diag_frame_potential.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra\n",
    "using Combinatorics\n",
    "using Statistics\n",
    "using PyPlot\n",
    "using BenchmarkTools\n",
    "using Profile\n",
    "\n",
    "using Symbolics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "test_true_frame_potential_estim (generic function with 1 method)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function n_choose_k(n, k)\n",
    "    if k==0\n",
    "        return [Bool[0 for _ in 1:n]]\n",
    "    elseif k==n\n",
    "        return [Bool[1 for _ in 1:n]]\n",
    "    else\n",
    "        a = n_choose_k(n-1, k)\n",
    "        b = n_choose_k(n-1, k-1)\n",
    "        return [\n",
    "            [Bool[0, i...] for i in a]..., \n",
    "            [Bool[1, i...] for i in b]...\n",
    "        ]\n",
    "    end\n",
    "end\n",
    "    \n",
    "function ind2mask(indices, n)\n",
    "    mask = zeros(Bool, 2^n)\n",
    "    for i in indices\n",
    "        for j in 0 : 2^i : (2^n-2^i)\n",
    "            mask[j+1:j+2^(i-1)] .⊻= true\n",
    "        end\n",
    "    end\n",
    "    return mask\n",
    "end\n",
    "\n",
    "\n",
    "function diag_rand_U1(n, k)\n",
    "    eles = zeros(2^n)\n",
    "    for l in 1:k\n",
    "        for indices in combinations(1:n, l)\n",
    "            x = rand()\n",
    "            mask = zeros(Bool, 2^n)\n",
    "            for i in indices\n",
    "                for j in 0 : 2^i : (2^n-2^i)\n",
    "                    mask[j+1:j+2^(i-1)] .⊻= true\n",
    "                end\n",
    "            end\n",
    "            eles[mask] .+= x\n",
    "            eles[.!mask] .-= x\n",
    "        end\n",
    "    end\n",
    "    return exp.(1im .* 2pi .* eles)\n",
    "end\n",
    "    \n",
    "\n",
    "function diag_rand_U2(n, k)\n",
    "    eles = Diagonal([0 for _ in 1:2^n])\n",
    "    Z  = Diagonal([1, -1])\n",
    "    II = Diagonal([1,  1])\n",
    "    for l in 1:k\n",
    "        for ar in n_choose_k(n, l)\n",
    "            x = rand()\n",
    "            eles += x * kron([b ? Z : II for b in ar]...)\n",
    "        end\n",
    "    end\n",
    "    return exp.(1im .* 2pi .* eles.diag)\n",
    "end\n",
    "\n",
    "function diag_frame_potential_estim1(n, k, ts, avg)\n",
    "    tmp = [abs(\n",
    "                sum(diag_rand_U1(n, k))\n",
    "                )\n",
    "        for _ in 1:avg]\n",
    "    return [mean(tmp.^(2t)) for t in ts], [std(tmp.^(2t)) / sqrt(avg) for t in ts]\n",
    "end\n",
    "\n",
    "function diag_frame_potential_estim2(n, k, ts, avg)\n",
    "    tmp = [abs(\n",
    "                sum(diag_rand_U2(n, k))\n",
    "                )\n",
    "        for _ in 1:avg]\n",
    "    return [mean(tmp.^(2t)) for t in ts], [std(tmp.^(2t)) / sqrt(avg) for t in ts]\n",
    "end\n",
    "\n",
    "function test_true_frame_potential_estim(n, ts, avg)\n",
    "    tmp = [abs(\n",
    "                sum([exp(2pi * 1im * rand()) for _ in 1:2^n])\n",
    "                ) / 2^(n/2)\n",
    "        for _ in 1:avg]\n",
    "    return [mean(tmp.^(2t)) for t in ts], [std(tmp.^(2t)) / sqrt(avg) for t in ts]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tGhs3buTYsWPExcVdMDPyd55//nmmT5/O5MmTOXjwIOPGjWP+/PkMGzYMgJtuuok6derQp08ffv31V1avXs1LL730p9eJjo5m+/btREdH43A42L59O9u3byctLa3ofhEiIiXUJ6uPFBST/m2r8VaPhsRmnqXfj/3Ym7CXYJ9gPuvyKU32LoPvnwNMaDkQ7vrYpYsJqJy4rbCwMNauXYvD4aBLly40bNiQZ555hqCgIGy2/GEdNmwYdrud+vXrU758eaKjoy/ptXv06MH48eMZM2YMDRo0YMqUKUybNo0OHToAYLPZWLBgAdnZ2bRq1YqBAwfy1ltv/el1XnnlFZo2bcqrr75KWloaTZs2pWnTpkRFRRXZ70FEpCSKXH6IN7/PPw/w8Q41eeW2+kSnRtP3h74cTT5KaKlQZnSZRt3NM2H5m/kb3TAcuo0Fm+t/9BvmxU4gcGEpKSkEBQWRnJxMYGDgBc9lZWVx9OhRqlevjo+Pz+W/SU76/77hcxnfupHLU2TjJyJSTJmmyfvLDvDhL4cAePam2jzd6RoOJB5g0LJBxGfFUy2wGlM7TaTiz2/Dr3PyN+wyGiKesDD5339+/5HbnHMSGRlJZGTkZZ1DISIi4u5M02T0D/uYuuoIACO61uWx9jXZHrudJ35+gtScVOoG12Vyh/GU/e8w2P89GHa4IxKa9LI4feFo5kRchsZPROTinE6T1xbtZub64wC81r0+/dpWZ/3p9Tyz/Bky8zJpWqEpE9qOJnD+IDi2Guze0HM61O1mbfjziuXMiYiISEnkcJq8OH8nX0adwDDg7TuvpVerKvx8/GeeX/U8uc5c2oS14f1WL+M39wGI2Q5eAdBrLlS/3ur4l0XlRERExEXlOZwM+/pXFm4/jc2AsT0bc1ezynx3+DteWfsKDtPBzVVv5p1GT+I1806IPwh+ZeGheRDW1Or4l03lRERExAXl5DkZ8uU2Fu88g4fN4IP7m3BbozBm751dcGfhHtf04NVaD+IxvTuknITAyvk38Ctf2+L0/47KiYiIiIvJynXw5Jyt/LQ3Fi+7jQkPNOXm+iFM+XVKwZ2FH6r3EM9Xugnb9G6QEQ9la+UXk9Lh//Dqrk/lRERExIVk5jh4dFYUqw/G4e1hY2qfFtxQqxxjo8Yyc89MAJ5o8gSPBTTAmHEH5KRCxSb5h3JKlbM2fBFROREREXERadl5PDx9MxuPJuDnZeeTvi1oXb0Mr61/jfkH5wMwotUIHjTKwOx7wJEN1a6H++eAz99/A8adqJxcREZuBq3ntAZg4wMb8buMm/iJiIgURkpWLv0+28TW6CT8vT2Y3r8ljcMDGL5qOEuPL8Vm2BjVZhR3pGXAtw+B6YA6t8I9n4Fn8br8gutfw1aK1IoVKzAMg6SkpCJ/bcMwWLhwYZG/rohIcZeYnsODH29ka3QSQb6ezB7YmgaVfXlq+VMsPb4UT5sn77V/jzvOnYKFj+UXkyYP5t9ZuJgVE1A5KdY6dOjAkCFDLHnvY8eO8fDDD1O9enV8fX2pWbMmr776Kjk5OZbkERFxVXFp2fT6eAM7TyUTXMqLuY9cR40QO48te4y1p9bi6+HLhBsncNPhDbBkZP5G1w2G2yeAvXgeAHGbvdLl693Lvn37cDqdTJkyhWuuuYZdu3bxyCOPkJ6eztixY