slope-analysis_lspu_gr.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mFailed to start the Kernel. \n",
      "\u001b[1;31mUnable to start Kernel 'base (Python 3.7.3)' due to a timeout waiting for the ports to get used. \n",
      "\u001b[1;31mView Jupyter <a href='c/https://github.com/mew-two-github/Spatial-Matching-Simulations/blob/master/ommand:jupyter.viewOutput'>log</a> for further details."
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pickle\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mFailed to start the Kernel. \n",
      "\u001b[1;31mUnable to start Kernel 'base (Python 3.7.3)' due to a timeout waiting for the ports to get used. \n",
      "\u001b[1;31mView Jupyter <a href='c/https://github.com/mew-two-github/Spatial-Matching-Simulations/blob/master/ommand:jupyter.viewOutput'>log</a> for further details."
     ]
    }
   ],
   "source": [
    "import utils\n",
    "def run_extremes(N, W, pmf_cust, pmf_serv, gurobi_flag = 0):\n",
    "    Ex = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    print(\"Expected cost for c = 0 case:\", Ex )\n",
    "    if gurobi_flag == 1:\n",
    "        fluid_sol = utils.fluid_solution_gurobi(N, W, pmf_cust, pmf_serv)\n",
    "    else:\n",
    "        fluid_sol = utils.fluid_solution(N, W, pmf_cust, pmf_serv,0)\n",
    "#     print(\"\\nFluid Solution:\\n\")\n",
    "#     print(fluid_sol)\n",
    "    return([Ex,fluid_sol])\n",
    "def plot_from_sim_paths(file_name, save_file= 0, frac = 0):\n",
    "    with open(file_name,'rb') as f:\n",
    "        C_paths_M, Q_paths_M, average_cost_B, average_queue_B, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M, frac)\n",
    "    # (average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B, frac)\n",
    "    [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    utils.qc_plot(Ex,fluid_sol,average_queue_B,average_new,average_queue_M,average_cost_M, save_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost B [3.74046052 3.51405085 3.42862927 3.39667979 3.35759114 3.34246078\n",
      " 3.34328065 3.32450379 3.30075713 3.28766352 3.27960868 3.25483721\n",
      " 3.25339483]\n",
      "average cost new [3.74046052 3.51405085 3.42862927 3.39667979 3.35759114 3.34246078\n",
      " 3.34328065 3.32450379 3.30075713 3.28766352 3.27960868 3.25483721\n",
      " 3.25339483]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_gr_batch_new.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, C_paths_B, Q_paths_B, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B = average_new\n",
    "#Q_paths_B = np.transpose( np.asarray( Q_paths_B )  )\n",
    "#C_paths_B = np.transpose( np.asarray( C_paths_B ) )\n",
    "average_cost_B = np.sum(C_paths_B,axis=0)/(Q_paths_B.shape[0] - Q_paths_B[-1,:])\n",
    "average_queue_B = np.average(Q_paths_B,axis = 0)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost new\", average_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.5    ,  4.5    ,  6.49984,  7.99975,  9.4996 , 10.5    ,\n",
       "       10.99981, 12.49936, 15.499  , 20.5    , 25.5    , 37.99375,\n",
       "       45.496  ])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost B [3.74046052 3.51405085 3.42862927 3.39667979 3.35759114 3.34246078\n",
      " 3.34328065 3.32450379 3.30075713 3.28766352 3.27960868 3.25483721\n",
      " 3.25339483]\n",
      "average cost M [4.39096514 3.40043199 3.34147486 3.30648575 3.297759   3.29579503\n",
      " 3.29411162 3.28478793 3.27180523 3.26732104 3.269119   3.24033086\n",
      " 3.22763015 3.19774973]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_gr_mwm_scaled.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, dummy, dummy, dummy, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M_sc = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M_sc = np.average(Q_paths_M,axis = 0)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M_sc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 4.311\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n",
      "3.2353891814339213\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "Cstar = fluid_sol['Cost']\n",
    "print(Cstar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.02433084  2.55877145] [0.12844861]\n",
      "[-0.84588093  0.46085391] [0.07626542]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b6b9cb0dd8>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M_sc[1:10]-Cstar)\n",
    "yM2 = np.log(average_queue_M_sc[1:10])\n",
    "xB2 = np.log(average_cost_B-Cstar)\n",
