plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Required packages\n",
    "numpy, matplotlib, statsmodels, numba, seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from signals import *\n",
    "from frequencyestimator import *\n",
    "from scipy.optimize import curve_fit\n",
    "import scipy.stats as st \n",
    "from pathlib import Path\n",
    "import statsmodels.api as sm\n",
    "\n",
    "\n",
    "from chebAE import chebae\n",
    "\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "sns.despine(left=True, bottom=True)\n",
    "sns.set_context(\"poster\", font_scale = .45, rc={\"grid.linewidth\": 0.8})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Helper function to simulate the chebAE approach from Quantum 7, 937 (2023) and store output values needed for plots\n",
    "\n",
    "def simulate_chebAE(amplitude, epsilons, delta, num_mc):   \n",
    "    np.random.seed(7) # Seed for reproducible results\n",
    "    errors = np.zeros((len(epsilons), num_mc), dtype = float)\n",
    "    queries = np.zeros((len(epsilons), num_mc), dtype = float)\n",
    "    time_complexity = np.zeros((len(epsilons), num_mc), dtype = float)\n",
    "\n",
    "    for i, eps in enumerate(epsilons):\n",
    "        q,d,t=0,0,0\n",
    "        for j in range(num_mc):\n",
    "            res = chebae(amplitude, eps, delta)\n",
    "            q += res['queries']\n",
    "            t += res['time_complexity']\n",
    "            \n",
    "            time_complexity[i,j] = res['time_complexity']\n",
    "            queries[i,j] = res['queries']\n",
    "            errors[i,j] = np.abs(res['a_hat']-amplitude)\n",
    "\n",
    "    return errors, queries, time_complexity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_parameter_fits(epsilons, queries):   \n",
    "\n",
    "    epsilons = np.array(epsilons)\n",
    "    queries = np.array(queries)\n",
    "\n",
    "    mod_wls = sm.WLS(epsilons, sm.add_constant(1.0/queries), weights=1.0 / (epsilons ** 2))\n",
    "    res_wls = mod_wls.fit()\n",
    "    \n",
    "    return res_wls.params[1], res_wls.bse[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data in Table I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load precomputed data from run_ae_sims.py and compute fit line to estimate constant factor.\n",
    "# Average fit line over each amplitude to compute average constant factor independent of a\n",
    "\n",
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "\n",
    "#Setup storage containers\n",
    "C_csae99 = {}\n",
    "C_csae_time99 = {}\n",
    "C_csae95 = {}\n",
    "C_csae_time95 = {}\n",
    "C_csae68 = {}\n",
    "C_csae_time68 = {}\n",
    "C_csae50 = {}\n",
    "C_csae_time50 = {}\n",
    "\n",
    "ninetyninepercentile = {}\n",
    "ninetyfivepercentile = {}\n",
    "sixtyeightpercentile = {}\n",
    "median = {}\n",
    "num_queries = {}\n",
    "max_single_query = {}\n",
    "errors = {}\n",
    "thetas = {}\n",
    "num_queries99 = {}\n",
    "max_single_query99 = {}\n",
    "errors99 = {}\n",
    "thetas99 = {}\n",
    "\n",
    "for a in amplitudes:\n",
    "\n",
    "    # Use a sampling parameter C=1.3 for confidence intervals <= 95%\n",
    "    dir='sims_C1.3_final/'\n",
    "    with open(dir+f'a{a:0.3f}_mc0500.pkl', 'rb') as handle:\n",
    "        errors_a, thetas_a, num_queries_a, max_single_query_a, arrays, num_lengths, num_mc = pickle.load(handle)\n",
    "\n",
    "    # Use a sampling parameter C=1.8 for confidence intervals == 99%\n",
    "    dir='sims_C1.8_final/'\n",
    "    with open(dir+f'a{a:0.3f}_mc0500.pkl', 'rb') as handle:\n",
    "        errors99_a, thetas99_a, num_queries99_a, max_single_query99_a, arrays99, num_lengths99, num_mc99 = pickle.load(handle)\n",
    "\n",
    "    # First 2 are for very high error rates and not useful\n",
    "    errors[a] = errors_a[2:]\n",
    "    thetas[a] = thetas_a[2:]\n",
    "    num_queries[a] = num_queries_a[2:]\n",
    "    max_single_query[a] = max_single_query_a[2:]\n",
    "    num_lengths = num_lengths-2\n",
    "\n",
    "    # First 2 are for very high error rates and not useful\n",
    "    errors99[a] = errors99_a[2:]\n",
    "    thetas99[a] = thetas99_a[2:]\n",
    "    num_queries99[a] = num_queries99_a[2:]\n",
    "    max_single_query99[a] = max_single_query99_a[2:]\n",
    "    num_lengths99 = num_lengths99-2\n",
    "\n",
    "    ninetyninepercentile[a] = np.percentile(errors99[a], 99, axis=1)\n",
    "    ninetyfivepercentile[a] = np.percentile(errors[a], 95, axis=1)\n",
    "    sixtyeightpercentile[a] = np.percentile(errors[a], 68, axis=1)\n",
    "    median[a] = np.percentile(errors[a], 50, axis=1)\n",
    "    \n",
    "    C_csae99[a]      = one_parameter_fits(ninetyninepercentile[a], num_queries99[a])\n",
    "    C_csae_time99[a] = one_parameter_fits(ninetyninepercentile[a], max_single_query99[a])\n",
    "\n",
    "    C_csae95[a]      = one_parameter_fits(ninetyfivepercentile[a], num_queries[a])\n",
    "    C_csae_time95[a] = one_parameter_fits(ninetyfivepercentile[a], max_single_query[a])\n",
    "\n",
    "    C_csae68[a]      = one_parameter_fits(sixtyeightpercentile[a], num_queries[a])\n",
    "    C_csae_time68[a] = one_parameter_fits(sixtyeightpercentile[a], max_single_query[a])\n",
    "\n",
    "    C_csae50[a]      = one_parameter_fits(median[a], num_queries[a])\n",
    "    C_csae_time50[a] = one_parameter_fits(median[a], max_single_query[a])\n",
    "\n",
    "# Compute max constant and max deviation across amplitudes\n",
    "C_csae_ave99          = max(C_csae99.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_time99     = max(C_csae_time99.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_dev99      = max(C_csae99.values(), key = lambda i: i[0])[1]\n",
    "C_csae_ave_time_dev99 = max(C_csae_time99.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_csae_ave95          = max(C_csae95.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_time95     = max(C_csae_time95.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_dev95      = max(C_csae95.values(), key = lambda i: i[0])[1]\n",
    "C_csae_ave_time_dev95 = max(C_csae_time95.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_csae_ave68          = max(C_csae68.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_time68     = max(C_csae_time68.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_dev68      = max(C_csae68.values(), key = lambda i: i[0])[1]\n",
    "C_csae_ave_time_dev68 = max(C_csae_time68.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_csae_ave50          = max(C_csae50.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_time50     = max(C_csae_time50.values(), key = lambda i: i[0])[0]\n",
    "C_csae_ave_dev50      = max(C_csae50.values(), key = lambda i: i[0])[1]\n",
    "C_csae_ave_time_dev50 = max(C_csae_time50.values(), key = lambda i: i[0])[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=0.100\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.200\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.300\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.400\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.500\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.600\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.700\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.800\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n",
      "a=0.900\n",
      "99% ChebAE Load\n",
      "95% ChebAE Load\n",
      "68% ChebAE Load\n",
      "50% ChebAE Load\n"
     ]
    }
   ],
   "source": [
    "# Simulates the approach from Quantum 7, 937 (2023) for the output epsilons obtained from the csAE approach \n",
    "# for 99%, 95%, 68%, and 50%. Saves the files for future use to save time when plotting.\n",
    "\n",
    "# Same number of samples as for csAE\n",
    "num_mc_chebae=500\n",
    "\n",
    "# Setup storage containers\n",
    "ave_num_queries_chebae99 = {}\n",
    "max_num_queries_chebae99 = {}\n",
    "min_num_queries_chebae99 = {}\n",
    "ave_time_complexity_chebae99 = {}\n",
    "max_time_complexity_chebae99 = {}\n",
    "min_time_complexity_chebae99 = {}\n",
    "errors_chebae99 = {}\n",
    "queries_chebae99 = {}\n",
    "time_complexity_chebae99 = {}\n",
    "\n",
    "ave_num_queries_chebae95 = {}\n",
    "max_num_queries_chebae95 = {}\n",
    "min_num_queries_chebae95 = {}\n",
    "ave_time_complexity_chebae95 = {}\n",
    "max_time_complexity_chebae95 = {}\n",
    "min_time_complexity_chebae95 = {}\n",
    "errors_chebae95 = {}\n",
    "queries_chebae95 = {}\n",
    "time_complexity_chebae95 = {}\n",
    "\n",
    "ave_num_queries_chebae68 = {}\n",
    "max_num_queries_chebae68 = {}\n",
    "min_num_queries_chebae68 = {}\n",
    "ave_time_complexity_chebae68 = {}\n",
    "max_time_complexity_chebae68 = {}\n",
    "min_time_complexity_chebae68 = {}\n",
    "errors_chebae68 = {}\n",
    "queries_chebae68 = {}\n",
    "time_complexity_chebae68 = {}\n",
    "\n",
    "ave_num_queries_chebae50 = {}\n",
    "max_num_queries_chebae50 = {}\n",
    "min_num_queries_chebae50 = {}\n",
    "ave_time_complexity_chebae50 = {}\n",
    "max_time_complexity_chebae50 = {}\n",
    "min_time_complexity_chebae50 = {}\n",
    "errors_chebae50 = {}\n",
    "queries_chebae50 = {}\n",
    "time_complexity_chebae50 = {}\n",
    "\n",
    "ninetyninepercentile_chebae = {}\n",
    "ninetyfivepercentile_chebae = {}\n",
    "sixtyeightpercentile_chebae = {}\n",
    "median_chebae = {}\n",
    "\n",
    "\n",
    "C_cheb99          = {}\n",
    "C_cheb_max99      = {}\n",
    "C_cheb_time99     = {}\n",
    "C_cheb_time_max99 = {}\n",
    "\n",
    "C_cheb95          = {}\n",
    "C_cheb_max95      = {}\n",
    "C_cheb_time95     = {}\n",
    "C_cheb_time_max95 = {}\n",
    "\n",
    "C_cheb68          = {}\n",
    "C_cheb_max68      = {}\n",
    "C_cheb_time68     = {}\n",
    "C_cheb_time_max68 = {}\n",
    "\n",
    "C_cheb50          = {}\n",
    "C_cheb_max50      = {}\n",
    "C_cheb_time50     = {}\n",
    "C_cheb_time_max50 = {}\n",
    "\n",
    "# Load or simulate chebAE for confidence levels 99%, 95%, 68%, and 50% for each amplitude\n",
    "for a in amplitudes:\n",
    "    print(f'a={a:0.3f}')\n",
    "\n",
    "    chebae_file = dir+f'chebae_a{a:0.3f}_mc{num_mc_chebae:04d}_99.pkl'\n",
    "    if Path(chebae_file).is_file():\n",
    "        # file exists\n",
    "        print('99% ChebAE Load')\n",
    "        with open(chebae_file, 'rb') as handle:\n",
    "            errors_chebae99[a], queries_chebae99[a], time_complexity_chebae99[a] = pickle.load(handle)\n",
    "    else:\n",
    "        print('99% ChebAE Sim')\n",
    "        errors_chebae99[a], queries_chebae99[a], time_complexity_chebae99[a] = \\\n",
    "            simulate_chebAE(amplitude=a, epsilons=ninetyninepercentile[a], delta=0.01, num_mc=num_mc_chebae)\n",
    "        with open(chebae_file, 'wb') as handle:\n",
    "            pickle.dump((errors_chebae99[a], queries_chebae99[a], time_complexity_chebae99[a]), \n",
    "                        handle, protocol=pickle.HIGHEST_PROTOCOL)  \n",
    "\n",
    "    # compute the average, max, and min number of queries both for total complexity and time complexity.\n",
    "    # Time complexity is the maximum coherent depth and indicates the parallelizability of the algorithm\n",
    "    ave_num_queries_chebae99[a]     = np.mean(queries_chebae99[a], axis=1)\n",
    "    max_num_queries_chebae99[a]     = np.max(queries_chebae99[a], axis=1)\n",
    "    min_num_queries_chebae99[a]     = np.min(queries_chebae99[a], axis=1)\n",
    "    ave_time_complexity_chebae99[a] = np.mean(time_complexity_chebae99[a], axis=1)\n",
    "    max_time_complexity_chebae99[a] = np.max(time_complexity_chebae99[a], axis=1)\n",