62OJyLiEs6mZPHAxxs4fC6dCgHezB7YmuDAHB5e8jh7E/YS4BXAxI4TaLJlNmz+JH+jG1+G64eBYVgb/gpym5mTwYMHs2fPHjZv3mx1lCuiQ4cOPPXUUwwZMoQyZcoQEhLC1KlTSU9Pp3///gQEBFCzZk1++OGHgm327NlDt27d8Pf3JyQkhN69exMXFwdAv379WLlyJePHj8cwDAzD4NixYwXbbtmyhRYtWuDn50ebNm3Yv3//BXkmTZpEzZo18fLyok6dOsyaNeuC5w8ePMgNN9yAj48P9evXZ9myZRc8f8sttzBt2jQ6d+5MjRo1uP322xk2bBjz588v4t+ciIh7OpmYwb1T1nP4XDphQT58OSiCAP90+v3Yj70Jewn2CWbaTVNpsibyfDEx4Nb34Ibni3UxATcqJ5fLNE0ycjMK9ZOZl1mwfWZeZqG3z8jN4HJuWTRjxgzKlSvHpk2beOqpp3j88cfp2bMnbdq0YevWrXTp0oXevXuTkZFBTEwM7du3p0mTJkRFRfHjjz9y9uxZ7r33XgDGjx9PREQEjzzyCDExMcTExBAe/r/vvr/00ku89957REVF4eHhwYABAwqeW7BgAc888wzPPfccu3btYtCgQfTv35/ly5cD4HQ6ueuuu7Db7WzYsIHJkyfzwgsv/OP+JScnExwcXOjfi4hIcXM8Pp37pmzgeHwG4cG+fDkoAptXHH1+6MOxlGOElgplRqcp1FnyGuz6BmwecPcn0HKg1dGvimJ/47/ff/Pmairst3w6dOiAw+Fg9erVADgcDoKCgrjrrruYOTP/e+1nzpyhYsWKrF+/nsWLF7Nx40aWLFlS8BonT54kPDyc/fv3U7t2bTp06ECTJk344IMPCtZZsWIFHTt25KeffqJTp04ALF68mFtvvZXMzEx8fHxo27YtDRo0YOrUqQXb3XvvvaSnp/P999+zdOlSunXrxrFjx6hcuTIAP/74I127dmXBggX06NHjT/t3+PBhmjVrxnvvvcfAgRf/y6Ub/4lISXAoNo0HP9nA2ZRsapQrxexHWpPiiGbQskHEZ8VTLbAaU68fS8Vvn4YTG8DDF+6bBbVutjr6v1KYG/8V+5kTd9KoUaOCP9vtdsqWLcu1115bsCwkJASA2NhYtmzZwvLly/H39y/4qVu3LpBfBArzXhUrVix4XYC9e/fStm3bC9Zv27Yte/fuLXi+SpUqBcUEICIi4i/f6/Tp09xyyy307NnzL4uJiEhJsO9MCvdPXc/ZlGxqh/jzxaDrOJu9n/5L+hOfFU/d4LpMbzeGil8PyC8mPkHQZ6HbF5PCcpsTYi+Xr4cvGx/YWKhtMvMy6fBVBwBW3LsCXw/fy3rfwvL09LzgsWEYFywzzh9jdDqdOJ1Ounfvzrvvvvun1/mtbFzqe/3+df+47DemaRYsu9hk2x/X/83p06fp2LEjERERF8zEiIiUNLtOJfPQpxtJysilfsVAPh/Ymn3JUQxZPoTMvEyaVmjKhObDCZxzPyQehVIV8i9HH9rQ6uhXXbEvJ4Zh/KuLqPl6+LrkRdiaNWvGvHnzqFatGh4eFx9GLy+vy/p2U7169VizZg19+vQpWLZu3Trq1asHQP369YmOjub06dOEhYUBsH79+j+9zqlTp+jYsSPNmzdn2rRp2GyaqBORkmnL8UT6TdtEalYeTcJLM6N/K6LOreL5Vc+T68ylbVhb3m8wCN+Zd0PaGShdNX/GJLiG1dEtoU8LNzV48GASEhLo1asXmzZt4siRIyxdupQBAwYUFJJq1aqxceNGjh07Rlxc3AUzI3/n+eefZ/r06UyePJmDBw8ybtw45s+fz7BhwwC46aabqFOnDn369OHXX39l9erVvPTSSxe8xunTp+nQoQPh4eGMHTuWc+fOcebMGc6cOVO0vwgRERe38Ug8fT7dSGpWHi2rlWHWw61YcXoxQ1cOJdeZy81Vb+aj2n3xndkjv5iUrwcDlpTYYgIqJ24rLCyMtWvX4nA46NKlCw0bNuSZZ54hKCioYIZi2LBh2O126tevT/ny5YmOjr6k1+7Rowfjx49nzJgxNGjQgClTpjBt2jQ6dOgAgM1mY8GCBWRnZ9OqVSsGDhzIW2+9dcFrLF26lEOHDvHLL79QuXJlKlasWPAjIlJSrD54jr7TNpGe46DtNWWZMaAV3x39ipfXvozTdHLnNXcypnI3PD+/G7KSoHJL6L8YAkv2/yuL/bd1LofurWMNfVtHRIqTn/ee5fHZW8nJc9KxTnkmPtiMGXs/IXJ7JAC96/fmed9aGPMfAWcu1LwR7vscvEpZnPzKKMy3dYr9OSciIiJX2w87Y3j6i23kOky6NAhh/P1N+Gj7+8zck39piMFNBjMo1xtj3gAwnVC/B9w1FTy8rQ3uIlROLsLP04+dfXdaHUNERNzQt9tPMfSrX3E4Tbo3DmPMPQ0ZvfkN5h/Mv0L2iFYjeDA+Fn46f/HKZn3htvfBZrcwtWtRORERESkiX20+wQvzd2CacE/zyrzZox4vrR3B0uNLsRk2RrV5nTuObIF1H+Zv0O5Z6PRqsb8cfWG5TTnRjf9ERMSVzVp/jP/7djcAD7auwshuNRiy4mnWnl6Lp82TMde/S6dfv4Vt5+9VdvMb0PZpCxO7Lrf5tk5xv/GfiIi4r09WHykoJgPaVmd4tyo88cvjrD29Fl8PXyI7fECnjTPzi4lhg9s/UjH5G24zc1IYbvYFJDlP4yYi7mjCLwcZu/QAAE90qMmAG8oxcOlA9iXsI8ArgIk3vEeTn9+BIyvA7gV3fwr1b7c2tIsrVuXkt0uyZ2Rk4Otb+MvHi7VycnKA/PsKiYi4OtM0eW/pASYsPwTAczfXpud1AfRf0p9jKccI9glm6vVjqPP9CDi1BTxLQa85UKODtcHdQLEqJ3a7ndKlSxfcwM7Pz+8v7/kirsXpdHLu3Dn8/Pz+8nL8IiKuwjRN3vp+L5+sOQrAi93q0rmxnT4/9CEmPYaKpSrycZu3qLrgSTi3D3zLwIPzoHJzi5O7h2L3KRAaGgr87w674j5sNhtVqlRRoRQRl+Z0mrz63W5mbTgOwOu3N+C6utn0/XEACVkJVAusxsctXyL0ywGQHA0BYfk38KtQ1+Lk7qPYlRPDMKhYsSIVKlQgNzfX6jhSCF5eXro5oIi4NIfTZOT8HXwVdRLDgNF3Xkvdagn0X/IEqTmp1A2uy+Rrn6bs3Icg/RwE18wvJmWqWh3drRS7cvIbu92ucxdERKTI5DmcPPf1r3y7/TQ2A967tzEhIdE8umwImXmZNK3QlAm1+hA49wHIToHQa+Gh+eBfwerobqfYlhMREZGikpPn5Om52/hx9xk8bAYf9mqKd+Aenvz5eXKdubSt1Jb3K92K7xcPQl4WVGkDD3wBPkFWR3dLKiciIiJ/IyvXwROzt/LLvli87DYmPtiMNK/1jFz5Kk7TSeeqnXmndAs8v+4Hzjyo1QV6Tgcv3TT2cqmciIiI/IXMHAePzopi9cE4vD1sTO3TghN5S3h37bsA3FXrLl6xVcS+8LH8Da69F3pMBLunhandn8qJiIjIRaRl5zFg+mY2HU3Az8vOJ31a8Gv610zcPhGAPvX7MCzNgbHy/A38Wg2CW94Bndj/r6mciIiI/EFyZi79pm1iW3QSAd4eTOvfgl/OfcqsPfn3xXmy8WAePX0EY9OU/A3aj4AOI3QDvyKiciIiIvI7iek59P5sI7tOpRDk68mMAc2ZHz2eBYcWADCixXAe3L8GdnyRv8Et78J1j1mYuPhRORERETnvXGo2D32ykf1nUylbyotpA5oy/eBbLDu+DJth443W/8ftW76BAz+AYYcek6DxfVbHLnZUTkRERIAzyVk88MkGjpxLp0KAN5/1b8SE3S+z9vRaPG2ejIl4jU6rJ8PxteDhk/+NnDpdrY5dLKmciIhIiXcyMYMHPt5IdEIGYUE+TO3XgP9sH8a22G34evgy/rpRRCx7C87sAO9A6PUFVGtrdexiy23KSWRkJJGRkTgcDqujiIhIMXIsLp0HP9nIqaRMqgT7Edm7Fq9HPcW+hH0EeAUwsfWrNPn+RYg/BH7loPd8qNjY6tjFmmGapml1iMJISUkhKCiI5ORkAgMDrY4jIiJu7FBsKg98vJHY1GxqlC/FBw9U46UNT3Es5RhlfcoypcVI6nz7LKScgqBw6L0Qyl1jdWy3VJjPb7eZORERESlKe2NSeOiTjcSn51AnJIDR94Xy3NpHOJN+hoqlKvJx4yFU/eYxyEyAcrXzi0lQJatjlwgqJyIiUuLsPJlM7882kpSRS4OwQF65uzTPrn6EhKwEqgVW4+O6DxP69SOQkwZhzeDBb6BUWatjlxgqJyIiUqJsOZ5Iv882kZqdR5Pw0gy73ZtnVw4iNTeVesH1mFz1LoK/eQQcOVD9Brh/DngHWB27RFE5ERGREmPDkXgGTN9MRo6DVtWCeayrg6GrniAzL5NmFZoxofwNBCx4HEwn1L0N7v4UPH2sjl3iqJyIiEiJsOrAOR6dFUVWrpN215SjV8ckhq0aSa4zl7aV2vK+Tx18/zs0f+UmD0H38WDXx6QV9FsXEZFi76c9Z3li9lZyHE5urFuBrhEneHHt6zhNJ52rduadvAA8f3otf+WIJ6Hzm7pPjoVUTkREpFhbvDOGp+duI89pckuDUK5ruodRG/4DwF3X3Mkr8cnYt76fv3KnV6HdsyomFlM5ERGRYmvhtlMM/Wo7ThO6N6pI3XobeG/LJAD61nuI547txdizADDgtnHQYoC1gQVQORERkWLqy83RjJi/E9OEe5qFUa7qUibv+ByApxoN4pGdP2Mc+QVsnnDXVGh4l8WJ5TcqJyIiUuzMXH+MV77dDcADrSthKz+P2fsWAjCy6TM8sOlLOLkJPP3gvllwzU0WppU/UjkREZFiZeqqw7y9eB8A/dtWJsl/Oj8d/gm7YWdUs+e4fdUkiN0NPkH5F1cLb2VxYvkjlRMRESk2Pvr5IO8tOwDAoPaVOWafyLrodXjaPBnT7Hk6/fQOJB4D/xDovQBCGlgbWC5K5URERNyeaZqMXbqfyOWHAXiyUyV+zR3L9pjt+Hr4Mr7JUCJ+eAXSzkKZavn3yQmubmlm+WsqJyIi4tZM0+TN7/fy6ZqjADzbpSJr0t5iX8I+ArwCmNjwSZosGg5ZyVChAfSeDwGhFqeWv6NyIiIibsvpNHnlu118viEagGHdyrMk/lWOpRyjrE9ZptQdQJ3vnoPcDKjcCh78CnzLWJxa/onKiYiIuCWH0+SFeTv4ZstJDAOevzWYBWde4kz6GcJKhTG12j1U/XYoOHPzv41z70zwKmV1bLkEKiciIuJ2ch1OnvvqV7779TR2m8Gw2/z54sQIErISqB5UnakhnQj97/OACQ3ugjungIeX1bHlEqmciIiIW8nJc/LU3K0s2X0WD5vBc929mHV0BKm5qdQLrsfkgMYEL3klf+UWA6DbWLDZrQ0thWKzOsClioyMpH79+rRs2dLqKCIiYpGsXAePfb6FJbvP4mW3MaS7ybQjL5Kam0qzCs341KMawSvy75vD9cPg1nEqJm7IME3TtDpEYaSkpBAUFERycjKBgYFWxxERkaskIyePR2duYc2hOHw8bTzeLYPph94kz5lHu7C2jEsD31/n5q/c+S1o86S1geUChfn81mEdERFxealZuTw8PYpNxxLw87Lz8C1xfHZwDE7TSZcqNzH6zBk89y8Gwwa3T4CmD1odWf4FlRMREXFpyZm59P1sE9tPJBHg7cEDnY8z/eBHANxdozv/d2QH9qOrwe4F90yDerdZnFj+LZUTERFxWQnpOfT+dCO7T6cQ5OfBnR32MOfQZwD0rXUvz+36GeP0NvDyh/vnQI32FieWoqByIiIiLulcajYPfbKR/WdTCS7lwc3tNjHv6FcAPFWvL49s+hIj7gD4BsND30Cl5hYnlqKiciIiIi4nJjmTBz/eyJG4dMoHeNCm9XIWR38PwMgGj/DA6qmQfAICK+XfwK98HYsTS1FSOREREZdyIiGDBz7ZwImETMJKe3Jt0//yy6nl2A07b9QfSPdf3oeMOCh7Tf4N/EqHWx1ZipjKiYiIuIyjcek8+PEGTidnUaWsneoNvmLdmY142jwZU+9hOi17B7JToGJjeHAe+Je3OrJcASonIiLiEg6eTeXBTzYSm5pN9QoGFWrNYuu5Hfh6+PJhrYe47sdRkJcFVdtBr7ngo2tdFVcqJyIiYrk9p1Po/elG4tNzqFXRpFTVz9iTcIAArwAmVb2bxj+8BqYDaneFntPA09fqyHIFqZyIiIildpxMovenm0jOzKVu5TyMilM5nBxNWZ+yTAm5iTpLR+Wv2Oh+uGMC2D2tDSxXnMqJiIhYJupYAv2nbSY1O48GVbPIKjeZ2LQzhJUK4+PA5lRZMSZ/xdaPQ5e3weY2t4STf0HlRERELLH+cDwPz9hMRo6DRjXSSQqcQGJGItUDqzPVoyqh6yLzV+z4EtzwPBiGtYHlqlE5ERGRq27lgXM8OjOK7DwnTWslcsY3krTsNOoF12VydimCf52Zv2K3sdDqEWvDylWnciIiIlfVsj1nGTx7KzkOJy3qxnLcYyJZuVk0K9+ECQkZBBxaADYP6DEZGvW0Oq5YQOVERESumu93xPDMF9vIc5q0bHCCQ0whz5FHu9DrGHcqGt/oDeDhA/fOgtqdrY4rFlE5ERGRq2LBtpM899WvOE1oee0hDjg+w2k6uaVyB94+uBXPM7vAOwge+BKqRlgdVyykciIiIlfc3E3RvLhgJ6YJLRvvYl/O5wDcXbUL/7fjJ+wJR6FUeXhoPlRsZHFasZrKiYiIXFEz1h3j1e92AyYtmkSxL3seAP2qd2fo5gUYqachqAr0WQhla1qaVVyDyomIiFwxU1YeZvQP+wAnzZuuZn/WDwA8XfNuBq6djpGZCOXr5t9ZODDM2rDiMlRORESkSGTk5FH/lSUA7H69M5+uOca4ZQcAB02b/cSBzOUAvFjjHnqtnAK56VCpOTz4DfgFW5hcXI3KiYiIFLkPfjrIx6uPgpFHo6b/5VDmBuyGnTeq3Un3FRPAkQPV28P9c8Db3+q44mJUTkREpMjlF5McGjSdz9HM7XjaPBkbfis3Lv8ATCfUux3u/gQ8vK2OKi5INykQEZEikZaTgWfpDfkPbJnUbTKX6Mzt+Hr4MjH0Jm5c8WF+MWnaG3pOVzGRv6SZExER+dfSs/N4/us95CZdh2FPpnrDuZzKOkagVyCTgprTaO2U/BXbPgM3va775MjfUjkREZF/JSY5k4enR7EnJgXD8xylqn/EuZwcyvmWY4pndWpvmpG/4k2vQ7shlmYV96ByIiIil23nyWQenrGZ2NRsSgfFkhc6HsPmIMS3Ap85y1Hl13lg2OC2D6B5X6vjiptQORERkcvy464Yhny5naxcJ1UqHyEjaCYOpwPDNJmWZic8+keweeaf+Nqgh9VxxY24TTmJjIwkMjISh8NhdRQRkRLNNE0mrTzMf37cD5jUqbOZ07b54AS7aRJ5JpbwrBPgWQru/xxq3mh1ZHEzhmmaptUhCiMlJYWgoCCSk5MJDAy0Oo6ISImSk+fkxQU7+WbLSTByqX/tj5zIXQtAzyqd6bluBvVyczF9gjAenAfhLS1OLK6iMJ/fbjNzIiIi1kpMz2HQ51vYdDQBu2cKNRp8zYnsg3gYHoysdR89V0/ByM3lrN1O4ANf4KtiIpdJ5URERP7R4XNpDJi+mePxGQQEniao2mzOZMdT2rs04yreRMtlY8CZB0CIwwGhjS1OLO5MF2ETEZG/te5QHHdGruV4fAYVKu7BK3wyybnxXBNUkzm+DWi5fFx+Mal3u9VRpZhQORERkb/0xaZo+ny2iZSsHKrUXEFm6ZnkOHPoULENsxKzCN82FzCg0yvQY5LVcaWY0GEdERH5E4fT5J0f9ubfI8eWTfUG3xLn3ArAw9Vv56kt32FPjgavALj7Y6jTNX/D15ItTC3FhcqJiIhcID07j2e+2M5Pe89ieCYQXvdL4vKO42Xz4rWq3em+egrkZkBwDbh/LlSoa3VkKWZUTkREpMDvL0Xv7X+c0tXmkJiXTDnfcowPaEqjX97PX7HmjXDPZ+BbxtrAUiypnIiICAA7TiYxcEYUsanZlAnZill2PhmOPOqVqcOHaQahGz/NXzHiyfz75Nj1ESJXhv7LEhERftgZw7NfbScrN5fQ6j+R7rMcTOgS1pY3DmzD99w+sHtD9/HQpJfVcaWYUzkRESnBTNNk4orDjFmyH2yZVKr7DSnGbgCerHIrj26ci5GVBP6hcP9sqNzC2sBSIqiciIiUUNl5Dl6cv4t5W09ieJ0jtNYcUpwx+Hr48HaF9ty0aiqYDqjUHO6bDYEVrY4sJYTKiYhICZSQnsNjs7aw6VgCnv4HCar6BWnOdEL9QvjIVom6az/OX7FxL7jtA/D0sTSvlCwqJyIiJcyh2DQenrGZ4/HpBJTfgFFuEdlOJ02C6/P+2VjKnVwIhg06vwnXPQGGYXVkKWFUTkRESpC1h+J4/PMtpGRlEVz1e3L91mMCPSpez//tXI5X6mnwCcr/mvA1N1kdV0oolRMRkRJi7qZo/m/hLhxGKhVqf0Gm/RA2w8bQsE702TAbIy8LytWBXnOhbE2r40oJpnIiIlLMOZwmoxfv5ZM1R7F5n6Fcjc/JJA5/T3/+438t1685f/2S2rfAXR+DT6C1gaXEUzkRESnG8i9Fv42f9sbi4b+bwCpfk2VmUcW/Mh9leFBj65f5K7YbCje+DDa7tYFFUDkRESm2Tidl8vCMKPbGJONbfiWe5ZaQa5q0LtuI947uJSj+MHj4Qo9IaHi31XFFCqiciIgUQ7+eSGLgzCjOpaURVGUBzlJbMYFeoW15fuv3eGanQGDl/AurhTWxOq7IBVRORESKmcU7Yxj61XayzSSCr5lNrsdxPAwPRpZtzb3rvwBMqBIB984E/wpWxxX5E5UTEZFi4veXorf5nKBMtdnkGkkEeQXyvq0SLTfPzV+xeT/oOgY8vCzNK/JXVE5ERIqB7DwHI+fvZP7WU3gEbqdUpXnkkss1AVX5MC6J8NNLwOYBt7wDLQfqwmri0lRORETc3P8uRR+HT4Wf8Cz7C06gfdlGvLNvE/5pseAbnH8Yp/r1VscV+UcqJyIibqzgUvQJiQRU+RpK7QJgQPlWPB31LXZnLoQ0hPvnQJmqFqcVuTQqJyIibmrNwTgen72FNEcsQTU/x+l5Gi+bF6+Vqkv3Td/kr1TvdugxCbz9rQ0rUggqJyIibmj2xuO88u1u8D5CUM3ZOIw0ynoHMz7bi8Y7/pu/UseX4PphYLNZG1akkFRORETciMNp8vbivXy65iieQZvxDVuIAwf1AqvzYfRRQhOjwcsf7pwC9W6zOq7IZVE5ERFxE2nZeTwzdxs/74vBO2QxXsFrMYEuwdfyxs4V+OakQ+mq0OsLCKlvdVyRy6ZyIiLiBk4nZTJg+mb2xcZSqspcbKUOADA4qBGDtvwXA6D6DdBzBvgFW5pV5N9SORERcXHbTyTxyMwo4rJPElhjJqbnOXztPrxlC+Xm7efPL2k1CLq8BXZPa8OKFAGVExERF/b9jvxL0ed57yeg+hxMWyahvuX5KCGDumdWgc0TbhsHzfpYHVWkyKiciIi4INM0iVx+iLFL9+NZZh1+Id9jGk6aBNbg/UM7KZceD6UqwH2fQ5XWVscVKVIqJyIiLiY7z8HIeTuZv+043qHf4VVmEwB3BNXjlR0/4+XMg4pN8u8oHFTZ2rAiV4DKiYiIC0lIz2HQrCiiTpzAr+ps7H5HsRk2hvrUoM/2Jfknvl7bE27/CDx9rY4rckWonIiIuIhDsakMmB7FyfQj+FefAZ6J+HuU4j/ZPly/5xfAgJteg7bP6MZ9UqypnIiIuIDVB8/xxOytZHr8SqlqX4Etm3DfCkyIOUONxL3gHQh3fwq1O1sdVeSKUzkREbHY5xuO8+p3u7CXWY5v+aVgmLQOqM57+zYTlJMBZa+B++dC+dpWRxW5KlROREQs4nCavPX9Xj5bdwCfivPwDNoOwP2lajJ8x3I8Aa65KX/GxLe0hUlFri6VExERC6Rl5/H03G0sP3QIv6ozsfuexMOwM9KowL27luev1Obp/HNMbHZLs4pcbSonIiJX2amkTB6evpkDSXspVX0mhkcKQZ4BvJ+cTcuzG8HDJ//bOI3utTqqiCVUTkRErqLtJ5IYOCOKJNsmSlX9Bmy51PQN5aPjBwlPT4SAsPzrl1RqZnVUEcuonIiIXCX/3XGa577ahllmCb7l8g/dtC9VhXf2rMff6YDKreC+WRAQanFSEWvZrHjTO++8kzJlynDPPfdY8fYiIleVaZp89PNBnpy7ASN0Jt7ni0l/r0qM37Umv5g0fQj6/VfFRASLysnTTz/NzJkzrXhrEZGrKjvPwdCvfmXcig34VZuEZ8AePG2evJ0XwND967EbdrjlXbh9Anh4Wx1XxCVYclinY8eOrFixwoq3FhG5auLTshk0awvbYrdSqtrnGB7plPUKZPzZeBonHQaf0tBzOtTsaHVUEZdS6JmTVatW0b17d8LCwjAMg4ULF/5pnYkTJ1K9enV8fHxo3rw5q1evLoqsIiJu4+DZVHpMXMuvSUvxq/oJhkc69XxD+eLoYRonxUD5evDochUTkYsodDlJT0+ncePGTJgw4aLPf/nllwwZMoSXXnqJbdu2cf3119O1a1eio6P/dVgREXew+uA57pq4mliPr/AJmweGg84+YczYu5nQnEyocysMXAbBNayOKuKSCn1Yp2vXrnTt2vUvnx83bhwPP/wwAwcOBOCDDz5gyZIlTJo0idGjRxc6YHZ2NtnZ2QWPU1JSCv0aIiJXy6wNx3ntv1F4VZyDl/8BAJ4wgnls74b8OwrfMBw6jASbJaf8ibiFIv3bkZOTw5YtW+jc+cIbU3Xu3Jl169Zd1muOHj2aoKCggp/w8PCiiCoiUqQcTpPXF+3mlcXL8a4SiYf/AXzs3oxLt/H4ke0Ynn7555fc+JKKicg/KNK/IXFxcTgcDkJCQi5YHhISwpkzZwoed+nShZ49e7J48WIqV67M5s2b//I1R44cSXJycsHPiRMnijKyiMi/lpadx8AZm5m5fRmlqkVi9z5HqFdpZsWc4+bYYxBUBQYsgQZ3Wh1VxC1ckW/rGIZxwWPTNC9YtmTJkkt+LW9vb7y99fU6EXFNJxMzeHjGZo5kL8E3/HsMw0lj7/J8cGA75ZwOqNoO7p0BpcpZHVXEbRRpOSlXrhx2u/2CWRKA2NjYP82miIi4u23RiQycuZE0/6/xCd0EwB32sryybwteAC0ehq7vgt3T0pwi7qZID+t4eXnRvHlzli1bdsHyZcuW0aZNm6J8KxERSy369TT3ffIzGcET8SqzCRs2huX68MahbXjZPOC29+G2cSomIpeh0DMnaWlpHDp0qODx0aNH2b59O8HBwVSpUoWhQ4fSu3dvWrRoQUREBFOnTiU6OprHHnusSIOLiFjBNE0++uUQH6xahW/4DGxeiZSy+/CfuCRuSDoGfuXy749TVf8gE7lchS4nUVFRdOz4v4sGDR06FIC+ffsyffp07rvvPuLj4xk1ahQxMTE0bNiQxYsXU7Vq1aJLLSJigaxcByPm7WDRoZ/wq/oFhj2HcM8gPjp+iJrZmRB6Ldw/B0pXsTqqiFszTNM0rQ5RGCkpKQQFBZGcnExgYKDVcUSkhIhPy+bRWVHsTFuAV/mlGIZJa89gxh7aQWmnM/+bOHdEglcpq6OKuKTCfH5bcm+dyxEZGUlkZCQOh8PqKCJSwhw8m0r/GWuJ85mNd4XtANxvBjD8wHY8MeDG/4Prn4M/fFNRRC6PZk5ERP7GqgPnGPzFchwVpmH3PYndsPNimoN7Y6PBKwDu/hjq/PVVs0UkX7GcORERudpmbTjOqCVL8Ko0A7tnCoF2X94/c4ZWaclQpjr0+gIq1LU6pkixo3IiIvIHeQ4nb36/l893fYtPla8xbHnU8AhkwtF9hOflQY0OcM808Au2OqpIsaRyIiLyO6lZuTw5dwvrE+biW+kXAG6wBfDuod34myZc9wTc/AbY9b9PkStFf7tERM47mZhB/+lrOOHxGd7ldgPQP8eTZ07txm73gts+gKYPWhtSpARQORERAbZGJ/LI7KVkBn+Cp88ZPAw7ryemcXtiNPiHwH2zIbyl1TFFSgSVExEp8b779TTPL1qIR8WZ2D3SCbb5Mv5UNE2yMiGsGdw/GwLDrI4pUmK4TTnRdU5EpKiZpsmHPx9iwubZeFdeiGE4qGvz56Nj+wl1OKDR/dB9PHj6WB1VpETRdU5EpETKynXw/DfbWBrzCV5l1wLQ2enDG9EH8cOAm0dBxJO6sJpIEdF1TkRE/kZcWjYDZ61mv3MSXmUPAPBEhpPHzh7A8A6Cnp/BNTdZnFKk5FI5EZES5cDZVPrO+p7kwKl4+J3Dy/Bg9Ll4OqcmQ7nacP9cKHeN1TFFSjSVExEpMVYeOMeT87/ArDATuz2LCoYPE04epV5OLtTqkn8pep8gq2OKlHgqJyJSIsxYd5S31nyMV+j3GIaTRvgw/vghyjmc0G4o3Pgy2OxWxxQRVE5EpJjLczgZ9d+dfHn0Q7xDNgFwe46NV08dwMvDF+6eANfeY3FKEfk9lRMRKbZSs3J5fO4qtmSOx6vMUQxgaHImfRPOYQRWgvvnQFgTq2OKyB+onIhIsXQiIYM+ny8k1ncyHqUS8cWTsWdjuCEjA8Kvg/tmgX8Fq2OKyEWonIhIsbPleCIDv55ObvDn2Ow5VMKbyJNHqZmbB836Qrex4OFldUwR+QtuU050hVgRuRQLt51k5C/jsZdbgmGYtHR4MO7kYUqbRn4paTlQF1YTcXG6QqyIFAumafLeT7v4ZO9/8AzaDsB9GQ5eOHsKT99guHcGVL/B2pAiJZiuECsiJUpWroNnvl7F6pQxeAadwIbByIQk7k9OhgoNoNccKFPN6pgicolUTkTErZ1Lzabv7Hkc94jE7puCv+nB+DOnaJWVDXVvgzungLe/1TFFpBBUTkTEbe0/k0rvL6aQETQbmy2Pqk4PJp2KJjwvDzqMhBuGg81mdUwRKSSVExFxS7/sO8PTP76LUeYnDKBdDow5fRR/Dz+4dxrUv93qiCJymVRORMTtfLxmL+O2v45Hmd0A9EvNZEjcOeylq0KvuRDSwOKEIvJvqJyIiNvIczgZ8d1KFse+jUfAGeymwai4OG5PS4dq10PPGVCqrNUxReRfUjkREbeQkpVL/zlfsc/8CLtPOqWddj46c4om2TnQ6lHo8jbYPa2OKSJFQOVERFzeiYQMes39kKRSX2AzHNTOM4g8HU2oaYPuH0LzvlZHFJEipHIiIi5t09FzPPLf13EGrsQAbsrM462zMfj5lYP7Pocq11kdUUSKmNuUE12+XqTk+WLLft7Y+CK2wAMAPJ6UwmOJSdgqNs6/o3BQZYsTisiVoMvXi4jLMU2T139cyVcnRmH3PoenafBObCydMzKh4T1w+0fg5Wd1TBEpBF2+XkTcTkZOHvVfWQJARIM4duZOwO6dRXmHjcgzp6iXkwc3vQZth+jGfSLFnMqJiLiEzLxMStV6g9zkpux0rMOwO2mY4+SjMycp5+EPD3wCtbtYHVNErgKVExFxCSsOnMKRfg3eZdcAcFtaJq/FncM7+Bq4fy6Ur21xQhG5WlRORMRS6dl5DP3uG9YkTcQzKBFMeC4hkb4pqRg1O8E9n4FvaatjishVpHIiIpZZefAEQ396mxy/Ndi8IDgP/nPuLK2zsqHNU3DT62CzWx1TRK4ylRMRueqych08/9/5/BI3AZtfAgD3pGUzLC4WD0xSu7xLQMRjFqcUEauonIjIVbX+yCmeXvoWWb6rsXlBOYed0bGnuS4ru2Ad7+a9LUwoIlazWR1AREqG7DwHz303j4E/P0CW72oA7k7L4r8njnFdLtBhpLUBRcRlaOZERK64LSfOMHjxm6T7rDw/W2Lj7dgYIrKyoXJLuCMSyteBDiOsjioiLkDlRESumFyHk1eWfMd3p97H5pN/bsndqZkMi4/D3+6Tfyfh1o/ppFcRuYDKiYhcETtPxfLY4jdI8VpxfrbE4K3Ys7TJyoKq7eD2D6FsTatjiogLcptyohv/ibgHh9Nk1LJFzIseh+EVD8BdqRk8Hx+Pv4cfdBsLLR4Gm055E5GL043/RKTI7DsTxyP/fYNEj+UYhkm5PIO34s7SJjMLanSE7uOhTFWrY4qIBXTjPxG5qpxOk3eWL2bOkTEYXvEYwJ3nZ0sCvALg9jHQtLdu2Ccil0TlRET+lUPnEhi4aBRxtl8wvEzK5cGbcbG0zcyCWp3htg8gqJLVMUXEjaiciMhlMU2T91YtYfrBdzE8487PlqTzfHwCAd5BcOd4aHSfZktEpNBUTkSk0I4nJDHgu1Gc5ScMz/zZkjfiYmmXmQV1b4Nbx0FAiNUxRcRNqZyIyCUzTZOP1i3j472j4fxsSY/UdIbHJxDgWxZ6Tob6PTRbIiL/isqJiFySU0nJDPjuDU45l2J4mpTNM3kj7hzXZ2ZBw3ug67tQqpzVMUWkGFA5EZF/NHnDT0Tuehs8z2EY0CM1jecTEgn0qwD3fwZ1b7U6oogUIyonIvKXYlNT6f/tKI7nLSmYLRkVd44bMrOg8QNwy9vgW8bqmCJSzKiciMhFfRq1nPHb38A8P1tyR2oawxMSCfQPg7vGQ62brY4oIsWUyomIXCAuLZUB373JkZwf/jxb0rw/3DwKfHR1ZhG5clRORKTArG0rGbt1FE6PWAwDbj8/WxIUGA49P4IaHayOKCIlgMqJiJCYkc7D373JgazvMTxMyuY5eT0ujvaZWdBqEHR6Bbz9rY4pIiWEyolICffljtWM3vw6Do+zF86WlK4B90+Aqm2sjigiJYzKiUgJlZyVwSOL3mJP+qKC2ZLX4uLpkJUNEU9ChxfBy8/qmCJSArlNOYmMjCQyMhKHw2F1FBG3t2D3Ol7f8ErBbEn31HReSEgkqGxteDASKrewOqKIlGCGaZqm1SEKIyUlhaCgIJKTkwkM1DcGRAojLSeTRxe9zY7UbzEMk+A8J6/Fx9MxMwfaPQvth4OHt9UxRaQYKsznt9vMnIjIv7No3wZeWfd/5NnPYBhwW1o6I+ITCSrfAHpHQsXGVkcUEQFUTkSKvfScTB7/fjRbkxdi2PPPLXk1Pp6OWXnQfiS0HQIeXlbHFBEpoHIiUowtObiJF9e8TI4tBsOAW9PSGRmfSFBoY7gjEkIaWB1RRORPVE5EiqGs3GyeWDyaTYnzMWz555a8Eh/PjdlOjBtfzf82jl1//UXENen/TiLFzM9Honhh5Ytkn58t6XZ+tqR0WIv82ZLyta2OKCLyt1RORIqJ7LxsnvrxP6yL+wbD5qRMnoNX4xO4MQeMm9+C1oPAZrc6pojIP1I5ESkGVh7bwrAVL5JlnMYwoGtaOi/GJ1I6vA3c8REE17A6oojIJVM5EXFj2XnZPLt0DKtjvwbDSXCeg/+LT6BTnh2j6xhoPgBsNqtjiogUisqJiJtaG72dZ5ePIJNTcH62ZGR8ImWqd4Du46F0FasjiohcFpUTETeT48hh2LKxLD/zJRhOyjgcvBKXQCeHJ8ZtH0LTh8AwrI4pInLZVE5E3MiGk78y5JcRpJsnwYBbzp9bUuaaznDb+xAYZnVEEZF/TeVExA3kOnIZ8ct7LD01t2C25OW4BG42fTB6TIFre2q2RESKDZUTERe3+fQOnv5pBGnmCTCgy/nZkuA6t0K39yAgxOqIIiJFSuVExEXlOnJ5ecX7LD4x+8LZEkph3P0ZNLjT6ogiIleEyomIC9p6ZhdPLXuBFGc0GNA5LZ2X4hMJbnA33PIulCprdUQRkStG5UTEheQ6cnl11XgWHZ9VMFvyYnwinY0AbPfOhrrdrI4oInLFqZyIuIhfY3fz5NIXSHIcBwNuTs/gpbgEyjZ6ALq8Cb5lrI4oInJVqJyIWCzXkcsbaz5iwdEZYDgp7XDwUnwine1lsPX6GmrdZHVEEZGrSuVExEK7zu3liaXDScw7duFsSdO+cPMo8Am0OqKIyFXnNuUkMjKSyMhIHA6H1VFE/rVcZy5vr43km8PTCmZLXoxP5GaPcng89BnUaG91RBERyximaZpWhyiMlJQUgoKCSE5OJjBQ/6oU97Mnbh+Dlw4nLvcoAJ3SM3g5LpFyLR+BTq+AVymLE4qIFL3CfH67zcyJiLvLdeYyZsMkvjjwGabhIOj8uSU3eYXi2fdzqBphdUQREZegciJyFeyN38/gpcM5l3MEjN9mS5Ioe90TGB1fBE9fqyOKiLgMlRORKyjXmct7GyczZ/+nBbMlI+MTudm7Ml4DvoLKza2OKCLiclRORK6Q/fH7GbzsBc5mHwYDOqZn8HJCMuUjnsFoPxw8vK2OKCLiklRORIpYrjOX8ZunMnPvx5iGg8DfZkt8q+H98Hyo2NjqiCIiLk3lRKQIHUg4wOBlwzmT9b/ZkpcSUijf7nls1z8Ldk+rI4qIuDyVE5EikOfM46MtU5m2e2rBbMmI+ERuLlULn0cWQUh9qyOKiLgNlRORf+lg4kGeWvYCpzIPggEd0jN4MTGNkBtGYmvzJNj110xEpDD0f02Ry5TnzGPi1k/4dNdknIaDAIeTkQkJdPKvh9+gKVCultURRUTcksqJyGU4lHiIp356gZMZBwpmS0YmZhBy4yvYWz8KNrvVEUVE3JbKiUgh5DnzmLztUz7eNQkn+bMlIxIS6RhwLQGPT4LgGlZHFBFxeyonIpfocNJhnvnpBY6n7wfghoxMRiZkEnLTKDxbDgCbzeKEIiLFg8qJyD/Ic+bx8Y5pTP41smC25IWERDoENSVo8GQoHW51RBGRYkXlRORvHE46zLM/j+Bo2j4gf7bkhcQsQm9+B68WvcEwLE4oIlL8qJyIXESeM49Pdkxn8q+ROMgjwOFkeEIi15duTdknJ0JgRasjiogUWyonIn9wJPkIQ39+gcOp+bMl7TIyeSExh9BbxuHT9D7NloiIXGEqJyLnOZwOPts1nchtH+E4f27J8wmJtCnTjpCnJ4B/BasjioiUCConIuTPljz38wsc+t1sybBEB6FdP6JU07stTiciUrKonEiJ5nA6mLZrBhO2fYgDB/5OJ8PjE2kV3JFKz3wIpcpaHVFEpMRROZES62jyUZ5fPoL9yXsAaJuRybOJJmG3Tiag8e0WpxMRKblUTqTEcTgdzNwziw+3jCePPPydTp6PT6R52c5UffYD8C1tdUQRkRJN5URKlKPJRxm+fAT7fjdb8kyiQcXbPqN0o1ssTiciIqByIiXEH2dLSp2fLWlU9lauGToWwyfI6ogiInKeyokUe8eSj/HC8hfYc362JCIzkycTPKjYfQblr73Z4nQiIvJHKidSbDmcDmbvnc0HUe+Te3625Ln4JBqUvZ16z43B8Pa3OqKIiFyEyokUS8eSjzFixQh2J+0G8mdLnkjwIrT754Re29HidCIi8ndUTqRY+d9syThyceDndDI0Pok6Ze/m2ufewe7tZ3VEERH5B25TTiIjI4mMjMThcFgdRVxQRm4Gree0xsNpkGczAbguM5NHE3wJ7f4F4ddeb3FCERG5VIZpmqbVIQojJSWFoKAgkpOTCQwMtDqOWCzPmcfKEyv5bPvH7Dh/CMfP6WRIfDI1g++l2YNv4eHta3FKEREpzOe328yciPxecnYy8w7OY86uWZzNjgPAbprclJ7BXUkBhHT/mpqNIixOKSIil0PlRNzKgcQDzNnzOYsOLyLHzAOgtMNBz9Q0IpJ8yMkLof6z31I6WHcQFhFxVyon4vIcTgcrTqxg1s5pbIn/tWB53ewc7k9OI9TZCN/Wj9H4+u7Y7TbrgoqISJFQORGXlZydzPwD85i9awZncxKA/EM3ndIzuC3ZCWVuo9pdT1G9Zh2Lk4qISFFSORGXcyDxAHN2z2TR4e/J4cJDN43TKmDWGkTTPv0JCtBF1EREiiOVE3EJDqeDFSdX8PmvnxKVsLNged3sHO5NzqCM2YqANo/Tok0n7DbDwqQiInKlqZyIpQoO3eycztncROB/h246p9hxBt9J7Z6DqVmtqsVJRUTkalE5EUscSDzAnF3TWXRkMTnkX1ivtMPBPalp1Emrgq3eUFr3fYAgfx+Lk4qIyNWmciJXTcGhm+1TiUrcU7C8TnYOdydnEWBcT5l2T3BdqwgduhERKcFUTuSKS85OZv7+b5i9axpnc5OB/EM3N2Zk0iHZB2e5B2hw/6PUCq9ocVIREXEFKidyxRxMPMicnZ+y6OiPZP/u0M1dKelUTa+FV8NHub5vD4JKeVmcVEREXInKiRSp3y6Y9vn2SUQl7S9YXic7h9tT8vAxbiTkhido17yJDt2IiMhFqZxIkUjOTmbB/q+YvXM6Z/JSgP8dummdHIQZ0pdmvfpRu1I5i5OKiIirUzmRf+Vg4kHm/DqFRceXkY0TyD900yMlk9CMBvg2GsSNN3ahtJ8O3YiIyKVROZFCczgdrIhezuxtE9mccrBgeZ3sHLqmmHgYXQnvOIj2Terp0I2IiBSayolcsuTsZBbsncOcXbOIcaQCYDNNOmVk0ii5PEbo47R+oBd1w8pYnFRERNyZyon8o0OJh5izLZJFJ34h6/yhmyCHg9tTsimT0ZSApo9zS/vrdehGRESKhMqJXJTD6WBl9C98vvUjNqceLVheOzuHTske2D1up0aHgXRsVAMPu83CpCIiUtyonMgFkrOTWbB7FnP2fE6MIx3IP3TTMT2T2smVsVfqzw0P3km9sCCLk4qISHGlciIAHEo8yJyo8Sw6vfqCQzfdUnPxT29NmeaPc1u7lpTRBdNEROQKUzkpwRxOByuPL2P2lglsSj9esLx2dg7tkn3B8x7qd+xHp4bhOnQjIiJXjcpJCZScnczCHZ8xe98XxDgzgPxDNx3Ss6iSXB3PygO5uXtX6lUMtDipiIiURConJcihhAPM2fQei86sJ8swgfxDN51TnXiltyOkxWP0aNtIh25ERMRSKifFnMPpYNXRH/l8y0dsyjyVv9DIP3TTIjkIp9c9NOv4ADc3CNOhGxERcQkqJ8VUcnYyC7dPYc7+rzltZgH5h25uyMghNKk2nlUGcdtt7akfpkM3IiLiWlROipnD8fuZvfFdFsVGXXDopmOKgZHZkfCWj3B3RD2CdehGRERclMpJMeBwOlh1aBGfb4tkU9aZ/IUG1MrOoVFyOfK87yfixrvp3CBUh25ERMTlqZy4sZTsZBZEfcScQws5TTaQf+imbUYuZZIa4lv1Ue687Toa6IJpIiLiRlRO3NDhuN3MXv8Oi+K3k3X+pr+BDgftUjxxZt5MjVYDuO+6a3ToRkRE3JLKiZtwOB2s3j+Pz7dPZmPOufyFBlyTnUvdpFDyfB/ihhtvpXODEDx16EZERNyYyomLS8lKYsGm95h79HtOkQvkH7q5LsNBqaQm+FcbxL23NqVhJR26ERGR4kHlxEUdPrudORve4bvE3Rccummd4ktOZlfqt+7Nfa2qUdbf29qgIiIiRUzlxIU4nA5W757