    "yB2 = np.log(average_queue_B)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Iterative Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 13)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_paths_B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "279.5402156712974"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(C_paths_B[C_paths_B[:,-1] > 0,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b6bd647128>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3jHuysLQ4M0ktW/vb8GzeWvi1b+X8/eN1WLR5HwB7M6mfdySTPusEM+PTNbvAzFJ5O7nSZgtP3jLMvA/AR4jb0kFE1wK4GMBVnFQJtgDoaLisA4CtmVbUC+ygPcoi4xfd7a4peGjKStz22mJPeTMzJs7b7Ml/XESJw4SxH2aZpFuZe1qZfIOSa5mO4398vhGDTFEq7fJ8d8k29L9XvPjFItwFrpBhu+iZMX/lAvH9hv3IEwAenLISo5/8DABw73+XZ5SvDEFtTv72oq24+rk5eHn2Jqn+lguxbWS8ZSp1TxgiagBgJICVRDQKwB0ALmVm44zW2wDGEFEZEXUG0B3AHN9rLkEmssTLw/G6jHnuxm9w+2uL8du3l2VUrpOwrHN5OckUIzs59f6y7eg8/l2s3XnQ0YLz1Z5ggmYFMYzs2vzKHGt44GQ9rNfUm+wDdnUNKza43k4//c3t2vj5OrHJx8+Xvm7X9/t26j76W745mvKcP1+7W5heN8sYn3+2xb2M5t4WwAwiWgxgLuI293cAPAGgMYCpRLSQiJ4GAGZeBmAigOUA3gNwIzOHsj2MXaeRiW/hyWbm8akdqom/DESbJvhl6vfHz13OFfL9pXFvh0Wb9yeX2XsYsGt2HMQDk5fHP3nT2ExC6jPZ4+2we/5Ok4JCDwlLGnG+H2cpfKxdfV6ebf/S8lyGx5udibnug2XbMf+rvcm8AvaWIUodo99/1jz9mCz/zS+/Rre7pmBTgLHznZDxllnMzAOZuR8z92Xme7Xj3Zi5IzMP0P791HDNA8zclZl7MvMU+9yDQe9cuw6KhYScmcHPGonzFk5OOBRsHgROdRSd++v0NdjqIY53ws+d2dmEZLDfJmy4HsbruY99gv/7dAN2H6rFXz9ci+r7p2H7/mPYf7QOr8zZ5Cos0n2ezq6QyQveXbIt4b3keI3gmG4e07Oze3n7qTk//N5KrN/lNsns/xqGdObfgcw097H/mo/L/zbLUodMhftjU1djqsE91BgbSFaZeGdx3BodlnNGQa5Q1W/lUx+tSzsPLw+Ewbj+H+5RCBPpHeYE/PIpF53709TVUtfq6LX7aNUu9Pnt+5izYS/mbtxru9Lu4DF785RIQF/21Gd4NKVOjA9XxgfUtv1HccdrizF+0hIs8WEjaeHkpoPGaHwOP3t5AUY++jEAZ81dNOj1Q/rXot1cjij6p5mNuw9LacVPfbQO174gZwkNRMMNWJZ9tGon/vCeOD5U4mszwzo8Pn0NfmzYack4NyEzWRqNseMcTDYoSOHuB56EO8NT4CY957poDPe/szwlUp7XT1o7W62b6cnp/Muzv8KSLfsTbmX6gqj/LtqKK5+ehdv+kzqBrAvJe/673H71puD4l5v2JdwZgbgpJBLRbaZJ80yNYXn6nA178c1hsXfSI++vxLcemWHbLjNOGqOd0HNaF+cUxiAp5NPji/V7MPyPH+E/8+U2O9GD563deTBFizfXMQil0mtYX6/+79e9MBd/s1Hc9OdjHL9rdx5E1bjJWJqBkmD0KpJpX4yDDm7sTkEKdzf56Pdst9eHqOf96ZrdeHbmBvz1w6SAcyrWPAamLN2O7ndNES4fz0RLuOuNpbjkiZkWzXafNnG8YtsB23rpbbOYkCTKjQdbSgp3Ed/5+yx895lZwnNPzlgnPWm7dd9RPOQQythunYCjIBJcYrbde+lXG3Yfxj9nbQSQDBGwZIucgNI12JGPfoIRf/rYNl0girvHPP11orK6Qk5dHle8/rvYH6c9Udfcd6Q2ZWMdZrGi9tCUlfgi4IiUOoUp3H14Z3rT3L2VZ05uFCReBr++bHuxYMC75cIcD0T2b4eJNLMcW7Jln3bClM7wOyHcTWlk7lEsxglf6KiD5rN6h/dFS8byj9VFcZXNRJgejM0ufIOzbBeYZUwfVl66yuV/+xx3v7UMddFYwpzzry++QtW4yYb8MuvrQblmRmOMeRv3uif0GZH7bibyoLY+hjteW4yXvvgKALBxz2HhGL3sqc9TwhdHY+JSn/54HcZksArYCwUj3HcdrMHgB6YJt6UzI+Ut48nm7hX7K/waam4vCQZw0ytf4s43lmCd9tk+7MHpuOmVLxNpzHMCG2204hTN3cYeKae5J4W7MZ/ERJ1Pgui+d5bbTmDq5duZu5xt7qJjqWaZ+hjjuZkbcLTW3YHs0LH6RB52C469mlWsL11v14u49ImZuPHfyQWBjHiwrCueFn9hWSuVeR0SWelmGUHDRHMsbn1q5tpdeHXeZuzUnDPeWbxNOLbM/SnGVpt7timYeO7TV+zAzoM1eG7meseVm7J4cYX0+hDN6UWarxQOCzZkstmr2a71jZ637j+GrYuSn66ycdeMg8Zc/72HazFl6TYM6NjMNZ8YJ4VrfSxmXSqfwWAxZrV06wHbdKVFEdTUx9IS7qLnYO5H7yzaiv/M34KtgsBwZhJufTH7iVivE6JWm3vmEmjxlv1YvGU/vj2gXaKMVQJToR1+mmX05yO9oQqnvvBW7ziIBiXJOIfCPSGkzLqiZNmV9gUj3L0g89z91Nx3HjyGlg3LEoLLnN74t9BXmhlE9r4d4vJdNHcbLTkdUm3uqedOuW+qdD5Rg1mmLspYsGlfSv5+ae5tmpRhkc05PUx0nY2q7NUVMqG5a38f1LRxXSt3wviis1M27ISY7BylnxOqyXUR7ElgHzhWjxtfXoBHv9sfX+05gq/3HcXZPVunWYf4/8Z2OXqVmf4+77HUnaFEeyYM/v1013rENffU3O3qsfdwLVo0LHXN0ysFY5Yx4kd//dMHq90TJQq0L3HPoRoMfmA6Hn4vPpGycbfYZieRlUP53vNhIMW+LSKdgZ9cxORdH2PmxGBK3cDBX5/sYocvO/1cnc0GEl5dITfuPoLdh2oS9yWauD+C6003PKGFxuQ3CJFHf+n4r02mU6fJS7Zh1ro9OO+xT/BDic3NRfz6zSWJbfxEioDonu85HDe3bN57JGUuQ8dpQxwd0WYjoueV+sJJ/nH7a3aqRmYUpnD3ob9+6HFPSju+0YKKTV2xA2Oe+QLD//iRY/2cfKXNJBeNpPcBqAv3TXuPoOud7wrKFeey27Q4zDhoEsJLonwzUeaEQBNtYp7JczXeI1sTR4xR4mpzdyzEwnf+PgunPpCMW5OMwiha42AW7vH/4yYqcZFeNXc9deIyyXu6/0id9I5JjDRf7p6vSOWlL5LOAdEYo2rcZDw4xXn9wDXPxdcD2O06JbPhzyDB12ksJnCcMHwiG88dOBrMDk0FKdzd8FtXOegYAEwwiWP+23BAKNz1nGy3DYwLI6MpyXVClZNuh+8u3iY0Q9nlcMBiUjDa3PW6OhYvZOGmfYnrjDZbtzjhMrjdY/24rrk/O3ODMI2jzV2ibN0LR/SSMD8C45eV+fnoL167ryu3Jf36ZbK26f73foDrX3TWqBMlsjezTBDo9+XvHyfj7S8XzLWs3xWfCC212dVs3OtLXMsSjf+4n3vqvbU19QZ0swrU5i5hk/ARvYOY2XlQvNTfyXacjnb68uxNGDdpCfp3aCrMZ8bKnUJNOOJilnG6T8yMNTsP4bzHPkF/w2RpJnbxcZOWYORJJwBIHZTJvL3lN8EQ5Mt4qV1QqShzQlOb/9U3qI/GrCYcj4uYLGUkhLu75l5kWNBlPqdvwJzuhKh+mRfT26drxEGyLHmnUR+/EfVD0T66+v2zc8JYk+aG9yJvGaN7rfFUBhvGOVJwwj3MmOFG3lu6DT99aQHuG90nfkCyx9tNqIqkiq7J68vzFxn83Y35/FAYGoETmrudQHbSlOuijGkr4qEC9HjdQHKwPPPJepzQpNz2ejtEG6uk+0THTRJrXU72a+PWhURkuTd2mvuxuqij2SLpChnT8rFPYywfAI7WRvHq3M0p5/TJZ7ul8LYfGAnXzNSJXj8xe6CEgaxDhJ7KKXx2OnywbIfleb46J/kMjdFFg5JZBSfcAX9s7mZiseTSePfyGXM3xm14y7dZXcJkt3DLBAZj2/6jaFxeYlPHpD3RPva7ff610ZiwU+p5Ld6yH1fK+jkbcDJx+fVc7e5xNMYpWxcyW/0+RFs3MjN6/eY9nNCkzLZMPSx01IPNXS/r//1jLraZAr7paW1t7rY10epsqLtXZPY6SEtcmbLd8s0RnPGHGSgviWBAx2aYMHZoyvkvN4nt5ID8HsJ6+0t9cJ828sSMtRjSpUXKsVfnJYX7r99cmvgd1IvwuBfuupuhG4dr620FpZkYG/Zx1fqMsUrm+hk1ZFHV05FpzMDQBz9EGwftORH72s4q4yTcbbTUQHedz8jmbpyPEKeJMadsXcgQTHIKZICen9Pu9tsPxIWz3i/+8flGYflAPAb4fe8sT5j1RIvH3IS7G8zxfWh3OtTZjr997ByQT3ZMWa4zjgNm/OG9VQCAY3UxfLE+vtr1o1VJR4fLnvrcNi9j/3R6genPrsTG5p4Jso8mqL1lC0a4G++j++rM5PnnP9uI68/o7Jr/ht2H0a9DM6m6iGykxg7ml7eME/o1ulCxnAcMfu52Zhl76qIxocYRxHL25Ebd/uRnV8cYp7q+ia1h7hq3E07mghgD33pkhlR8HD0bu9w27jmCP09LuvOu2XEQ3U9onPibwbj4rzOl6mz2HDLGnhcuoJPK1Rl9TsHMdZJukl7D7NptAZgJsjUISnMvOG8ZIvfVpcbTz3263jG+is6lT3wmXYdoLOndQAIfbafaOcZz99AJXKNCsvtqPqe61NbHhJ/eQcSu9iP8QOqEqo1wN3ukwPqSlrGVO+FkLmBm6cBn0RijLhrDPwVfADp/npYMSHeutjgnUbqHOvf7nXhbQcC0u5Ihrks68ur1+cm9W+uiMWkzqIg6Dyvzfvqv+VjmsGo5bUKeWS444Q54G2xb9x/DnW8sEXqTpEuUnTfRNQspo5+rcEIVqS8KGWTuwbb98SXwdtufOWVRa6O5B2GWMW/mLMIcqdKC4WInV8iUS9h6H0Uanl+au9dgdf+c9RX+8uFa6WuMeHlOR+vsx4YoABsDaUn