    "    min_time_complexity_chebae99[a] = np.min(time_complexity_chebae99[a], axis=1)\n",
    "    ninetyninepercentile_chebae[a]  = np.percentile(errors_chebae99[a], 99, axis=1)\n",
    "\n",
    "    # Fit the curves to get the constant factor\n",
    "    C_cheb99[a]          = one_parameter_fits(ninetyninepercentile_chebae[a], ave_num_queries_chebae99[a])\n",
    "    C_cheb_max99[a]      = one_parameter_fits(ninetyninepercentile_chebae[a], max_num_queries_chebae99[a])\n",
    "    C_cheb_time99[a]     = one_parameter_fits(ninetyninepercentile_chebae[a], ave_time_complexity_chebae99[a])\n",
    "    C_cheb_time_max99[a] = one_parameter_fits(ninetyninepercentile_chebae[a], max_time_complexity_chebae99[a])\n",
    "\n",
    "    # Do the same for the rest of the percentiles. Probably should be done in a function, but this is the lazy way.\n",
    "    chebae_file = dir+f'chebae_a{a:0.3f}_mc{num_mc_chebae:04d}_95.pkl'\n",
    "    if Path(chebae_file).is_file():\n",
    "        # file exists\n",
    "        print('95% ChebAE Load')\n",
    "        with open(chebae_file, 'rb') as handle:\n",
    "            errors_chebae95[a], queries_chebae95[a], time_complexity_chebae95[a] = pickle.load(handle)\n",
    "    else:\n",
    "        print('95% ChebAE Sim')\n",
    "        errors_chebae95[a], queries_chebae95[a], time_complexity_chebae95[a] = \\\n",
    "            simulate_chebAE(amplitude=a, epsilons=ninetyfivepercentile[a], delta=0.05, num_mc=num_mc_chebae)\n",
    "        with open(chebae_file, 'wb') as handle:\n",
    "            pickle.dump((errors_chebae95[a], queries_chebae95[a], time_complexity_chebae95[a]), \n",
    "                        handle, protocol=pickle.HIGHEST_PROTOCOL)  \n",
    "    \n",
    "    ave_num_queries_chebae95[a]     = np.mean(queries_chebae95[a], axis=1)\n",
    "    max_num_queries_chebae95[a]     = np.max(queries_chebae95[a], axis=1)\n",
    "    min_num_queries_chebae95[a]     = np.min(queries_chebae95[a], axis=1)\n",
    "    ave_time_complexity_chebae95[a] = np.mean(time_complexity_chebae95[a], axis=1)\n",
    "    max_time_complexity_chebae95[a] = np.max(time_complexity_chebae95[a], axis=1)\n",
    "    min_time_complexity_chebae95[a] = np.min(time_complexity_chebae95[a], axis=1)\n",
    "    ninetyfivepercentile_chebae[a]  = np.percentile(errors_chebae95[a], 95, axis=1)\n",
    "    \n",
    "    C_cheb95[a]          = one_parameter_fits(ninetyfivepercentile_chebae[a], ave_num_queries_chebae95[a])\n",
    "    C_cheb_max95[a]      = one_parameter_fits(ninetyfivepercentile_chebae[a], max_num_queries_chebae95[a])\n",
    "    C_cheb_time95[a]     = one_parameter_fits(ninetyfivepercentile_chebae[a], ave_time_complexity_chebae95[a])\n",
    "    C_cheb_time_max95[a] = one_parameter_fits(ninetyfivepercentile_chebae[a], max_time_complexity_chebae95[a])\n",
    "    \n",
    "    chebae_file = dir+f'chebae_a{a:0.3f}_mc{num_mc_chebae:04d}_68.pkl'\n",
    "    if Path(chebae_file).is_file():\n",
    "        # file exists\n",
    "        print('68% ChebAE Load')\n",
    "        with open(chebae_file, 'rb') as handle:\n",
    "            errors_chebae68[a], queries_chebae68[a], time_complexity_chebae68[a] = pickle.load(handle)\n",
    "    else:\n",
    "        print('68% ChebAE Sim')\n",
    "        errors_chebae68[a], queries_chebae68[a], time_complexity_chebae68[a] = \\\n",
    "            simulate_chebAE(amplitude=a, epsilons=sixtyeightpercentile[a], delta=0.32, num_mc=num_mc_chebae)\n",
    "        with open(chebae_file, 'wb') as handle:\n",
    "            pickle.dump((errors_chebae68[a], queries_chebae68[a], time_complexity_chebae68[a]), \n",
    "                        handle, protocol=pickle.HIGHEST_PROTOCOL)  \n",
    "    \n",
    "    ave_num_queries_chebae68[a]     = np.mean(queries_chebae68[a], axis=1)\n",
    "    max_num_queries_chebae68[a]     = np.max(queries_chebae68[a], axis=1)\n",
    "    min_num_queries_chebae68[a]     = np.min(queries_chebae68[a], axis=1)\n",
    "    ave_time_complexity_chebae68[a] = np.mean(time_complexity_chebae68[a], axis=1)\n",
    "    max_time_complexity_chebae68[a] = np.max(time_complexity_chebae68[a], axis=1)\n",
    "    min_time_complexity_chebae68[a] = np.min(time_complexity_chebae68[a], axis=1)\n",
    "    sixtyeightpercentile_chebae[a]  = np.percentile(errors_chebae68[a], 68, axis=1)\n",
    "    \n",
    "    C_cheb68[a]          = one_parameter_fits(sixtyeightpercentile_chebae[a], ave_num_queries_chebae68[a])\n",
    "    C_cheb_max68[a]      = one_parameter_fits(sixtyeightpercentile_chebae[a], max_num_queries_chebae68[a])\n",
    "    C_cheb_time68[a]     = one_parameter_fits(sixtyeightpercentile_chebae[a], ave_time_complexity_chebae68[a])\n",
    "    C_cheb_time_max68[a] = one_parameter_fits(sixtyeightpercentile_chebae[a], max_time_complexity_chebae68[a])\n",
    "    \n",
    "    chebae_file = dir+f'chebae_a{a:0.3f}_mc{num_mc_chebae:04d}_50.pkl'\n",
    "    if Path(chebae_file).is_file():\n",
    "        # file exists\n",
    "        print('50% ChebAE Load')\n",
    "        with open(chebae_file, 'rb') as handle:\n",
    "            errors_chebae50[a], queries_chebae50[a], time_complexity_chebae50[a] = pickle.load(handle)\n",
    "    else:    \n",
    "        print('50% ChebAE Sim')\n",
    "        errors_chebae50[a], queries_chebae50[a], time_complexity_chebae50[a] = \\\n",
    "            simulate_chebAE(amplitude=a, epsilons=median[a], delta=0.5, num_mc=num_mc_chebae)\n",
    "        with open(chebae_file, 'wb') as handle:\n",
    "            pickle.dump((errors_chebae50[a], queries_chebae50[a], time_complexity_chebae50[a]), \n",
    "                        handle, protocol=pickle.HIGHEST_PROTOCOL) \n",
    "    \n",
    "    ave_num_queries_chebae50[a]     = np.mean(queries_chebae50[a], axis=1)\n",
    "    max_num_queries_chebae50[a]     = np.max(queries_chebae50[a], axis=1)\n",
    "    min_num_queries_chebae50[a]     = np.min(queries_chebae50[a], axis=1)\n",
    "    ave_time_complexity_chebae50[a] = np.mean(time_complexity_chebae50[a], axis=1)\n",
    "    max_time_complexity_chebae50[a] = np.max(time_complexity_chebae50[a], axis=1)\n",
    "    min_time_complexity_chebae50[a] = np.min(time_complexity_chebae50[a], axis=1)\n",
    "    median_chebae[a]                = np.percentile(errors_chebae50[a], 50, axis=1)\n",
    "    \n",
    "    C_cheb50[a]          = one_parameter_fits(median_chebae[a], ave_num_queries_chebae50[a])\n",
    "    C_cheb_max50[a]      = one_parameter_fits(median_chebae[a], max_num_queries_chebae50[a])\n",
    "    C_cheb_time50[a]     = one_parameter_fits(median_chebae[a], ave_time_complexity_chebae50[a])\n",
    "    C_cheb_time_max50[a] = one_parameter_fits(median_chebae[a], max_time_complexity_chebae50[a])\n",
    "\n",
    "\n",
    "# Compute max complexity and max deviation across amplitudes\n",
    "C_cheb_ave99          = max(C_cheb99.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time99     = max(C_cheb_time99.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev99      = max(C_cheb99.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev99 = max(C_cheb_time99.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave_max99          = max(C_cheb_max99.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time_max99     = max(C_cheb_time_max99.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev_max99      = max(C_cheb_max99.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev_max99 = max(C_cheb_time_max99.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave95          = max(C_cheb95.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time95     = max(C_cheb_time95.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev95      = max(C_cheb95.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev95 = max(C_cheb_time95.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave_max95          = max(C_cheb_max95.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time_max95     = max(C_cheb_time_max95.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev_max95      = max(C_cheb_max95.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev_max95 = max(C_cheb_time_max95.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave68          = max(C_cheb68.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time68     = max(C_cheb_time68.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev68      = max(C_cheb68.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev68 = max(C_cheb_time68.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave_max68          = max(C_cheb_max68.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time_max68     = max(C_cheb_time_max68.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev_max68      = max(C_cheb_max68.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev_max68 = max(C_cheb_time_max68.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave50          = max(C_cheb50.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time50     = max(C_cheb_time50.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev50      = max(C_cheb50.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev50 = max(C_cheb_time50.values(), key = lambda i: i[0])[1]\n",
    "\n",
    "C_cheb_ave_max50          = max(C_cheb_max50.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_time_max50     = max(C_cheb_time_max50.values(), key = lambda i: i[0])[0]\n",
    "C_cheb_ave_dev_max50      = max(C_cheb_max50.values(), key = lambda i: i[0])[1]\n",
    "C_cheb_ave_time_dev_max50 = max(C_cheb_time_max50.values(), key = lambda i: i[0])[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table 1 parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99% Fits Average Case\n",
      "  99% CS Sequential Constant Factor: 8.543 +- 1.604\n",
      "  99% CS Parallel Constant Factor: 0.551  +- 0.102\n",
      "  99% Cheb Sequential Constant Factor: 5.847 +- 0.415\n",
      "  99% Cheb Parallel Constant Factor: 5.581 +- 0.316\n",
      "  99% Sequential Ratio: 0.684\n",
      "  99% Parallel Ratio: 10.134\n",
      "\n",
      "\n",
      "95% Fits Average Case\n",
      "  95% CS Sequential Constant Factor: 4.945 +- 0.602\n",
      "  95% CS Parallel Constant Factor: 0.398  +- 0.048\n",
      "  95% Cheb Sequential Constant Factor: 3.992 +- 0.128\n",
      "  95% Cheb Parallel Constant Factor: 3.767 +- 0.090\n",
      "  95% Sequential Ratio: 0.807\n",
      "  95% Parallel Ratio: 9.456\n",
      "\n",
      "\n",
      "68% Fits Average Case\n",
      "  68% CS Sequential Constant Factor: 2.006 +- 0.102\n",
      "  68% CS Parallel Constant Factor: 0.162  +- 0.008\n",
      "  68% Cheb Sequential Constant Factor: 1.550 +- 0.075\n",
      "  68% Cheb Parallel Constant Factor: 1.441 +- 0.048\n",
      "  68% Sequential Ratio: 0.772\n",
      "  68% Parallel Ratio: 8.924\n",
      "\n",
      "\n",
      "Median Fits Average Case\n",
      "  50% CS Sequential Constant Factor: 1.388 +- 0.072\n",
      "  50% CS Parallel Constant Factor: 0.112  +- 0.005\n",
      "  50% Cheb Sequential Constant Factor: 1.041 +- 0.049\n",
      "  50% Cheb Parallel Constant Factor: 0.955 +- 0.029\n",
      "  50% Sequential Ratio: 0.750\n",
      "  50% Parallel Ratio: 8.549\n",
      "\n",
      "\n",
      "99% Fits Worst Case\n",
      "  99% CS Sequential Constant Factor: 8.543 +- 1.604\n",
      "  99% CS Parallel Constant Factor: 0.551 +- 0.102\n",
      "  99% Cheb Sequential Constant Factor: 8.249 +- 0.450\n",
      "  99% Cheb Parallel Constant Factor: 7.971 +- 0.315\n",
      "  99% Sequential Ratio Max: 0.966\n",
      "  99% Parallel Ratio Max: 14.474\n",
      "\n",
      "\n",
      "95% Fits Worst Case\n",
      "  95% CS Sequential Constant Factor: 4.945 +- 0.602\n",
      "  95% CS Parallel Constant Factor: 0.398 +- 0.048\n",
