=2, bbox_to_anchor=(0.5, 1.35))\n",
    "ax.legend()\n",
    "fig.tight_layout(pad=0)\n",
    "plt.grid()\n",
    "plt.savefig(Path(FIGURES_DIRECTORY, \"exponent_relative_error.pdf\"), bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd1d7fcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "******************** k = 2 ********************\n",
      "[ 1  2  3  4  5  6  7  8  9 10]\n",
      "[0.1188702  0.06473071 0.04111148 0.03071493 0.02341345 0.01814162\n",
      " 0.01476605 0.01244213 0.01059493 0.00932065]\n",
      "exponent = 0.13417782388875002*p^-1.128465555937889\n",
      "******************** k = 4 ********************\n",
      "[ 1  2  3  4  5  6  7  8  9 10]\n",
      "[0.52997227 0.40648098 0.33795859 0.29253021 0.25883296 0.23231049\n",
      " 0.2106802  0.19282664 0.17838665 0.16549626]\n",
      "exponent = 0.5678138097368761*p^-0.5115584482890002\n",
      "******************** k = 8 ********************\n",
      "[ 1  2  3  4  5  6  7  8  9 10]\n",
      "[0.67575593 0.55782387 0.4909771  0.44719298 0.41495542 0.38989858\n",
      " 0.36921589 0.35190173 0.33865189 0.3265543 ]\n",
      "exponent = 0.6893888446598346*p^-0.32019991393434205\n"
     ]
    },
    {
     "data": {
      "image/png": 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deI7gHSgc/FV8o9rvqTMUFbUOJQUImTGDkF27CLl6lRYGDMOgk7DNlJQU9O/fH0VPnJcHDBiA9957r8P7SkpK4OzsLPd75TgOQqEQxcXFCunq6+sxf/58pKamgq+C32RdXR2qqqoUDmnLoWEtwnEcEv0TW12X7aVsCnh4tA5MefNNYNgwup1wQADg5kaXWf7kE7oyazOXhlawQTj9o7awr1y5ghUrVsDc3BwA0KNHD61GQq1atQpTpkzBkCFDVEq/du1a2NnZKRxisW7DLgf3GwwOitN9ndlL2RhpGZiydi3wxht08O3OHdpPDwujc+giEV2ddfRo6vK6fz/tuxOi/ZU/GSqibjNg+PDhhBBChg0bRggh5OHDh2To0KEd3qdqUzw8PJwIhULi7u5OXF1dCcdxxN3dnZSXlyvNt7a2llRWViocEyZMUPdrqc2OP3YQ3js8eVN805lNOn+mMXPzJiHffEPI8uWEREcTYmNDSL9+rZvzbHWYzqOTPvabb75JVq9eTQYPHkyOHTtGxo8fL19lsSMiIiIUBs+CgoLaTV9UVGR0fezmlFSWkF8KfyEzM2aSIf8dQoruFenluV2BxkZCPvtM+SDciBGErFhByIEDrL+uCTrpY7/77rvg8XiwtbXFv//9b4waNUrl6K7U1FSkpqbCx8cH69atQ3o63aM6KSkJ3333nbqmGByBrQAxnjHYO2Uvnh36LEamjcQfN/8wtFlGAY8HxMYq35V05kzg4UPgv/8FAgPphoZRUcCSJXSzhfPn215ggvXXVUQPBYze0VeN3ZJdObuI/Tp78nXe1wZ5vjHS0cqfUikdhT94kJCVK+kKrt7ehJiZEeLpSYhIRJv3e/cS8vbbTaP13Tl6TSfRXQ0NDThw4IDJR3dpwhz/ORhgPwDTM6bj3I1zWDt2Lcx43WazFaW05Q0ng+PoKLyHB3V3lfHwIXDpEl2PPS+PusEeP970uVQKzJ9Pa/aRI4FBg+gAHoOi9q9uxowZuHXrFkJDQ1WajupujHYfjQvJFzBt/zTEfh6LfVP3ob91f0ObZVBarg6jCj170mZ6YCB9n5mpKGyA9ti/+opun3T1KtCnDxW47PDxoecBA4AnkzhyTH1BChbdpQOcbZyROTcTb/zyBp7e+jS2JWzDM4OfMbRZXRrZTh3NXRT4fCpsgQCor6fivnKFhqpeugR89x19fecO4OlJhT5wIFBeDnz5JS0YOI7O2ZuaH7zawpZFd1laWurCHpPBnG+Oj+I+wjivcXj+2+dx+MphbIjbABtLG6XpJVUSiO+I4d3H22gWdTAmZNFrKSk0zpzPB1JTm2pbc/OmmjohQfHe+/ep4MViIDsb2Lev6TNCgKQkKu4hQ6jwPT2bzn37tl4euiXGWPuz6C4dEzswFn+99BdeOvISnv70aWydsBXxXvEKadIupCH5cDKkRAoex8O2idswL9DEqhAt0FF/vS3s7YHQUHq4uNAtjlsiEgG9egGFhcDZs/RcVARYWND+v1BIHWzc3ZteC4XA0aM0sMbYouDUFnbz6C4ZrFnePg49HPDl1C9x8O+DmPfdPIxxH4MNcRvQ37o/JFUSuagBQEqkSDmcgjivOFZzK0GT/npz2mrSz5nTOl+pFLh5k3reyY6iIuptV1xMPfOaT8vJBvTu3aOryrq7U9fbHj1Ut09btb/awpbNPTPUg+M4TH1qKsZ6jsWKEyvg+4kvVkWuwqA+g+SiliHzO2fC1j4dNembw+M1FSSjRrX+/MQJICZG8Roh1O12/35aEJSXA717A66uNJ+WZ9lre3s68q+tGHiNprs2bNiAY8eOAQDi4uLw6quvarSoeXfEzsoOW8ZvwWz/2Xj1x1dx+8FtcOBA0ORvb2p+58aGpk36lvj4KK/99+xpyvPxY6C0lNbEEglw4wY9X7zY9P7GDTpG8KjZLs6dXYxSbTUuWbIEhYWFePnll8FxHHbs2IHr169j8+bN6j+9GxPqGorfX/gd+y/ux4KjC1DxsAIAFXXqxFRWW+uYzjbpZXl0VPtbWDT1zdtCKgUOHaJr0zVHtjmjXoR98uRJ5OTkgPfEV3DChAkIlE02MtSC4zhM952OSYMm4d3f3sWWc1sQ6hqKYf2HGdo0hopoo/bn8YDhw5XX/l4aNtzU9hUnhCjEOxMaSKLZ0xkAAEszS6yOXg3JvySI9ohG3J44iPaJcP7meUObxlABbWy9q2wxyrb6/qqgtrDj4+Pxj3/8A7t378bu3bsxbtw4jBs3TrOnMxSwsbTB8tHLUfRqEcLcwjBu7zhE7YrC4SuHWw2wMUyP5jHw1651btqMI2pWt1KpFKmpqTj+xL9v7NixSE5OljfNjQGRSNQlo8Va8qj+ET7/63N8dOYjAMC/RvwLs/1no6d5zzbvYY4upo8qv2+1hS1DdpsxzmGbirBlSIkUP4h/wPoz65F9Kxuzn56N5KBk+Dn6KaRjji7dA1V+32pXs8XFxYiLi0OPHj3Qo0cPjBs3rtW6ZQztwuN4mOAzASfmnsDvL/wOc545IndGIiwtDDtzduJh/cM2HV2MaWlkhv5QW9hz5szB2LFjUVZWhlu3biEmJgZz5szRhW0MJQzpNwTr49ZDskSChaELsTNnJ/p/2B/zvp3XpqMLo/uhtrBv376N119/HXZ2drC3t8fSpUtRUVGhC9sY7WBlZoVnhz6Lk4knkfNiDp7u/3SrNDzwmKNLN0VtYXt5eeHKlSvy91euXIG3t7dWjWKoh2dvT3wQ+wG2T9wOXrN/qUMPB6z/fT1+u/6bUe4WytAdajuo1NTUwN/fH2FhYQCAM2fOICwsDFOmTAEAHDx4ULsWMlQmKSgJ8d7xKLhbAM/enrhRdQOHLh3CC9++gKq6KogGiTB58GTEeMbAyqzjbTfZCHvXRe1R8V27drX7+dy5cztlkDYwtVHxzkIIQV55Hg5dOoRDlw7hyp0riPSIRPzAeMR7xcPLwavV7AYbYTdedDrd1ZzHjx/DwsKis9loDSbs9rlZfRM/F/6MHwt+xM+FP6N3j96IGxiHeK94RLhHoPpxNdw3uisMxvE5Pq4tvsZqbiNAJ9Nd48ePx927d+Xvr169Km+WM7oGLjYuSByWiC//+SVuv34be6fshWMvR6w5tQaOHzoiZncMG2Hv4qgt7OjoaISEhODMmTP4+uuvERkZiTfffFMXtjH0AJ/HxwjBCLwT+Q7OJp1FxesVWDmm9TrxHDgU3itEWU2Z2s8wxu2GTR21B8+WLl2KkJAQREVFoU+fPjh16hQ8PT11YRvDANhY2mDW07NQ11CHlMMpaCSN4IGHOK847MrZhUVHF6G/dX+MEIzASMFIjBCMgH9/f1jwlXfFWF/dMKjdx7527RqmT5+OgIAA5OXlYfDgwfj4448V1j8zNKyPrR0kVRIU3C2Al4OXvG9d31iPv8r+whnJGZyVnMUZyRncrL6JIOcgDHcdjiCXIAQ6B8LbwRulNaWsr64DVPl9q11jjx49Gh988AFmzJiBxsZGvPHGGwgNDcVff/2lsaEM40RgK2glQHO+OYJcghDkEoSFoQsBAOUPynFWchbnbpzD3ty9WPLTEtQ8roGHvQdb9slAqCzs/Px8+Pr64vjx43B/shwEn8/Hhx9+iMOHD+vMQIbx49jLEaJBIogGieTXSqtL8XPhz3j+2+cVln0CgI/PfYysG1nwc/SDn6MfBLYClYOJ2Ny6aqg8eDZ79mwAgI+PD0aOHKnwmarb+4jFYoSFhcHHxwchISHIz89vlebEiRMIDQ3FU089BV9fXyxbtkynG9kzdIOzjTPmDpuL7Qnbwefo6gE88PDayNcwxn0MCu4WYPWp1fDb6gf79+wx6rNRSPk+BVv+3xZkFmWirKas1QIeaRfS4L7RHdG7o+G+0R1pF9hm222hco3d/I/c8g+uajc9JSUFycnJSExMREZGBhITE5GVlaWQpnfv3vjyyy/h6emJ2tpajB07Frt370ZiYqKqpjKMiHmB8xDnFdeqry6DEAJJlQR55XnIK8/D+dLz2PnnTly8fRGWfEsM6jsIg/oMgpO1E9b/vl5e+7NlmttHZWE3byq1bDap0owqLy/H+fPn8fPPPwMApk6dioULF6KgoABezRZ2CggIkL+2srLCsGHDcO3aNVXNZBghyvrqMjiOg5udG9zs3DDOu2klHimRQlIlweWKy7h85zJOFJ1o1aRvJI1YdHQRogZEYWDvgfDs7QkPew/0MO94IW9Tb9KrLOxHjx4hNzcXhBCF17LPOqKkpATOzs7yZYo5joNQKERxcbGCsJtz69YtZGRktNuHr6urQ11dncI11nTv+vA4HoR2QgjthIgdGItnBj+Dby9/qzAYxwMP3n288UfpH8i4mIGr966itKYUTr2c4NnbU+nR37o/0rPTTX4KTi1hi0RNgyPNX+tiFZWqqiokJCRg2bJlCA4ObjPd2rVrsWrVKoVrPj4+WreHYVgEtgJsm7hNPrcuW6a5pSBrG2px7f41FN0rwtV7V3H13lUcunRI/rq+sR51jU0VgZRIMf/7+bC2sEaQSxAEtgKVAmSMHa34iqtCeXk5vLy8cPfuXZiZmYEQAmdnZ5w+fbpVjV1dXY24uDiMHz8eK1asaDdfZTX2s88+y0bqTRRlc+uqQgjBN5e+wZSvp7T6bFCfQbhfex/lD8rRr1c/uNm6yVsMstdudm5wsXFBf+v+Cg45+m7W62QeW1McHR0RGBiIPXv2IDExEQcOHIBAIGgl6pqaGsTHxyM+Pr5DUQOApaVlq50/jWlhRYZ2aa+/3hEcxyHENQQ8jtfKaeaXOb9AYCtAbUMtJFUSlFSWoLiyGCVVJbh85zKOXT2GkqoSlFaX4n7tffTt2RcuNi5oJI3IK8+j+YPDyyEvY67/XLjYuMDJ2glmPMPskKPXp6ampiIxMRFr1qyBra2tfB+wpKQkiEQiiEQibNq0CefOncODBw/ksd3Tpk3DW2+9pU9TGSZKW016WWFhZWYFLwevdleeeVT/CKU1pci5lYN/ft20fQcBwcdZH+Onwp9Q/qAc1XXVcLJ2grO1s7ymd+rlBCdrJ4XXTr2cYG9lD47jtFb7660prk+YSymjIzrTpJeRWZSJ6N3Rra/PzUSkRyQePH6A0ppS3Ky+iRtVN1D2oAxlNWUoe1CGWzW3FN7zOB6sza1xt5ZGTrY3qGdUTXEGw5joTJNehncfb6XNellt38uiV4e1P/BkIYzbefDf6i+/1tl5etYZZTA0RNasl3nWabqhIsdxqHhQoXSeXtMYeFZjMxidoCPPOlXpqPZXF1ZjMxidRGArQKRHZKea9tqq/WWwGpvBMBK0VfsDTNgMhlGhjUE9oDs2xSsrge3bDW0Fg6FTup+wi4uBFSuALVsMbQmDoTO6l7