3yUu2JX7Xx1g4vyFLXb18A99bth2/MdjA/ULWjBiUWabghHt9jPHGl867t4tuudcZ608EblU60WhSc9cfsHH8m2XB6wuSMbpFg27CnM3Wg0gvHnmijjF21VbcbO7pBGLKBKesL3j8U+l87JS6KLNrYC3RLffSZDezjJd8ZBcVGXFa+OY5ExuYWbBrmLfy6qMxy4t0sR6VVOb6TGNq+IBsk5VZxgX9Rr4msZmB2E7obXbdKJDN1Mdijhv0OpUlEsqijbQB5zHm1ppdUvuUuphlsqS5S1THlaN1Ubw8+yss/Xq/oyuk+SVsflYyXi5OOAl3LwIwxkCjcu9TZnoJQW/InWn0yXW7DqVs0gLYryIVIestEyTSNveAyi+YCVUviG66TOdbuHkfvv3kZ3jlx0NSIseZMZplkjZ3uQlVp3OebO4u7ZGJSuiUh51wCGLbNtE99Mq2/cdw1xvxT++BnZoJ01hWgYItLyvRSkYvtXISOl7kUYwZTdIQ7jo1df4L98Rz4vhYMeL1yRn3RU3mL099VLzUP5vIvqzT8SySoWA0dy/3x26XHTfmbIjbpqev2IHGDgPLOKEqwmkQ2wnHqnGTEzZyOZzbKBNP3NlbRuzuFsSE6iVPzMSyrfv983OXDJ/LbD0mWuzin7eMF82d0agsA+GehklHx3Z9lNZjFm7Zl9hQXMePfuFFCE6cl/yyDkuHD1tzLxjh7mXgi7ROmev1hQ419THbWBRAqiukSNt08uZxqsdK04Iop87uNpZkBpvzF4Y4fkhQWtK8jd/4Nki/tvlqicVSlQSGtT2iZeoyGybr+CXcox4W1Ynw04FAZ9KC+FzXToH7bY9fT8k4/7BXvXpF2dxDoFYk3CVER5lmiqmpjzoKT7Gfe/K3KJys/gl3yDEImTxuHUvGJul0T95dus3G5h6MdD9UU49/fLbBl7x2HxJvsC1am2D8tN5/pE7qOiecXSGls8GeQ7WocfBicSsjnclYr2X4TZ7Jdg/KiFrEZMuxuiimLN3mnlBDZJbRO2SE7LXe8pKk5u40oEVmGWNykWtZTX0M5SVF+N7/ye+vqO+kJMLN3heV8CZwyuKlLzbhd5f0thyX9dP2yiPvrwokXyMW4Y7Ue7By+wEbV1V5nO67l5fE6Cfl112IyMQs40ZQZpCgbNOBIfk8gwoc5qq5E1E5Ec0hokVEtIyI7tGOtyCiqUS0Rvu/ueGa8US0lohWEdH5wVQ9yTXPzZGOWAfYmGW0/506UFmxprnX2cfXBsSLmIymgCO1Vu1cZrB5GTRf7XUWsjKau5uwEd0r0VdRvuBmc2eIn4Ffmns2HTzmbJDbvPpxw0IoHTcZG9TXW74hbXMP0SxTA2AEM/cHMADAKCIaAmAcgOnM3B3AdO1vEFFvAGMA9AEwCsBTRGTvWuIDcxx2WRd5hYi2UNM1Xae3aEnC5h511Izj3jJavoJHfEQwmZnOJ7YTt7+22PG8PxNcGWchTUVpoF0IgCAUMJtWFouM8PA4EerTIqZ00fvjB8t3SKV/bFrqjmRBrmNwQxSPJ5eRtrkHZJZxFe4cR5/6LtH+MYDRAF7Ujr8I4Nva79EAJjBzDTNvALAWwGA/K+2FYQ99aDmWruaud+zaaMxRy6o3LGISDViRp0pNfQxrXDYV9nNgSdncXZJk8yO5eYX/e0yaMfeLrfuP4huD6UvkGgl4XMTkYeVyLiKzTD+oZpg9cGTJpD5lGQQUk3XdDTUqpKZ5zwfQDcCTzDybiE5g5m0AwMzbiEjf0bY9AKPheIt2zJznWABjAaBTp07ptyAN6h28ZUSae/8OTbF6x6GkB4zARc7Ix6t3JQSFyL4/Ya51xemZD8+QqbpvSHnLuHXOLKruDbKguV/815k4tSphXbSuemXxPfEiPI45+JfnwLobX8i1l1Qm6yMymZuQvQ2hRoVk5iiAAUTUDMAbRNTXIbnQQ06Q5zMAngGA6urqrPaGOqH6Ff9P9IlUUhRJNbWw84MzTv79R2LFrCx+3iQZX/9c0tztdsrJJjZWGd9szPlgq44QSW/hl01Em7yEjfTjzAVXSGbeB+AjxG3pO4ioLQBo/+uBlrcA6Gi4rAOArZlW1E/EZhnG/iN1Qs29pCiCmGGSNOYSGCwfkKm/W5Js3oFSn3fKscNtgVmmE6rOZed+n5IJjRtGM67WNrrOJUKW7VLeMpWaxg4iagBgJICVAN4GcK2W7FoAb2m/3wYwhojKiKgzgO4AcurOizrflKXb0f/eD3BYYA8vLY6g3rgwycUsExR+FikTWMm1uCzeg2xp7m7mKr/i7YvIA9ku5baXUVCyNAkiHnumyJqnwjTLtAXwomZ3jwCYyMzvENEsABOJ6HoAmwBcCQDMvIyIJgJYDqAewI2aWSen+WytvSulLlh0U4Zo89ts4OegkVuh6uYrn72bkMlqTC+4bl6e4YSqEzMd+mCuQEQ5uVK0OAeFuyyhTagy82IAAwXH9wA4x+aaBwA8kHHtJJjn4AbpBacBWqrtq6mbcxjhTH75qrm72NyJ3DX3QpkANOLozQJvfu5FEfL0AnxoykrptOmSaR+S0txD6BdFDma78AKHyaVTUSFtuCKNTZhFOA1CXXMfN2kJAF1zz2/J5iZ0CHCV7vlgI/aK0xqsGLPQT93uhVDsUbgHTdW4yRlFkgTk7MhhdItc1NylN+sIqO7huyDkCE4a2+It+1P+Dsvm7idufu4RItfOmc17kK2h6/bSFp09UiO2OuaCh4+ZA8cyi10U3/zaOU0YY8PJ5i4T3tpvKkqLpF9yrRqVBVKH3Ot9IeE0qFs2TF1AUwhmGVfNndzLyyGl1DecBNO6nYfw3MwNluN7j4hj/IjCA+c7L32xCVu+yb6wdMNpSz4/3ZFlqSgtzn1vmeOFfTYR/wDgt5f0SfmbC8AV0s1bhkASNvfs3YNsleT00rt/8grh8W9sArjlouaeKf/4fKNrcLhcs7mHQYxZGPpYRFC3q/B6X5rMc9jCq0mDYpzYsiLxd4w5nJUaPuKH5p7NQewUk8XXctIo5htbzf34HF5huEKWRHLrXseYpU1gQfXt3LojOUqEKOWzLxYrfJt73Fsmd1whneZE/GTD7sOer7nnv8uFx4tzTJvMFmEMDdlJST1sd9B4EdhKcw+RSIRSOk9YNvfDglDB6eLuLUPuG35kMbxvtjR3PzleNfdcVnyCisBoxut+uEFwfPY+jxSZNPewbO6ieQHzZK8sbsI9IuHnXpvmXrRO2LUnW5q7nxy/wj2MMuUKzdYCLC/yIaiunde9T7TpRRBEIqmffWGtUBWRro+su1mGXN0Cl3693/F8OtgNPqePhCsGdfC9Hn5wnMr2UHz7w47AaMbLPQhqzUxed79V253jn/tFhChlkUSMw5k0EuHkAuaETIdySyK7XP6uC0+SShdH3J4V2+zjiJ/UtomH/LNHtkwAuYYXwfbn7w7wpUxZAZnOE0lngZSXUMHK5i6gvCT4GN9AXICaNWSJuFtZId2ASW7jL+4t40+3K/MwiZXOuypX5y1zcNFkVvAi3Du2aOBLmX59LAw6sbnlWNBxjZRZRkC2hHskQhYBkiuTRul6gEmF/E0vawvFHiqZzjDKxYiAALK7D2EOsV3SvzuOP/dok82eweau4danv1vd0XKsNGD7mppQFZAtt6YIWQVIrjhvpGtDdK0/w/NKxCe+b4kvB8DbZ21amnuO+Tgr5An6vex1fIi09KBdWpVZRkB5cZbMMhFK6SRrdx7CPpuFK9kmXa3VzeRSF4sJl9o71sVmIHmpYzp26uN14rIQcNqz2A9khHsLg4eWqC95+fJMBzWhKiBrZhkii4ByWtGaTdLV3N3sok57fdphN1C9aD6FpLnLNOUXI3vgD5efHHhdcpWgDVfm/mQWpD8b3hVz7xqZ+Fs0noLeBSwoC29eh/zNZGdyLxRFrMI9V0j3re+3Wemv3xto+4nt5QUkm7KsOAJmoDYay8lwr7K0a1aO3u1y09snGwQ9LWEet+Zu365Zg5Q0onFeHPCnoZpQFZCt3XkiRL74x7Zv5o9ngB+s3G7vWpgOl/Rvl7hH5rkQT2YZyftcHKHEmyBb/SAISGLD6XzC64s2iLaP6tMm8ds8bt0Eqci0GLTNXU2ohkiE/NEwHr6iX+aZmChNc94hiP6kW0dO6dQcAzs1Sxz3Jtzl0hUXRRJiIV1f/1zAr76VK3h90QbRdqNyYc7eXF7TBiWm8yKzTMCae0D55rVZBgAGdmqGLzftC7QMPyZ9Ft59LppVpBcqwIlseQzJoN8n5vhmBTpBCN+SIkKNtkA5TJNZhDIzcREFu2qyS6uGWJ9GMLR0KY4QvLgaBNF0tvkNJJWaq07rhIGdmuPifm1Tzov6UtBhJJTmbkO2PGb22sTslsWLYH/0O/2l02ar/TIYhfiQzi2Txz181soKOqMHQ5g290w9KSIBbzjdvrm7KfDk9k0952v3QvX6Ig/aJGUXoqSkKIIrBnWwKG5CbxlB/z2jWytf6gcgMNU974V7tsIAmLfaC5IGHryAcklzNwrmG8/ulvjtZcDLJq0oK0oIhjA1dz/Kls3itvN7ZlyWiHQ0R9tdprTDHVs0wKX927nm4/eLrV+H1BeV+avKTV6IlAuz8jC4cwuc2/sES7p//+g0yVqmojT34wgvdstsuYOa6dve6uGhjwui1DZ4WsQkma5xWXGivDAnVDP9aogLE7k80tGwZWiZxh6edqYKvSXnntQGPds0ds3Hb+HuFtTPdUJV8DzNxwg29U6zLWoRU46QDY8XLwIjLOH+5PdPkU7rRfjK2jcbl5ckxlKYZhknk5OM4Irb3OXKCsJ8M+6CXmkF7zJOMvbv2CzxWzdzlBTLVdZsljm7Z6Xnuhhx2yTNTZAKvWVMpje755Du3ElorpBE1JGIZhDRCiJaRkQ3a8cHENEXRLSQiOYR0WDDNeOJaC0RrSKi84Opejg0Lg9+DtrLp76MdhQEXl4qXtoj61Pcpml54ne2wriK8Mfmnp4g9IPrhlWlrNCUJRIh3P/tvgCA3oaonHpTZF+4RjNJaVEEF5zc1iG1O26L89zWhYgUEavmLm5buk8nTLNMPYBfMfNJAIYAuJGIegN4GMA9zDwAwN3a39DOjQHQB8AoAE8RUWDqZbbjd2VDkHgRhmEprU6D1/xMzPfMybXM1pZr4IxurfDbS3onhGKY29ll+tUgb5Rx1tzvHd3H/qQNt53fM+0vP4LxuVoHoew8C3M8JtGt5/XA6gcuQKcWFe4XZYD7JjUibxnrMVHr9BdDozJ5BfD7p3XCnZ5CYsvjKtyZeRszL9B+HwSwAkB7xJ+o/spuCmCr9ns0gAnMXMPMGwCsBTAYec5Htw7Hv398mutn3Vs3np5xWZm4DsoIRz8Qadh2JZsF4Ls3n2mbr4xZ5obhXVPMMmFq7plOqJJggdyvzu0hTuuQzzVDqzw/+0xWeJPBP18U/joSkfMCYgYu7tcO/zuiezzftGuUzE/Xzo3uuDpubqsysWXibbcX+E08fN13btkQ7QIy9Xp6ukRUBWAggNkAbgHwCBFtBvBHAOO1ZO0BbDZctkU7FgjZUtyrWjXEsK7u7k/dT2iUcVlmgeFlK71V912Aq07rlHEd3PCysMPyWeswgmU0YTL9CNUV0snmLpUDW+6H7f1xydCPkBKXDZQbqvFV2/HfRtOKvtet7AvXq0ni8lOcd92KcbI2pWm8vET1Ni90skuXWOfhobwgvf2kW09EjQC8DuAWZj4A4AYAv2DmjgB+AeA5PangcksLiGisZquft2vXLu81t805WFxtdpKd+i/fG2h7ziwwvuVhkokIOFobtT3/1FXyE6FOBBUMTGpClVL+y7orZL8OTTGkSwvPZT97TTUm//yMlGPRmPX+2Nng3WzuXgWlqJzxF/SSu9ZQH+NLRf8pe1/MVXabf7h0gLN7ZRODIK71sBuSjrneHVs0wPVndk45ZvxqMR8HvJmKgzQrSwl3IipBXLC/zMyTtMPXAtB//wdJ08sWAMaI9x2QNNkkYOZnmLmamasrKzObIdf5X4NvdRh8dOtw6bT9Tf64RswvCKdBbT5HLhN0Ii3EjIzN0Iu23L116qSv05UyLw1zm7Mt3J+9phq/vyweyfHifu6+3DpDu7ZEn3apzz3KbHledo/P7SVpFBQ/PL3KtT4i+7bs5G5NfSzxII3l6r8jkjFzzC8kt+LdHrXRi0sk3AdXxV/Ko21eEuax95Ozulq+UptXlIpt7gnNXV5iB7kvhIy3DCGula9g5kcNp7YC+Jb2ewSANdrvtwGMIaIyIuoMoDuAOf5VORXjjfTb9Dqsa0v3RAaqWjWUroOThm+28RnbeKVpM+hL+rdDZeNUP2Wnz1GZL4sOzRu4anBOQsDcuUuLI7j+jM42qVOR0dz1Aa7XIZvC/XeX9EbrJuXoUtkI639/IS7pl5l3BzNb45/44I0xvGdrx/Ov3zBUuBBHtv8SAZ1bNQSQuuZBF9ayVjuLcHcr1yXFCU3KEp8Pok3gO7WswMaHLsLATs2F15v7UrEpImznVg3x+/85WTiOIoKXnRthm2VOB3A1gBGa2+NCIroQwI8B/ImIFgH4PYCxAMDMywBMBLAcwHsAbmRmezuBj/g9xF+6/jSs+/2FHuuQeS0s3nXa8+/QvAFuMU22tWlanhKPGojHqB5g8D02Yu6837exzwepUTi9GGRs+fr1iUVMWZxQNd6WiEsoaBmNPBpj65eareaePPGnK+VDVHx6+9mWY4NObCEuQzLPGAOnVrXA+7echeuGVRmOJ23uopeHGdlu1k5zfXV71ETkKDDdvGXMz7PIMDHcvlkDzLh1OJqUl4jNMnC3uT98eWrwwFDNMsw8k5mJmfsx8wDt37va8UHM3J+ZT2Pm+YZrHmDmrszck5mnBFd9083JYJCLJi3dBq8IPxakmLVXvYmyzevYogJv2njtmGWnbl4w48V+mwiBINt2h3PNG5Zg0d3n4bphVTinl1j7TKyE1f7O5oSq+bY4+bkb52fO73OCMKxENGadULVrjjHd5YOsE4v6dad1ThXcHT24F8qaZfRYSz3bNE65RpedRRFCt9aNsPr+Cxzzsdrcxemm3HwWPr5teMZf515dIYuLKLEO4JqhJxrqKZpQjf/vNHQ6tQzW1dNIQa1QFQ2KoV3kTCuyM+tuMk92cDibZdKbUDMjWkUq7cXgQXVfeZ94AHvx8gGAn5zVBT86owuaVpTgd5f2wfgLxaYhcwuyaZZp2Si1TbJB0R6+or+wb8RY4C0jeM5lxRHXp6+7pz5w2cko1/pzc4+RSPUyulQ29HSdDhs0d0BmnsDcz8QXNK0owYktG2b8ZRx1GcBWs0wEFaXF2PjQRfjJt7o61rJJeXw+S59sF2FWmryMM6/kfcjfFMVdcMtlvTr8EhCyuXjS3LUOQeRt56UGpdYXlmw70+pzpmum3HwmNn8T35XeWKpd28dbFnOIE+qLRczmGSPNK0rwzZE6txp7xhwMy+mrYd/RZPl2PujRmGhS3Jpu0s+G4Vids3VTD7dbFCEM7twC947ug29LujYay1553ygcqY3ilPumeroWSPabxDNySX9Ck3KXFNb6ueE0RKJR545tfp52z1f0wdapZQXeu+VMVLVsiHcWb5OqW5DOfnmvufc4IemJIXrw8iFk5dK5TYBIT0g5dHs7Aez19SMqQ1bz8WNJdOsm5ba2XRn0e2n+Aig2CQ6RRvzodwakXa5znaw2WTvW70rGUbebKBZq7oL2xB+H87PT61IciXtMXTO0KqFNykJEKC8pSnvVb2JCNfHitc9n1vgRFpORKPni352X+N1KIsiZo3C3Oan3qQamhU99bYK12cmVXm2aOK767aCFYNYXWIXuCpnL/PaS3qg+MT7zLbrdspqqbHAr/8wy9ufMAytpc/c44DL4GAlqR3ZA/gVjJ7xlPvmbVsgJNS9LxUU4KQXfG9zRNV2MBROqNvm5PX79BZJJlEynSeqRJyUnSO3MNnq3KZKYhmnb1Loy08ncAQDdWjeyhPX1gp0Z5NM7zsbMO85OaffGhy7yNF8hw4ktG2L+r0fiR5r3WFBxZYACEO7lJUUYrE0giTq/rHDP+ipHJ7OM6ZuvbdP4Jr63nuctnrd4FZ01ne7SZsTNNilCt/lWlDoLTHl3u3hCs9KbfPklNfiK0iLcel7Sk8guhENZcQQv/PDUZBlyVbHFqX8ZfdrtXszRmNUV0nZC1aUueh/OpCuT6X8jxrUZdt5YOul6MMkoMHbatJlfCsI42PXrtk0boEPzCul7l4mHVstGZf77bQvIe+EOOGu2skJb9mEZZ8wzgUB4+geDLD7qgFVzb1BShHW/vxAXefSplu0+r/5kiGW7MTube7um5ZZVljqnVjXHL8/t4dtesXr9zc/GLLiJgOX3jkrEJwHshe5lA9vjbKMPeIZjzMlbRhTbxIzYFVJslnETfLrm7uYR4oTTPIaXbIsi9vlkSnOXrzLddNq9dSOcWtU85ZzbvZH+qsywXfrlyubuQsww4WjG6RN10InJBy9rY7x6aJV0/A0nIgSM6tsGE8YOsZzza89G2RdW68blFp9k8+errgUNqmphWWWpQ0T4+TndpeyiMhhNBHeMSnrOREyCQzi34NL0e0f3watjh0jdo79fPcj2nJPmLiPcY8yWF4yoSgyrhm9G9+TJ5Es/qblbSzOaENyEYNJ0lprue4Od4x7J9NibRnR3jIKpV5PIWs8H/0fs+psoX3LoZeq1k+h3AZpl8t5bBkDi9Sf0lnEYfEYNUP9dHCE88f2BgWxmbUTv9EdqrB4Qfi3KES60kMxaZuXgv398GsoC3MM1ab8l3DC8Kx55fyVibJ1QFWEndPU8rxlaFc/D5X48/YNTcJ7DYhyn/iUTTldkCiAitG5chp0Ha0zHnfN65upqTF6yLSM7sdN8htM8zIUnt8Hew7X4Yv3eeD5p2oZk+md5SRGuGVqFu99a5pab5UiH5s73RnbsmZt3ejdvq9n1YkINP5AP2C3y6VrZMGGPF2H8ojYKg1F922KIpH98uuilNRKEB7V6T2RWRuoxcWbmTm3udKLBOqxrq5SvH8e6kPi3E7p9VH82CTc7kwASeTBFiHCfRIxzt6qM6tsWRIQTW1bgIsFGEsb78t4tZ+Iugzun/oVjt2vVaz8digv6trGuZAXwwS/OSjkWV/Cda9umabl0mAc7El9DNmYZ3eRmPv/UVYMwYezQxN/phq32Y4V3JvJStnTjM7t9VE+8cJ23qOZJs4yaUHUkuXAi9fj0Xw1HYwdXMKNA9+Lnrpd3+6ieuGlEesHKdAHVuVVDy9Zi/mnu8vlYhXtqp/MjbrnXetk9V92E5iQIIkS4emgV5tx5jmMZsvf649vOxpMOETVHnnQCerVpgh+f1SVxrLJxGTY+dJHtXEl1VYt4oDfTcSKkfDmWl0TQtXWjjOy8/+90b0LfzSzjhk+Wxawj2x+MyRqVFXsOL5wFq0xhCPeYg1nGCeODTEd4tWlSLpyRl8JQnNFX33RKmpeuPw03n9M95ZgXs4z5uDl6ZBgx06NaUD+3CVXRANGr29q0SMasKfnxHp3/65EZhVI2t8/898r7LsjYZfNXBk+i926x3ywlOc9hPRdjGEygztgLSX/WiQBxP3lhCQabu1fNWH6dSmakE/vdKwVhczc+TC8YBbqXvTDT0UKteSR/m6PXWcwyEvmd0b0VzuieupmI0CxjJ9xNf98wvCtaNizFbzS7pp/BuWRzipnMMjpmTwzRAJF/WWferpYZTiCn87y9on/tXNC3DXq1aWKbTleQxB478hFYsxESQuQnDwBNGsTFWllxxLNmLG9zN8gA17RWM2fS5q7MMo44vZ0dJ90MDyiThR/pYOwcZvesdF8YljI8tMlcZllxEa7WJh0Bf/cplba5x3QvKBvhrv0tmuhLd2IsDGTnWDLpFmXFRfjktrPx2HcHOKZLhFM2HLtTi/ET3+VIThil7+ee1mV4+UenJYLg/e7SPrjzwl74Vo9Kz5qxbPle9kUXrjdJBMOXz8