      "  95% Cheb Sequential Constant Factor: 5.652 +- 0.152\n",
      "  95% Cheb Parallel Constant Factor: 5.417 +- 0.135\n",
      "  95% Sequential Ratio Max: 1.143\n",
      "  95% Parallel Ratio Max: 13.599\n",
      "\n",
      "\n",
      "68% Fits Worst Case\n",
      "  68% CS Sequential Constant Factor: 2.006 +- 0.102\n",
      "  68% CS Parallel Constant Factor: 0.162 +- 0.008\n",
      "  68% Cheb Sequential Constant Factor: 2.520 +- 0.081\n",
      "  68% Cheb Parallel Constant Factor: 2.226 +- 0.091\n",
      "  68% Sequential Ratio Max: 1.256\n",
      "  68% Parallel Ratio Max: 13.782\n",
      "\n",
      "\n",
      "Median Fits Worst Case\n",
      "  50% CS Sequential Constant Factor: 1.388 +- 0.072\n",
      "  50% CS Parallel Constant Factor: 0.112 +- 0.005\n",
      "  50% Cheb Sequential Constant Factor: 1.502 +- 0.043\n",
      "  50% Cheb Parallel Constant Factor: 1.303 +- 0.051\n",
      "  50% Sequential Ratio Max: 1.082\n",
      "  50% Parallel Ratio Max: 11.657\n"
     ]
    }
   ],
   "source": [
    "# Gets the fit parameters for csA and chebAE for both total query complexity as well as parallel query complexity (denoted as time). \n",
    "# This is the query complexity assuming access to as many quantum computers as required to fully parallelize the problem.\n",
    "\n",
    "# Computes fits for both average case and worst case for chebAE. For csAE there is no variation in schedule, so \n",
    "# average case and worst case are the same. \n",
    "\n",
    "print('99% Fits Average Case')\n",
    "print(f'  99% CS Sequential Constant Factor: {C_csae_ave99:0.3f} +- {C_csae_ave_dev99:0.3f}')\n",
    "print(f'  99% CS Parallel Constant Factor: {C_csae_ave_time99:0.3f}  +- {C_csae_ave_time_dev99:0.3f}')\n",
    "print(f'  99% Cheb Sequential Constant Factor: {C_cheb_ave99:0.3f} +- {C_cheb_ave_dev99:0.3f}')\n",
    "print(f'  99% Cheb Parallel Constant Factor: {C_cheb_ave_time99:0.3f} +- {C_cheb_ave_time_dev99:0.3f}')\n",
    "print(f'  99% Sequential Ratio: {C_cheb_ave99/C_csae_ave99:0.3f}')\n",
    "print(f'  99% Parallel Ratio: {C_cheb_ave_time99/C_csae_ave_time99:0.3f}')\n",
    "\n",
    "print('\\n\\n95% Fits Average Case')\n",
    "\n",
    "print(f'  95% CS Sequential Constant Factor: {C_csae_ave95:0.3f} +- {C_csae_ave_dev95:0.3f}')\n",
    "print(f'  95% CS Parallel Constant Factor: {C_csae_ave_time95:0.3f}  +- {C_csae_ave_time_dev95:0.3f}')\n",
    "print(f'  95% Cheb Sequential Constant Factor: {C_cheb_ave95:0.3f} +- {C_cheb_ave_dev95:0.3f}')\n",
    "print(f'  95% Cheb Parallel Constant Factor: {C_cheb_ave_time95:0.3f} +- {C_cheb_ave_time_dev95:0.3f}')\n",
    "print(f'  95% Sequential Ratio: {C_cheb_ave95/C_csae_ave95:0.3f}')\n",
    "print(f'  95% Parallel Ratio: {C_cheb_ave_time95/C_csae_ave_time95:0.3f}')\n",
    "\n",
    "print('\\n\\n68% Fits Average Case')\n",
    "\n",
    "print(f'  68% CS Sequential Constant Factor: {C_csae_ave68:0.3f} +- {C_csae_ave_dev68:0.3f}')\n",
    "print(f'  68% CS Parallel Constant Factor: {C_csae_ave_time68:0.3f}  +- {C_csae_ave_time_dev68:0.3f}')\n",
    "print(f'  68% Cheb Sequential Constant Factor: {C_cheb_ave68:0.3f} +- {C_cheb_ave_dev68:0.3f}')\n",
    "print(f'  68% Cheb Parallel Constant Factor: {C_cheb_ave_time68:0.3f} +- {C_cheb_ave_time_dev68:0.3f}')\n",
    "print(f'  68% Sequential Ratio: {C_cheb_ave68/C_csae_ave68:0.3f}')\n",
    "print(f'  68% Parallel Ratio: {C_cheb_ave_time68/C_csae_ave_time68:0.3f}')\n",
    "\n",
    "print('\\n\\nMedian Fits Average Case')\n",
    "\n",
    "print(f'  50% CS Sequential Constant Factor: {C_csae_ave50:0.3f} +- {C_csae_ave_dev50:0.3f}')\n",
    "print(f'  50% CS Parallel Constant Factor: {C_csae_ave_time50:0.3f}  +- {C_csae_ave_time_dev50:0.3f}')\n",
    "print(f'  50% Cheb Sequential Constant Factor: {C_cheb_ave50:0.3f} +- {C_cheb_ave_dev50:0.3f}')\n",
    "print(f'  50% Cheb Parallel Constant Factor: {C_cheb_ave_time50:0.3f} +- {C_cheb_ave_time_dev50:0.3f}')\n",
    "print(f'  50% Sequential Ratio: {C_cheb_ave50/C_csae_ave50:0.3f}')\n",
    "print(f'  50% Parallel Ratio: {C_cheb_ave_time50/C_csae_ave_time50:0.3f}')\n",
    "\n",
    "\n",
    "\n",
    "print('\\n\\n99% Fits Worst Case')\n",
    "print(f'  99% CS Sequential Constant Factor: {C_csae_ave99:0.3f} +- {C_csae_ave_dev99:0.3f}')\n",
    "print(f'  99% CS Parallel Constant Factor: {C_csae_ave_time99:0.3f} +- {C_csae_ave_time_dev99:0.3f}')\n",
    "print(f'  99% Cheb Sequential Constant Factor: {C_cheb_ave_max99:0.3f} +- {C_cheb_ave_dev_max99:0.3f}')\n",
    "print(f'  99% Cheb Parallel Constant Factor: {C_cheb_ave_time_max99:0.3f} +- {C_cheb_ave_time_dev_max99:0.3f}')\n",
    "print(f'  99% Sequential Ratio Max: {C_cheb_ave_max99/C_csae_ave99:0.3f}')\n",
    "print(f'  99% Parallel Ratio Max: {C_cheb_ave_time_max99/C_csae_ave_time99:0.3f}')\n",
    "\n",
    "print('\\n\\n95% Fits Worst Case')\n",
    "\n",
    "print(f'  95% CS Sequential Constant Factor: {C_csae_ave95:0.3f} +- {C_csae_ave_dev95:0.3f}')\n",
    "print(f'  95% CS Parallel Constant Factor: {C_csae_ave_time95:0.3f} +- {C_csae_ave_time_dev95:0.3f}')\n",
    "print(f'  95% Cheb Sequential Constant Factor: {C_cheb_ave_max95:0.3f} +- {C_cheb_ave_dev_max95:0.3f}')\n",
    "print(f'  95% Cheb Parallel Constant Factor: {C_cheb_ave_time_max95:0.3f} +- {C_cheb_ave_time_dev_max95:0.3f}')\n",
    "print(f'  95% Sequential Ratio Max: {C_cheb_ave_max95/C_csae_ave95:0.3f}')\n",
    "print(f'  95% Parallel Ratio Max: {C_cheb_ave_time_max95/C_csae_ave_time95:0.3f}')\n",
    "\n",
    "print('\\n\\n68% Fits Worst Case')\n",
    "\n",
    "print(f'  68% CS Sequential Constant Factor: {C_csae_ave68:0.3f} +- {C_csae_ave_dev68:0.3f}')\n",
    "print(f'  68% CS Parallel Constant Factor: {C_csae_ave_time68:0.3f} +- {C_csae_ave_time_dev68:0.3f}')\n",
    "print(f'  68% Cheb Sequential Constant Factor: {C_cheb_ave_max68:0.3f} +- {C_cheb_ave_dev_max68:0.3f}')\n",
    "print(f'  68% Cheb Parallel Constant Factor: {C_cheb_ave_time_max68:0.3f} +- {C_cheb_ave_time_dev_max68:0.3f}')\n",
    "print(f'  68% Sequential Ratio Max: {C_cheb_ave_max68/C_csae_ave68:0.3f}')\n",
    "print(f'  68% Parallel Ratio Max: {C_cheb_ave_time_max68/C_csae_ave_time68:0.3f}')\n",
    "\n",
    "print('\\n\\nMedian Fits Worst Case')\n",
    "\n",
    "print(f'  50% CS Sequential Constant Factor: {C_csae_ave50:0.3f} +- {C_csae_ave_dev50:0.3f}')\n",
    "print(f'  50% CS Parallel Constant Factor: {C_csae_ave_time50:0.3f} +- {C_csae_ave_time_dev50:0.3f}')\n",
    "print(f'  50% Cheb Sequential Constant Factor: {C_cheb_ave_max50:0.3f} +- {C_cheb_ave_dev_max50:0.3f}')\n",
    "print(f'  50% Cheb Parallel Constant Factor: {C_cheb_ave_time_max50:0.3f} +- {C_cheb_ave_time_dev_max50:0.3f}')\n",
    "print(f'  50% Sequential Ratio Max: {C_cheb_ave_max50/C_csae_ave50:0.3f}')\n",
    "print(f'  50% Parallel Ratio Max: {C_cheb_ave_time_max50/C_csae_ave_time50:0.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fig. 3 95%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ms=2\n",
    "lw=1\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "a=0.5\n",
    "\n",
    "#QUERY COMPLEXITY\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "plt.rcParams[\"text.latex.preamble\"] = r'\\boldmath'\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Helvetica\"]})\n",
    "\n",
    "colors = ['r.', 'b.', 'c.', 'g.', 'k.']\n",
    "for k in range(num_lengths):\n",
    "    plt.plot([num_queries[a][k]]*num_mc, errors[a][k], colors[k % len(colors)], ms=ms)\n",
    "    plt.plot(queries_chebae95[a][k], errors_chebae95[a][k], colors[k % len(colors)], ms=ms)\n",
    "\n",
    "plt.plot(num_queries[a], ninetyfivepercentile[a], '^g', label=r'\\textbf{csAE}', ms=6)\n",
    "plt.plot(num_queries[a], C_csae95[a][0]/(num_queries[a]), '--g', label=rf'${C_csae95[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(ave_num_queries_chebae95[a], ninetyfivepercentile_chebae[a], '*r', label=r'\\textbf{chebAE Ave}', ms=6)\n",
    "plt.plot(ave_num_queries_chebae95[a], C_cheb95[a][0]/(ave_num_queries_chebae95[a]), '--r', label=rf'${C_cheb95[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(max_num_queries_chebae95[a], ninetyfivepercentile_chebae[a], '*c', label=r'\\textbf{chebAE Worst}', ms=6)\n",
    "plt.plot(max_num_queries_chebae95[a], C_cheb_max95[a][0]/(max_num_queries_chebae95[a]), '--c', label=rf'${C_cheb_max95[a][0]:.2f}/x$', linewidth=1)\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.xlabel(r'\\textbf{Total query complexity}')\n",
    "plt.ylabel(r'\\textbf{Estimation error}')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/a5_max_query.pdf')\n",
    "\n",
    "# TIME COMPLEXITY\n",
    "plt.figure()\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "\n",
    "colors = ['r.', 'b.', 'c.', 'g.', 'k.']\n",
    "for k in range(num_lengths):\n",
    "    plt.plot([max_single_query[a][k]]*num_mc, errors[a][k], colors[k % len(colors)], ms=ms)\n",
    "    plt.plot(time_complexity_chebae95[a][k], errors_chebae95[a][k], colors[k % len(colors)], ms=ms)\n",
    "\n",
    "   \n",
    "# plt.plot(max_single_query, 0.1/(max_single_query), 'r', linewidth=1)\n",
    "plt.plot(max_single_query[a], ninetyfivepercentile[a], '^g', label=r'\\textbf{csAE}', ms=6)\n",
    "plt.plot(max_single_query[a], C_csae_time95[a][0]/(max_single_query[a]), '--g', label=rf'${C_csae_time95[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(ave_time_complexity_chebae95[a], ninetyfivepercentile_chebae[a], '*r', label=r'\\textbf{chebAE Ave}', ms=6)\n",
    "plt.plot(ave_time_complexity_chebae95[a], C_cheb_time95[a][0]/(ave_time_complexity_chebae95[a]), '--r', label=rf'${C_cheb_time95[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(max_time_complexity_chebae95[a], ninetyfivepercentile_chebae[a], '*c', label=r'\\textbf{chebAE Worst}', ms=6)\n",
    "plt.plot(max_time_complexity_chebae95[a], C_cheb_time_max95[a][0]/(max_time_complexity_chebae95[a]), '--c', label=rf'${C_cheb_time_max95[a][0]:.2f}/x$', linewidth=1)\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.xlabel(r'\\textbf{Parallel query complexity}')\n",
    "plt.ylabel(r'\\textbf{Estimation error}')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/a5_max_time.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fig 3 99% (Not shown in paper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ms=2\n",
    "lw=1\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "a=0.5\n",
    "\n",
    "#QUERY COMPLEXITY\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "plt.rcParams[\"text.latex.preamble\"] = r'\\boldmath'\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Helvetica\"]})\n",
    "\n",
    "colors = ['r.', 'b.', 'c.', 'g.', 'k.']\n",
    "for k in range(num_lengths):\n",
    "    plt.plot([num_queries99[a][k]]*num_mc, errors99[a][k], colors[k % len(colors)], ms=ms)\n",
    "    plt.plot(queries_chebae99[a][k], errors_chebae99[a][k], colors[k % len(colors)], ms=ms)\n",
    "\n",
    "\n",
    "plt.plot(num_queries99[a], ninetyninepercentile[a], '^g', label=r'\\textbf{csAE}', ms=6)\n",
    "plt.plot(num_queries99[a], C_csae99[a][0]/(num_queries[a]), '--g', label=rf'${C_csae99[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(ave_num_queries_chebae99[a], ninetyninepercentile_chebae[a], '*r', label=r'\\textbf{chebAE Ave}', ms=6)\n",
    "plt.plot(ave_num_queries_chebae99[a], C_cheb99[a][0]/(ave_num_queries_chebae99[a]), '--r', label=rf'${C_cheb99[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(max_num_queries_chebae99[a], ninetyninepercentile_chebae[a], '*c', label=r'\\textbf{chebAE Worst}', ms=6)\n",
    "plt.plot(max_num_queries_chebae99[a], C_cheb_max99[a][0]/(max_num_queries_chebae99[a]), '--c', label=rf'${C_cheb_max99[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.xlabel(r'\\textbf{Total query complexity}')\n",