DT0oBhw4DycuCVV4D//MfQFjEYOqH7CFsiAZKTgeYhnStWAGytNoYJ0n2ELRYrilrGzJnAw4f6t4fB0CHdR9je3kDLqC8eD/DwAOLjgaoqg5jFYOiC7iNsgQDYtg3gUwcA8Pn0/bffAu7uQEwMcOuWYW1kMLRE9xE2AMybB1y7BmRm0vO8eYCZGbBrFxARAQQHA2fPGtpKBqPTdD8HFYGAHs3h8YAPPwQCA4Fx44A33gCWLqWiZzC6IN2rxu6IZ58FzpyhzfNRo4A//zS0RQyGRjBht2TwYOD0aWD6dCAyEkhKAkpLDW0Vg6EWTNjK4POB114DLl8GLCyAQYOABQuAoiLFdBIJ7a9L2PawDOOCCbs9HB2BTz6hTix8PuDvD0ybBvz4I/U3d3cHoqPpOY1tN8MwHpiwVcHDA9i8GSgsBEJDgYULFb3YpFIgJYXV3AyjgQlbHfr1A15/nc5/t6SxEdi3D3jwQP92MRgtYMLWBB+f1l5sHAd8/jnQty+dE1+1Cjh+nIaJqgLrrzO0CBO2JijzYtu+nfbFJRLg1VeB27eBZctoLT94MDBnDg0V/fVXoKJCMb+0NNZfZ2gVtq54Z5BIgIICwMurtdOLjEeP6Hz4uXP0yMsDLl0C7OyAp56iQt69G2j+b+DzqWdcW3l2ZJNYTH3jNbmfYfSwdcV1jTIvtpb06AGMGEEPGQ0NwNWrQH4+8P33iqIGaH99wgQgIAAQCgEXF3q4utKzo2NTa6E5aWlNg3o8Hm1VzOvELpKskOiyMGEbAjMz2k/38QFCQqivevOQUh4P+Ne/aMSZREIdZm7eBG7coMejR0D//lTkTk60X29pSbsDskJCKqUiDwkBfH2VFwTtoc1CghUQeocJ29DI+uspKbSm5vOB1FQgMbHte6qrm4R++zbts2dlta75pVIa2NLQANjY0Oa/Kkd9PTB/futCYswY2u1QZ9tkY21FaLOwMcKCS6/CFovFmDt3LioqKmBnZ4edO3fC19e3Vbq0tDSsW7cOUqkU0dHR+OSTT2Bubq5PU/XLvHlAXFzH/XUZNjbUG27QoKZrEgkdlW9e8/P5dO69d286Ot/ecfMm8Pff9PX168oLCdm+4z17Ar16KT969qTdD0tLWqB89pliHvPnA/fu0daGlZXyw9Ky6WxhAZib0/POndopJLRZ2BhpwaVXYaekpCA5ORmJiYnIyMhAYmIisrKyFNIUFRVh5cqVuHDhApycnDBp0iRs27YNCxYs0Kep+keV/npH9yur+d3c6OfW1rSPrgoSCR3UU1ZI9OlD5+rbO+rqgNpa4OLF1nkTAhw5Atja0jSyQ3ZPy6O+XvnKN1Ip9eNfuZIWJDLxm5srvm55rb4eOHBAMZ/584HsbMDBgXaT+HzFc1vX7t+nzkotWzY2NoCzs+r58Pn02LsXWLyY5tfJQsLoNr7/4IMPUFhYiE8//RQAcPToUaxZswanT59W+VnderdNVUbqVSEtrXUhoe6PrK0CQt0Rf6kUOHaMrnTTkl276CDj48dUtLJz89fNz3l5wKZNrfN57jlqU0MDPRobFc/KXpeVKY/fHzyYtlw6yqfltbo6xXza+FsZ1ah4SUkJnJ2dYfYkxpnjOAiFQhQXFysIu7i4GO7u7vL3Hh4eKC4ubjPfuro61LX4g0iVlfDdhc7W/DLU7R60ZYuyVoS6efF4dACQx2tdSERHq5efREL9CVrms26d+na1VXAdO6Z+XpmZ9Ls0p7GR/v01+Nt3eQeVtWvXws7OTuEQi8WGNss0EAho6GpnCgplq9ZoaktLpyBNCglt5aPtvJStycfn00JVE4ieKCsrIzY2NqS+vp4QQohUKiVOTk5ELBYrpHv//fdJSkqK/P2RI0fIqFGj2sy3traWVFZWKhwTJkzQzZdgGJ6SEkIyM+nZGPLRZl47dhDC5xMC0POOHUqTJSQkdJiV3oRNCCEREREkPT2dEELI/v37SVBQUKs0hYWFxNnZmZSWlhKpVEoSEhLIli1b1HqOKl+cwTBKVCgkVPl967UpnpqaitTUVPj4+GDdunVIT08HACQlJckHAzw9PbFq1SqMGjUKXl5e6NevH1JSUvRpJoNhOLTR/QHzFWcwuhxGNSquTwoLCyESiXT+HKlUCrFYDG9vb/BaDnwYCGaTahijTYBqdhUWFnaYj0nW2PqiqqoKdnZ2qKyshK2traHNAcBsUhVjtAnQnl3GU1QxGAytwYTNYJggTNgMhgnChN0JLC0t8fbbb8PS0tLQpshhNqmGMdoEaM8uNnjGYJggrMZmMEwQJmwGwwRhwmYwTBAmbA2ora3FM888Ax8fH/j7+yM2NhYFBQWGNktOeno6OI7DN998Y2hTANCY+YULF8Lb2xtDhw7FrFmzDG0Sjh49isDAQAwbNgx+fn7YtWuX3m145ZVX4OHhAY7jkJOTI78uFosRFhYGHx8fhISEID8/X/3MtRKR0s149OgROXLkCJFKpYQQQrZs2UIiIiIMa9QTioqKyMiRI8mIESPIoUOHDG0OIYSQxYsXk4ULF8r/XqWlpQa1RyqVkt69e5M///yTEEL/ZpaWlqSqqkqvdvz666+kpKSEuLu7k+zsbPn1qKgohSjI4OBgtfNmwtYCWVlZxN3d3dBmkMbGRhITE0POnz9PIiIijELYNTU1xMbGhlRWVhraFDlSqZQ4ODiQX3/9lRBCyJ9//klcXFxIXV2dQexpLmxV1y3oCNYU1wKbNm3CpEmTDG0GPvroI4waNQpBQUGGNkVOYWEhHBwcsGbNGgQHB2P06NE4fvy4QW3iOA5fffUVpkyZAnd3d4SHh2PXrl2wsLAwqF1A+0uIqYNJRnfpkzVr1qCgoMDgP9a8vDwcOHAAv/32m0HtaElDQwOuX7+Op556CuvWrUN2djZiY2ORn58PJycng9m0evVqHDx4EGPGjEFWVhZEIhFyc3PRt29fg9ikbViN3Qk+/PBDHDx4ED/88AN69uxpUFtOnTqFa9euwdvbGx4eHjh79iySk5OxdetWg9olFArB4/Hw3HPPAQACAgIwYMAA5ObmGsymnJwc3Lx5E2PGjAEAhISEQCAQIDs722A2yXBzc0NpaSkaGhoAAIQQFBcXQygUqpeRlrsL3Yb169eTwMBAcvfuXUObohRj6WMTQkhsbCw5cuQIIYSQq1evkj59+hCJRGIwe27dukWsra3JxYsXCSGEiMVi0rt3b3L9+nWD2NNy8EyVJcQ6gglbA0pKSggA4unpSfz9/Ym/vz8JDQ01tFkKGJOwCwsLSWRkJPHz8yNPP/00ycjIMLRJ5IsvvpDb4+fnR/bu3at3G5KTk4mrqyvh8/nE0dGRDBw4kBBCyKVLl8iIESOIt7c3CQoKIn/99ZfaeTNfcQbDBGF9bAbDBGHCZjBMECZsBsMEYcJmMEwQJmwGwwRhwmYwTBAmbAbDBGHCZjBMECZshkZwHIcVK1YgICAAPj4+2Lt3r6FNYjSDRXcxNIbjOGRnZ+Pq1asIDg7GqFGj4OHhYWizGGA1NqMTJCUlAaBbH48ZM8boQka7M0zYDK3BcZyhTWA8gQmboTHp6ekAgGvXruHUqVMYPXq0gS1iyGB9bIbGNDY2IiAgAA8ePMDmzZtZ/9qIYGGbDI3gOA737t2Dvb29oU1hKIE1xRkME4Q1xRkawRp6xg2rsRkME4QJm8EwQZiwGQwThAmbwTBBmLAZDBOECZvBMEGYsBkME4QJm8EwQZiwGQwT5P8Dtq5K9b8kD/EAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "\n",
    "cols = [\"r\", \"g\", \"b\", \"k\"]\n",
    "\n",
    "for index, k in enumerate(sorted(summary_results_df[\"k\"].unique())):\n",
    "    print(f\"******************** k = {k} ********************\")\n",
    "    summary_results_fixed_k_df = summary_results_df.query(f\"k == {k}\")\n",
    "    # Show analytic results for all p\n",
    "    pvals = summary_results_fixed_k_df[\"p\"].to_numpy()\n",
    "    exps = -summary_results_fixed_k_df[\"analytic_exponent\"].to_numpy()\n",
    "    # Discard NaN values\n",
    "    if len(pvals) > 10:\n",
    "        pvals = pvals[:10]\n",
    "        exps = exps[:10]\n",
    "    print(pvals)\n",
    "    print(exps)\n",
    "    a, b = np.polyfit(np.log(pvals), np.log(exps), 1)\n",
    "    print(f'exponent = {np.exp(b)}*p^{a}')\n",
    "    #    log y = b log x + a\n",
    "    #    y = e^a*x^b\n",
    "\n",
    "    xrange = np.arange(1,np.max(pvals),0.01)\n",
    "    \n",
    "    ax.plot(pvals, exps, 'o', label=f\"k={k}\", color=cols[index])\n",
    "    ax.plot(xrange, [np.exp(b) * p ** a for p in xrange], color=cols[index])\n",
    "    ax.set_ylabel(\"Exponent\")\n",
    "    ax.set_xlabel(\"p\")\n",
    "    index += 1\n",
    "    \n",
    "ax.legend()\n",
    "fig.tight_layout(pad=0)\n",
    "fig.savefig(Path(FIGURES_DIRECTORY, f\"k_{k}_scalingwithp.pdf\"), bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0fc863c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "\n",
    "cols = [\"r\", \"g\", \"b\", \"k\"]\n",
    "\n",
    "k = 8\n",
    "\n",
    "summary_results_fixed_k_df = summary_results_df.query(f\"k == {k}\")\n",
    "# Show analytic results for all p\n",
    "pvals = summary_results_fixed_k_df[\"p\"].to_numpy()\n",
    "exps_analytic = -summary_results_fixed_k_df[\"analytic_exponent\"].to_numpy()\n",
    "exps_numeric_prob = -summary_results_fixed_k_df[\"empirical_exponent\"].to_numpy()\n",
    "exps_numeric_prob_error = summary_results_fixed_k_df[\"empirical_exponent_error\"].to_numpy()\n",
    "exps_numeric_median = summary_results_fixed_k_df[\"empirical_exponent_runtime\"].to_numpy()\n",
    "exps_numeric_median_error = summary_results_fixed_k_df[\"empirical_exponent_runtime_error\"].to_numpy()\n",
    "# Discard NaN values\n",
    "#if len(pvals) > 10:\n",
    "#    pvals = pvals[:10]\n",
    "#    exps = exps[:10]\n",
    "\n",
    "a_analytic, b_analytic = np.polyfit(np.log(pvals[:10]), np.log(exps_analytic[:10]), 1)\n",
    "a_numeric_prob, b_numeric_prob = np.polyfit(np.log(pvals), np.log(exps_numeric_prob), 1)\n",
    "a_numeric_median, b_numeric_median = np.polyfit(np.log(pvals), np.log(exps_numeric_median), 1)\n",
    "a_numeric_median_short, b_numeric_median_short = np.polyfit(np.log(pvals[:10]), np.log(exps_numeric_median[:10]), 1)\n",
    "#print(f'exponent = {np.exp(b)}*p^{a}')\n",
    "#    log y = b log x + a\n",
    "#    y = e^a*x^b\n",