crBaa5e+sZxvTZ3mPZWFy9aBNKG7wMGi8Tqm7Zttf2eezeOr1tBDs2975PpHm1o445towIuxebXRTCLpUNU8IFZMLDl/fzFonRElvG5hllqNPLRCQU+bnrfc6LZ4fs/feL07u1wuna9FeT8hKMPSse5MurZixtc/fwLOJ5sulY/H/l5y6JrBYmWslXpL2KZZ6t16X5jwgW9RjLaeiyotNI26blthsoO5UBxLdQs2ufW6ce2rUl/vPTobgxzd2urjrNEC7V40IRc3wUs/3fyebuWoZWl39df5rcBRJ859SOGOphoxdZs0wQC4IsZSTKShbWULP3NygpkhbOYXrLGPFulpFM6KGaIi0/YZYJ0BeyIIR7YhGT4Jyoj00YOwTPXD3IZHMPbuSc1cO6jaBRmN4ysof83pVEuMk0ceqQOuUvpxWubs0vihBOrWqRti01HbNXn3ZNcMeoXnh8zMDUvCQEh6xwyQWzjMwK1fjx4OsiKuPKQR1wx6he+F+DZ5jrIqY0JYvfbfSqiMl+/XupppNZRmnuLpRpbkilkgtqKhuX4bw+bVI6UhATQHpoAbecG5QWpcSKNuNnh09XK0xXE0unrGS6+OIlc4iGYvOEqmCESA9S3eQQ5GoStzqY/raPLRO8dBeG8CiK4IbhXVFeUiS9cYxbfKFske5T7dPOftIZ8GYeFY2dbLhC5sYTyJBbRvZAaXEEVwzqgDvfWOKaPiaw0QcxodqyYSl2HawR5p0NLcxaJtmW6yY4/Hz5ZZqT1VvGOkKyvWl2JmRjQjXbNLPZiN09qqq/9dDLO6FJGf505QCpa9688XR0bum8WYmnuS9B0qQrpDLLONKwrBi3nd9LuJBAF1ojT0oGi9K9MFL83Ck1vR/844eD8eD/nCyMteKtc/jpeeD+yZ+JJpwN9LroAcBEC9Wko/tpXSZIDcoNu5DGlnTZqIwLsvfJvE5CFr+/TnST7T2X9rW4CtsxoGMz15DRKY/IZWyIFI3h2sJF8+YvflIQwt3I+7ecJTxeWhzB42MGAIhPSgKpg8Vvzb2ycRnaNC23DZQkKu3T28/GOzeJIy76RZnNSjqjgAlSm4gX5k82d1/cG5+NG5HY49KI3fNsZTLx9GvfDABQLti1yrxyOGxy6P3qWpcm6Qp3LV/Z4HN//u6AlDjzZox7uvpJSm4ubzzRy7prZSNsfOgiDOzU3Nd6GSkIs4wRO1c9ZmD0gPYYPSAZ0dF4z3U77skZbASgM/UXZ7kubBFpwh1bVKCjIK2f2Ap3w+8wtVgvFBdFEi6aZkQD6o9X9scl/dtajl1/Zme0bmzd7u2FH3qLF+IX9l9JqeYonS/GO4dY8BPZF3/m4Srk0n17YHvHrQT1CVW/HSa8fMmG9dVbcMJd1n4JpAq0Ds0rMOlnw9DNgx+3Xd7dTeEERGTDJGwugmC/EbhRGAa5ai5ej/Qa//oNwzBr3W6ptKJJrCsGdbAca1BahFMC1J7sSMdzSW+SWVClawKR4aS2qROL/Ts0A4DUmPg+4vew0Bff+f1l7iW7sKZ/ClC4axq4xG4tukD7Vo9K3DC8q29x1GUI621uL9yTv4NW3I1Nv+jktpi8RLyZsJlBJzZPKwplrrHxoYssx5bdcz763/MB6mOcePmNPasLSg19Um9StiaLp/3yWzihSeoXaN/2TbHq/lFph3r2aw9iWfSwIn5r7r2ML700bO7ZoOBs7gDwxs+G4SWZRSnaPb+4X9usCna/aCa5T6gOEVKEhRGjhpZNs4xTpMVMyCdvGSDuFKCbzHRZceeFJ+HW85NbK+oKgTkOUlAvsm6tGwknq4OM4Z8wPfmUW3LBor83qWmDElx1mvPGIzp+ly2Lq0Qjoo5ENIOIVhDRMiK62XDuJiJapR1/2HB8PBGt1c6dH1Tl7RjYqblltlu8ijH4hQRmWgom/9Lh+euqMfnn9tH9AHufZR2jmaJ5w1JM+tkwAMFujg1kx+vDOKB+Nrwrykty/+UdSQgi8Xn9sJ9xfnIVv+Shfq+C6NOyOYb1FSljlqkH8CtmXkBEjQHMJ6KpAE4AMBpAP2auIaLWAEBEvQGMAdAHQDsA04ioBzNbtxzKAk73VT8XtDAz8uaNp+PLzfsyzmdEL3sPATvMtu4/Xtk/5e+iEF52QWEUkLeP6oXbR8mtAA6TpOnA2V01jPDLfpFtP3f9i7wuxEVqOau5M/M2Zl6g/T4IYAWA9gBuAPAQM9do53Zql4wGMIGZa5h5A4C1AMJxO3DhV+f1xDm9WuOift58TTPpJh1bVHj2bU23b5gvqyhz/pxO7ngUsOYuaFB/H7yU3MrIddziG+kvZ7PJKZ+aOmZw3B/Mvo3+or8I66PywflkkalrxxYNcM+l7juCBYGnCVUiqgIwEMBsAI8AOJOIHgBwDMCtzDwXccH/heGyLdqxUBFN5LRpWo7nrjs147xfuO7UnB5gvdo0xv9dU20JwGUmYabKspv7R7cOt/ifH4/oFjPbRUwJzd1kc8+J5U3ubHzoIhyuqZdK61ebdDNkXTQcs8ynt4s3FMkG0sKdiBoBeB3ALcx8gIiKATQHMATAqQAmElEXiF9olvtARGMBjAWATp3kJibSIQiha87y7F7+u4U99D8n462FWzFr/Z6MO3pJUSQlBO3jYwagSrC8WrRac/LPz8DOAzWWtH5S1cp5qffxgi607Z623eYluaRY3DSim6Nrpl5X+xeYv41prO1RHOQ9ksn64Sv6oXOW+7mUcCeiEsQF+8vMPEk7vAXAJI4brOcQUQxAK+24cS1OBwBbzXky8zMAngGA6urqQjDz+sqYwZ2wYc9hzFq/J+0Vo3Yd2riQy4jIN7xPu6bo4/MK6VwSRrmEOWaOGV37zGWb+6/O6+meCA4B7PyrCgDgtxf3QYdmDRxXsWaD71QHvTzRioy3DAF4DsAKZn7UcOpNACO0ND0AlALYDeBtAGOIqIyIOgPoDmCOz/X2TL6sugyTSJZs7kHSpkk5OnnYKMPIq1oo6LAocnHb0zd1MXvL5K6ot5Lcxs/mvM+NaVpRgl+e1zPvXGP9QEZzPx3A1QCWENFC7didAJ4H8DwRLQVQC+BaTYtfRkQTASxH3NPmxrA8ZQBgaNdWqGpZgZtHysZAdyfboi9Ts4z0kvGs2dyDG2h2mybLcFoX+Q02giAhgGxuT31UN8uY/dzzT3C59YE8bFLO4SrcmXkm7JWDH9hc8wCABzKol280bVCCj247O+xqpEeGQtarEM2Wt0yQqmY+CjodXbbbae56NNNcNsu4kWiai0eQInNyf2WHImMtRlZW62aZ/DXK5De6ULd73N1aN0Jl4zLcYfLZzydxmNjv2OZ8Hr+bc46Ciy2jSOJ1oCTNMkH7uQeafca0alSGitIgl9iLEW1ObaRhWTHm3jVScF2QtfIX3UToVmeCt7hDYZDrU1NKuOcw2e47ubBxRS4w79dWAZoN3MwyhUBSc3ezuROevOoUPJmFOmVKrj4uZZbJgGzZBzMtRdosk6XwAzk6FkLHzSxjRz7NM+jzOl0qxT7fedSUnEdp7ooE2Yq1k0/CKJu4hJYpCMpLivDCD09FP4mQ3PlCrn7pKuGew/z4zC5YveMgvntqegsgOjaP+3tfO+xEqfRBa+4tG5Ziz+HagHLPf/SXXiGbZQDnjT5yVVDmI0q4p0GDkvhkW9ChVysbl+EfGWz11rSiRLgxhB26TIkFFEFv1vhzwOCEv7YiFRc3d0WOcUHfNnhlziYM7twi7KoIUcI9De686CS0blyGUX3ahF0VX6GANXd9F6hoTC541PFGwuZe4Jp7oXBWj0pb5WniT4biWF1oazcBKOGeFk3K40uaC42GpUUoLY7g1xedFHZVjksiWXJFVQRPLmjzSrgrEhQXRbD6/gsCL0etQhSTMIuFINuvHNQB01bsyH7BNqiPl8xRwl2hyBHC1NwfMe3KFRbqo8U/lJ+7IusorUxMmJp7rqH6SOYo4a5Q5Ai65p7PIZft6NiigVS6dPcuUFhRZhmFIkdIau6FJeAW3n1uwlNKFjUvkzlKuCuyjvrkFpOt8A/ZpllFadhVOC5RZhmFIkeIBLyITHF8oYS7IuuoT24xSZt7yBUJkQKzSIWKEu6KrKPMMmLIoytk99aNgqxOqKg+kjnK5q5Q5AgRj66Qr/10GLbuPxpchRR5jRLuiqyjlDIxXhcxNa0oQdOKkiCrlHWUVcY/lFlGocgR+rRrAgA4oWl5yDUJjxNbVODqISfi2Wuqw65K3qM0d0XWUVEPxfzs7G44q0cl+ndsFnZVQiMSIdz37b5hV6MgUJq7Iuso0S6mKELHtWBX+IsS7gqFQlGAuAp3IupIRDOIaAURLSOim03nbyUiJqJWhmPjiWgtEa0iovODqLgif1FWGYUieGRs7vUAfsXMC4ioMYD5RDSVmZcTUUcA5wLYpCcmot4AxgDoA6AdgGlE1IOZw92WRKFQKI4jXDV3Zt7GzAu03wcBrADQXjv9GIDbkerBNBrABGauYeYNANYCSH8jUEXBoSZUFYrg8WRzJ6IqAAMBzCaiSwF8zcyLTMnaA9hs+HsLki8DY15jiWgeEc3btWuXt1orFAqFwhFp4U5EjQC8DuAWxE01dwG4W5RUcMyyNoGZn2HmamaurqyslK2GQqFQKCSQEu5EVIK4YH+ZmScB6AqgM4BFRLQRQAcAC4ioDeKaekfD5R0AbPWz0gqFQqFwRsZbhgA8B2AFMz8KAMy8hJlbM3MVM1chLtBPYebtAN4GMIaIyoioM4DuAOYE1gKFQqFQWJDxljkdwNUAlhDRQu3Yncz8rigxMy8jookAliNuvrlRecooFApFdnEV7sw8Ey6LCjXt3fj3AwAeyKhmCoVCoUgbtUJVoVAoChAl3BUKhaIAUVEhFaHwm4t74/RuLcOuhkJRsCjhrgiF68/oHHYVFIqCRpllFAqFogBRwl2hUCgKECXcFQqFogBRwl2hUCgKECXcFQqFogBRwl2hUCgKECXcFQqFogBRwl2hUCgKEGK27KOR