    "plt.ylabel(r'\\textbf{Estimation error}')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/a5_query99.pdf')\n",
    "\n",
    "# TIME COMPLEXITY\n",
    "plt.figure()\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "\n",
    "colors = ['r.', 'b.', 'c.', 'g.', 'k.']\n",
    "colors_cheb = ['r*', 'bo', 'co', 'go', 'ko']\n",
    "for k in range(num_lengths):\n",
    "    plt.plot([max_single_query99[a][k]]*num_mc, errors99[a][k], colors[k % len(colors)], ms=ms)\n",
    "    plt.plot(time_complexity_chebae99[a][k], errors_chebae99[a][k], colors_cheb[k % len(colors)], ms=ms)\n",
    "\n",
    "\n",
    "plt.plot(max_single_query99[a], ninetyninepercentile[a], '^g', label=r'\\textbf{csAE}', ms=6)\n",
    "plt.plot(max_single_query99[a], C_csae_time99[a][0]/(max_single_query[a]), '--g', label=rf'${C_csae_time99[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(ave_time_complexity_chebae99[a], ninetyninepercentile_chebae[a], '*r', label=r'\\textbf{chebAE Ave}', ms=6)\n",
    "plt.plot(ave_time_complexity_chebae99[a], C_cheb_time99[a][0]/(ave_time_complexity_chebae99[a]), '--r', label=rf'${C_cheb_time99[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.plot(max_time_complexity_chebae99[a], ninetyninepercentile_chebae[a], '*c', label=r'\\textbf{chebAE Worst}', ms=6)\n",
    "plt.plot(max_time_complexity_chebae99[a], C_cheb_time_max99[a][0]/(max_time_complexity_chebae99[a]), '--c', label=rf'${C_cheb_time_max99[a][0]:.2f}/x$', linewidth=1)\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.xlabel(r'\\textbf{Parallel query complexity}')\n",
    "plt.ylabel(r'\\textbf{Estimation error}')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/a5_time99.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate the Expected Shortfall for both chebAE and csAE (Not shown in paper)\n",
    "\n",
    "Here we calculate the expected error if we happen to fall in the region outside the $\\delta$ confidence level. These results are not shown in the paper. Specifically what this computes is the mean of the error values above the 99%, 95% and 68% error targets respectively. This tells you in a sense, if this algorithm fails, how badly does it fail. We find our approach is generally better, especially for lower confidence levels where it can be orders of magnitude better than chebAE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.5 # Do the calculation for amplitude a = 0.5\n",
    "\n",
    "csae_es_99 = []\n",
    "csae_es_95 = []\n",
    "csae_es_68 = []\n",
    "for err_index in range(len(errors[a])):\n",
    "    errors_95 = 0\n",
    "    errors_68 = 0\n",
    "    es_95 = 0.0\n",
    "    es_68 = 0.0\n",
    "    for error in errors[a][err_index]:\n",
    "        if error >= ninetyfivepercentile[a][err_index]:\n",
    "            errors_95 += 1\n",
    "            es_95 += error\n",
    "        if error >= sixtyeightpercentile[a][err_index]:\n",
    "            errors_68 += 1\n",
    "            es_68 += error\n",
    "    \n",
    "    csae_es_95.append(es_95/errors_95)\n",
    "    csae_es_68.append(es_68/errors_68)\n",
    "\n",
    "for err_index in range(len(errors99[a])):\n",
    "    errors_99 = 0\n",
    "    es_99 = 0.0\n",
    "    for error in errors99[a][err_index]:\n",
    "        if error >= ninetyninepercentile[a][err_index]:\n",
    "            errors_99 += 1\n",
    "            es_99 += error\n",
    "    \n",
    "    csae_es_99.append(es_99/errors_99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "chebae_es_99 = []\n",
    "chebae_es_95 = []\n",
    "chebae_es_68 = []\n",
    "for err_index in range(len(errors_chebae95[a])):\n",
    "    errors_99 = 0\n",
    "    errors_95 = 0\n",
    "    errors_68 = 0\n",
    "    es_99 = 0.0\n",
    "    es_95 = 0.0\n",
    "    es_68 = 0.0\n",
    "    for error in errors_chebae99[a][err_index]:\n",
    "        if error >= ninetyninepercentile_chebae[a][err_index]:\n",
    "            errors_99 += 1\n",
    "            es_99 += error\n",
    "    for error in errors_chebae95[a][err_index]:\n",
    "        if error >= ninetyfivepercentile_chebae[a][err_index]:\n",
    "            errors_95 += 1\n",
    "            es_95 += error\n",
    "    for error in errors_chebae68[a][err_index]:\n",
    "        if error >= sixtyeightpercentile_chebae[a][err_index]:\n",
    "            errors_68 += 1\n",
    "            es_68 += error\n",
    "    \n",
    "    chebae_es_99.append(es_99/errors_99)\n",
    "    chebae_es_95.append(es_95/errors_95)\n",
    "    chebae_es_68.append(es_68/errors_68)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ninetyninepercentile[a],csae_es_99, \"^g\", label=r'\\textbf{csAE}')\n",
    "plt.plot(ninetyninepercentile_chebae[a],chebae_es_99, \"*r\", label=r'\\textbf{chebAE}')\n",
    "plt.gca().invert_xaxis()\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'\\textbf{99\\% Error}')\n",
    "plt.ylabel(r'\\textbf{Expected shortfall}')\n",
    "plt.legend()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ninetyfivepercentile[a],csae_es_95, \"^g\", label=r'\\textbf{csAE}')\n",
    "plt.plot(ninetyfivepercentile_chebae[a],chebae_es_95, \"*r\", label=r'\\textbf{chebAE}')\n",
    "plt.gca().invert_xaxis()\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'\\textbf{95\\% Error}')\n",
    "plt.ylabel(r'\\textbf{Expected shortfall}')\n",
    "plt.legend()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sixtyeightpercentile[a],csae_es_68, \"^g\", label=r'\\textbf{csAE}')\n",
    "plt.plot(sixtyeightpercentile_chebae[a],chebae_es_68, \"*r\", label=r'\\textbf{chebAE}')\n",
    "plt.gca().invert_xaxis()\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'\\textbf{68\\% Error}')\n",
    "plt.ylabel(r'\\textbf{Expected shortfall}')\n",
    "plt.legend()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fig. 4 Constant factor vs Amplitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load noisy simulations\n",
    "\n",
    "def load_sims(dir, amplitudes, percentile=95, idx=4):\n",
    "\n",
    "    C = []\n",
    "    C_time = []\n",
    "    \n",
    "    for a in amplitudes:\n",
    "        filename = dir+f'a{a:0.3f}_mc0500.pkl'\n",
    "        \n",
    "        with open(filename, 'rb') as handle:\n",
    "            errors, thetas, num_queries, max_single_query, arrays, num_lengths, num_mc = pickle.load(handle)\n",
    "\n",
    "        p_error = np.percentile(errors, percentile, axis=1)\n",
    "\n",
    "        C.append(p_error[idx]*num_queries[idx])\n",
    "        C_time.append(p_error[idx]*max_single_query[idx])\n",
    "\n",
    "    return C, C_time\n",
    "\n",
    "cs_C_eta = {}\n",
    "cs_C_eta_time = {}\n",
    "etas = ['1e-4', '1e-5', '1e-6']\n",
    "for eta in etas:\n",
    "    dir = 'sims_C1.5_eta'+eta+'_final/'\n",
    "    temp = load_sims(dir, amplitudes)\n",
    "    cs_C_eta[eta] = temp[0]\n",
    "    cs_C_eta_time[eta] = temp[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vp36Nrle60LCxAYIgFDosIiIiysJSx9tut0MURRbdRAU0dGEIY++MAQDG3hnD0IWhAkdERERE87FUeB86dAiJRGLRd6n0er2orq5GfX09mpubUV1djVAotKh9Eq0Eqqqi+5Vu2ITUbbxtgg3dr3Rn3NSKiIiIioelwvuhhx6CIAjweDzYvHlz2j+73W56f9pFmn6/H01NTVZCIlpRhi4MYfTtUSTVJAAgqSYx+vYou95ERERFzNIY7/m6amY7bn6/H06n00oYRCvSzG63VngDN7veDXdzrDcREVExslR4nz17NmcBRKNRRKNRAIAkSXnreCeTSSSTyYU3zIHr16/j2vQ1XLl6BTabLS/HXK6SySRztQCt2z2b1vX++7N/j4a7GwoQWXHja8sc5ss45soc5ss45sqcZDIJVVXzVt9pxzRDUC0OCo3H4xnzdScSCSiKgn379hnaRzgchqIoaGpqgqIo2L59OyRJWpK7Yk5NTeHcuXM53+9CVFXFd2PfxU/jP4VzvRN3rr0z7zFQaXnp4kv44KMPsq6/fc3t2FW1K48RERERFYdP3PoJ/JH0RwU781tdXT3v1NqWOt6RSAR79+6dc11jY6Ph/fh8PrhcLgDQZ0nROuAOh8NKaIZt3LgxL3OOT09P45/+6Z8wcW0C/5z4Z3z2U59d8mMuZ6qq4r333sMdd9zB4RJzuPCbC/MW3QDwwUcf4Ldrfou7f+fuPEW1PPC1ZQ7zZRxzZQ7zZRxzZY6qqoAC1NbWYtUqSyWuaVNTUzh//rzh7S1F5fV6oaoqJEmCLMuw2+363N7btm0ztA9FURCNRqEoStoyAHmZptBms+XltM3wr4fxZuJNAMA7U+9gy51b0LCRwwCySSaTeP311/GZz3yGp9VmUVUV257bhjKUYRrTWbcrQxnO/es5PPe/P8df1DPwtWUO82Ucc2UO82Ucc2VOMplE9JdRrFq1Km/5MnscyzfQcTgcePHFF7FlyxYcOHAADzzwALZs2YLJyUlD+xBFEQ6HQ7+wUlEUyLKM/fv3QxRFK2EVndkXwdkEG3r+7x48uOlBFkRZJJHE6rLVuMV2C3/JzDJ4fhA/f+fnC243jWn8/J2f49V/eRWNG42fgSp1fG2Zw3wZx1yZw3wZx1yZk0Sy6OsrS9MJiqKoF9g1NTUYHx+HKIqw2+04duyY4f0cPXoUzzzzDNrb29HR0QG3243Ozk4rIRUlTvlGuTJ73u6FcF5vIiKi4mOp4+1wOHDq1CkcPnwYdrsd/f39SCQSiMViqKioMLwfURTR19dnJYSixynfrBn+1TC+9OqX8EPxh2j8NLu1mmwzmWQz80Meu95ERETFwVLH2+12Q1VVyLIMl8sFVVURCAQAmLu4spTN7nZr2PXOTlVVdL3ShV9P/Rpdr3SxW3uD2W63hl1vIiKi4mK54z06OgpZliFJEl588UWcOHECVVVVaGlpyXWMy062breGXe+5DV0Ywtg7YwCAsXfG2K29wWy3W8OuNxERUXEx3fGWZRlHjhxBeXm5fnt4h8MBt9sNSZLwwgsv5DzI5SZbt1vDrnem2V1ddmtTtLyUWTs5hTKUMY9ERERFwnDHW7thzsjICJ5//nlUVVVl/DH3er2Ix+PYvXt3zgNdLhbqdmvY9U43u6vLbm3K1eRVXExcnHf6wPlMYxqyIuNq8irWrFqT4+iIiIjIDMOF97Fjx3DkyBEAqeKyvb09YxtVVVFVVZW76JYho8MCWFjexAtRs1uzag1G20Zx6fKlOdcnk0m88cYb2LRpU9apptbftp5FNxERUREwXHhXVVVh8+bNmJycRDwex+bNmzO2qayshNvtzmmAy4nRbreGhWVKtg8r/HCSIlVIkCrmvqlUMplE2XtluO+T93GOVyIioiJnuPBuaWlBS0sLwuEwfD4fgsHgUsa1LHHKN/N4ISoRERGtFKav2HI6nQgGgzhz5gwikQgA4IUXXsC+fftW9IWVnPLNGl6IukhjY/j0gQPA2FihIyEiIqIFWJoqIRKJoLm5GaFQCLFYDN3d3RgZGYHH41mxxfdCBWQ2K7mwNPphZaV/OJmP8OMfQxwbg/CTnxQ6FCIiIlqApcLb6/UCSE0jeOzYMQiCgP3790NVVQwMDOQ0wOWAU75ZM9eHlc++Bbx8NPVVs5I/nGSIx4Ff/EL/J9y4cZUQCKQtx1tvLbAjIiIiyjdLlWI8HofdbkdLSwsikQhEUYTb7cbWrVtx8eLFXMdY9HI55dtKka3b/V9eB37/X4D/45fp27PrfcODDwKf/ezNfx98kFp+6VL68p07CxsnERERZbB050pNPB6HLMtoamoCACQSCYiimJPAlpOFpnxb84vT+N2ub+NfD30NH/1vtXNus9KmfNO63XcmgPW/vbncFU19fWQc+KvP3Fz+3rokRtWVfSEqAODhh4Ff3vxUItz4ICLM/kCygufSJyIiKlaWbxl/6tQpPPTQQxAEAdu2bcPg4CBisRgcDkeuY1wW5pvybTrkR9lrMawf/DnKHvxiniMrPjO73f/zb5K4772b67RzBh//LfCLZ28uf+0O4P7/kzOcoLs79dXjyb7NwYNAV1d+4iEiIiLDLA01cbvdWLdund7h3r17N0ZGRvR1Kx7H4c5r5tjuF+3p68pmfdX8nZ1jvXXd3cATT8y97sknWXQTEREVKcsd79HRUcRiMdjtqcppx44deOSRR/THK9qDD6YNB4DWndXG4WruvRd4/fX8xlZgMy9EncY0Dv1eavnBV7I/p+vzwLdubKddiLqiu94AcP06IAhQkRpmogoCBG05ERERFSVr03DcUFVVhXg8jng8DkmSIIoi4vF4rmJbvh5+OO0hx+HeNNeFqId+Dzi8de7tfVtvFt3AyrwQNcP0NHDsGKCqQEUF3m5rAyoqUo//9m9T64mIiKjoWOp4x2IxPP7445BlOWOdIAiIxWKLDmxZ4zjcrLJdiLpB9kI9dWNIzo0OLgD8F8cj+P1H04cvrbQLUTNcuQJIErBtG6Z/8AO88/bbuOPP/xy2L38ZkOXU+ttuK3SURERENIulwrurqytt2sCVOJPJgrq7gYkJ4DvfyVy3wsfhZlyIOj0N/MM/AqoKtbISb+/ejU++8AKEiQms//uXsf6ZHwNlizo5U1puuw342c8Amw1IJoG33wbWrweCwdRjm7m7pxIREVF+WO54C4KAoaEhSNLcM3kQOA7XKHZwzctWXLPoJiIiKlqW2oh2ux2iKLLong/H4RqndXCDwVTnFrjZwT11ikU35cbYGD594AAwNlboSIhWNr4XaQWzVHgfOnQIiUQCL7zwQq7jKR1aF3fXLkzHYnjnsccwHYsBu3YBVVWp9XQTO7i0xIQf/xji2BiEn/yk0KEQrWh8L9JKZmmoiXbjHI/HA8+sCwgXc3Flc3MzDh48WBo34eE4XKLCiseB99/XH6bNp79nz83t7rgDuPPOPAdHJWVsDJ/+yleA738f+NznCh1N8eF7kUhnqfBWZ0+LZ3DdfFpbWxGNRi09t2ixi0tUOJxPn/JE6+BO/+QnLLznwvcikc5S4X327NmcBtHf38/x4kSUWw8/nPbHnvPpU86wg2sO34tEOkuFt+bMmTMYHx8HANTW1uKee+4xvY9wOAwAcDqdCNz45UVEtGicT5+WCju45vC9SKSzXHh3dHRgaGgobVlTUxOefvppw/uQZRmhUAg9PT0IhUJWQ7EkmUwimUzm7Vgzv1J2zJU5zNcCvv51CP/2byj77nczVk3/6Z9C/bM/S11zQRn42spOaG5GmYEO7vRDD0Fl/lL4XrSE70NzCpEvs8eyVHgPDAxgcHAQANDY2AgAGBwcRCgUQm1tLfbu3WtoP16vF319fVZCWLTz58/n/ZinT5/O+zGXK+bKHOYruw3vvov1NzqSM++KeunddxF/7bUCRrY88LU1hz/4A3zi3Xdx549+lHWTtw4cwLsPPgjwNabje9E6vg/NKeZ8CaqFqyG/8IUvIB6P4+TJk9iwYQMAQFEUbNmyBXfddZdelM/H6/UiEonoz4/H44hGo3A6nWhqaoLL5TIb1rympqZw7tw5/fHGjRuxbt26nB4jm2QyidOnT6O2thY2Xlg5L+bKHOZrAdPTKLvzTgiXLkGtrMQ7M+6Kqq5fj+l4nHdFzYKvrYUJbnf2Dq7Xm/+Aihnfi5bwfWhOIfI1NTWV1sytrq6et7601PGWZRkOh0MvmoHUbeOdTicikYihfXR2dqY97u/vRzQahdvtzst0gjabLe8v4kIcc7lirsxhvrL48MPUvPn/4T9k3BVVkGXYrl7lDZoWwNfWPKan57w7cdn0NGevmo3vxUXh+9CcfObL7HEsfbzcsGEDYrEY3nrrLX3Z1NQUxsfHLc1O0t7ejhMnTgAAfD4fL7IkotzgXVFpqfDuxObwvUgEwGLH2+Vy4fDhw6ivr08b4w0Ajz32mOn9FWqcNxGtAJxPn5aCdnfibdsyOriQ5dR6FpPp+F4kslZ4t7W14fTp0xgaGkqbjaSpqQn79u3LWXBERERFacbdiYf/v0F86dUv4Yd/9EM08u7ERDQPy9MJ9vX1IRaL6fN419TUwG635ywwIiIqnOFfDaeKSfGHaPx0Y6HDKU42G1RVRdcrXfj11K/R9UoXGjY2QGDRTURZWCq8p6amsG7dOtjtdtjtdv0xEREtf3MWk9pNYijN0IUhjL0zBgAYe2cMQxeG0LiRH1SIaG6mLq48c+YMGhoasGfmLXEBbN++HY2NjTm/lTwREeXfXMUkZVJVFd2vdMMmpDrcNsGG7le6YWGWXiJaIQwX3pOTk/jiF7+IixcvZvxSmZ6exptvvonm5mbE4/