    "\n",
    "xrange = np.arange(1,np.max(pvals),0.01)\n",
    "\n",
    "ax.plot(pvals, exps_analytic, 'o', label=\"Analytic\", color=\"r\")\n",
    "ax.plot(pvals, exps_numeric_prob, 'o', label=\"Numerical (inverse probability)\", color=\"g\")\n",
    "ax.fill_between(pvals, exps_numeric_prob - exps_numeric_prob_error, exps_numeric_prob + exps_numeric_prob_error, alpha=0.3, color=\"g\")\n",
    "ax.plot(pvals, exps_numeric_median, 'o', label=\"Numerical (median running time)\", color=\"b\")\n",
    "ax.fill_between(pvals, exps_numeric_median - exps_numeric_median_error, exps_numeric_median + exps_numeric_median_error, alpha=0.3, color=\"b\")\n",
    "ax.plot(xrange, [np.exp(b_analytic) * p ** a_analytic for p in xrange], color=\"r\")\n",
    "ax.plot(xrange, [np.exp(b_numeric_prob) * p ** a_numeric_prob for p in xrange], color=\"g\")\n",
    "ax.plot(xrange, [np.exp(b_numeric_median) * p ** a_numeric_median for p in xrange], color=\"b\", linestyle=\"dashed\")\n",
    "ax.plot(xrange, [np.exp(b_numeric_median_short) * p ** a_numeric_median_short for p in xrange], color=\"b\")\n",
    "ax.set_ylabel(\"Exponent\")\n",
    "ax.set_xlabel(\"p\")\n",
    "ax.axhline(0.325, color=\"k\", linestyle=\"dashed\")\n",
    "    \n",
    "ax.legend()\n",
    "fig.tight_layout(pad=0)\n",
    "fig.savefig(Path(FIGURES_DIRECTORY, f\"k_{k}_scalingwithp_multiple.pdf\"), bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "87670c8a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  4  5  6  7  8  9 10 14 30 60]\n",
      "Loading p=1\n",
      "[12, 13, 14, 15, 16, 17, 18, 19, 20]\n",
      "[3.53852578e-03 2.27544864e-03 1.44764647e-03 9.16658286e-04\n",
      " 5.90210874e-04 3.69698895e-04 2.31894704e-04 1.42023112e-04\n",
      " 9.44307111e-05]\n",
      "p=1 2**(-0.658520375254191n + -0.2191994921686201)\n",
      "Loading p=2\n",
      "[12, 13, 14, 15, 16, 17, 18, 19, 20]\n",
      "[0.00921642 0.0063651  0.00432873 0.00295155 0.00203876 0.0013775\n",
      " 0.00092817 0.00061383 0.00044112]\n",
      "p=2 2**(-0.5534164862595246n + -0.10587771228997693)\n",
      "Loading p=4\n",
      "[12, 13, 14, 15, 16, 17, 18, 19, 20]\n",
      "[0.02651263 0.01968768 0.01429012 0.01055434 0.0078362  0.00569508\n",
      " 0.0041006  0.00293852 0.00226742]\n",
      "p=4 2**(-0.4485814653242474n + 0.15778426097013867)\n",
      "Loading p=8\n",
      "[12, 13, 14, 15, 16, 17, 18, 19, 20]\n",
      "[0.07506239 0.05984873 0.04583239 0.03632174 0.02872177 0.02219467\n",
      " 0.01693452 0.01309617 0.01087561]\n",
      "p=8 2**(-0.35513204987163444n + 0.537054181857411)\n",
      "Loading p=30\n",
      "[12, 13, 14, 15, 16, 17, 18, 19, 20]\n",
      "[0.33408651 0.29084842 0.24142863 0.20943259 0.17724713 0.15295147\n",
      " 0.12654304 0.10410626 0.09252376]\n",
      "p=30 2**(-0.236221415930034n + 1.2735022024410916)\n",
      "Loading p=60\n",
      "[12, 13, 14, 15, 16, 17, 18, 19, 20]\n",
      "[0.51954879 0.46394754 0.39987756 0.35495424 0.30834978 0.26939719\n",
      " 0.22926701 0.19172078 0.1761391 ]\n",
      "p=60 2**(-0.20116664063436931n + 1.4995676656102865)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Empirical vs theoretical fit for k=8\n",
    "\n",
    "# Demonstrates empirical probabilities match the theoretical values very well;\n",
    "# that they fit exponential decay very well; and that the constant factors aren't too bad.\n",
    "k = 8\n",
    "summary_results_fixed_k_df = summary_results_df.query(f\"k == {k}\")\n",
    "pvals = summary_results_fixed_k_df[\"p\"].to_numpy()\n",
    "#for p in pvals:\n",
    "print(pvals)\n",
    "colours = {1: 'r', 2: 'g', 4: 'b', 8: 'm', 30: 'lime', 14: 'c', 30: 'c', 60: 'k'}\n",
    "\n",
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "\n",
    "for p in [1,2,4,8,30,60]:\n",
    "    print(f\"Loading p={p}\")\n",
    "    summary_results_fixed_kp_df = summary_results_fixed_k_df.query(f\"p == {p}\")\n",
    "    #print(summary_results_fixed_kp_df)\n",
    "    analytic_exp = -summary_results_fixed_kp_df[\"analytic_exponent\"].to_numpy()[0]\n",
    "    empirical_x = summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_x\"].to_numpy()[0]\n",
    "    empirical_y = np.array(summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_y_mean\"].to_numpy()[0])\n",
    "    empirical_y_errs = summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_y_std\"].to_numpy()[0]\n",
    "    empirical_y_count = summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_y_count\"].to_numpy()[0]\n",
    "    empirical_y_prob = [1/y for y in empirical_y]\n",
    "    empirical_y_med = summary_results_fixed_kp_df[\"empirical_runtime_exponent_fit_curve_y_median\"].to_numpy()[0]\n",
    "    empirical_y_med_errs = summary_results_fixed_kp_df[\"empirical_runtime_exponent_fit_curve_y_median_abs_deviation\"].to_numpy()[0]\n",
    "    empirical_y_med_count = summary_results_fixed_kp_df[\"empirical_runtime_exponent_fit_curve_y_count\"].to_numpy()[0]\n",
    "#    y = 2^{en}\n",
    "#    e = log y / log n\n",
    "    print(empirical_x)\n",
    "    print(empirical_y)\n",
    "#    y = 2^{-e x}\n",
    "#    log y = -e \n",
    "#    plt.plot(empirical_x, [np.log2(y) / x for x,y in zip(empirical_x,empirical_y_runtime)])\n",
    "#    plt.plot(empirical_x, [np.log2(y) / x for x,y in zip(empirical_x,empirical_y_med)])\n",
    "    a, b = np.polyfit(empirical_x, [np.log2(y) for y in empirical_y], 1)\n",
    "    print(f\"{p=} 2**({a}n + {b})\")\n",
    "    ax.semilogy(empirical_x, empirical_y, 'o', color=colours[p])\n",
    "    ax.fill_between(empirical_x, empirical_y - empirical_y_errs / np.sqrt(empirical_y_count), empirical_y + empirical_y_errs / np.sqrt(empirical_y_count), color=colours[p])\n",
    "    ax.semilogy(empirical_x, [2**(a*x+b) for x in empirical_x], color=colours[p], label=f\"p={p}\")\n",
    "    ax.semilogy(empirical_x, [2**(-analytic_exp*x) for x in empirical_x], color=colours[p], linestyle='dashed')\n",
    "#    plt.axhline(analytic_exp, color=\"k\", linestyle=\"dashed\")\n",
    "\n",
    "ax.set_xlabel(\"n\")\n",
    "ax.set_ylabel(\"Mean success probability\")\n",
    "ax.legend()\n",
    "fig.tight_layout(pad=0)\n",
    "fig.savefig(Path(FIGURES_DIRECTORY, \"8_sat_fits.pdf\"), bbox_inches=\"tight\")\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "91ab99b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  4  5  6  7  8  9 10 14 30 60]\n",
      "Loading p=1\n",
      "p=1 2**(0.6595928896436642n + 0.5268349914227465) [median] or p=1 2**(0.658520375254191n + 0.2191994921686201) [prob]\n",
      "[350.5792564185915, 549.6185740270289, 860.6837328336115, 1378.4695915664172, 2113.514892719282, 3393.7676168881494, 5431.222722770085, 9083.66912790143, 12931.434971646471]\n",