/UoQ7QLwVQZZtAKw26fq5BKF2i5AtS1fUW3LLU5kZuFuRzkh3DOFiOYxc3XY9fCbQm0XoNqWr6i25Q/KLKNQKBQFiBLuCoVCUYAUinB/JuwKBEShtgtQbctXVNvyhIKwuSsUCoUilULR3BUKhUJhIK+FOxGNIqJVRLSWiMaFXR+vEFFHIppBRCuIaBkR3awdb0FEU4lojfZ/c8M147X2riKi88OrvTtEVEREXxLRO9rfhdKuZkT0GhGt1J7d0AJq2y+0vriUiF4hovJ8bRsRPU9EO4loqeGY57YQ0SAiWqKd+wsROe4pnTMwc17+A1AEYB2ALgBKASwC0DvsenlsQ1sAp2i/GwNYDaA3gIcBjNOOjwPwB+13b62dZQA6a+0vCrsdDu37JYB/A3hH+7tQ2vUigB9pv0sBNCuEtgFoD2ADgAba3xMBXJevbQNwFoBTACw1HPPcFgBzAAwFQACmALgg7LbJ/MtnzX0wgLXMvJ6ZawFMADA65Dp5gpm3MfMC7fdBACsQH2CjERcg0P7/tvZ7NIAJzFzDzBsArEX8PuQcRNQBwEUAnjUcLoR2NUFcaDwHAMxcy8z7UABt0ygG0ICIigFUANiKPG0bM38CYK/psKe2EFFbAE2YeRbHJf0/DdfkNPks3NsD2Gz4e4t2LC8hoioAAwHMBnACM28D4i8AAK21ZPnU5j8DuB1AzHCsENrVBcAuAC9oJqdniaghCqBtzPw1gD8C2ARgG4D9zPwBCqBtBry2pb3223w858ln4S6ye+Wl6w8RNQLwOoBbmPmAU1LBsZxrMxFdDGAnM8+XvURwLOfapVGM+Kf+35h5IIDDiH/e25E3bdPsz6MRN0u0A9CQiH7gdIngWE62TQK7tuRtG/NZuG8B0NHwdwfEPyHzCiIqQVywv8zMk7TDO7TPQWj/79SO50ubTwdwKRFtRNxcNoKIXkL+twuI13ULM8/W/n4NcWFfCG0bCWADM+9i5joAkwAMQ2G0TcdrW7Zov83Hc558Fu5zAXQnos5EVApgDIC3Q66TJ7RZ9+cArGDmRw2n3gZwrfb7WgBvGY6PIaIyIuoMoDvikz05BTOPZ+YOzFyF+HP5kJl/gDxvFwAw83YAm4mop3boHADLUQBtQ9wcM4SIKrS+eQ7i80CF0DYdT23RTDcHiWiIdk+uMVyT24Q9o5vJPwAXIu5hsg7AXWHXJ436n4H4J95iAAu1fxcCaAlgOoA12v8tDNfcpbV3FfJg1h7AcCS9ZQqiXQAGAJinPbc3ATQvoLbdA2AlgKUA/oW490hetg3AK4jPHdQhroFfn05bAFRr92MdgCegLf7M9X9qhapCoVAUIPlsllEoFAqFDUq4KxQKRQGihLtCoVAUIEq4KxQKRQGihLtCoVAUIEq4KxQKRQGihLtCoVAUIEq4KxQKRQHy/wFvw/sbcoB+4QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(C_paths_B[C_paths_B[:,-1] > 0,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "209.00044742093016 244.11279086151194 0.0035072453173666876\n"
     ]
    }
   ],
   "source": [
    "idx = -2\n",
    "var = np.var(C_paths_B[C_paths_B[:,idx] > 0,idx])\n",
    "mu = np.mean(C_paths_B[C_paths_B[:,idx] > 0,idx])\n",
    "print(var, mu, var/(mu**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = \"../longest_spatial_uniform_25_all_good.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M_og = M_res[\"Q_paths\"]\n",
    "C_paths_M_og = M_res[\"C_paths\"]\n",
    "Q_paths_B_og = B_res[\"Q_paths\"]\n",
    "C_paths_B_og = B_res[\"C_paths\"]\n",
    "#(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.857\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n",
      "1.414213562444884\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "Cstar_og = fluid_sol['Cost']\n",
    "print(Cstar_og)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "C_paths_B_og = np.transpose( np.asarray( C_paths_B_og ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 38)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_paths_B_og.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b70dac7898>]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = -20\n",
    "plt.plot(C_paths_B_og[C_paths_B_og[:,idx] > 0,idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "145.05939504426988 335.810135157606 0.001286347369895206\n"
     ]
    }
   ],
   "source": [
    "locs = C_paths_B_og[:,idx] > 0\n",
    "var = np.var(C_paths_B_og[locs,idx])\n",
    "mu = np.mean(C_paths_B_og[locs,idx])\n",
    "print(var, mu, var/(mu**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "2.0\n",
      "3.0\n",
      "4.0\n",
      "5.0\n",
      "8.0\n",
      "10.0\n",
      "12.0\n",
      "15.0\n",
      "18.0\n",
      "20.0\n",
      "30.0\n",
      "40.0\n",
      "50.0\n",
      "60.0\n",
      "100.0\n",
      "135.0\n",
      "150.0\n",
      "200.0\n",
      "250.0\n",
      "300.0\n",
      "325.0\n",
      "350.0\n",
      "400.0\n",
      "450.0\n",
      "475.0\n",
      "500.0\n",
      "550.0\n",
      "600.0\n",
      "650.0\n",
      "700.0\n",
      "1200.0\n",
      "1400.0\n",
      "1600.0\n",
      "1800.0\n",
      "2000.0\n",
      "2200.0\n",
      "2400.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Variances')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts = C_paths_B_og.shape[1]\n",
    "vals_og = []\n",
    "vars_og = []\n",
    "for i in range(counts):\n",
    "    queue_size = max(Q_paths_B_og[:][i])\n",
    "    print(queue_size)\n",
    "        \n",
    "    vals_og = vals_og + [np.mean(C_paths_B_og[C_paths_B_og[:,i] > 0,i])/queue_size]\n",
    "    \n",
    "    vars_og = vars_og + [np.var(C_paths_B_og[C_paths_B_og[:,i] > 0,i])/(queue_size**2)]\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(vals_og,'x')\n",
    "plt.title('Means')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(vars_og,'x')\n",
    "plt.title('Variances')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([345.1983887 , 331.72894007, 335.12411756, 346.34002109,\n",
       "       329.82013838, 346.60593613, 331.33870721, 333.7901979 ,\n",
       "       338.53491503, 342.87368237, 339.5356905 , 338.89777891,\n",
       "       322.04725251, 341.49588858, 325.10517491, 332.19039716,\n",
       "       340.34841224, 359.30386272, 356.72931593, 333.64062068,\n",
       "       327.52600789, 332.41907024, 319.31495205, 341.17775497,\n",