GcB0lERPnBYtK4oQtDGH17FEn1xt3y1CRG3x7lBxUiyspw4e31eqEoCpqamnD06NG0df/4j/+IhoYGTE9P4/Dhw7mOkYiI8oTFpDGzP6Bo+EGFiOZjuPCORCIQBAGHDh1CeXl52rry8nJ9SsBoNJrbCImIcmD4V8PY/epuDP9quNChFC0Wk8bN/oCi4QcVIpqP4cJblmUAmPciSlEU9e2IiIrF7IsFWUDOjcWkMdk+oGj4QYWIsjFceGtTBZ46dWrO9bIsQ1EUTilIREWHFwsujMWkcdk+oGj4QYWIsjFceG/duhWqqqKjowMnT55MWxeJRLBv3z4IggCn05nzIImIrOLFgsawmDRmoQ8oGr7OiGguhufx7uzsxODgIOLxONrb2wGkhpYoigIg9cuoqqoKTz755NJESkRkgVZQamYWkJxvOWVmMZmt8AZuFpMNd6/ceb1nv56y4euMiOZiah7vl156CS0tLVBVFaqqIpFI6N+3tLTgxRdfXKo4iYhM48WCxizU7das9K630W63hq8zIprN1J0ry8vL0dPTg56eHsRiMSQSCVRUVHBcNxEVpWzdSXYjbzLa7das5K630W63hq8zIprNVMd7Jrvdjq1bt7LoJqKixIsFjTHa7das1K632W63hq8zIprJcuFNRFTMeLHgwlhMGmf2A4qGrzMimomFNxGVHM48YQyLSWO011OZxT+ZZShb0a8zIrqJhTcRlRxeLLgwFpPGXU1excXERUxj2tLzpzENWZFxNXk1x5ER0XJj6uJKIqJix4sFjcllMblm1ZocR1dc1qxag9G2UVy6fGnO9clkEm+88QY2bdoEm23usyzrb1tf8nkiooUZLrynpqYM73S+28oTES0lzjxhDItJc6QKCVKFNOe6ZDKJsvfKcN8n78uaKyIiwEThXVdXZ2g7QRAQi8UsB0REZJXZbrdmpXa9WUwSEeWX4cF92o1yFvo3PW3ttCUR0WLxYkEiIipmhjveZ8+eXco4iIgWZebFglbGLWsXC660rjcREeWP5Ysr4/F4xpCSRCIBRVGwb98+Q/uQZRn9/f369wDQ09MDSZr71CcRUTa8WJCIiIqdpcI7Eolg7969c65rbDR+cZLH40EikUAwGAQAVFdXo7W1FcPDw1bCIqIVjBcLEhFRsbNUeHu9XqiqCkmSIMsy7HY7YrEYBEHAtm3bDO9HkiQkEgkANzve7HYTkVW8WJCo+A3/ahhfevVL+KH4QzR+euXMJEQEWCy8Y7EYHA4HXnzxRWzZsgUHDhzAAw88gC1btmByctLwfnp6egCkim6v1wtJkuB2u62EZFoymUQyae4CrMUca+ZXyo65Mof5Mo65Mof5Mo65Mk5VVTz1ylP49dSv8dQrT2H7v9/OayrmwdeWOYXIl9ljCaqF245t2bIFlZWVGBoawt69e1FTU4MnnngCzc3NmJqawtCQ8ZkBFEVBIBDAxMQEIpEIXC4XXC6X2ZAWNDU1hXPnzuV8v0RERGRM5P0Ivvr/flV//L0t38PW9VsLGBFRblVXV897PxtLHW+Hw4FTp07h8OHDsNvt6O/vRyKRQCwWQ0VFhaF9KIqC7du3o6WlBZ2dnQCA5uZmeDweVFRUoKmpyUpohm3cuDFvN/pJJpM4ffo0amtreYp7AcyVOcyXccyVOcyXccyVMaqq4sBzB/R59m2CDX8l/xUOfOEAu95Z8LVlTiHyNTU1hfPnzxve3lLh7Xa78dBDD0GWZTz55JMYGBhAIBAAAMMF8/j4OBRF0cd2A6liHMjPOG+bzZb3F3EhjrlcMVfmMF/GMVfmMF/GMVfzGzw/iLF3xvTHSTWJsXfG8PK/vLyi7hprytgYPv2Vr8D2/e/D9rnPFTqaZSOf70Wzx7Hc8R4dHYUsy5AkCS+++CJOnDiBqqoqtLS0GNqH0+mEKIrYuXMnAOhFuNPphMPhsBIWERERFaFsd5VdqXeNNUr48Y8hjo1h+ic/AVh4lwTDhffU1BQAYN26dZiamoIgCKiqqsLU1BTuuusuHDhwQN/O6BCOYDAIj8eD48ePIx6PY//+/fqwEyIiIioN2l1lZ5t511h2vQHE48D77+sPhRujCYRAANiz5+Z2d9wB3HlnnoOjXDBceNfV1aGqqgoDAwNoaGjIup0gCBk31slGkiT4/X6jIRAREdEyk63brWHXe4YHHwR++cubj7V8XLoEfPazN5ffey/w+uv5jY1ywnDhraoqtAlQ5psIxcIkKUVBVVV88MEH+O1vf4tr167lfN8AcOHCBf5SWYCWq4sXL2LdunW4/fbbmTMiomUsW7dbw673DA8/nFZ4Czf+Jgqza6vdu/MZFeWQ4cL77Nmzc35fClRVxXvvvYff/OY3S7b/VatW4fr16ywiF6CqKmw2G65cuYIPP/wQyWQSd9xxB/NGRLQMLdTt1rDrfUN3d+qrx5N9m4MHga6u/MRDOWf64kpZljE0NIR9+/ZlrItEIojH49i9zD6JffDBB2lFt81my/kbv6ysjFe7GzQz97/5zW9gs9nw8Y9/vIARERGRFQt1uzXses/Q3Q1MTADf+U7muiefZNG9zBkuvOPxOGKxGEZGRvD888+jqqoqY1iJ1+tdloX3b3/7W/37T37yk6isrFzU/oZ/NYz2E+3o29GH+k/VQ1VVXL58GWvXrl3Zn+QN0HJ17do1vPPOOwBSPx8W3kREy4vRbreGXe+b1GvXoAoAVKAMwDQACIBw7RpWdmaWP8OF97Fjx3DkyBEAqTdTe3t7xjaqqqKqqip30eWJNqbbZrMtuuhWVRVff/nrOPPBGXz95a9j+7/fnoMIV56Kigq8//77SCaTuH79eqHDISIik4x2uzXset8wPY2rf/PXWKMC//Yx4HufA776M+DffQh89JO/xpqnnwbKygodJVlkuPCuqqrC5s2bMTk5iXg8js2bN2dsU1lZCbfbndMA8ykXn7Bn/qLRfoE03J19FhjKTvt5LNcLdomIViqz3W4Nu96AevkyfnXbNZxZDxx4ELi0DvhBHfCjnwL3XL6KzZcvQ8jTnbcp9wwX3i0tLWhpaUE4HIbP50MwGFzKuJal2b9otF8gX/jUFwod2rzC4TBaW1sBAL29vRl3H62rq9PvKjqb3++H0+lc8hiJiGj5MNvt1rDrDQy9O4Kdey5jekZT+9I64CEXUDZ9GcffHVmxuSkFpi+udDqdetE9NTWFiYmJjG02bNiw6MCWo9m/aGb+AvmP/8t/LGBk8zt27Jj+/fHjxzMKb43D4UBFRUXastmPiYhoZdOaUGUow3RqdLIpZShbsV1vLXeCzQbMcaZAsPGMwHJn6ZbxZ86cQUdHB2RZzlhn5gY6pWTe2+G+2o1X/viVnB9TURR0dXUhEokAAHbs2AG32w1RFAFAPzsRjUYhiiJ27NiBnp6ejP0MDg5CkiT9+2yOHj2q75uIiGguV5NXcTFx0VLRDQDTmIasyLiavIo1q9bkOLrixjnPS5+lwvupp57CxYsX9ccsxua/He7Y22N4+V9exh85/iinx2xuboYsy2hsbEQ8HkcgEMDExAT6+vqgKApaW1shiiJcLhfGx8cRuHHr2ZnFdygUAgC4XC5MTExgYGAAoVAoa9ebiIhoPmtWrcFo2yguXb405/pkMok33ngDmzZtyjrN7vrb1q+4optznq8MlgrvWCwGQRAwNDSkd0pXMiO3w+35px78of0Pc/YmCYVCkGUZTqcTfX19AID6+nq9+z0+Pg4AkCRJ74J7vd6MWVu0YrypqQmKomBgYACBQGDOwruuri7tsSiKGB01P4aPiIhKm1QhQaqYuz5IJpMoe68M933yPt7fYgbOeb4yWCq87XY73nrrLRbdNxg5NfSL936BoQtDaPp0bjrJ2jCfmRc2Dg8P699ry6PRKOrq6uBwOLBjxw60tbXp2yiKgnA4DEmS9J+lKIoIh8NQFCXjTMbsMd7l5eU5+b8QERGtZJzzfOWwVHgfOnQIzc3NeOGFF5bdzXJyzdSpoVe70bixMadvkvmG+YyOjiIQCODEiROIRqOIRqM4ceKEfnHsiRMnAKSK+Orq6rTnnjhxAi6XK20Zx3gTERHlHuc8XzkszcD+0EMPQRAEeDwebN68Oe2f3W7PdYxFTXuzLPQJVRvrPXRhKCfH1TrUIyMj+rLm5mZ9OEg4HEYgENBnoRkeHoYoiohGo/r22jATp9Op/3M4HABujv0mIiKipTOzgWeG1vXmvS6WF0sd7/l+yCvpBVDIU0NNTU2QJAmDg4Nob29HPB5HNBpFY2Pqk6+iKPD5fPpsJhMTE1AURS/YZVnWZzvx+/1p+66rq5tzuElHR0dGHC6XixdiEhERWcQ5z1cWS4X32bNncx3HslToU0N+vx8ej0e/oNLlcukzljQ1NaGnpwf9/f0IBAIQRRFOp1Nfr3W0d+zYkbHfrVu3YnBwMGO4STgcztjWbrez8CYiIrKAc56vPJYKbwCIx+Po7+9HNBrFo48+CiA1/GGuW8mXomK4Ha4kSRnd6plcLlfGOG1NW1tb2oWWM2mzpGg4cwkREVHucc7zlcdS4S3LMhoaGqCqKgRBQCKRwJtvvomOjg689NJLuOeee3IdZ9HhqSEiIiJaDM55nmNjY/j0V74CfP/7wOc+V+ho5mSp8P7GN74BANi/fz8GBgYAANu2bcPAwAC8Xi+OHDmSuwiLEE8NERERUS5wzvPcif/gL3DX2Bje/L/+End97n8UOpw5WSq8x8fH4XQ64Xa79cJ769atcDqd+o1bShlPDREREREVWDwOvP8+gFRTtPx/HAcAlL/0U6jtP7/Z3LzjDuDOOwsVZRrLY7wTiUQu41hWFjo1NJuqqvjwww/xsY99TH8R8NQQERER0SI8+CDwy18CAAQAlTcWV05eh3D//Te3u/de4PXX8x3dnCwV3g888ABOnjyJxx9/HIIgYGRkBCMjI4hEIvp0dqVuvlNDs6mqisuXL2Pt2rUcWkJERESUCw8/rBfewM2b02TcpKaIbvZoqfD+1re+hVgspk9JNzg4CFVVIYoiDh06ZHg/iqKgq6sLk5OTkGUZLpcr60wbRERERES67u7UV48n+zYHDwJdXfmJxwBLhXd5eTmGh4cRCAT0OyHW1NSgpaXF1H727NmjT3kXCoXQ0dGBiYkJdHZ2WgmLiIiIiFYQtasLf/P//AD/+eR7Get+/IU78J+fegrFNNbAUuE9NTUFAHjwwQfx4IMPpi1ft26doX0oioJoNKoX7tpNWAYGBlh4ExEREdGChi4M4QPlPX26izJA//4D5b2im77ZUuFdV1eXdV1TUxOefvrpBfchiiIkSUJ5ebm+zOFw6MW4w+GwEpphyWQSyWTqxjeqquq3ul+KW94v5b5LzexcaT8b7WdF6bS8MD8LY67MYb6MY67MYb6MY67mp6oquoefwj+Mpwruf/sY8L3PAV/9GfDvPgT+eBz4w+GnsP1/3b5k19iZ/dlYKrznKyDNFJfDw8Npj6PRKCRJWvKiGwDOnz+f9njVqlUoKyvD5cuXl+yYV65cyfk+JycncfDgQZw9exbxeBz33HMP9u7di/r6ekv7i8fjeOutt/C5eSaej8fj+Na3voWf/exn2LBhA9rb27Meb/b+Dh06hGAwmLZNe3s79uzZk7bsypUrSCaTuHbtGq5cuYLXXnvN0v9npTh9+nShQ1g2mCtzmC/jmCtzmC/jmKu5Rd6PICr/HLII/JMEfOkPgEvrgB/UAT/8n0CVAkTln+NHJ3+Ereu3FjpcABYL77Nnz2YsCwQC+OY3v4nHHnvMUiDNzc1wuVxwu92Wnm/Wxo0b9WExFy5cwPXr12Gz2bB27dqcH0tVVVy5cgW33nprTj9xybKML3zhC2hpaUFvby8AIBKJ4Gtf+xq++93v6sN3zPjyl78Mu92Oz3/+83OuVxQFf/Inf4KWlhZ873vfw/j4OB5//HHcfvvtcDqdC+7v3Xffxf79+7Fjxw59G0mS9LzPzJXNZsPq1atx66234u677zb9f1kJkskkTp8+jdraWt5cYQHMlTnMl3HMlTnMl3HMVXaqquLAcwfw0RobPteWxPSMqUwurQMefgQomwYEmw1/Jf8VDnzhwJJ0vaempjKaufOxPI/3bC6XCwMDA+ju7sbf/d3fGX6eNrPJwYMH4XA4EAgE4HQ6IUnGpuqzymaz6S9iQRD0H8ZSTvc38zi58I1vfAMulws9PT36spqaGgDA4cOH04pbIzweD2RZht1uzxpnJBJBRUWFPg5/27ZtePTRRzEwMIBt27YtuD9ZltHW1qbHmc3Mn4cgCPyFs4CZr2eaH3NlDvNlHHNlDvNlHHOVafD8IMbeGUs9yJg/MGW6DICaxNg7Y3j5X15ekrHeZn8uOSu84/E4ZFlGPB43/JxoNIo9e/ZAkiT4fD4kEglEo1GMjo7mKqxFUVUV16av5WQ/V5NXsSq5at7Ce3XZasOFuaIoCIfDGcN1AKCtrc10tzscDiMcDsPlcmFiYiLrdtlunCTLsqH9ybKM/v5+tLa2QhRFtLS08GJaIiIiMkxVVXS/0g2bYENSXXiMtU2wofuVbjTc3VDw+6lYKrw3b96cdZ3dbje0D0VR0NzcDAD6zCZA6qJLURSthJVTqqriuX9+DrIiL7yxgX1du3YNq1fPX1hXVVSh9b5WQy+K8fFxAMh6ZsDMGQNFUdDR0YGjR4/i+PHj8xbeTqcTHo8HgUAALpcL0WgUzz77rKH9acW53W5HT08PZFlGR0cHKisrOX87ERERGTJ0YQijbxtv0ibVJEbfHi2KGU5yenGlJEmGb6AjiiLOnTtn5fB5U+hPRbmgzY8+F7/fD6fTiY6ODjz66KNwOBw4fvz4vPuTJAl+vx8ejwcejweSJKGlpQWDg4P6Ntn2J0lS2s9ckiS43W709/ez8CYiIqIFme12a4ql622p8D558mTGssrKyrSpAZc7QRDQel9rzoaaGLllvJmhJtoYaVmWM7rbWie5t7cXTU1N837ACQQCSCQScLlcUBQFk5OTmJychKIoWc88OJ3OtCEugUBA39bs/iRJyhimQkRERDQXs91uTbF0vS0V3r/zO78z53LtxjozGb2hTjESBAG32G5Z9H5UVcV123XcYrslZ5+yRFGEw+FAf39/2sWVQKrLPVdBPhdt3vTZc7PX1dVhdHQ0o1iWZRlerxd9fX1px9Mu5Jxvf3/5l3+Jf/iHf4Df70/b31JfSEtERETLn9btLkMZpvXb5BhXhrKCd70tFd67du0ydBGlIAiIxWJWDkEG9Pb2or6+HhMTE/o0juFwGD6fTy/GFxpq0tPTk1a4e71eyLKcUViLoqjPNhOJRODxeNDW1oZQKITx8XF9OsP59ifLMv7sz/4MXq8XjzzyCGRZhs/ny9sUkkRERLR8XU1excXERUtFNwBMYxqyIuNq8irWrFqT4+iMsTzG28iNcninxqUlSRKGh4fh8XiwZ88eKIoCh8OhDzEBsOBQEyOeffZZ1NTU6PN0Hz16FN3d3aivr4fT6UQwGDR0QawkSQgGg+ju7sbAwIA+xtvlci0qPiIiIip9a1atwWjbKC5dvjTn+mQyiTfeeAObNm3KOs3f+tvWF6zoBiwW3gcPHkRrays6OzvR0NCAyspKHDt2DN/5znfw3HPPYevW4rg70EqgXeyYK3NN7Tf7TpMOhyNjmdH9mXkuERER0UxShQSpYu4hqslkEmXvleG+T95XtPOeZ5lyfH5erxdVVVXYt28fJElCeXk52trasHnzZnzzm9/McYhERERERMufpY53PB6HIAiYmprSL56cmprSlxMRERERUTpLhfcDDzyAoaEhbN++XR9WEolEMDk5icbGwk5MTkRERERUjCwV3t/61rcQj8cRi8UQCoX05Xa73fANdIiIiIiIVhJLhXd5eTmCwSAikQhGRkYAALW1tex2ExERERFlYeniSiA1zjsUCiESieDee++FIAg4c+ZMLmMjIiIiIioZljresiyjoaEBqqpCEAQkEgm8+eab6OjowEsvvYR77rkn13ESERERES1rljre3/jGNwAA+/fv12+Ss23bNqiqCq/Xm7voiIiIiIhKhKXCe3x8HE6nM+1W31u3boXT6cT4+HjOgiMiIiIiKhWWx3gnEolcxlFaxsaA3//91NcCUBQF1dXVqK+vt/T8aDSK6upqtLa2LrhtOBxGdXU1qqur02a40dTV1enrZ/8Lh8OW4iMiIiJajizP433y5Ek8/vjjEAQBIyMjGBkZQSQS4cwmAPDXfw288grw3/87cP/9hY5mSR07dkz//vjx42hqappzO4fDgYqKirRlsx8TERERlTLL83jPnMNb+yqK4sqcxzseB95//+bjQCD19dgx4ItfBFQVZR9+CNx1F7BhQ84OqygKurq6EIlEAAA7duxIG/6TCiUAn88HAHj00UfR1tYGIHWBrMfjQTgchiiKaetm8ng8OHHiBCRJgtvthtPpTFs/ODgISZL077M5evQoRFG0/p8lIiIiWuYsz+M9PDyMQCCAaDQKAKipqUFLS0tOg1s2HnwQ+OUvbz4WhNTXS5eAz34WAoBbAaj33gu8/nrODtvc3AxZltHY2Ih4PI5AIICJiQn9w48sy/D5fJAkCdFoFD6fD01NTaioqEB9fT1EUYTL5cL4+Dh8Pp/+WKMV5Vu3bsXg4CBaW1sRDAbhcDgA3PzA5XK5MDExgYGBAYRCoaxdbyIiIqKVzPIYbyBVcP3xH/8xamtr9a7nivTww+mPb8z0on/Ntt0ihEIhyLIMp9OJvr4+BINBSJKkd781L7/8MoLBoD4EKBqNInCjI+92u9HT04NgMAgg1d2eLRgMoq+vT++ka8+d+X1TUxN27tyZsX6m2WO96+rqFvPfJyIiIlp2THW8n3/+eRw+fBhutxu7d+/GwMAADh8+rK93Op04cuRIzoMset3dqa9zFK6aq93dWN3VlbNDyrIMAGlDP4aHhwGkhqAAgCRJ+vAO7YNRIpHA6dOnb4TrySi2tedqz9Ge19TUBJ/Pp89aoygKwuFw2jaiKCIcDkNRlIxhJbPHeJeXly/mv09ERES07BguvCORSEaRpo0dttvtiMfjCIfDeO6557B3797cRrkcdHcDExPAd76TsUp94glc+6//FauX4LBWxk1XVlYCSHW8tWEjZvd34sQJAKkPANXV1RnrZg5ZATjGm4iIiMjwUJP+/n4IgoDOzk7s3r1bH9Kwbds2BINBvPjii1BVFT/96U+XLNiid/16any3NsZb+/769ZwfSusyj4yM6Muam5sNDeGY2aF2Op1wOp36zDQzybKsd9a18dw1NTUAbg4p0Z7vdDozxn4TERER0U2GO97aEIN9+/YBSI0VFgRBv5BOG9YQj8cNH1xRFAQCAQQCAX2YxLI1PZ2axURVgcpKoL0d6OtLdcGPHQNyPNtLU1MTJEnC4OAg2tvbEY/HEY1GDU3n6HK54PP54PF4cPHiRcRiMYTD4YwuNZAq5rWLKwGgra0NsiwjGo1CFEX4/f607evq6uYcbtLR0TFnHLwQk4iIiFYKw4W3oiioqqrSH2vjhLUOKJCal9lo4e31ejE5OYlwOKx3VZe1K1cASQK2bQN+9CNg/Xrgy18GDhwAZDm1ft26nB7S7/fD4/HoZx9cLhd6enrSxmnPRRRFBINBdHd3Y2BgAKIowu1269MJiqKIxsZGSJKEyclJfTrBnp4eSJKE/v5+AKnpC2fTivTZw03mulmO3W5n4U1EREQrhuHCW5IkyLKMt956C3feeade7G3evBkAEIvFIMtyWnE+n87OTgBAa2traRTet90G/OxngM12c9n69UAwmBpq8tFHOT+kJEkZHWcgVTifO3cubVlnZ6eecyB1saM2m8lc++3r69Mf9/T0pK1va2ubc85vAGnPA4DR0dH5/xNEREREK4ThwruhoQFHjhzR53+enJzUZ9QYHBzU72I513CFYpRMJpFMJgEAqqpCvTH1nzp7CkAzysoypxAEoJaVLX7fK8Tsn4P2s9F+VpROywvzszDmyhzmyzjmyhzmyzjmypxC5MvssQwX3p2dnYjFYohEIkgkEgCgz+0syzJUVcW2bdv0MeDF7vz582mPV61ahbKyMly+fHnJjnnlypUl23epuXLlCpLJJK5du4YrV67gtddeK3RIRU0b+kULY67MYb6MY67MYb6MY67MKeZ8mZrH2+/3Q5ZlxONx1NTU6HMxO51O+P1+bN26dUmCXAobN27Euhtjri9cuIDr16/DZrNh7dq1OT+Wqqq4cuUKbr31VgjajCc0p5m5stlsWL16NW699VbcfffdhQ6tKCWTSZw+fRq1tbWwzRzmRBmYK3OYL+OYK3OYL+OYK3MKka+pqamMZu58TN8yfuYNUzR2u93sbgrOZrPpPxRBEPSCeCkL45nHofnN/HkIgsBfOAuY+Xqm+TFX5jBfxjFX5jBfxjFX5uQzX2aPs6hbxhMRERERkTGmO965EggEMDIyos9o0t7ejsrKyowZNIiIiIiISkHBCm+Xy7VsZkAhIiIiIlosDjUhIiIiIsoDFt7LnKIoaG9vR319Paqrq9Hc3IxQKGRqHx6PB9XV1Wn/tLtTZtPf34/6+nrU1dXB6/Ua3p+iKGhtbUVdXR3q6urg8XjM/YeJiIiIlqmCDTWhxZNlGfX19XC5XOjt7QWQujV7R0cHent7Dd+OXZZl7N+/Hzt37tSXzZ65Ziav14vBwUH09vYikUigo6MDVVVV+tCh+fbX3NwMu92OYDAIRVHQ0dEBj8fDsf1ERERU8lh4L2MejwculyutaHU4HAAAn89nqvBua2vTn7uQ559/Hr29vfr2brcbiqIsuL9oNApZljE8PKwvc7vd6O7uZuFNREREJY+F93xUFbh2LTf7uXoVWLUKmG8e79Wr518/g6IoCIfDaUWspq2tzXDRDaQK5f7+frS2tkIURbS0tKCzs3PObaPRKBRFgdPp1JfNvkg22/5EUcwosLW7oBIRERGVOhbe2agq8NxzwI3pDhe7r9XXri1cWFdVAa2thorv8fFxANmHhMw3VGQmbTpHu92Onp4eyLKMjo4OVFZWoq2tbc7tJUmC1+vFwMAAAKCxsRGHDh2CKIoL7m9mkS7LMnw+Hx599FFDsRIREREtZ7y4cj4lcJfJUCiUcaGj9i8cDkOSJJw7dw6dnZ2QJAlOpxNutxuBQGDO/SUSCciyjMnJSYyOjmJ4eBjxeBxdXV0AYHh/2sWZjz766JwFPhEREVGpYcc7G0FIdZ9zNNTk2uXLWL12bc6GmtTU1AC42YGeSesyaxdYnjt3zlS4kiTpnevZKioqAEAfMiKKItxuNzo6OgztT5ZlfQhKMBg0PK6ciIiIaLljx3s+ggDcckv+/pnosIuiCIfDMee0f6FQaM6CfC6hUAitra1py+Z77lyF8swLKxfaX2trK5xOJ4tuIiIiWnHY8V7Gent7UV9fj4mJCTz22GMAUtMJ+nw+vSMdCoWydqP9fj8cDgfC4TC8Xi8eeeQRfdy12+3WtwuFQhBFEU6nUx8+0t7ejs7OTiiKAp/Ph5aWFgCYd3/hcBiyLMPlcmV01I2OSSciIiJarlh4L2OSJGF4eBgejwd79uyBoihwOBxpc3gbGWoSDAbR3d2NgYEBSJIEt9uddhHks88+i5qaGn0mk97eXnR1daG5uRkA0mZBkSQp6/607rz2PI0oihgdHc1NUoiIiIiKFAvvZU6SJPj9/kXtw+FwIBgMZl0/e50oiujr6zO9v7a2Nl5ISURERCsWx3gTEREREeUBC28iIiIiojxg4U1ERERElAcsvImIiIiI8oCFNxERERFRHrDwBiDcuHHN9evXcfXq1QJHQwBw9epVXL9+HcDNnw8RERHRcsbpBAHccsstuHbj1vAXLlyAzWbLebGXTCZhs9lyus9SpRXcmjVr1hQoEiIiIqLcYeEN4Pbbb8fVq1f14juZTOZ0/6qq4tq1a1i9ejW7twtQVRVXr17FLbfcAkEQsHr1avzu7/5uocMiIiIiWjQW3gDWrl2LT33qU7h06RIuX76c0XFdLFVVceXKFdx6660svBeg5epjH/sYbrvtNnz84x9HWRlHRBEREdHyx8L7hrKyMtxxxx1Lsu9kMonXXnsNd999N4ebLEDL1V133cVcERERUUkpeOHd3t6ufz85OYne3l6IoljAiIiIiIiIcq+g5/BbW1sBAH19fejr64MkSdizZ08hQyIiIiIiWhIF63grioJwOAy3260vczgcCAQCkGUZkiTl9HizL5i8fPlyTvdv5NhTU1McPrEA5soc5ss45soc5ss45soc5ss45sqcQuRrdj250AQdBSu8w+HwvOtcLldOj/fRRx+lPZZlOaf7N+L8+fN5P+ZyxVyZw3wZx1yZw3wZx1yZw3wZx1yZU8h8za43Z+N0EUREREREecDCm4iIiIgoDwo21MThcAAAJiYmMtbV1NTk/HiVlZVpj9esWcPxUkRERERkWTKZTBteMrvenK1ghbckSXA6nYjFYvqykZEROBwOvSjPpVtuuQXr16/P+X6JiIiIiIwQVFVVC3VwRVHQ1dWlP+Y83kRERERUqgpaeBMRERERrRS8uJKIiIiIKA9YeBMRERER5QELbyIiIiKiPGDhTURERESUByy8iYiIiIjygIU3EREREVEesPAmIiIiIsoDFt5ERERERHnAwpuIiIiIKA9YeBMRERER5QELbyIiIiKiPGDhTURERESUByy8iYiIiIjygIU3EREREVEesPAmIiIiIsoDFt5ERERUMOFwGLIsFzoMorwQVFVVCx3Ectfe3q5/Pzk5id7eXoiiOO9zFEVBIBBAIBDA8PDwUodYVMzmS1EUdHV1YXJyErIsw+Vyoa2tLR+hFpzZXMmyjP7+fv17AOjp6YEkSUsbaJGw8l6cqbm5GQcPHoTD4ViK8IqK2Vx5vV4MDAxAkiSIoohoNIre3l40NTXlI9yCs/LaikajeOaZZ1BZWYmJiQns3LlzReTLbK6am5sRjUYzljudTvj9/iWJsZhY+Zv4zDPPAEj9np+cnITb7ebvrTnIsgyPx6P/DZyYmMChQ4dM/V3IOZUWZc+ePepXv/pV/XF3d7e6a9eueZ/z7W9/W+3u7la3b9+ubtq0aalDLCpW8rVr1y712LFjqqqq6okTJ9RNmzap3/72t5c0zmJgJVd79uxJ22bTpk3q9u3blyzGYmIlX7Ofv2nTJnV8fHwpwisqVn9vbdq0Sd20aZO6a9cudWRkZKnDLBpW8jU+Pq5u2rRJz1N3d7d6//33L2mcxcBKru6//351165d6q5du9Q9e/ao27dvV++//341kUgsdbgFZyVfX/3qV9PefydOnFgRv+cX89qauQ8zfxeWAoeaLIKiKAiHw6itrdWXORwORKPReU+bdXZ2rqgupMZKvhRFQTQa1bshWrdoYGBg6QMuIKuvrZmvKW27lfA6s5ovTX9//4rIE7C4XPn9fpw7dw7BYBBOp3OpQy0KVvPV0dEBh8Oh58nhcKClpWXJ4y0kq7mqqalBMBhEMBiE3++HKIoIBoOF7UrmgdV8xWIx+Hw+/e+iKIrM1RzC4TAURcGGDRv0ZZIkGf67sFRYeC9COBy2tG6lspIvURQhSRLKy8v1ZdrptLlOTZYKq6+tnp4eBINByLIMr9cLSZLgdruXIsSispj3orZ+pRSSi8lVNBpFf38/+vv7EQqFch1aUbKSL0VRIMsyNmzYgHA4DK/Xi4qKCnR2di5VmEXB6mtr5nCS1tZWuFyuFfFB2Gq+XC4XotEompub0draCp/Ph97e3qUIsWhYyVVFRUXGsomJCQCFrR9YeFPRGx4eTvuDFY1GIUnSihjPZoWiKAiFQvpY3PHx8UKHVLRkWUYoFFox1wwsxrZt2yBJEtra2uByudDd3Y3m5uZCh1WUtPdcJBJBRUUFHnvsMfh8vrTxqZQpFAphfHwcLper0KEUtZkfTMLhMKLR6Ir5IGyGw+FAY2MjYrGYfvY8FosVOiwW3rS8NDc3w+VyIRgMFjqUoqMoCurq6vDMM8+gra1N/7Di8Xj4SzkLr9eLnp6eQoexLPh8PiQSCQA3z0TNHAZGmbQGgSiKcDqdGBwc5NnQeTz77LPYunVrocMoetu3b0dbWxvOnTuH/fv3A0Da0BO6qa+vDz09PXjmmWcgy7J+ZrOQZ1RYeC+C1nHVTl3MVFNTo3+vKEq+Qipqi8mXoihob2/HwYMH0dPTgxMnTpT09FNWcjU+Pq6f4p69vtRP21rJl9frRTweR3t7O9rb2/Hss88CSP0BCwQCSxtwAVnJldYtmr0M4GtLMzM32vKZY0vn2q7ULPZ3fDQaRWVl5VKFV3Ss5Esbt6ydFejs7NRnRuPfxMzXVn9/P2RZRmdnJ5qamiDLMkRRLOgZcxbeiyBJEpxOZ9qpi5GRETgcDv2HGggEUFdXp0/xtpJZzVc0GsX27dsRj8fh8/nQ3NwMj8cz5/itUmElV06nE6IoYufOnQBujjN1Op0lPyzHSr46OzsRDAbR19eHvr4+7NixAwDgdrtL+lS3lVxpf6i0bpH22tq/f3/JX9RlNV/aKW6N9ge/lK8lWMzfxJV0MbjGSr60/MwssrVhhXxtZb62AoEARkZGAKRyFg6HcfDgwfwGP8uqgh69BPT29qKrq0sfuzc5OYmjR4/q67U3xMxfJtoLQXvjtLe3o7KyckWc8jabL0VR9HGkM0+jrYSruK28toLBIDweD44fP454PI79+/eX/AVdGiv50rS3tyMejwNIdbybmppKuvi2kqujR4+iq6tL397tdq+YsfFW8tXX1wePx5M2rvvo0aP8vZXlfaj9Ti/1JsFsZvMlSRL8fj86OjpQUVEBSZIwMTHB1xbmfm319PSgv79f/x3v9/sL/gGFN9AhIiIiIsoDDjUhIiIiIsoDFt5ERERERHnAwpuIiIiIKA9YeBMRERER5QELbyIiIiKiPGDhTURERESUByy8iYiIiIjygIU3EREREVEesPAmIipCdXV1qK6uRl1dXV6PW11djerqaiiKMufjQCAAr9ebdsvqxR4rF/siIloOeMt4IqIiEw6H9UJXURREo9GC3Up79q29A4EAotEoamtrM9YREdH82PEmIioyx44dS3scCAQKFAng9/vh9/shimLaB4JwOMxONRGRSSy8iYiKzODgIACgsbERAHDixIm09Yqi6MM0AoEA6urqUFdXB4/HA0VR0N7ejrq6OtTX1yMUCunPqa+vR319PcLhMOrr6/XnzEd7jqIo8Pl8erEdCAQQCoUgy7Iey0yzh6gAgMfjyYhr9v9Li72urg6tra0s7omopLDwJiIqIlpBKooiDh06BCBVkIbD4Tm393g8qKiogKIoehGuFe6yLKOjowOKoiCRSECWZciyjNbWVn2/gUAAzc3NhmILBoP6kJfe3l60tbUZ/n81NzcjEAjohXhHR8ec2wwODkKSJNTU1OgfEFh8E1GpYOFNRFREtGElLS0tEEVR73rP1SEGUkNBhoeH4XK5AKQK9nPnzmF0dBSiKAIAxsfH057jdrsxPDyM0dFRAEA0Gs1a2OdCOBxGNBoFAIyOjmJ4eBhutzttm0AgAFmW0djYiGAwCL/fj/379wMA+vv7lyw2IqJ8YuFNRFQkZna2d+7cmfZ19nATjdPpBHDzIsitW7fq67Jd/DizSNeerxXGS0Hbd2Njo/5hQIth9jaDg4P6MJWBgQEAmR8ciIiWK85qQkRUJGYW17OHf2hFuVYo50p5eXlO9zeXiYkJw9s2NjZi27ZtacsqKipyHBERUWGw401EVCRmju+WJEn/p5k924lV2nAWRVH08eBWpyucWRTPvPByJq2QHhwcTJsPfKaZx3e5XHC5XJAkCRcvXrQUFxFRMWLHm4ioCMwcZhIMBtMK7lAohI6ODr1IXiyfz4cTJ07ohbLD4TDcSdcKbZ/Ppw9VkSQJsiyjvr5e/34mp9MJh8OBaDSK7du3Q5KkjKEtLpcLPp8Pg4OD+sWfM/NBRFQK2PEmIioCWgd4dpcbAJqamvTvs11kaYbf79c7z9rFjEa53W69uNYK7N7eXr1jLYoigsEgGhsb08Z0a8uA1IeM3t5efRutmH/55ZfR2NiI8fFxjI+Pw+l0ps2kQkS03AmqqqqFDoKIiJaW1pEGgHPnzhU4GiKilYkdbyIiIiKiPGDhTURERESUBxxqQkRERESUB+x4ExERERHlAQtvIiIiIqI8YOFNRERERJQHLLyJiIiIiPKAhTcRERERUR6w8CYiIiIiygMW3kREREREecDCm4iIiIgoD1h4ExERERHlwf8P/gz1NU4B6/QAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ms=7\n",
    "lw=1.5\n",
    "\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "cs_C = [c[0] for c in C_csae95.values()]\n",
    "cheb_C = [c[0] for c in C_cheb_max95.values()]\n",
    "\n",
    "#QUERY COMPLEXITY\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "plt.rcParams[\"text.latex.preamble\"] = r'\\boldmath'\n",
    "\n",
    "plt.plot(amplitudes, cs_C,  '^g', label=r'\\textbf{csAE}', linewidth=lw)\n",
    "plt.plot(amplitudes, [C_csae_ave95]*len(amplitudes), 'g', linewidth=lw, alpha=0.5, label=rf'C={C_csae_ave95:0.3f}')\n",
    "plt.plot(amplitudes, cheb_C, '*r', label=r'\\textbf{chebAE}', ms=ms, linewidth=lw)\n",
    "plt.plot(amplitudes, [C_cheb_ave_max95]*len(amplitudes), 'r', linewidth=lw, alpha=0.5, label=rf'C={C_cheb_ave_max95:0.3f}')\n",
    "\n",
    "plt.xlabel(r'\\textbf{Amplitude}')\n",
    "plt.ylabel(r'\\textbf{Sequential Constant Factor}')\n",
    "plt.ylim([0,8])\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/fixed_error_query.pdf')\n",
    "\n",
    "# TIME COMPLEXITY\n",
    "plt.figure()\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "\n",
    "cs_C = [c[0] for c in C_csae_time95.values()]\n",
    "cheb_C = [c[0] for c in C_cheb_time_max95.values()]\n",
    "\n",
    "plt.plot(amplitudes, cs_C,  '^g', label=r'\\textbf{csAE}', linewidth=lw)\n",
    "plt.plot(amplitudes, [C_csae_ave_time95]*len(amplitudes), 'g', linewidth=lw, alpha=0.5, label=rf'C={C_csae_ave_time95:0.3f}')\n",
    "plt.plot(amplitudes, cheb_C, '*r', label=r'\\textbf{chebAE}', ms=ms, linewidth=lw)\n",
    "plt.plot(amplitudes, [C_cheb_ave_time_max95]*len(amplitudes), 'r', linewidth=lw, alpha=0.5, label=rf'C={C_cheb_ave_time_max95:0.3f}')\n",
    "\n",
    "plt.xlabel(r'\\textbf{Amplitude}')\n",
    "plt.ylabel(r'\\textbf{Parallel Constant Factor}')\n",
    "plt.ylim([0,6])\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/fixed_error_time.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot of physical and virtual arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fig. 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 750x350 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x210 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style(\"white\")\n",
    "\n",
    "sns.despine(left=True, bottom=True)\n",
    "sns.set_context(\"poster\", font_scale = .45, rc={\"grid.linewidth\": 0.8})\n",
    "plt.rcParams[\"text.latex.preamble\"] = r'\\boldmath'\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Helvetica\"]})\n",
    "plt.figure(figsize=(10, 2.1))\n",
    "\n",
    "ula_signal = TwoqULASignal(M=[2]*4)\n",
    "ula_signal.get_idx()\n",
    "virtual_locations = ula_signal.virtual_locations\n",
    "\n",
    "colors = ['r.', 'b.', 'c.', 'g.', 'k.']\n",
    "plt.plot(ula_signal.depths, [0]*len(ula_signal.depths),  'g*', label=r'\\textbf{Physical array}', ms=8)\n",
    "plt.plot(virtual_locations[0], [(1)*0.2]*len(virtual_locations[0]), 'b.', label=r'\\textbf{2nd order virtual array}', ms=8)\n",
    "plt.plot(virtual_locations[1], [(2)*0.2]*len(virtual_locations[1]), 'c^', label=r'\\textbf{4th order virtual array}', ms=6)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "\n",
    "plt.legend()\n",
    "plt.savefig('figs/virtual_locations.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fig. 5\n",
    "## Parallel query complexity versus number of quantum computers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to divide the queries evenly among the n quantum computers, we view depths as the weight of n objects and n_samples the number of each such item\n",
    "# we want to divide these objects as evenly as possible according to the weight\n",
    "# this is related to the partition problem, which is an NP-complete problem\n",
    "# we will use the greedy approach mentioned here: https://en.wikipedia.org/wiki/Partition_problem#Approximation_algorithm_approaches\n",
    "\n",
    "ula_signal = TwoqULASignal(M=[2]*5)\n",
    "ula_signal.get_idx()\n",
    "\n",
    "n_samples = np.array(ula_signal.n_samples)\n",
    "n0 = n_samples[0]\n",
    "n_samples = 2*n_samples\n",
    "n_samples[0] = n0\n",
    "\n",
    "depths = ula_signal.depths\n",
    "depths[0] = 1\n",
    "\n",
    "def part_sums(n_samples, depths, num_parts):\n",
    "    S = []\n",
    "    for i, d in enumerate(depths):\n",
    "        S = S + [d]*n_samples[i]\n",
    "\n",
    "    partitions = []\n",
    "    for _ in range(num_parts):\n",
    "        partitions.append([])\n",
    "\n",
    "    while len(S)!=0:\n",
    "        S.sort(reverse=True)\n",
    "        part_sums = []\n",
    "        for part in partitions:\n",
    "            part_sums.append(np.sum(part))\n",
    "        idx = list(np.argsort(part_sums))\n",
    "        partitions = [partitions[i] for i in idx]\n",
    "\n",
    "        x = S.pop(0)\n",
    "        partitions[0].append(x)\n",
    "    part_sums = []\n",
    "    for part in partitions:\n",
    "        part_sums.append(np.sum(part))      \n",
    "\n",
    "    return part_sums\n",
    "\n",
    "quantum_computers = list(range(1, 16))\n",
    "fractions = np.zeros(len(quantum_computers))\n",
    "\n",
    "for i, num_parts in enumerate(quantum_computers):\n",
    "    p_sums = part_sums(n_samples=n_samples, depths=depths, num_parts=num_parts)\n",
    "    fractions[i] = max(p_sums)/(np.sum(n_samples*depths))\n",
    "\n",
    "# now plot constant factor against number of quantum computers\n",
    "ms=5\n",
    "lw=0.8\n",
    "\n",
    "a=0.5\n",
    "\n",
    "#C= 6960*4.6*10**(-4) # this is the constant factor for the query complexity for amplitude 0.5 for q=5\n",
    "C = C_csae_ave95 # This is the constant factor determined from the fit\n",
    "\n",
    "sns.set_style(\"whitegrid\")\n",
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "plt.rcParams[\"text.latex.preamble\"] = r'\\boldmath'\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Helvetica\"]})\n",
    "\n",
    "plt.plot(quantum_computers, C*fractions, '.-b', ms=ms, linewidth=lw)\n",
    "\n",
    "plt.ylim([0.0, 5.0])\n",
    "plt.xlabel(r'\\textbf{Number of QPUs}')\n",
    "plt.ylabel(r'\\textbf{Constant factor}')\n",
    "plt.tight_layout()\n",
    "plt.savefig('figs/constant_factors_qpus.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fig. 6 Impact of Noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "plt.rcParams[\"text.latex.preamble\"] = r'\\boldmath'\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Helvetica\"]})\n",
    "\n",
    "eta_label = ['$10^{-3}$', '$10^{-4}$', '$10^{-5}$', '$10^{-6}$', '$0$']\n",
    "etas = [1e-3, 1e-4, 1e-5, 1e-6, 0]\n",
    "dirs = ['sims_C1.5_eta1e-3_final/', 'sims_C1.5_eta1e-4_final/', 'sims_C1.5_eta1e-5_final/', 'sims_C1.5_eta1e-6_final/', 'sims_C1.3_final/']\n",
    "\n",
    "a=0.5\n",
    "for idx in range(len(etas)):\n",
    "    etal = eta_label[idx]\n",
    "    eta = etas[idx]\n",
    "    dir = dirs[idx]\n",
    "    \n",
    "    with open(dir+f'a{a:0.3f}_mc0500.pkl', 'rb') as handle:\n",
    "        errors_eta, thetas_eta, num_queries_eta, max_single_query_eta, _, _, _ = pickle.load(handle)\n",
    "\n",
    "    ninetyfivepercentile_eta = np.percentile(errors_eta, 95, axis=1)\n",