      "[282.6035648279715, 439.4737737795216, 690.7763879123048, 1090.9190651848778, 1694.3096836420216, 2704.903948793777, 4312.302027007059, 7041.107508461349, 10589.775171987894]\n",
      "Loading p=2\n",
      "p=2 2**(0.5511299614511248n + 0.41376832432419786) [median] or p=2 2**(0.5534164862595246n + 0.10587771228997693) [prob]\n",
      "[131.68513658122043, 191.06731564680857, 278.64520032969017, 407.11675435411263, 599.3108925059356, 872.3096752379365, 1279.7336336630074, 2002.2054383452737, 2686.1044357708215]\n",
      "[108.50196626063345, 157.10677259809623, 231.01483632078518, 338.80553821065166, 490.4934126550551, 725.9514469503507, 1077.3869134486486, 1629.1086932114158, 2266.942472601179]\n",
      "Loading p=4\n",
      "p=4 2**(0.4529181093339734n + 0.044489075822630085) [median] or p=4 2**(0.4485814653242474n + -0.15778426097013867) [prob]\n",
      "[45.078924921410305, 60.83290131216403, 83.96209922136714, 113.37986451260758, 155.656138958002, 210.9512874457959, 294.5352741574345, 414.14002363628913, 542.5097118561824]\n",
      "[37.71787335250456, 50.79318053495855, 69.97841352022121, 94.7477688510129, 127.61291437960263, 175.59018446316864, 243.866891506722, 340.30742100453233, 441.0295119454915]\n",
      "Loading p=7\n",
      "p=7 2**(0.3861966690680686n + -0.3903760348015343) [median] or p=7 2**(0.3725949932478318n + -0.46984327379168594) [prob]\n",
      "[19.10790206148014, 24.471025882612906, 32.76483243393403, 41.84245136818913, 54.457419781401114, 71.53540765178722, 97.67400696629335, 125.83777773009855, 157.13903156451792]\n",
      "[16.170202532191556, 20.531969038947253, 27.059335294695057, 34.57617257528306, 44.20879419620327, 57.88301098207688, 76.59258880251208, 100.32637160820791, 123.7464523086427]\n",
      "Loading p=8\n",
      "p=8 2**(0.3697958962408101n + -0.4689030269093524) [median] or p=8 2**(0.35513204987163444n + -0.5370541818574105) [prob]\n",
      "[15.720728459426283, 19.914379228597085, 26.53221911259285, 33.639534410632905, 43.109385838342526, 56.101049758517014, 74.95625728792555, 95.88426077731506, 118.3817338751505]\n",
      "[13.322251431648011, 16.708792654015106, 21.81862898292827, 27.531718902609494, 34.81679814898999, 45.0558705169062, 59.050962597858195, 76.35821163713483, 91.94885631659504]\n",
      "Loading p=30\n",
      "p=30 2**(0.31315595979202526n + -2.1127859628768046) [median] or p=30 2**(0.23622141593003396n + -1.273502202441091) [prob]\n",
      "[3.140063257251409, 3.78168933409342, 4.9305830075175425, 5.9551447533937205, 7.502039390103621, 9.31080745988452, 11.534453198793798, 14.578573592513848, 17.313443045501916]\n",
      "[2.9932367080552273, 3.43821707396999, 4.142010883583422, 4.774805998013956, 5.6418404384117, 6.538021708181673, 7.902449891021419, 9.605570750436232, 10.808034282826677]\n",
      "Loading p=60\n",
      "p=60 2**(0.3017633429182282n + -2.842403349100193) [median] or p=60 2**(0.20116664063436931n + -1.4995676656102865) [prob]\n",
      "[1.7920967335890072, 2.1004250217329794, 2.582769973668996, 3.1224388557827543, 3.834064967962451, 4.7974304135712424, 6.05152558210112, 7.953793694193282, 8.927710596910448]\n",
      "[1.9247470542138716, 2.155416100065403, 2.500765500627229, 2.8172645755118166, 3.2430702191507894, 3.711991171926413, 4.361726495310141, 5.215918729764203, 5.677331230717234]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Empirical inverse success probability vs median runtime\n",
    "\n",
    "k = 8\n",
    "summary_results_fixed_k_df = summary_results_df.query(f\"k == {k}\")\n",
    "pvals = summary_results_fixed_k_df[\"p\"].to_numpy()\n",
    "#for p in pvals:\n",
    "print(pvals)\n",
    "colours = {1: 'r', 2: 'g', 4: 'b', 8: 'm', 30: 'lime', 7: 'c', 30: 'c', 60: 'k'}\n",
    "\n",
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "\n",
    "for p in [1,2,4,7,8,30,60]:\n",
    "#for p in [1,2,4,8]:\n",
    "    print(f\"Loading p={p}\")\n",
    "    summary_results_fixed_kp_df = summary_results_fixed_k_df.query(f\"p == {p}\")\n",
    "    #print(summary_results_fixed_kp_df)\n",
    "#    analytic_exp = -summary_results_fixed_kp_df[\"analytic_exponent\"].to_numpy()[0]\n",
    "    empirical_x = summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_x\"].to_numpy()[0]\n",
    "    empirical_y = np.array(summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_y_mean\"].to_numpy()[0])\n",
    "    empirical_y_errs = summary_results_fixed_kp_df[\"empirical_exponent_fit_curve_y_std\"].to_numpy()[0]\n",
    "    empirical_y_prob = [1/y for y in empirical_y]\n",
    "    empirical_y_med = summary_results_fixed_kp_df[\"empirical_runtime_exponent_fit_curve_y_median\"].to_numpy()[0]\n",
    "#    y = 2^{en}\n",
    "#    e = log y / log n\n",
    "#    print(empirical_x)\n",
    "#    print(empirical_y)\n",
    "#    y = 2^{-e x}\n",
    "#    log y = -e \n",
    "#    plt.plot(empirical_x, [np.log2(y) / x for x,y in zip(empirical_x,empirical_y_runtime)])\n",
    "#    plt.plot(empirical_x, [np.log2(y) / x for x,y in zip(empirical_x,empirical_y_med)])\n",
    "    a_prob, b_prob = np.polyfit(empirical_x, [np.log2(y) for y in empirical_y_prob], 1)\n",
    "    a_med, b_med = np.polyfit(empirical_x, [np.log2(y) for y in empirical_y_med], 1)\n",
    "    print(f\"{p=} 2**({a_med}n + {b_med}) [median] or {p=} 2**({a_prob}n + {b_prob}) [prob]\")\n",
    "    print(empirical_y_med)\n",
    "    print(empirical_y_prob)\n",
    "    #plt.fill_between(empirical_x, empirical_y - empirical_y_errs, empirical_y + empirical_y_errs, color=colours[p], alpha=0.1)\n",
    "    ax.semilogy(empirical_x, empirical_y_prob, 'o', color=colours[p])\n",
    "    ax.semilogy(empirical_x, empirical_y_med, 'o', color=colours[p], label=f\"p={p}\")\n",
    "    ax.semilogy(empirical_x, [2**(a_med*x+b_med) for x in empirical_x], color=colours[p])\n",
    "    ax.semilogy(empirical_x, [2**(a_prob*x+b_prob) for x in empirical_x], color=colours[p], linestyle=\"dashed\")\n",
    "    #ax.semilogy(empirical_x, [2**(-analytic_exp*x) for x in empirical_x], color=colours[p], linestyle='dashed')\n",
    "#    plt.axhline(analytic_exp, color=\"k\", linestyle=\"dashed\")\n",
    "\n",
    "ax.set_xlabel(\"n\")\n",
    "ax.set_ylabel(\"Running time\")\n",
    "ax.legend()\n",
    "fig.tight_layout(pad=0)\n",
    "fig.savefig(Path(FIGURES_DIRECTORY, \"running_time.pdf\"), bbox_inches=\"tight\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5d9d8a01",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_21638/1797470480.py:47: FutureWarning: Passing 'suffixes' which cause duplicate columns {'benchmark_id_x'} in the result is deprecated and will raise a MergeError in a future version.\n",