       "       321.27761667, 318.90653572, 348.66550355, 334.8921218 ,\n",
       "       340.7120983 , 335.85090105, 336.88536225, 318.90653572,\n",
       "       334.24005577, 336.61355722, 334.60456401, 337.89198167,\n",
       "       321.41098528, 350.34591174, 334.19614768, 346.93073587,\n",
       "       341.90512709])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_paths_B_og[C_paths_B_og[:,i] > 0,idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n",
      "8.0\n",
      "12.0\n",
      "15.0\n",
      "18.0\n",
      "20.0\n",
      "21.0\n",
      "24.0\n",
      "30.0\n",
      "40.0\n",
      "50.0\n",
      "75.0\n",
      "90.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Variances')"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts = C_paths_B.shape[1]\n",
    "vals = []\n",
    "vars = []\n",
    "for i in range(counts):\n",
    "    queue_size = max(Q_paths_B[:,i])\n",
    "    print(queue_size)\n",
    "    \n",
    "    vals = vals + [np.mean(C_paths_B[C_paths_B[:,i] > 0,i])/queue_size]\n",
    "    \n",
    "    vars = vars + [np.var(C_paths_B[C_paths_B[:,i] > 0,i])/(queue_size**2)]\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(vals,'x')\n",
    "plt.title('Means')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(vars,'x')\n",
    "plt.title('Variances')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.     ,  9.     , 12.99968, 15.9995 , 18.9992 , 21.     ,\n",
       "       21.99962, 24.99872, 30.998  , 41.     , 51.     , 75.9875 ,\n",
       "       90.992  ])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.5    ,  4.5    ,  6.49984,  7.99975,  9.4996 , 10.5    ,\n",
       "       10.99981, 12.49936, 15.499  , 20.5    , 25.5    , 37.99375,\n",
       "       45.496  ])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.average(Q_paths_B,axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 13)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_paths_B = np.asarray(Q_paths_B)\n",
    "Q_paths_B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "2.0\n",
      "3.0\n",
      "4.0\n",
      "5.0\n",
      "8.0\n",
      "10.0\n",
      "12.0\n",
      "15.0\n",
      "18.0\n",
      "20.0\n",
      "30.0\n",
      "40.0\n",
      "50.0\n",
      "60.0\n",
      "100.0\n",
      "135.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b6b7e49f60>]"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counts = C_paths_B_og.shape[1]\n",
    "vals_og = []\n",
    "vars_og = []\n",
    "for i in range(counts):\n",
    "    queue_size = max(Q_paths_B_og[:][i])\n",
    "    print(queue_size)\n",
    "    if queue_size > 100:\n",
    "        break\n",
    "        \n",
    "    vals_og = vals_og + [np.mean(C_paths_B_og[C_paths_B_og[:,i] > 0,i])/queue_size]\n",
    "    \n",
    "    vars_og = vars_og + [np.var(C_paths_B_og[C_paths_B_og[:,i] > 0,i])/(queue_size**2)]\n",
    "# plt.figure(figsize=(10,5))\n",
    "# plt.subplot(1,2,1)\n",
    "# plt.plot(vals_og,'x')\n",
    "# plt.title('Means')\n",
    "# plt.subplot(1,2,2)\n",
    "# plt.plot(vars_og,'x')\n",
    "# plt.title('Variances')\n",
    "plt.plot(np.log(vars_og),'x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b70c95b2e8>]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(vars),'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b6b7f5e780>]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(vals),'x')\n",
    "plt.plot(np.log(vals_og),'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3.8552543385903726,\n",
       " 3.4506327023420864,\n",
       " 3.202307524706063,\n",
       " 3.026906141568854,\n",
       " 2.9029078243367237,\n",
       " 2.6453190133666187,\n",
       " 2.525865859303159,\n",
       " 2.4463556177766304,\n",
       " 2.3410935396679986,\n",
       " 2.269375231235819,\n",
       " 2.2333818140651323,\n",
       " 2.0844576874910405,\n",
       " 1.9962485047431398,\n",
       " 1.9363727336899803,\n",
       " 1.88626051284473,\n",
       " 1.7824935149534915]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals_og"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        5.09901951, 5.38516481, 5.83095189, 6.40312424, 7.07106781],\n",
       "       [2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        5.38516481, 5.09901951, 5.38516481, 5.83095189, 6.40312424],\n",
       "       [3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        5.83095189, 5.38516481, 5.09901951, 5.38516481, 5.83095189],\n",
       "       [4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        6.40312424, 5.83095189, 5.38516481, 5.09901951, 5.38516481],\n",
       "       [5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        7.07106781, 6.40312424, 5.83095189, 5.38516481, 5.09901951],\n",
       "       [2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424],\n",
       "       [2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425],\n",
       "       [3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ],\n",
       "       [4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595],\n",