    "    colors = ['-xr', '-xb', '-xg', '-xk', '-xc']\n",
    "    plt.figure(0)\n",
    "    plt.plot(num_queries_eta[2:], ninetyfivepercentile_eta[2:], colors[idx], label=r'\\textbf{$\\eta=$}'+etal, ms=6, lw=1)\n",
    "    plt.yscale('log')\n",
    "    plt.xscale('log')\n",
    "    plt.xlabel(r'\\textbf{Total query complexity}')\n",
    "    plt.ylabel(r'\\textbf{Estimation error}')\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('figs/a5_query95_eta.pdf')\n",
    "\n",
    "    plt.figure(1)\n",
    "    plt.plot(max_single_query_eta[2:], ninetyfivepercentile_eta[2:], colors[idx], label=r'\\textbf{$\\eta=$}'+etal, ms=6, lw=1)\n",
    "    plt.yscale('log')\n",
    "    plt.xscale('log')\n",
    "    plt.xlabel(r'\\textbf{Parallel query complexity}')\n",
    "    plt.ylabel(r'\\textbf{Estimation error}')\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('figs/a5_parallel_query95_eta.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table 2\n",
    "To generate table 2, we first loop through all our precomputed data for the various noise values to find the number of samples required to achieve a target estimate error rate of 1e-3 at a given confidence level. Because we used an exponential schedule to generate scaling curves, in some cases, the max depth is too high. In that case, we tweak the parameters of the 2q array to try and find a \"sweet spot\" in between the powers of 2. The 2q array approach allows us to do this by varying the array parameters and not just use powers of 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta = 0E+00\n",
      "   99% Error: 6.766E-04\n",
      "   99% Total number of queries required: 32212\n",
      "   99% Max depth queries required: 2048\n",
      "\n",
      "   95% Error: 8.711E-04\n",
      "   95% Total number of queries required: 32212\n",
      "   95% Max depth queries required: 2048\n",
      "\n",
      "   68% Error: 3.195E-04\n",
      "   68% Total number of queries required: 8036\n",
      "   68% Max depth queries required: 512\n",
      "\n",
      "   50% Error: 9.467E-04\n",
      "   50% Total number of queries required: 1995\n",
      "   50% Max depth queries required: 128\n",
      "\n",
      "eta = 1E-03\n",
      "   99% Error: INF\n",
      "   99% Total number of queries required: inf\n",
      "   99% Max depth queries required: inf\n",
      "\n",
      "   95% Error: 9.039E-04\n",
      "   95% Total number of queries required: 109201\n",
      "   95% Max depth queries required: 8192\n",
      "\n",
      "   68% Error: 7.256E-04\n",
      "   68% Total number of queries required: 6807\n",
      "   68% Max depth queries required: 512\n",
      "\n",
      "   50% Error: 4.117E-04\n",
      "   50% Total number of queries required: 6807\n",
      "   50% Max depth queries required: 512\n",
      "\n",
      "eta = 1E-04\n",
      "   99% Error: 7.689E-04\n",
      "   99% Total number of queries required: 27284\n",
      "   99% Max depth queries required: 2048\n",
      "\n",
      "   95% Error: 9.865E-04\n",
      "   95% Total number of queries required: 27284\n",
      "   95% Max depth queries required: 2048\n",
      "\n",
      "   68% Error: 3.448E-04\n",
      "   68% Total number of queries required: 6807\n",
      "   68% Max depth queries required: 512\n",
      "\n",
      "   50% Error: 2.331E-04\n",
      "   50% Total number of queries required: 6807\n",
      "   50% Max depth queries required: 512\n",
      "\n",
      "eta = 1E-05\n",
      "   99% Error: 7.094E-04\n",
      "   99% Total number of queries required: 27284\n",
      "   99% Max depth queries required: 2048\n",
      "\n",
      "   95% Error: 9.480E-04\n",
      "   95% Total number of queries required: 27284\n",
      "   95% Max depth queries required: 2048\n",
      "\n",
      "   68% Error: 3.199E-04\n",
      "   68% Total number of queries required: 6807\n",
      "   68% Max depth queries required: 512\n",
      "\n",
      "   50% Error: 9.985E-04\n",
      "   50% Total number of queries required: 1690\n",
      "   50% Max depth queries required: 128\n",
      "\n",
      "eta = 1E-06\n",
      "   99% Error: 6.659E-04\n",
      "   99% Total number of queries required: 27284\n",
      "   99% Max depth queries required: 2048\n",
      "\n",
      "   95% Error: 9.571E-04\n",
      "   95% Total number of queries required: 6807\n",
      "   95% Max depth queries required: 512\n",
      "\n",
      "   68% Error: 3.176E-04\n",
      "   68% Total number of queries required: 6807\n",
      "   68% Max depth queries required: 512\n",
      "\n",
      "   50% Error: 8.368E-04\n",
      "   50% Total number of queries required: 6807\n",
      "   50% Max depth queries required: 512\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Here we go loop over our precomputed data with the exponential arrays and \n",
    "# figure out how many samples are required. We report the samples as well as \n",
    "# the error rate required to get a 1e-3 error rate\n",
    "\n",
    "ninetyninepercentile_eta = {}\n",
    "ninetyfivepercentile_eta = {}\n",
    "sixtyeightpercentile_eta = {}\n",
    "median_eta = {}\n",
    "\n",
    "etas = [0.0, 1e-3, 1e-4, 1e-5, 1e-6]\n",
    "dirs = ['sims_C1.8_final/', 'sims_C1.5_eta1e-3_final/', 'sims_C1.5_eta1e-4_final/', 'sims_C1.5_eta1e-5_final/', 'sims_C1.5_eta1e-6_final/']\n",
    "epsilon = 1e-3\n",
    "\n",
    "def find_max_query(error_percentile, queries, max_single_query):\n",
    "    largest_query = 0\n",
    "    largest_max_single_query = 0\n",
    "    largest_error = 0\n",
    "    \n",
    "    for key, val in error_percentile.items():\n",
    "\n",
    "        # If a given amplitude cannot achieve the target error rate, then we just exit\n",
    "        if min(val) > epsilon:\n",
    "            return np.inf, np.inf, np.inf\n",
    "            \n",
    "        # Otherwise loop through and figure out what the maximum number of queries \n",
    "        # one needs to achieve the target error rate\n",
    "        for idx in range(len(val)):\n",
    "            error = val[idx]\n",
    "            \n",
    "            if (error < epsilon) and (largest_query <= queries[idx]):\n",
    "                largest_query = queries[idx]\n",
    "                largest_max_single_query = max_single_query[idx]\n",
    "\n",
    "                if error > largest_error:\n",
    "                    largest_error = error\n",
    "                # break out of the loop because we found the first point where error < epsilon\n",
    "                break\n",
    "\n",
    "    return largest_query, largest_max_single_query, largest_error\n",
    "\n",
    "for idx in range(len(etas)):\n",
    "#for idx in [0]:\n",
    "    eta = etas[idx]\n",
    "    dir = dirs[idx]\n",
    "    \n",
    "    for a in amplitudes:\n",
    "    \n",
    "        with open(dir+f'a{a:0.3f}_mc0500.pkl', 'rb') as handle:\n",
    "            errors_eta, thetas_eta, num_queries_eta, max_single_query_eta, _, _, _ = pickle.load(handle)\n",
    "    \n",
    "        ninetyninepercentile_eta[a] = np.percentile(errors_eta, 99, axis=1)\n",
    "        ninetyfivepercentile_eta[a] = np.percentile(errors_eta, 95, axis=1)\n",
    "        sixtyeightpercentile_eta[a] = np.percentile(errors_eta, 68, axis=1)\n",
    "        median_eta[a] = np.percentile(errors_eta, 50, axis=1)\n",
    "\n",
    "    # Find the largest number of queries needed to get a target error of 1-3 at a given confidence interval\n",
    "    largest_query99, largest_max_single_query99, largest_error99 = find_max_query(ninetyninepercentile_eta, num_queries_eta, max_single_query_eta)\n",
    "    largest_query95, largest_max_single_query95, largest_error95 = find_max_query(ninetyfivepercentile_eta, num_queries_eta, max_single_query_eta)\n",
    "    largest_query68, largest_max_single_query68, largest_error68 = find_max_query(sixtyeightpercentile_eta, num_queries_eta, max_single_query_eta)\n",
    "    largest_query50, largest_max_single_query50, largest_error50 = find_max_query(median_eta, num_queries_eta, max_single_query_eta)\n",
    "    \n",
    "\n",
    "    print(f'eta = {eta:0.0E}')\n",
    "    print(f'   99% Error: {largest_error99:0.3E}')\n",
    "    print(f'   99% Total number of queries required: {largest_query99}')\n",
    "    print(f'   99% Max depth queries required: {largest_max_single_query99}\\n')\n",
    "\n",
    "    print(f'   95% Error: {largest_error95:0.3E}')\n",
    "    print(f'   95% Total number of queries required: {largest_query95}')\n",
    "    print(f'   95% Max depth queries required: {largest_max_single_query95}\\n')\n",
    "\n",
    "    print(f'   68% Error: {largest_error68:0.3E}')\n",
    "    print(f'   68% Total number of queries required: {largest_query68}')\n",
    "    print(f'   68% Max depth queries required: {largest_max_single_query68}\\n')\n",
    "\n",
    "    print(f'   50% Error: {largest_error50:0.3E}')\n",
    "    print(f'   50% Total number of queries required: {largest_query50}')\n",
    "    print(f'   50% Max depth queries required: {largest_max_single_query50}\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\eta = 10^{-3}$\n",
    "For $\\eta = 1e-3$ the number of queries can be slightly reduced at 95% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.2$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.1; a_est = 0.10002218196960742\n",
      "95% percentile: 8.169525e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.2; a_est = 0.19999030938681103\n",
      "95% percentile: 9.100088e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.30000000000000004; a_est = 0.2999907143902312\n",
      "95% percentile: 8.483941e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.4; a_est = 0.39998547755854946\n",
      "95% percentile: 7.077875e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.5; a_est = 0.4999716123608445\n",
      "95% percentile: 6.736306e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.6; a_est = 0.6000089313135039\n",
      "95% percentile: 6.116776e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.7000000000000001; a_est = 0.6999946189874507\n",
      "95% percentile: 5.611541e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.8; a_est = 0.8000003829013573\n",
      "95% percentile: 4.736107e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 3, 3, 3, 3]\n",
      "Depths: [   0    1    2    3    6    9   18   27   54   81  162  243  486  729\n",
      " 1458 2187 4374]\n",
      "Samples at each depth: [31, 29, 27, 26, 24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 89453\n",
      "Max Single Query: 4374\n",
      "a = 0.9; a_est = 0.9000150140897687\n",
      "95% percentile: 3.641856e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "eta=1e-3\n",
    "np.random.seed(7)\n",
    "narray = [3, 3, 3, 3, 3, 3, 3, 3] # 8399 C=1.1\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=1.8)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'95% percentile: {np.percentile(errors, 95):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\eta = 10^{-4}$\n",
    "For $\\eta = 1e-4$ the number of queries can be reduced at 99% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.7$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.1; a_est = 0.09999819640486839\n",
      "99% percentile: 7.256559e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.2; a_est = 0.2000282279675473\n",
      "99% percentile: 5.458186e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.30000000000000004; a_est = 0.2999928397582868\n",
      "99% percentile: 7.378559e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.4; a_est = 0.4000015916975476\n",
      "99% percentile: 4.155991e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.5; a_est = 0.4999888256543783\n",