D5zs+YWNeQv5CA2rk5FEjsTK5fv3odOONOnQjIiLFmsqJC0jJTGTh+tHMiV7KKcMB5B+6aZkOXsnNKV19EA90a6BDNyIiUiKonFjoyOko5mwYzXfJ+8m0GWBAgMNJs5QAMjJvo0mre7m/dVXK6dCNiIiUIConV5nDkcfqHdOYvWs6G5wp+QttBtVzHFROrE6OXz9uubEtXRqE6tCNiIiUSConV0lKeiwL177F3FMrOGlzAvmHbpqk27AlRVCuxsP06VqHayvr0I2IiJRsKidX2JHoNczZ+B++SzuSf+jGln/opmFKaVIy7qBF6zvp1bqKDt2IiIicp3JyBTgdeazeOpHP985hg5mev9BmUDXHSUhiLXJK9ee2ji3p2lCHbkRERP5I5aQIpaScZOGaN/nizFpO2POXGaZJo3RP8pLaElazH/26XkOjyqUtzSkiIuLKVE6KwJEjy5izaRzfZZ7IP3Rjzz90UzulHAmZd9GqVTd6tapC+QAduhEREfknKieXyZmXw+pN7zP7wDesN7LyF9oMwnNMghPrkufXj7s6NuOWBqF4eejQjYiIyKWypJz897//5bnnnsPpdPLCCy8wcOBAK2JcltTEoyxcM4q55zZzwp5/bRLDNKmX7kNWUntq1HiQfrfUoHF4aaujioiIuKWrXk7y8vIYOnQoy5cvJzAwkGbNmnHXXXcRHBx8taNcOtPkyP5FzNn6Id9lx5Bps4HdwN/hpEZKKHGZPWnTshO9WodTIcDH6rQiIiJu7aqXk02bNtGgQQMqVaoEQLdu3ViyZAm9evW62lH+kTMnnTXrx/L54YWst+flL7TZCMsxCEhoiOnfl3s7NKRrw4o6dCMiIlJECv2JumrVKrp3705YWBiGYbBw4cI/rTNx4kSqV6+Oj48PzZs3Z/Xq1QXPnT59uqCYAFSuXJlTp05dXvorJDV2D7MWPMBts1ox+Ng3rLfnYZgmddJ8CTt5K/UCZvDyAxOZN7gLdzSppGIiIiJShAo9c5Kenk7jxo3p378/d99995+e//LLLxkyZAgTJ06kbdu2TJkyha5du7Jnzx6qVKmCaZp/2sYwjMtLX5ScTo7s/pK52yfzbV5c/qEbDxulHCbhyZU4l9WTdi1v4IHWVXToRkRE5AoqdDnp2rUrXbt2/cvnx40bx8MPP1xwkusHH3zAkiVLmDRpEqNHj6ZSpUoXzJScPHmS1q1b/+XrZWdnk52dXfA4JSWlsJEvyXtf3sr0nJP5D2w2QrNt+CQ2wV7qIR7qWF+HbkRERK6SIv20zcnJYcuWLXTu3PmC5Z07d2bdunUAtGrVil27dnHq1ClSU1NZvHgxXbp0+cvXHD16NEFBQQU/4eHhRRm5QExGAwzTpGaaP2VO3En9gGmM6vUBC5+8WYduRERErqIiPSE2Li4Oh8NBSEjIBctDQkI4c+ZM/ht6ePDee+/RsWNHnE4nw4cPp2zZsn/5miNHjmTo0KEFj1NSUq5IQbm7w/Os//JaOrSK0KEbERERC12Rb+v88RwS0zQvWHb77bdz++23X9JreXt74+195a+sel2NCiwf3lszJCIiIhYr0nJSrlw57HZ7wSzJb2JjY/80m+JqDMPAy8MFTswVEREp4Yp0msDLy4vmzZuzbNmyC5YvW7aMNm3aFOVbiYiISDFV6JmTtLQ0Dh06VPD46NGjbN++neDgYKpUqcLQoUPp3bs3LVq0ICIigqlTpxIdHc1jjz1WpMFFRESkeCp0OYmKiqJjx44Fj387WbVv375Mnz6d++67j/j4eEaNGkVMTAwNGzZk8eLFVK1atehSi4iISLFlmBe7KpoLS0lJISgoiOTkZAIDA62OIyIiIpegMJ/fbvPVlMjISOrXr0/Lli2tjiIiIiJXkGZORERE5IorljMnIiIiUjKonIiIiIhLUTkRERERl6JyIiIiIi5F5URERERcisqJiIiIuBS3KSe6zomIiEjJ4HbXOUlOTqZ06dKcOHFC1zkRERFxEykpKYSHh5OUlERQUNDfrlvoe+tYLTU1FYDw8HCLk4iIiEhhpaam/mM5cbuZE6fTyenTpwkICMAwjCJ97d9aXXGdldH+ub/ivo/aP/dX3PdR+3f5TNMkNTWVsLAwbLa/P6vE7WZObDYblStXvqLvERgYWCz/o/uN9s/9Ffd91P65v+K+j9q/y/NPMya/cZsTYkVERKRkUDkRERERl6Jy8jve3t68+uqreHt7Wx3litD+ub/ivo/aP/dX3PdR+3d1uN0JsSIiIlK8aeZEREREXIrKiYiIiLgUlRMRERFxKSonIiIi4lJKTDlZtWoV3bt3JywsDMMwWLhw4T9us3LlSpo3b46Pjw81atRg8uTJVz7oZSrs/q1YsQLDMP70s2/fvqsTuJBGjx5Ny5YtCQgIoEKFCvTo0YP9+/f/43buNIaXs4/uNI6TJk2iUaNGBRd3ioiI4Icffvjbbdxp/Aq7f+40dhczevRoDMNgyJAhf7ueO43hH13KPrrTOL722mt/yhkaGvq321g1fiWmnKSnp9O4cWMmTJhwSesfPXqUbt26cf3117Nt2zZefPFFnn76aebNm3eFk16ewu7fb/bv309MTEzBT61ata5Qwn9n5cqVDB48mA0bNrBs2TLy8vLo3Lkz6enpf7mNu43h5ezjb9xhHCtXrsw777xDVFQUUVFR3Hjjjdxxxx3s3r37ouu72/gVdv9+4w5j90ebN29m6tSpNGrU6G/Xc7cx/L1L3cffuMs4NmjQ4IKcO3fu/Mt1LR0/swQCzAULFvztOsOHDzfr1q17wbJBgwaZ11133RVMVjQuZf+WL19uAmZiYuJVyVTUYmNjTcBcuXLlX67jzmNompe2j+4+jmXKlDE/+eSTiz7n7uNnmn+/f+46dqmpqWatWrXMZcuWme3btzefeeaZv1zXXcewMPvoTuP46quvmo0bN77k9a0cvxIzc1JY69evp3Pnzhcs69KlC1FRUeTm5lqUqug1bdqUihUr0qlTJ5YvX251nEuWnJwMQHBw8F+u4+5jeCn7+Bt3G0eHw8EXX3xBeno6ERERF13HncfvUvbvN+42doMHD+bWW2/lpptu+sd13XUMC7OPv3GXcTx48CBhYWFUr16d+++/nyNHjvzlulaOn9vd+O9qOXPmDCEhIRcsCwkJIS8vj7i4OCpWrGhRsqJRsWJFpk6dSvPmzcnOzmbWrFl06tSJFStWcMMNN1gd72+ZpsnQoUNp164dDRs2/Mv13HkML3Uf3W0cd+7cSUREBFlZWfj7+7NgwQLq169/0XXdcfwKs3/uNnYAX3zxBVu2bCEqKuqS1nfHMSzsPrrTOLZu3ZqZM2dSu3Ztzp49y5tvvkmbNm3YvXs3ZcuW/dP6Vo6fysnfMAzjgsfm+Yvp/nG5O6pTpw516tQpeBwREcGJEycYO3asy/2F+qMnn3ySHTt2sGbNmn9c113H8FL30d3GsU6dOmzfvp2kpCTmzZtH3759Wbly5V9+gLvb+BVm/9xt7E6cOMEzzzzD0qVL8fHxueTt3GkML2cf3Wkcu3btWvDna6+9loiICGrWrMmMGTMYOnToRbexavx0WOcvhIaGcubMmQuWxcbG4uHhcdGGWRxcd911HDx40OoYf+upp57iu+++Y/ny5VSuXPlv13XXMSzMPl6MK4+jl5cX11xzDS1atGD06NE0btyY8ePHX3Rddxy/wuzfxbjy2G3ZsoXY2FiaN2+Oh4cHHh4erFy5kg8//BAPDw8cDseftnG3MbycfbwYVx7H3ytVqhTXXnvtX2a1cvw0c/IXIiIiWLRo0QXLli5dSosWLfD09LQo1ZW1bds2l5xmhfy2/tRTT7FgwQJWrFhB9erV/3EbdxvDy9nHi3Hlcfwj0zTJzs6+6HPuNn4X83f7dzGuPHadOnX60zc7+vfvT926dXnhhRew2+1/2sbdxvBy9vFiXHkcfy87O5u9e/dy/fXXX/R5S8fvip9y6yJSU1PNbdu2mdu2bTMBc9y4cea2bdvM48ePm6ZpmiNGjDB79+5dsP6RI0dMPz8/89lnnzX37Nljfvrpp6anp6f5zTffWLULf6uw+/f++++bCxYsMA8cOGDu2rXLHDFihAmY8+bNs2oX/tbjjz9uBgUFmStWrDBjYmIKfjIyMgrWcfcxvJx9dKdxHDlypLlq1Srz6NGj5o4dO8wXX3zRtNls5tKlS03TdP/xK+z+udPY/ZU/fpPF3cfwYv5pH91pHJ977jlzxYoV5pEjR8wNGzaYt912mxkQEGAeO3bMNE3XGr8SU05++7rXH3/69u1rmqZp9u3b12zfvv0F26xYscJs2rSp6eXlZVarVs2cNGnS1Q9+iQq7f++++65Zs2ZN08fHxyxTpozZrl078/vvv7cm/CW42L4B5rRp0wrWcfcxvJx9dKdxHDBggFm1alXTy8vLLF++vNmpU6eCD27TdP/xK+z+udPY/ZU/fnC7+xhezD/tozuN43333WdWrFjR9PT0NMPCwsy77rrL3L17d8HzrjR+hmmeP7tFRERExAXohFgRERFxKSonIiIi4lJUTkRERMSlqJyIiIiIS1E5EREREZeiciIiIiIuReVEREREXIrKiYiIiLgUlRMRERFxKSonIiIi4lJUTkRERMSlqJyIiIiIS/l/RqruiB6xiTMAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x000000004F697850>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 5\n",
    "k = n\n",
    "ts = 1:5\n",
    "avg = 10000\n",
    "\n",
    "y1, e1 = test_true_frame_potential_estim(n, ts, avg)\n",