      "  lambda df1, df2: pd.merge(df1, df2, how=\"outer\", on=(\"n\", \"k\", \"r\", \"instance_id\")),\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WalkSAT QAOA scaling: 2^(0.294661666762821n+-3.2323811123290676)\n",
      "QAOA (p=14) scaling: 2^(0.32638748345993424n+-1.0636440846742952)\n",
      "QAOA (p=60) scaling: 2^(0.3017633429182282n+-2.842403349100193)\n",
      "WalkSATlm scaling: 2^(0.3245940329322641n+-0.3085224542219832)\n",
      "MapleSAT scaling: 2^(0.46053677508303426n+1.5311571374694621)\n",
      "Glucose4 scaling: 2^(0.4983789278274395n+2.99833004563839)\n"
     ]
    },
    {
     "data": {
      "image/png": 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lJfj2228tJUuLQSJ5pNgAcx8fDwwfDhjzPdOXoOHl5YWCggKUlZVBLBbD3t4efn5+yMnJwd27d+tM6CgrK4NKpYKHhwdiYmJw+vRpDB48mD2voKBAS0FLSkqwdOlSiMVixMbGYubMmbh27RpWr16tNb63tzd+/PFHvfKrVCrs3r0bv/76q5Zyd+3aFUlJSVCpVCgtLdVSbAAoKiqCj48PunTpAjs7O3h5eWHs2LGGf3Bof84vFokESE0FxGLjvmx6MEq5w8LC8M8//xiVwtYcNNZbnpr6SLE1qFRAWppxn7ePjw/S09O1XissLISbmxu2b9+OS5cuYcSIESguLsbevXsxYcIEvQkdI0eOxIEDB5Ceno4RI0agqqoKhYWFWspdGwcHB4SEhABg/m6ZmZmIi4tDXFycwfJ///33mDRpEmshKBQKVFRUoKioCFVVVbh69apOSLIGJycnrpyVsZjDXKyBUQ61goIChIaGYuTIkRg3bhx7a2k0NuVTLGY+25oIBICxPp1Ro0Zh3759KCgoAMCYuIMGDYKNjQ2OHDmCs2fP4tChQzhz5gwOHz6Mzp07Q6VSsTngqampuHLlCiIjI7F3714cO3YMhw4dwsmTJ3Hr1i0tp5anpycePHjAPq+oqEBqaiqICNevX0dAQACOHj2K2NhYxMTEaDn59EFEuHbtGrZt24bo6GgkJyfjX//6FwoKCiCRSNCzZ0+EhYWxPyC1qZkeymEAycnAvHm65mIjShwbNXPPmDEDM2bMMPlirQU/P+ZHMz6embEFAmDzZuOtJHd3d3zyyScYN24cKisr4ejoiIMHDyI1NRUuLi6sVWFlZQUbGxvk5OSwCR0VFRUQCAT44YcfIJPJkJeXx67dAaawxalTp9jZm8fjITg4GBKJBH5+fnB1dcXGjRtx6dIljB07Fh06dEBcXBx69+6tZUZr6sffvHkTCxYsQHJyMgYOHIgFCxZg1qxZWLBgAezt7fHUU09h165d4PF4OHToECZOnAgrKyt2jNpj1jWjcwBQKoFbt4Dz54Fz55j727eB2jsQppiLNWi2uuVNRWNiyyUS5rMNCmr08gclJSV46qmnsHXrVpMrzDTEjRs38PPPP+Pdd99FeHg4Ll68qHVcoVDg+vXrOu8TCoWQy+UQiURwcHBgb/oUlIgwZcoU7Nq1S8uhp1AoIJfLYWtrq/O+NhvPb8j6mAjIzn6kxOfPA5cuAR4eQL9+QP/+zH2HDkCPHtrrQYEAyMrSGdusseXr16/H0qVLsWTJEr3Ha6YItiX8/Bqv1BpcXV1Zc9tS9OzZU+8Ph1qthlQqrTNGwcPDA56engb5J3g8Hn766Sed121sbNrXbF3X+rioCLhw4ZEinz8PKBSMAvfrB7z2GhARAfj46I5pDnOxBgYpt8YxUtd2iaU5f/48Xn31VRARhg4dilWrVjWLHK0FpVKJP//8ExKJBJWVlaisrIS1tXWd5X/c3Nza/NamWdG3nTJvHrBqFZCXB/TuzSjy5MnA+vX6nTj6mDOH2ZIxk7lokHLHx8cDAMaOHYtevXppHdNn5pmbxx9/HKdPnwYAPPHEEygrK4OTk5PFr9sSUCgUkMlkEAqFdZrJcrkcFRUV7E0ul8POzg4ODg7w8vKCg4MDrK2tAejuSXPrYwNRq4E7d5iZ+JdfdLdTiIBly4Dnnwca40w0o7lolENt1qxZuHz5coOvmRvNF1OlUqFjx44tpgCdpdGniO7u7qisrERFRQV7D4BdJ7u7u8Pe3r7O3lyenp5wdnauc33M8ZB//nlkVp87B1y8CNjZMWvkkBCAx9N2gAkEwJgxjVNsM2OQcufn5+PevXuQSqVabU9KS0tRWVlp1AUXLlyI/fv3Izs7G1euXGEbAQLM1s/MmTNRWFgIZ2dnfP311+jRowcAYOfOnXj33XcxfPhw1ktbG00jwJq01ha+CoVCJzgkOzsbOTk5sLW1hYODA1xcXODn5wdbW1uDSwMB7XB9rKEuB1hZGaO8Nb3XpaVAeDhjXr/8MnPv58coNcAouBnXxxbBkBjVjRs3UkBAANnY2FBAQAB7CwsLMzru98SJE5Sbm6u348iQIUO0Oo6Eh4drHVepVDRu3Lg6mxW88847OqV0ajcXbOqSPwkJCTRo0CCKjo6myZMnazUS0DR/y8rKIiKm5FFKSgrFxcVRREQEhYeH065du+jChQt04cIFSkhIIKFQSCdOnNB7rRs3bjSq7NXHH39MQ4cOpZiYGMrIyCAi5m8/cOBAGjNmDJWWlhIR0b/+9S+2UKMhtIjSVtu2EfH5RAARj0c0fTrRzJlEjz1GZG1N1Ls3UXw80fbtRDduEOnpCKJDbi5RQoLpyQcmYpGOI//5z39MEkYftZX7/v375OjoSNXV1UTEfNE7dOhAqampWhUoZ86cSSkpKXrHlMlkVFpaqnUbNWqU1jlGtROS5lJx8TGSSk374zWUOLJy5UqaM2cOrVixgpKTk+ny5cvUp08f2rNnD0kkEvr5558pKCiIzp49SxcuXKCVK1fS/PnzLZI4cvHiRXr11Ve1XisoKKChQ4eSWq2m77//ntasWUNERL/++it9+eWXBo/dbMqtVhOlpBB9+imj1DVvPB7R228TnTpFVFnZPPKZiEU6jliyomVubi58fHxYk5vH46Fz587IycnB/v37ERsbi+joaPj5+UEsFusdw9bWFk5OTvjuu+8QGRmJyMhIHdPWUO7e3Y7ERH9cuzYUiYn+uHt3u0HvUygUKCsrg0Kh0EkcGT9+PM6cOYPMzEwkJSXh999/R3x8PE6cOAF3d3c4OjrCwcEBEyZMgK+vLwYPHgyxWMymfZ4/fx6rV6/G7du39Xa8qJ04Mn/+fAwYMADr1q1rUO7ffvsNUqkUQ4cOxSuvvAKVSoULFy4gJiYGPB4PI0aM0HJqGtQfuqnJzwcOHgTefhsYMQJwdwcGDAC+/173XCJgyBAgKopZS7dBWkUL34kTJ2LixIlNdj2ZTILk5Pmo2U8oOTkerq7DIRTWva6q7QC7ffs2XF1dkZGRgYqKCiiVSri4uKC0tBQqlQqPP/44IiIiIBaLUVlZiaKiIq3EEU9PT4SGhsLa2hoBAQGwsrKyWOLI/fv3YWVlhWPHjmHZsmXYs2cP1Go1uyvh7OyM4uJiAIzzThNSazEaChCprAQuX9Z2et2/D/Tpw6yPZ84EvvgC6NKFcY75++sGiLTxHPEWo9w1W/haWVk1uoVvYyqxSKWp0NdPSCpNq1O5pVKpjpVga2uLnJwcODg4wNvbGyKRCBUVFejevTvWrVuHy5cvN5g4cvfuXYwZMwaHDx+2aOKIi4sL+vXrB4CZmU+dOoUBAwawvdxKS0vh5uZW5/XMSu0Akf/+F4iM1A3XDA5mFHnoUODf/wZCQ4GHOytamCueuJXRYpTby8sLffr0wffff49Zs2bh559/hp+fn0kVOBqbFSYSicHk1NRUcAFEIkYWImIzpDQ3mUy3SWBUVBQWLVqEt99+G3Z2dnoTRwQCAZRKJUaNGoUlS5awiSORkZFaiSMbNmzAsWPHWBN/2LBhICLWS15X4khQUJBW4khdM3dUVBQuXLiA8ePH4+rVq+jatSsiIiLY6MPDhw8jKiqKHbtmnLtZyc1lAkI020yaBAofH8bE7t8fmD4d6NsXqKcgog5mDhBpDRil3LNnz9bZcnFxccGAAQMMNpvj4+Px+++/4969exg+fDgcHR3Z2WHz5s2YNWsW1qxZAycnJ3z11VfGiMfS2JlbKPRDSMgWJCfHA1ABEMDf/xM8eGCFioo0VFZWQq1Ws3vLnTt3hrW1NW7evKk1jouLCzZs2NCiEkfqmrlHjRqFAwcOIDY2Fu7u7ti5cydsbW0xatQoREVFwdXVFT/88AMA4K+//mKbQTaa4mLtcM3Tp3UTKABg506gsTXUzBlP3AowKnHkhRdewJkzZzB58mTweDzs3r0bvXv3Rnp6OgYPHow1a9ZYUlaDqT1z16xDVjOJoa7oL6VSiYqKCjx4kIrS0ttQKDwgFHbSSqoQCoU6P3T6gk40CtkSEkfMxcyZM/HFF1/A3t7eoPPZz1wmA65e1Y67zs4GwsIexV537syY2bUDRPQkULRXDE0cMWorLDo6msrLy9nn5eXlNHjwYKqsrKTHHnvMmKGajLpqqOXn57P7xxcuXKCMjAzKzMykGzdu0MWLF+n27duUk5NDxcXFbA0zQ5DL5VRWVqZTS6ypqV0LzeLI5USlpcw9EbMNVVVFVFBAOUeOEIWHE9nYEAUHE82YwWxPJSYS6Wu0t20bkUDAbFkJBMxzDhaL1FArKCjQqq7h4OCAwsJC2NnZtarkfH3RX5rSQAEBAbCzs6szfLMhWkr0l6Vmbb0UFDAzsAahEKiuZqK57O2ZkMw1a5iIL1fXhsdrh+tjS2CUcvfq1QvPP/88Zs+eDYCpJd2zZ0/I5fIWlVXUkENNn/ML4EoDGYxKxWxFVVYC5eVM+GZNZDKgWzdGsXk8RtmNzeduZ+tjS2DU9LRt2zZ4eHhg8eLFWLx4MVxdXdkm5A01fG9KGiqzJBTqb8fbmqyPJkOtZpQ4Px/IzARu3mTWzbm5TJ6ySKT/fUSP4rA5mgWjZm4HBwd8+OGHeo9ZbGvEAtjY2LTv0kAKBTO7CoVAzf8zESCXP5qVKyuBqipm79jenrl5eDARXRqLSKFggkdqw/1QNjtGKbdSqcTPP/+M9PR0rUaAb7/9ttkFawyG7HO329TH2utjLy/AygqoqGAUmeiRIvv4MPf6AkM02Ngw0V81x/T31/7R4GgWjDLLp0yZgk2bNqGwsBDl5eXsraVhaPVTGxsbODo61qnYkjIJEjITICkzrQLl3Llzce7cOQDAxo0b8dRTTwFggmC6d++uc/7XX3+Nzz77DAAQHh6udUypVOK5555DdHQ0Bg4ciO3bH8W6Hz58GI6OjpBKpfjll18QGxuL3r17o1OnToiNjcWyZcswa+ZM3Dx9WlsJAcbcViiYOOxu3ZgqIsHBgK8v4OJSv2Jr8PQEevVi0iB79WKeczQ7Rs3cN27cwJ07d4zKHW6tbL+8HfMPzoea1ODz+Ngyegvm9DGuhnRkZCTOnTuH/v374/Lly2xSTEpKCrp162bUWIcPH4a3tze+++47ANDqObZnzx4899xz+N///ofx48dj7LPP4viRIzj422/4aPlyoLISs5YvB+7dY2bV2ri7GxftpQ8bG262bmEYNXN36tQJCoXCUrK0GCRlElaxAUBNasQfjDd6Bo+MjGSLIlZVVaFnz55ISUlBYmIi+vfvj5iYGERERGDt2rV1jrFq5UqsXrECIisrXL16lfUTuD7cUlJWVyMrIwMrFizAvu+/Z+pfX7nyyOFlY8N4nV1dga5dcfzSJQx/5RWMfe01hE2bhp+OHMHwcePQr18/FBUVmfJxcbRQjJq5g4KCEBsbi7Fjx2p5nBcuXGh2wRpDozuOFKWyiq1BRSqkFafBz8nw7Znu3bvj9u3byM/Ph5eXF/r3749z587h3LlzmDx5MpYvXw61Wo3+/ftj0aJFOu9/89VX4UaEpQ9rxSc98QQmT5qEyooKbFm7FgMeewzHjh7FsB494CMQoKKyElJHR4i6dGG2p+7ceVRlk89nTOwOHaBWq/HLunXYsm8ffjx1CoePHsUnn3yC3377Dc8//7zRnxdHy8Qo5ZbL5ejWrRtu377NvtYSTfTGxpaL3cXg8/haCi7gCRDkZlwSC5/Ph4eHBw4ePIh+/fqhX79+WL16NS5fvoypU6di2LBhqK6uRlZWFvLz87Xem52djcNVVTi7Ywf72oJhw7AgLg537t7F3JUrceqPP7D3wgUkp6fj+KJF+OfuXfyRmFh/FxgXF/QaMAAICUHHiAj0erim9vX1NTn3naNlYpRym5rI0drwc/LDltFbEH8wHipSQcATYPPozUbN2hr69++PTz/9FLt27WJ7h/F4PHz44Yf48ssv0bVrV/Tp0wekVjNRXZWVQE4O/L288PrMmZj57rv4buVK5JeUwMneHva9esHD3x+wtYXSxQUpGRk4ceIEAOD+/ft49dVXG2zxxLOyYtbY1tZaP87UtvtTtDsMUu4TJ04gJiamzmB1U2bHls6cPnMwPGg40orTEOQWZLhi19pDjoyMxKZNm1gHmoODAwIDAxH++OMY+/TT6BkcDEcrKyApCbh7l2k1Y2UFWFtj/NChkMpkmLd6NeLHjcOSjz+GlbMzlCoVVq9ejYSEBISFhbGX7tChAzIyMiCVSi3xkXC0MgzKCps3bx62bt2KIUOG6A7A4+HYsWMWEc4cNKadkNHU3kP292e2hVQqZg+5ZnCIUskEg2j2lO3tGedXzWVOXeO1MtpsO6FmwqzthLZu3QoASEhIaJxUTURjHWomoVDo7iFnZzPRW3I5M5Pb2wNOToyTSyRqODzT0xNwdmbeb2vLbTVxGIXRlVju3r2LzMxMrQi16OhoswrVWBrrUDMYIkapKyuBGvvOWnh6MiGbpv7IcPvHHCZilHKvXr0a69atQ9euXdkZkcfj4fz58xYRrsVRXa1rXmvCNetIRoGrq+mKzcHRCIxS7h07diA9PR3u7u6WkqdpqSuBAmCyoWorskLxaJ3s5sakMdraPjKvRSIuxpqjxWCUcnfo0KHtKHZtZ1XHjowiahRZKmUU194ecHBg+ieLRPV3a+TWyBwtCKPCT+Pi4rB48WKcP38e169fZ2+W5tSpU4iMjMTAgQOxfv36xg+oz/mVl8cU69OEa4aFMYkTWVnM+fb2hrVhtbFh9pAfKnZWVhZ4PB7rjFQoFHB1dWUTRAzh3XffxcGDB+s8/vHHHyMyMhKDBw/GSy+9xL5eVlYGkUiEkydPIjMzE7GxsYiNjYWjoyNiY2Px5JNPGiwDR+vDqJn722+/BcB0p9DA4/GQkZFhXqlq0bVrV5w8eRI2NjYYMmQIXnzxxcZ1+qyjEgt8fB4lUNTVXN0EwsPDsW/fPgwZMgR//vlnnR1TTKG8vBw//fQTzp49Cx6Pp5VQsn//fsyePRt79uzBpk2bcPz4cVYezWOOtotRM3dmZqbOzdKKDQAdO3Zk0zIFAoHJ9c1Y6nJ+aQoM6GuuHh/PvG4C/v7+yMnJARHhl19+YSPIpk2bhpiYGAwaNAg5OTkAGm4DtGbNGsTExCA6Oho3btwAn89HYWEhLl26BCJiE0oA4JdffsF//vMfve2HONo+RmuJWq1GXl4ecnJy2JsxLFy4EAEBAeDxeLh69arWsdTUVAwcOBDBwcGIiIjArVu3tI4fPXoUgYGBdZZJMhhNgYGa1HR+pabqNldXqZiCfSYyYMAAnDx5EgUFBfD29gbAlK06ceIEli5dis2bNwN41Abo9OnTOHDggFbM+c2bN5GcnIwTJ07gxx9/xFtvvQV7e3t88cUXWLFiBQIDA7FlyxYAjEmuUqm02g9xtC+MMsu//vprLFy4ENbW1uzsyePxdJIe6mPChAlYtmwZBg0apHMsPj4e8+fPx6xZs7B3717MmjULFy5cAABIJBK8//779UbmGNWfuz7nl1jMmOJm7C01fvx4TJ48Gf/6178AACqVCsuWLcP169chlUoRGhoKQH8bIA1JSUk4c+YMYh8W59dsRz755JN48sknUV5ejqioKEybNg0HDhwwqv0QR9vDqJn7vffew4ULF1BUVISCggIUFBQYpdgA2E6dtcnPz8fFixcx42F64/jx45Gbm4u0tDTI5XLMmjUL//3vf+utTvr+++/D2dlZ65aamlq3MLWcXyya3lKa/Wkz9JYSi8UYNGgQJkyYAAB48OABHjx4gJMnT+Lf//43m7ShaQNERGwbIA3dunVDTEwMjh8/juPHj+PQoUOQyWTIzc0FALZZAgDs3bsXx44dw6FDh3Dy5EncunWLSwxpZxg1c3t4eLCzirmpr4Xv33//jaSkJMTHxwMAfvjhB/j6+uqM8frrr2PJkiXYunUrGzKrGc9oLFA7+9NPP2Ufu7i4IDs7G3FxcVpVWfS1AdLQq1cviMVixMTEgM/nIy4uDq+88gpmz54NmUwGlUqF5557DkTUYPshjnaAMZ0O1qxZQx9//DHdv39fq8G9Kfj7+9OVK1fY5xcvXqTg4GCtcyIiIuivv/4yaXwNdXUcaak0eaeQJqClf+YtidzSXDqWcYxyS3PrPMciHUfefPNNAMCSJUvA4/HYLpMqlarRPzLmbOHbLIkjHByN4IHsAdadXof3T70PAplct68mRim3JbdTzNnCt8kSRyxAk7YB4mgUkjIJUotSIXYXG5TvL1fKkVachpSilEe34hQkFyajRFYCpfpRMpambt/woOEmFQkBmqE/d1O08OVmbg5LU1d1XDWpkVuai5SiFCQXJWspck5pDrwdvBHiEYJgt2CEeoVi3GPjEOIRgqySLMR9r91e2ZS6fTUxqoUvn8/XWzPNHGa5pWjSYg0cemlrn3luaS78N/qDoK06Ie4hyC7Nhq3AllFg92CEuDP3we7BCHILgoON/t0eSZkE/hv9der2ZS3O0lFusxZr0FCzAYFUKsW3337bIhWbm7k59GGsGV1VXYXUolQtEzqlKAW38m/pKDYAvNzvZUzpMQUedh5GFw41Z90+DUbN3PrQlOttqTRm5pZIJEhNTYVYLNa7N28Ip0+fxltvvQUiAhFh4cKF2LRpEw4ePNikHUVHjBiB0NBQfPTRR012TQ0tYeauy4xWqpXIfpCtY0KnFKUgrzwPnZw7MTOvWzA7AzvZOiFqR5SWgtc1yxrLhWQJTiWlYVD3IESE6B/LIjN3be7cuYPCwsLGDGERzDFzb9++HfPnz4darQafz8eWLVswx8jEkaKiIrz00ks4dOgQfHx8UF1d3SwOs/Yeeppbmot5B+axyqgmNeYemIu1p9ci+0E2nIXOWib0sK7DEOwejEDXQIis9Xcx3Tpmq1lnWUCTq+QHtdqvsblKDMbswbm4uJCrqyu5urqSk5MTOTo60tdff23MEE2OKfvcubm5xOfzCQB7EwgElJtb996jPr799lt65513dF6PiYmh8vJy+uqrr2jTpk1ERHTgwAH23B07dlD//v0pJiaGjhw5QqWlpTRmzBiKjo6myZMnk1wup7Nnz1K/fv0oNjaWfd8ff/xBgwYNogEDBtDOnTvZ602aNIkOHDhAS5cuNUp+c2HKPrch+721KZWV0sV/LtLO6zvp3YR3aereqdR3c1+yW21HeBc6t8/Pf05FVUVGy1ZTxoTMBKNkrI1aTSSREP30ExGPR8SU9mFuAgGRvq+cRfa5ayZ6WFlZwdvbu02uaVNTU3W2/VQqFdLS0owyz/Py8uDzsOPHsWPH8J///AdOTk71vqegoABbtmxhU1zVajU2bNiAkSNH4oUXXsB7772HH3/8EampqXjnnXcwcuRIqNVqEBHee+89JCQkQCAQIDo6GpMmTcLp06cRFhbWpEuAxlJfnzaFSoGMkgwdEzq5KBkFlQXo4tqFNaOj/aMxt89cONo4ov+2/jpm9NMhT8NN5Ga6oGV+oEw/xv6t/8+K0lIgJeXRLTn50WMej8k2rr1A1uQqmRocabByq1QqzJkzB3/++adpV2pCGmuWi8Vi8Pl8LQUXCARG77l37NiRjW0fOnQohg4divDwcFbR9DUEyMjIQN++fdkUVz6fj7S0NMybNw8AEBERgdOnT+Pll1/GqlWr8MMPP2D69OkIDw9HSkoKW4DhwYMHKCgowCeffIKvvvoKly9fNvpzaA4kZRIdE3regXnYeXMnckpzkFmSCS97L3b9G+wejNHBoxHiHoIurl1gI9Bf/cbcZrS+dP/nngMyMnSVNzkZKCoCunRhGqEGBwNDhgAvvMA89vEB/vmHSUw0Y66S4cotEAhQVVXFrkFbMo0NYvHz88OWLVsQHx8PlUoFgUCAzZs3G+1UGzlyJGJjY/HCCy+gY8eOWhVjASaOXNOa6dq1awCAwMBAXL58GdXV1bC2toZarUZQUBDOnz+Pvn374sKFCxCLxXB2dsZnn30GhUKBvn374tq1a+jWrRuOHDkCGxsb9v1paWmYNGkSiouLUVBQgJiYGIwZM8boz6QhFCoFZEoZhFbCOhWsNiXSEp394Mt3L+t4ogmEgX4D8eGwDyF2F8PJtoFpUg8mN5moBRFw8SIwb96jmVatBubOZVL+PT0fKXC3bsDTTzOPu3atvxuyJlcpPp6Zsc2Qq2ScQy0iIgKjR4/GjBkztMy81hYFZghz5szB8OHDkZaWhqCgIJO85e7u7vjyyy8xbdo08Hg88Pl8LF68GNu2bQMADBs2DB999BFGjhwJX19f+Pr6wsPDA3PnzkVUVBTs7e3xxhtvYN68eZg+fTp+/PFHdOjQAcuXL8cXX3yBffv2QalUYtasWeDz+XjrrbcQFxcHPp8PT09P7N69m/3ROH78OA4ePGgRxS6oLEB26aOyVf7O/vC0Z5JW1KRGhaIC+27v01HkUlkpAt0CWWfWk4FPYlKPSZi0Z5KOCR0fHt9oh5UxZnRZme7sq3msVuua0ADw22/AqFGmi2fuXCWjtsK4jiMctVGoFLh+X7eOnoONAxQqBRQqBVIzU7E9fbtOUIe/iz+s+Lrzy/bL23VM6MbEWAN1m9GZmY8Ut+Z9UREz2wYHMzfNbBwSwjSLCQjQNaGzssySPNgghm6FNXqfuyVSe81948YN9hin3KaZ0EQEpVoJmVIGuUoOmVIGmVKGquoqKFS6Pds7OnaEi9AFtgJb5P2TZ/RnLimTNNqEZuRmzOj+/XVnWysrxoyuqbyax1261G9Gb9+ua0I3atvKCJpkn7ul0poTRyxNfSY0AKjUKi3llSllkCuZ52qoIRQIIbQSwtbKFi5CF7iL3JFekq5zHQ87D4N/OPRihAkNMGa0PkdWQ2b0yJGmiWeBdH+z0yaVuz6IiHWStTcUKoWWYgNAdmk2yhXlqFZVQ6aUoVpdDVuBLWytbCG0EsLBxgEeIg/YWtnCRmCjN6zSX+2v84OhUWyVSmV0BZi6Cs8qFI+80Q2Z0UOGMDNrfWZ0r15GiaWDn1/LVGoN7U65PTw8cPfu3VZTckiulKOyuhL21vawtbI17r0qOaoUVaiqrkJldSVK5aUolZXqnOfr6At3O3fYW9vDxdoFfBUfeGhpyx/+awgXpQuqqqtgZ20HWbEMucVM6ScejwcPDw+DZc7N1e+JXrWKOebl9UiBNd5oQ8xoc3uiWwPtTrnt7OwaV/O8CakvmENDqaxUJz9Y85iItPaDPew8sPj4YovEREskQG4W4CY2TGlqm9Ga+9u39ZvQ//43MHUq0yTVFFqDGW1ujFLurKwsfPDBB0hPT9fas23J3vLWiqRMwio2wGwpzT8wHxklGbhfeZ9V4CJpEbq6dmWjsmL9YzG/z3wEuwejo2NHHTPa3treQjHR+s1ofd7olBSgsFA7qGPoUCaow8EB6NdPW8EFAmaLyVTF1tDSzWhzY5S3vF+/fnjiiScwYMAArTXrqMZs7lmA+rzlLRU1qSEpk7BK+1fmX9h3e5/OeWOCxyA2IJadjbu4dIG1oB57VA/m8kQDjKns76872wYEMLO5Kd7o5vREtwYsshXWq1evJukNZk4M/SCaiqKqIr1ldlKLU2EjsGH3gb0dvLHh7AaLmdCpqUx5dkNnMo0ZXduUvn1bf3emL79snBktkbQvE9oYLLIVFhoaanLRwvaCpEyCm/dvQiAQ6K6Hi1JQrihHkFsQa0aPCByBRf0XIdg9GJ52nlpm9GMejzWZCQ3U7Y3WZ0ZrvNGOjkBEhPnN6PZmQlsCo5S7oKAAYWFhGDBggFZLn337dM3Hto5KrUJ2aTYTUlnIhFQmZCXgduFt9pzuHt0xpMsQ9PHpgymhU5ioLGd/CPiGbcOZKx5ag0Si64meNw/YtYtpepqZaZo3euvW9ueJbg0YpdwzZsxgO4K0BRoqu0NEyK/M10ktTClKQXpJOhxtHNm1r7eDN+4U3tF6f3JRMg4/d7hxSmlkMIcGfSmGly7pro2JgMhI4IMPGDPdlNm2PXqiWwNGKffMmTMtJUe9FBcXIy4uDsnJyaioqDDLmDW3mXjg4a3Bb6G7V3cdM1qhUkDsLmbN6LHdxiLEIwRiNzHc7dzZ8RIyE/DB6Q+0rtHY6pUNdRGuaUYbkmI4fjwwebKuCf3CC41XSM6MbnkYvc+9e/duXL16FbIaXpQNGzaYVajaODo64ujRo5g0aZJZxqu9zUQgvPf3exgSMAS9OvTCwE4DMav3LAS7B8PPyQ98XsMprmJ3Mfg8vk71yiA30xJy9XURnjcPSEwE8vIYJa7LjK4vxbCsjDOh2wtGKffChQuRmZmJS5cuYerUqdizZw/i4uIafmMjsba2hptbIypm1CK1KFVLCTW8HfM2YgNiTRqzsdUra5rRycnAqVO6XYSJgOpqYPp0ZkY2xYzmTOj2g1HKnZCQgGvXruHxxx/H+vXr8dprrxltqi9cuBD79+9HdnY2rly5gt69e7PHUlNTMXPmTBQWFsLZ2Rlff/01evToYfDYhrbwNfcsq2FOnznoZT+8zuqVDZnRNWOjhw8Hjh/XNaFXreJM6LaMTCaBVJoKkUgMobBxfySjlFsoFLKNCaqrq+Ht7Y28vDyjLmhqf25DeP/997Fy5Uqt14KDg3XOs0SNaIBZI8+b5wciP/B4zAzr6flIgWua0SEhjBn9zDPMc33eaA8PzoRuyZhTEQEgL28bUlLmg6nJyUdIyBb4+JgevWNUEMvQoUNx8OBBLFu2DAUFBfD29kZiYqJJdcsDAgLw66+/sjN3fn4+goKCUFxczDYC9PHxwalTp9jaZcOGDau3hpu+mXvatGk4ePCg3vMbE6lVOzb66lWgdlwBjwcsXszsA2tmZEdHoy7DBXO0UO7e3Y7k5PkA1DBGEYkICsVdSKVpkErT2fuqqiRUVtaOpBQgMjJL54fDIkEsu3btgkAgwLp167BhwwaUlJRg7969xgxRJ/X15w4KCsKwYcNw5coVDBs2DBs3bkRoaKjOGLa2trC1tTW8QGID20yGphiGhOgvZEfEOLhiY034QB7CmdAtD5lMUkOxAUCN5OR4uLoOh1DoB7VaCbk8R0t5pdI0yGTpkErTweMJIBQGQiQKgkgUCFfXJ+DoGIGMjP+rdSUVpNI0k60Co5S7ZiN4TTvfpsLcVVdrbjPxeMDSpUBgoLYi6zOj6wrqkEiAjRvNW72So2UilabikWJrUOHWrfFQKoshk2VBIHBmlVckCoKn5zj2ubW1l05Cj0wmQUbGslrjCiASmf4FMki5ly5divXr12Ps2LF6k/XNEaFmzv7cDVViqb3NRAR89BGjuI8/DkybZrw32hLVKznMi7FrZKWy7OGsW3PmTUNVVYqes3nw9p4FJ6d+EAoDYW3tYpRsQqEfQkK2IDk5HoAKgAAhIZsbtZY3SLljH9qVzz77rMkXaghz9uduyCxPTdXdZgKAV19tnAnNbTO1XPStkb29n0d1daEe05l5Xl1dDKHQn51x7eweg7v7aIhEQcj+fT/y3d8CBGpAxUeHog/hG/ti44T830jg9V1Ax3+Au77AmkFAI7LhmrxAYs3+3O7u7lr9uZOTkzFr1iwUFRWx/bl79uzZqOvpcz5IJPoLwDdV9UqOpoNIjbKyi7hyJRKoVQ9dIHCAWl0NkairlgktEgVBKAyEUOgPPl83EkgmkSHRPxFwKwB8/wH+8QVKPBGZFQmhn1DnfG15CIp7CsgyZJCmSyFNl0KWIUPl7UpUXKoVfSmA3jHN6lCbPXt2vS1Jd+zYYcgwAIDNmzfXeSwkJARnz541eKy6aGjm5kzolo8xJrRaXQ2ZLFtn5mXuM8DjCVBbsQEgOHg7vLwmgGdABGJNpKlSxgAo9GRumtfTpBD6CaFWqCHLkkGaIYUs/aESax5nSAEAoq4iCAOFEHUVwSnSCXahdrrKrXo0pikYpNzh4eEAgBs3buDkyZNskf1du3Zh8ODBJl3YkhhS/ZQzoVsu+kxoL6+pkEoz9ChvOmSybFhbu9VyYE1iH6tUMpw7F4Dazipn54FGKzYAiMQigAft3wsekPlmJu78cwfyXDmsPa0hChSxSuw53pN9bNNBt9CkTCJD5huZtUWEKEh/l1FDMEi5NYoSHR2NxMREtpndK6+8gtGjR5t88eaG22ZqWVRXP0Bp6RkkJ8/DI81RIzl5LpKT58PW1pdVWKEwEC4uQx8+D4SVVf2eT2OdVaQiyP+R659906UA/+FQAMADPCd4wmuaF0SBIgi7CGHlYFzahtBPiJAtIUiOT9aIiJDNISbP2oAJ+dw1u1Q6OTmhoKDA5ItbCnP05+YwDkPMaCJCdXV+jVlXewZWqUphbe0NfSZ0z55/wN39SZPl8/GZAzt5DMoyb8Opy2Nw9gmCqkoFWab22pdV4kwZ+CK+1uzr+oQrRPOYx8JOQsjvyiFNk0IUJGqUErIyzvGB63BXs41plENtypQpEAqFbBP6r776ClVVVfjxxx8bJYQlaWllltoi2mY0D127roWjY7jeIA4iFUSiwBpBHI9MaVvbTlAo7iEx0R+17VN9kVoNQUSoLqiGNF2Kezvu4e72u+zvhsBZAFW5CrYdbdm1ryjw4Tr4oUJbuVnV62tqLiwSobZt2zasXLkSixcvBsCEg65YscIkATlaL2q1AjJZFqTSdJSXX0RW1ts1jhIyMpbD3r4n7Oy6QyQKhLv7KFaBbWx86lUYY/d71dVqyHPkurPvw8fqajWEnYWME6wGqnIV+iX3g11Q6yhzbQpGKbeDgwPWrVtnKVnMBmeW148hJrRKVQmpNEPvHrBMlgtraw+IREEQCOz1vj8o6FO4usaaJJ+Pzxy4ug6HVJoGkSgIVgpvlF8p11FcaboUshwZrF2ttWZc96fd2ZnYxscGD048wLWh17QvogbkEjmn3Bpyc3Px4osvQiKR4OrVq7h69SoSEhLw6quvWko+k+B6hdVNbRO6c+c3YG8fqrONpFDch61tpxp7v4Fwc3uSNamtrJgWzjKZRK8ZbUzYJKkJirsKLadVxY0KSFPsoLifBWVpGoT+wkfbR0EiuD3pxprTVk71f41FYhHjADOjJ7o1YJRyx8fHY9q0aezsHRoaiueee67FKTcHA5OBdI+deSsqruCffz6teQZyclbDxWUo7O17wMHhcXh6TnjojQ4An99w+yKh0A8d8j/EffdlNaK1PtCxCFQyxnmld/bNlIFnxWNnX1WlCiVHSpj1MQ8I/m8wOsZ3NPlzsIQnujVglHLn5+djxowZWL9+PfNmKys2i4vDMjRkQhOpIJPloHbmkWYGBsDOvjye/vKl/v4rTDahZRIZ7k/tC7j9yEZr3S/yhM3FdFQXVrNKLM+Tw8bb5tHsGyiCUz8n9rG1hzV4PN6j6C+Nm5eAlJdT4DbKrVHKaG5PdGvAKM3UJHRoKCkpaZEN9drKmru2Ce3ruwAiUWCtdXAWBAIHLa+zu/vT7HMbG2/WgSWTSVBQsBemmtBqpRryXLnW7FuWWKY3WqsqrQou0S7weNaD3fsV2DX8t2Cjv2rSyEgtDUI/YbtQag1GKffEiRMRHx+PsrIybNu2DV9++SXmzp1rKdlMpjnX3KZW51Aqyx9GW2lM6OvIz99Z4wzCP/9sgqfnRNjb94KTUxQbwGFtbVh9OUM80coK5SNzuZYJLcuSQeAk0AqddB/jjtK/S7W3pgWA+FOxSYrUXtfHlsAo5V66dCl27dqF0tJSHDlyBEuWLMG0adMsJVuro77qHEwAR5He8EmpNA3V1UUQCjux0VcCgf6SLR07vmSyCQ0A3t7Pw/qfgSi+fhPWUn/IEjxxO+M2q8TVhdWw7WSrFbzhMsSFfWztomvaW7tam209217Xx5agybPCmpqmCmKRySRIPNsZ4NX4OIkHN/dRUCjyIJWmQ62WshlINStxMM/9wefb1BrPH+DVmMJIgMgBDQdz1Je4UJVSBVI8ktE1zhUez3pA2JVZ+wr9heDbGB9vLZPIzLqeNfd4bQmzBrEsWbKk3uOWrltuKUwxoZkSOtk6M29F6TVtxQYAHsFGFYhOgUsgEgXC1tb3YYaSARR6AOuXAK9uYL3Q+PhV4EsPwA+oflCtN+ZZmiHVTlwIFEHYlUlcEDgKcGvcLa3LlBwrQciOxs+M5l7Ptrf1sSUwSLk3btyIiIgIjBgxAny+8b/qTY0hDrX6TGiVSgaZLEOv+SyXZ8PKykVr5vX0nACHwonIVv8LENRQcBUfrqVz4eqqW++tIaqSq4DfRwHn+j3KGS70xLVh11BdUA1VmQrCACHrbbbrZge3UW71Ji6UJJTohm2byVnF0fIwSLn/+usv7NixAzt37sSkSZPw/PPPIzAw0NKymUxDDjX9Be7mIS9vGxQKCeTyPNjadnyowIwSu7jEsMpsZeWsO6ZShuwXrtWaaZfA+cu6PdEqqUo7WSFdO3EBgLYXmgcEvBsAp0gn2PrZgm9l3A8t56xqXxik3EOGDMGQIUNQVlaGXbt2Yfr06RCJRFi7di369+9vaRnNjv4CdwR399Hw9BwLobALBALjvvBCPyFCxi5B8vR+gPc/wD1fBK+KAt+Gj9KzpXqVWHFfAVtfW3a9K+oqglOUE/u44JcCpLyQouVY6jClQ4Oy1Csj56xqNxjlLXdycsIzzzyD4uJifPrpp7hz506rVG6RSAx9U5i390yjM49qJi6oFWr4PNsLVUlBqFZUI/3VdKS9kvbIWdVVCMe+jvCa5AVhVyGEAUIIhHWvwTvO7Qi3EW4tOq2Qo+VikHKrVCrs378f27dvR3Z2Np577jlcvnwZPj4+lpbPIhibeaQsU9aZtC/LkcHazVp79n3eiXVm2XjbgMc3PW3QEo4lzlnVPjBIuX19fdG5c2fMnj0bUVFRAJjCDZpCDb169bKchA955ZVXcPXqVTz11FN44403Gj2eVuaRMBC8Yi88OPlArxJXl1QziQsPZ19R4MPEha6GJS5wcDQHBn0rhUIhCgoK8OGHH4LH42mFnPJ4PGRkZFhMQAC4ePEirKys8Pfff2PChAm4f/++VoMEU1FluCJ1oh1kGZngWWVppQ06RzvDe7Y3RF1FsO1sC751y98l4OCoiUHKnZWVZWEx6ufcuXMYOnQoACAmJgaXLl3CyJEjGz+wAOj4Ukc4D3KGQy+HFll1g4PDVJp8Olq4cCECAgLA4/Fw9epVrWOpqakYOHAggoODERERgVu3mICLBw8esLXbHB0d8eDBg0bLcXf7XVzofgFpC9Jwqc8l3Ntxr9FjcnC0JJpcuSdMmIBTp07B399f55imhW9KSgqWL1+OWbNmAQBcXFxQVlYGACgvL4eLi4veseVyOcrKyrRu+vpzyyQyJM9PrrnNjeT4ZMgkMnP8Fzk4WgRNrtzR0dHw01NPOD8/HxcvXsSMGTMAAOPHj0dubi7S0tLQr18/JCQkAABOnjyJvn376h37/fffh7Ozs9YtNTVV57z60go5ONoKLcZLVF8L34iICMjlcgwePBhhYWF1OtNef/11lJaW4qOPPkJISAhCQkJgXbujPWpEatWEi9TiaGO0mj0cTax4fWj6cy9duhRLly4FoD/8lIvU4mgPtBjlNmcLX0MSR7hILY62Tosxy2u28AXQqBa+hiL0E8I11pVTbI62CTUx8+fPJ19fXxIIBOTl5UWBgYHssTt37lBkZCSJxWLq27cvXb9+vdHXGzNmTKPH4OBoSRj6nW7zlVh69OhRZ3qqWq1GamoqxGJxi81Tbw0yAq1DzrYiY3p6OhsDUh9tXrnro6ysDM7OzigtLdVqcNiSaA0yAq1DzvYmY8v8+eLg4Gg0nHJzcLRROOXm4GijtGvltrW1xTvvvANb24Z7YjUXrUFGoHXI2d5kbNcONQ6Otky7nrk5ONoynHJzcLRROOXm4GijtBvl1lcBRiaT4dlnn0VwcDDCwsIQFxeHtLS0FidnTb766ivweDz8+uuvTS6bhrpklMvlWLBgAcRiMXr27Mnm5rckGf/3v/+hT58+6N27N0JDQ/HNN980m4z1ff/y8/MxYsQIiMVihIaG4uTJk8ZfwGIBsC2MEydOUG5uLvn7+9OVK1eIiEgqldLvv/9OarWaiIg2bdpEMTExzSck6ZdTQ2ZmJg0YMIAiIyPpl19+aRb5iOqWcfHixbRgwQL287x7924zSahfRrVaTa6urnTt2jUiYj5PW1tbKisraxYZ6/v+zZ49m9555x0iIjp//jz5+vqSQqEwavx2o9wa9CmNhgsXLpC/v3+TylMXteVUqVT0xBNP0MWLFykmJqZZlVtDTRkrKirI0dGRSktLm1eoWtRWbjc3Nzpx4gQREV27do06duxIcrm8GSV8RM3vn729vdaPY0REBB09etSo8dqNWW4In3zyCZ555pnmFkMvGzZsQFRUVJ0lppqb9PR0uLm5Yc2aNQgPD8fgwYPx119/NbdYWvB4PPz0008YN24c/P39MWjQIHzzzTewsbFp+M1NgOb7V1RUhOrqanh7e7PHAgICkJOTY9R4LaZYQ3OzZs0apKWltbgvJADcvHkTP//8s2nrriZCqVQiOzsb3bt3x9q1a3HlyhXExcXh1q1bZqkxbw6USiVWrVqFffv2ITo6GhcuXMDTTz+NGzduwMPDo1llq/n9k0rNU8uPm7kBfPTRR9i3bx/++OMP2NnZNbc4Ovz999/IysqCWCxGQEAAEhMTMX/+fPz3v/9tbtFYOnfuDD6fj+nTpwMAHn/8cXTp0gU3btxoZskecfXqVeTl5SE6OhoAEBERAT8/P1y5cqVZ5ar9/XN3d4eVlRXu3XtUbjsrK8v4qkTmXDO0BmqvZdevX099+vSh4uLi5hNKD/X5BlrimpuIKC4ujn7//XciIsrIyCB3d3eSSCTNJB1DTRnv3btHDg4OlJSUREREqamp5OrqStnZ2c0mX13fv5kzZ2o51Dp27Mg51OpCXwWY3NxcAkBdu3alsLAwCgsLo379+rU4OWvT3Mpdl4zp6ekUGxtLoaGh1KtXL9q7d2+Lk3Hnzp2sfKGhofTDDz80m4z1ff/u3btHcXFxFBQURN27d6djx44ZPT4XW87B0Ubh1twcHG0UTrk5ONoonHJzcLRROOXm4GijcMrNwdFG4ZSbg6ONwik3B0cbhVNuDo42CqfcHBxtFC4rjKPRvPnmm8jPz0dhYSGSkpLg4+OD//3vfy0yCac9wc3cHI3m0qVLKCgowA8//IDk5GRUVlYiMTGxucVq93AzN0ejuXz5Mk6fPs3O1AqFAm5ubs0sFQc3c3M0itzcXAgEAojFYgBM0b/09HT06NGjmSXj4JSbo1FcunQJERER7PNr166he/fusLa2bkapOABOuTkayaVLlxAeHl7nc47mg8vn5uBoo3AzNwdHG4VTbg6ONgqn3BwcbRROuTk42iiccnNwtFE45ebgaKNwys3B0UbhlJuDo43CKTcHRxuFU24OjjbK/wNg8pK8LRHX0gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot scaling of solver running times on one graph\n",