      "99% percentile: 4.178383e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.6; a_est = 0.5999909204277397\n",
      "99% percentile: 9.013705e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.7000000000000001; a_est = 0.7000146220435493\n",
      "99% percentile: 9.762264e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.8; a_est = 0.7999689446886125\n",
      "99% percentile: 5.199019e-04\n",
      "\n",
      "Array parameters: [3, 3, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [   0    1    2    3    6    9   18   36   72  144  288  576 1152]\n",
      "Samples at each depth: [24, 22, 20, 18, 17, 15, 13, 11, 9, 8, 6, 4, 2]\n",
      "Number of queries: 18262\n",
      "Max Single Query: 1152\n",
      "a = 0.9; a_est = 0.8999977360285745\n",
      "99% percentile: 3.439443e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "eta=1e-4\n",
    "np.random.seed(7)\n",
    "narray = [3, 3, 2, 2, 2, 2, 2, 2, 2, 2] # 18262 C=1.8\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=1.8)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "\n",
    "        \n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'99% percentile: {np.percentile(errors, 99):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $\\eta = 1e-4$ the number of queries can be reduced at 95% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.1$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.1; a_est = 0.09992597576388526\n",
      "95% percentile: 9.590904e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.2; a_est = 0.19995293205651435\n",
      "95% percentile: 6.924465e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.30000000000000004; a_est = 0.29999607304326914\n",
      "95% percentile: 5.375237e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.4; a_est = 0.40000192727496714\n",
      "95% percentile: 5.960537e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.5; a_est = 0.5000121189359682\n",
      "95% percentile: 5.178090e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.6; a_est = 0.600056573170548\n",
      "95% percentile: 6.974145e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.7000000000000001; a_est = 0.6999933048934478\n",
      "95% percentile: 4.237754e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.8; a_est = 0.8000126181327335\n",
      "95% percentile: 3.398114e-04\n",
      "\n",
      "Array parameters: [3, 3, 3, 3, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6   9  18  27  54  81 162 324 648]\n",
      "Samples at each depth: [15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 8399\n",
      "Max Single Query: 648\n",
      "a = 0.9; a_est = 0.8999819896004505\n",
      "95% percentile: 3.168431e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "eta=1e-4\n",
    "np.random.seed(7)\n",
    "narray = [3, 3, 3, 3, 2, 2, 2, 2] # 8399 C=1.1\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=1.1)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'95% percentile: {np.percentile(errors, 95):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $\\eta = 1e-4$ the number of queries can be reduced at 68% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.3$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.1; a_est = 0.09991491487728353\n",
      "68% percentile: 7.916808e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.2; a_est = 0.2003798759233528\n",
      "68% percentile: 8.687281e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.30000000000000004; a_est = 0.29994119788151546\n",
      "68% percentile: 9.172225e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.4; a_est = 0.3999234625344838\n",
      "68% percentile: 7.472810e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.5; a_est = 0.5000562352818562\n",
      "68% percentile: 7.511928e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.6; a_est = 0.6000207586130026\n",
      "68% percentile: 7.562463e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.7000000000000001; a_est = 0.6999001873478986\n",
      "68% percentile: 6.549751e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.8; a_est = 0.7999562849518111\n",
      "68% percentile: 5.795263e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.9; a_est = 0.8999773815600269\n",
      "68% percentile: 4.096315e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(7)\n",
    "eta=1e-4\n",
    "narray = [3, 2, 2, 2, 2, 2, 2, 2] # 2311 C=1.1\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=1.1)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'68% percentile: {np.percentile(errors, 68):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\eta \\le 10^{-5}$\n",
    "For $\\eta \\le 1e-5$ the number of samples can be reduced at 99% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.1$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.1; a_est = 0.10002609884280733\n",
      "99% percentile: 8.359983e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.2; a_est = 0.2000266947722287\n",
      "99% percentile: 6.505989e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.30000000000000004; a_est = 0.3000033562712782\n",
      "99% percentile: 7.964034e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.4; a_est = 0.3999937155594981\n",
      "99% percentile: 4.931599e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.5; a_est = 0.4999853966013937\n",
      "99% percentile: 6.009079e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.6; a_est = 0.6000163109953865\n",
      "99% percentile: 5.000058e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.7000000000000001; a_est = 0.6999889738142461\n",
      "99% percentile: 4.188536e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.8; a_est = 0.7999878571194344\n",
      "99% percentile: 3.506508e-04\n",
      "\n",
      "Array parameters: [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   4   8  16  32  64 128 256 512]\n",
      "Samples at each depth: [24, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n",
      "Number of queries: 10214\n",
      "Max Single Query: 512\n",
      "a = 0.9; a_est = 0.900004364238074\n",
      "99% percentile: 3.893195e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "eta=1e-5\n",
    "np.random.seed(7)\n",
    "narray = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2] # 10214 C=2.1\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=2.1)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "\n",
    "        \n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'99% percentile: {np.percentile(errors, 99):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $\\eta \\le 1e-5$ the number of samples can be reduced at 95% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.2$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.1; a_est = 0.10004963567703462\n",
      "95% percentile: 6.736554e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.2; a_est = 0.20004865603706914\n",
      "95% percentile: 9.779548e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.30000000000000004; a_est = 0.3000454134261173\n",
      "95% percentile: 8.283761e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.4; a_est = 0.4000083860698776\n",
      "95% percentile: 8.233538e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.5; a_est = 0.4999677278950327\n",
      "95% percentile: 8.306939e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.6; a_est = 0.6000763444737155\n",
      "95% percentile: 8.229639e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.7000000000000001; a_est = 0.7000170099578487\n",
      "95% percentile: 6.237520e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.8; a_est = 0.7999863388226827\n",
      "95% percentile: 5.454716e-04\n",
      "\n",
      "Array parameters: [6, 5, 3, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   4   5   6  12  18  24  30  60  90 180 360]\n",
      "Samples at each depth: [20, 19, 17, 16, 15, 13, 12, 11, 10, 8, 7, 6, 4, 3, 2]\n",
      "Number of queries: 6004\n",
      "Max Single Query: 360\n",
      "a = 0.9; a_est = 0.9000092225903337\n",
      "95% percentile: 3.048803e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "eta=1e-5\n",
    "np.random.seed(7)\n",
    "narray = [6, 5, 3, 2, 2, 2] # 6004 C=1.3\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=1.3)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "\n",
    "        \n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'95% percentile: {np.percentile(errors, 95):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $\\eta \\le 1e-5$ the number of samples can be reduced at 68% confidence as demonstrated here. The estimation error for all amplitudes are below the $1e-3$ level with the max error at $a=0.3$. This cell takes a few minutes to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.1; a_est = 0.09993599082591796\n",
      "68% percentile: 7.862815e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.2; a_est = 0.20033686453116228\n",
      "68% percentile: 8.190978e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.30000000000000004; a_est = 0.2998801708572741\n",
      "68% percentile: 9.055884e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.4; a_est = 0.39992682114778444\n",
      "68% percentile: 7.402979e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.5; a_est = 0.500067361997145\n",
      "68% percentile: 7.407926e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.6; a_est = 0.6000340599160886\n",
      "68% percentile: 7.488634e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.7000000000000001; a_est = 0.6999162776006987\n",
      "68% percentile: 6.563467e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.8; a_est = 0.7999642753871531\n",
      "68% percentile: 5.566316e-04\n",
      "\n",
      "Array parameters: [3, 2, 2, 2, 2, 2, 2, 2]\n",
      "Depths: [  0   1   2   3   6  12  24  48  96 192]\n",
      "Samples at each depth: [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n",
      "Number of queries: 2311\n",
      "Max Single Query: 192\n",
      "a = 0.9; a_est = 0.8999955006763806\n",
      "68% percentile: 4.010263e-04\n",
      "\n"
     ]
    }
   ],
   "source": [
    "amplitudes = np.linspace(0.1, 0.9, 9)\n",
    "eta=1e-5\n",
    "np.random.seed(7)\n",
    "narray = [3, 2, 2, 2, 2, 2, 2, 2] # 2311 C=1.1\n",
    "espirit = ESPIRIT()\n",
    "\n",
    "for a in amplitudes:\n",
    "    theta = np.arcsin(a)\n",
    "    print(f'Array parameters: {narray}')\n",
    "    ula_signal = TwoqULASignal(M=narray, C=1.1)\n",
    "    num_mc = 500\n",
    "    thetas = np.zeros(num_mc, dtype = float)\n",
    "    errors = np.zeros(num_mc, dtype = float)\n",
    "    \n",
    "    for k in range(num_mc):\n",
    "        R = ula_signal.get_cov_matrix_toeplitz(theta, n_samples=ula_signal.n_samples, eta=eta)\n",
    "        theta_est = espirit.estimate_theta_toeplitz(R)\n",
    "\n",
    "        \n",
    "        \n",
    "        error = np.abs(np.sin(theta)-np.sin(theta_est)) \n",
    "        \n",
    "        thetas[k] = theta_est            \n",
    "        errors[k] = error\n",
    "    \n",
    "    num_queries = 2*np.sum(np.array(ula_signal.depths)*np.array(ula_signal.n_samples)) + ula_signal.n_samples[0]\n",
    "    max_single_query = np.max(ula_signal.depths)\n",
    "\n",
    "    print(f'Depths: {ula_signal.depths}')\n",
    "    print(f'Samples at each depth: {ula_signal.n_samples}')\n",
    "    print(f'Number of queries: {num_queries}')\n",
    "    print(f'Max Single Query: {max_single_query}')\n",
    "    print(f'a = {a}; a_est = {np.sin(np.mean(thetas))}')\n",
    "    print(f'68% percentile: {np.percentile(errors, 68):e}')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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