    "y2, e2 = diag_frame_potential_estim1(n, k, ts, avg) \n",
    "y3, e3 = diag_frame_potential_estim2(n, k, ts, avg)\n",
    "\n",
    "x = ts\n",
    "errorbar(x, y1, yerr=e1, label=\"true\")\n",
    "errorbar(x, y2, yerr=e2, label=\"method1\")\n",
    "errorbar(x, y3, yerr=e3, label=\"method2\")\n",
    "\n",
    "\n",
    "yscale(\"log\")\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  9.380 ms (138206 allocations: 16.44 MiB)\n",
      "  13.785 ms (185116 allocations: 17.13 MiB)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([8210.087308743094], [1447.9530776982933])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@btime diag_frame_potential_estim1(6, 3, [2], 100)\n",
    "@btime diag_frame_potential_estim2(6, 3, [2], 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Tuple{Array{Float64,1},Array{Float64,1}},1}:\n",
       " ([11.32359189258274, 236.29952481741904, 6681.723750343313], [0.8095773855868754, 29.21603967391721, 1228.773185569458])\n",
       " ([1.9821739361820156, 5.916940370068807, 24.498184541747033], [0.04535551581812609, 0.31735608384244407, 3.213941169455883])\n",
       " ([2.0134983605535663, 6.024465470311085, 24.367601772544873], [0.04507267206452266, 0.28367320085463194, 2.388595838180216])\n",
       " ([1.972154055267969, 5.791376352634025, 22.545154007589538], [0.043194476675490485, 0.24523836717578312, 1.755233622102816])\n",
       " ([1.9552757028228345, 5.588842662217546, 20.47011528611273], [0.04080279044351179, 0.20425369441296218, 1.2238814632605242])\n",
       " ([2.0086592139631074, 5.986897790456912, 23.262854915334792], [0.043852099247475386, 0.2361587407999351, 1.5230846450806175])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 6\n",
    "ks = 1:n\n",
    "ts = 2:4\n",
    "avg = 10000\n",
    "\n",
    "tmp1 = [diag_frame_potential_estim1(n, k, ts, avg) for k in ks]\n",
    "tmp2 = [diag_frame_potential_estim2(n, k, ts, avg) for k in ks]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x0000000042661E20>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for (i,t) in enumerate(ts)\n",
    "    y1, e1 = [a[1][i] for a in tmp1], [a[2][i] for a in tmp1]\n",
    "    y2, e2 = [a[1][i] for a in tmp2], [a[2][i] for a in tmp2]\n",
    "    x = ks\n",
    "    errorbar(x, y1, yerr=e1, label=string(t))\n",
    "    errorbar(x, y2, yerr=e2, label=string(t))\n",
    "end\n",
    "\n",
    "yscale(\"log\")\n",
    "xlabel(\"k\")\n",
    "ylabel(\"Phi(k, n=4)\")\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Tuple{Array{Float64,1},Array{Float64,1}},1}:\n",
       " ([5.012479229519372, 38.47921321709213, 359.6574788997936], [0.05783907643040237, 0.6399952594603849, 7.798663513504485])\n",
       " ([1.9508196862412623, 5.524201998152323, 20.470133396439735], [0.012909145050792178, 0.06965833433613633, 0.47678521491870823])\n",
       " ([1.9371202054202068, 5.453309148884202, 19.73453261397249], [0.012642095453801449, 0.06333782774159388, 0.38040352658242793])\n",
       " ([1.9283514108645337, 5.40131169035059, 19.54490625538273], [0.012580351885719675, 0.06406885862303688, 0.3991154693578115])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tmp2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x00000000426069A0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for (i,t) in enumerate(ts)\n",
    "    y1, e1 = [a[1][i] for a in tmp1], [a[2][i] for a in tmp1]\n",
    "    y2, e2 = [a[1][i] for a in tmp2], [a[2][i] for a in tmp2]\n",
    "    x = ks\n",
    "    errorbar(x, y1, yerr=e1, label=string(t))\n",
    "    errorbar(x, y2, yerr=e2, label=string(t))\n",
    "end\n",
    "\n",
    "yscale(\"log\")\n",
    "xlabel(\"k\")\n",
    "ylabel(\"Phi(k, n=4)\")\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[mean(samples1 .^ (2t)) for t = 1:max_t] = [7.992324777530755, 135.60713642178152]\n",
      "[mean(samples3 .^ (2t)) for t = 1:max_t] = [7.989637871596435, 119.80075963936285]\n"
     ]
    }
   ],
   "source": [
    "sampler1(d1, d2, d3) = exp.(1im * 2pi * (kron(rand(d1*d2), ones(d3)) + kron(ones(d1), rand(d2*d3))))\n",
    "sampler2(d1, d2, d3) = exp.(1im * 2pi * rand(d1*d2*d3))\n",
    "sampler3(d1, d2, d3) = exp.(1im * 2pi * (kron(rand(d1*d2), ones(d3)) + kron(ones(d1), rand(d2), ones(d3)) + kron(ones(d1), rand(d2*d3))))\n",
    "\n",
    "\n",
    "begin\n",
    "    avg = 1000000\n",
    "    d1,d2,d3 = 2,2,2\n",
    "    max_t = 2\n",
    "\n",
    "    samples1 = [abs(sum(sampler1(d1,d2,d3))) for _ in 1:avg]\n",
    "    # samples2 = [abs(sum(sampler2(d1,d2,d3))) for _ in 1:avg]\n",
    "    samples3 = [abs(sum(sampler2(d1,d2,d3))) for _ in 1:avg]\n",
    "\n",
    "    @show [mean(samples1.^(2t)) for t in 1:max_t]\n",
    "    # @show [mean(samples2.^(2t)) for t in 1:max_t]\n",
    "    @show [mean(samples3.^(2t)) for t in 1:max_t]\n",
    "\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Tuple{Array{Float64,1},Array{Float64,1}},1}:\n",