    "\n",
    "# Choose parameters\n",
    "p = 14\n",
    "#k, r = 2, 2.0\n",
    "k, r = 8, 176.54\n",
    "#selected_all_methods_df = all_methods_df.query(f\"k == {k} and r == {r}\")\n",
    "\n",
    "# Helper functions\n",
    "\n",
    "def agg_qaoa(benchmarks_df):\n",
    "    return benchmarks_df.groupby([\"k\", \"r\", \"n\"]).agg({\n",
    "        **{\n",
    "            \"instance_id\": \"count\",\n",
    "            \"eval_qaoa_runtime\": [\"mean\", \"median\", \"std\", median_abs_deviation, \"count\"]\n",
    "        }\n",
    "    })\n",
    "\n",
    "def agg(benchmarks_df):\n",
    "    return benchmarks_df.groupby([\"k\", \"r\", \"n\"]).agg({\n",
    "        **{\n",
    "            \"instance_id\": \"count\",\n",
    "            \"eval_qaoa_runtime\": [\"mean\", \"median\", \"std\", median_abs_deviation, \"count\"],\n",
    "#            \"schoning_runtime\": [\"mean\", \"median\", \"std\", median_abs_deviation, \"count\"],\n",
    "            \"schoning_qaoa_runtime\": [\"mean\", \"median\", \"std\", median_abs_deviation, \"count\"],\n",
    "            \"walksatlm_runtime\": [\"mean\", \"median\", \"std\", median_abs_deviation, \"count\"]\n",
    "        },\n",
    "        **{\n",
    "            solver_name + \"_runtime\": [\"mean\", \"median\", \"std\", median_abs_deviation, \"count\"]\n",
    "            for solver_name in analysis_helpers.pysat_solvers\n",
    "        }\n",
    "    })\n",
    "\n",
    "def plot_scaling(ax, name, label, colour, df):\n",
    "    xvals = df.index.get_level_values(2)\n",
    "    yvals = df[name][\"median\"]\n",
    "    a, b = np.polyfit(xvals, np.log2(yvals), 1)\n",
    "    ax.semilogy(xvals, yvals, \"o\", label=label, color=colour)\n",
    "    ax.semilogy(xvals, [2**(a*x + b) for x in xvals], color=colour)\n",
    "    print(f\"{label} scaling: 2^({a}n+{b})\")\n",
    "\n",
    "# Extract data\n",
    "\n",
    "selected_qaoa_benchmarks_df_1 = qaoa_benchmarks_df.query(f\"p == 14\")\n",
    "selected_qaoa_benchmarks_df_2 = agg_qaoa(qaoa_benchmarks_df.query(f\"p == 60 and k == {k} and r == {r}\"))\n",
    "all_methods_df = reduce(\n",
    "    lambda df1, df2: pd.merge(df1, df2, how=\"outer\", on=(\"n\", \"k\", \"r\", \"instance_id\")),\n",
    "    #[selected_qaoa_benchmarks_df, schoning_benchmarks_df, schoning_qaoa_benchmarks_df, walksatlm_df, pysat_benchmarks_df]\n",
    "    [selected_qaoa_benchmarks_df_1, schoning_qaoa_benchmarks_df, walksatlm_df, pysat_benchmarks_df]\n",
    "    #[selected_qaoa_benchmarks_df, schoning_benchmarks_df, walksatlm_df, pysat_benchmarks_df]\n",
    ")\n",
    "all_methods_agg_df = agg(all_methods_df)\n",
    "\n",
    "selected_all_methods_agg_df = all_methods_agg_df.query(f\"k == {k} and r == {r}\")\n",
    "\n",
    "# Create plots and fits\n",
    "\n",
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "\n",
    "plot_scaling(ax, \"schoning_qaoa_runtime\", f\"WalkSAT QAOA\", \"m\", df=selected_all_methods_agg_df)\n",
    "plot_scaling(ax, \"eval_qaoa_runtime\", f\"QAOA (p=14)\", \"b\", df=selected_all_methods_agg_df)\n",
    "plot_scaling(ax, \"eval_qaoa_runtime\", f\"QAOA (p=60)\", \"y\", df=selected_qaoa_benchmarks_df_2)\n",
    "plot_scaling(ax, \"walksatlm_runtime\", \"WalkSATlm\", \"g\", df=selected_all_methods_agg_df)\n",
    "plot_scaling(ax, \"maplesat_runtime\", \"MapleSAT\", \"r\", df=selected_all_methods_agg_df)\n",
    "plot_scaling(ax, \"glucose4_runtime\", \"Glucose4\", \"k\", df=selected_all_methods_agg_df)\n",
    "\n",
    "#plt.semilogy(selected_all_methods_agg_df.index.get_level_values(2), selected_all_methods_agg_df[\"eval_qaoa_runtime\"][\"median\"], \"-o\", color=\"b\")\n",
    "\n",
    "# def plot_runtime_agg_benchmark(name, runtime_agg):\n",
    "#     plt.semilogy(selected_all_methods_agg_df.index.get_level_values(2), runtime_agg[\"median\"], \"-o\", color=\"b\")\n",
    "#     plt.fill_between(\n",
    "#         selected_all_methods_agg_df.index.get_level_values(2),\n",
    "#         runtime_agg[\"median\"] - runtime_agg[\"median_abs_deviation\"] / np.sqrt(runtime_agg[\"count\"]),\n",
    "#         runtime_agg[\"median\"] + runtime_agg[\"median_abs_deviation\"] / np.sqrt(runtime_agg[\"count\"]),\n",
    "#         color=\"b\",\n",
    "#         alpha=0.2\n",
    "#     )\n",
    "    \n",
    "    \n",
    "ax.set_xlabel(\"$n$\")\n",
    "ax.set_ylabel(\"Median running time\")\n",
    "ax.legend()\n",
    "fig.tight_layout(pad=0)\n",
    "fig.savefig(Path(FIGURES_DIRECTORY, \"scaling_comparison.pdf\"), bbox_inches=\"tight\")\n",
    "plt.show()\n",
    "    # CHANGE AFTER DOING SCHONING-QAOA\n",
    "#    linreg = linregress(selected_all_methods_agg_df.query(\"n <= 16\").index.get_level_values(2), np.log2(runtime_agg.query(\"n <= 16\")[\"median\"]))\n",
    "#    return linreg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aca50c8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 226.927x170.195 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram comparing QAOA and WalkSATlm\n",
    "\n",
    "p = 60\n",
    "k, r = 8, 176.54\n",
    "\n",
    "selected_qaoa_benchmarks_df = qaoa_benchmarks_df.query(f\"p == {p}\")\n",
    "methods_df = reduce(\n",
    "    lambda df1, df2: pd.merge(df1, df2, how=\"outer\", on=(\"n\", \"k\", \"r\", \"instance_id\")),\n",
    "    #[selected_qaoa_benchmarks_df, schoning_benchmarks_df, schoning_qaoa_benchmarks_df, walksatlm_df, pysat_benchmarks_df]\n",
    "    [selected_qaoa_benchmarks_df, walksatlm_df]\n",
    "    #[selected_qaoa_benchmarks_df, schoning_benchmarks_df, walksatlm_df, pysat_benchmarks_df]\n",
    ")\n",
    "\n",
    "selected_methods_df = methods_df.query(f\"k == {k} and r == {r}\")\n",
    "\n",
    "ratios = (selected_methods_df[\"eval_qaoa_runtime\"] / selected_methods_df[\"walksatlm_runtime\"])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=figsize_revtex(2/3))\n",
    "ax.hist(np.log2(ratios), bins=100)\n",
    "ax.axvline(0, color=\"k\")\n",
    "\n",
    "ax.set_xlabel(\"$\\log_2($QAOA$/$WalkSATlm running time$)$\")\n",
    "ax.set_ylabel(\"Number of instances\")\n",
    "\n",
    "fig.tight_layout(pad=0)\n",
    "fig.savefig(Path(FIGURES_DIRECTORY, \"qaoa_walksatlm_hist.pdf\"), bbox_inches=\"tight\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e5ae6cd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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