       " ([11.32359189258274, 236.29952481741904, 6681.723750343313], [0.8095773855868754, 29.21603967391721, 1228.773185569458])\n",
       " ([1.9821739361820156, 5.916940370068807, 24.498184541747033], [0.04535551581812609, 0.31735608384244407, 3.213941169455883])\n",
       " ([2.0134983605535663, 6.024465470311085, 24.367601772544873], [0.04507267206452266, 0.28367320085463194, 2.388595838180216])\n",
       " ([1.972154055267969, 5.791376352634025, 22.545154007589538], [0.043194476675490485, 0.24523836717578312, 1.755233622102816])\n",
       " ([1.9552757028228345, 5.588842662217546, 20.47011528611273], [0.04080279044351179, 0.20425369441296218, 1.2238814632605242])\n",
       " ([2.0086592139631074, 5.986897790456912, 23.262854915334792], [0.043852099247475386, 0.2361587407999351, 1.5230846450806175])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tmp2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Array{Bool,1},1}:\n",
       " [0, 0, 1, 1]\n",
       " [0, 1, 0, 1]\n",
       " [0, 1, 1, 0]\n",
       " [1, 0, 0, 1]\n",
       " [1, 0, 1, 0]\n",
       " [1, 1, 0, 0]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_choose_k(4,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "diag_frame_potential_cal (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function diag_theta_expr(n, k)\n",
    "    all_terms = cat([collect(combinations(1:n, l)) for l in 1:k]..., dims=1)\n",
    "    nn = length(all_terms)\n",
    "    @variables iθ[1:nn]\n",
    "    expr = zeros(Num, 2^n)\n",
    "    for (i, indices) in enumerate(all_terms)\n",
    "        mask = ind2mask(indices, n)\n",
    "        expr += iθ[i] * mask\n",
    "    end\n",
    "    return expr\n",
    "end\n",
    "\n",
    "function diag_theta_expr_assign(n, all_terms)\n",
    "    nn = length(all_terms)\n",
    "    @variables iθ[1:nn]\n",
    "    expr = zeros(Num, 2^n)\n",
    "    for (i, indices) in enumerate(all_terms)\n",
    "        mask = ind2mask(indices, n)\n",
    "        expr += iθ[i] * mask\n",
    "    end\n",
    "    return expr\n",
    "end\n",
    "\n",
    "\n",
    "function sum_of_exp_expr_mult(a, b)\n",
    "    result = Num[]\n",
    "    for e1 in a\n",
    "        for e2 in b\n",
    "            tmp = e1+e2\n",
    "            push!(result, tmp)\n",
    "        end\n",
    "    end\n",
    "    return result\n",
    "end\n",
    "\n",
    "\n",
    "function diag_frame_potential_cal(n, k, max_t)\n",
    "    trU  = diag_theta_expr(n, k)\n",
    "    abs_trU_2 = sum_of_exp_expr_mult(trU, -trU)\n",
    "    tmp = [zero(Num)]\n",
    "    result = zeros(Int64, max_t)\n",
    "    for t in 1:max_t\n",
    "        tmp = sum_of_exp_expr_mult(tmp, abs_trU_2)\n",
    "        result[t] = count(x -> typeof(x.val)==Int64, tmp)\n",
    "    end\n",
    "    return result\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Array{Int64,1},1}:\n",
       " [8, 216, 8000]\n",
       " [8, 120, 2528]\n",
       " [8, 120, 2528]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 3\n",
    "# k = 3\n",
    "max_t = 3\n",
    "\n",
    "[diag_frame_potential_cal(n, k, max_t) for k in 1:n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Array{Int64,1},1}:\n",
       " [32, 7776]\n",
       " [32, 2016]\n",
       " [32, 2016]\n",
       " [32, 2016]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Profile.init(n=10^7)\n",
    "Profile.clear()\n",
    "\n",
    "@profile [diag_frame_potential_cal(n, k, max_t) for k in 1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       "  16.006837942882527\n",
       " 496.023124284127"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diag_frame_potential_estim1(n, k, 1:2, 1000000)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Array{Int64,1},1}:\n",
       " [1]\n",
       " [2]\n",
       " [3]\n",
       " [1, 2]\n",
       " [1, 3]\n",
       " [2, 3]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 3\n",
    "k=2\n",
    "cat([collect(combinations(1:n, l)) for l in 1:k]..., dims=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 4\n",
    "k = 2\n",
    "max_t = 3\n",
    "\n",
    "# diag_frame_potential_cal(n, k, max_t)\n",
    "tmp = begin\n",
    "    trU  = diag_theta_expr(n, k)\n",
    "    abs_trU_2 = sum_of_exp_expr_mult(trU, -trU)\n",
    "    tmp = [zero(Num)]\n",
    "    result = zeros(Int64, max_t)\n",
    "    for t in 1:max_t\n",
    "        tmp = sum_of_exp_expr_mult(tmp, abs_trU_2)\n",
    "    end\n",
    "    tmp\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "256"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 3\n",
    "# k = 3\n",
    "# max_t = 3\n",
    "\n",
    "@show diag_frame_potential_cal(n, 2, 4)\n",
    "@show diag_frame_potential_cal(n, n, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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