       "       [5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563],\n",
       "       [3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189],\n",
       "       [3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ],\n",
       "       [4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069],\n",
       "       [5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128],\n",
       "       [5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766],\n",
       "       [4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481],\n",
       "       [4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595],\n",
       "       [5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128],\n",
       "       [5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712],\n",
       "       [6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798],\n",
       "       [5.09901951, 5.38516481, 5.83095189, 6.40312424, 7.07106781,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951],\n",
       "       [5.38516481, 5.09901951, 5.38516481, 5.83095189, 6.40312424,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563],\n",
       "       [5.83095189, 5.38516481, 5.09901951, 5.38516481, 5.83095189,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766],\n",
       "       [6.40312424, 5.83095189, 5.38516481, 5.09901951, 5.38516481,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798],\n",
       "       [7.07106781, 6.40312424, 5.83095189, 5.38516481, 5.09901951,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356]])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = \"../longest_spatial_uniform_25_all_good.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W_og, pmf_cust_og, pmf_serv_og = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        5.09901951, 5.38516481, 5.83095189, 6.40312424, 7.07106781],\n",
       "       [2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        5.38516481, 5.09901951, 5.38516481, 5.83095189, 6.40312424],\n",
       "       [3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        5.83095189, 5.38516481, 5.09901951, 5.38516481, 5.83095189],\n",
       "       [4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        6.40312424, 5.83095189, 5.38516481, 5.09901951, 5.38516481],\n",
       "       [5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        7.07106781, 6.40312424, 5.83095189, 5.38516481, 5.09901951],\n",
       "       [2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424],\n",
       "       [2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425],\n",
       "       [3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ],\n",
       "       [4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595],\n",
       "       [5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563],\n",
       "       [3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189],\n",
       "       [3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ],\n",
       "       [4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069],\n",
       "       [5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128],\n",
       "       [5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766],\n",
       "       [4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481],\n",
       "       [4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595],\n",
       "       [5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128],\n",
       "       [5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712],\n",
       "       [6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798],\n",
       "       [5.09901951, 5.38516481, 5.83095189, 6.40312424, 7.07106781,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951],\n",
       "       [5.38516481, 5.09901951, 5.38516481, 5.83095189, 6.40312424,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563],\n",
       "       [5.83095189, 5.38516481, 5.09901951, 5.38516481, 5.83095189,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766],\n",
       "       [6.40312424, 5.83095189, 5.38516481, 5.09901951, 5.38516481,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798],\n",
       "       [7.07106781, 6.40312424, 5.83095189, 5.38516481, 5.09901951,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W_og"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        5.09901951, 5.38516481, 5.83095189, 6.40312424, 7.07106781],\n",
       "       [2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        5.38516481, 5.09901951, 5.38516481, 5.83095189, 6.40312424],\n",
       "       [3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        5.83095189, 5.38516481, 5.09901951, 5.38516481, 5.83095189],\n",
       "       [4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        6.40312424, 5.83095189, 5.38516481, 5.09901951, 5.38516481],\n",
       "       [5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        7.07106781, 6.40312424, 5.83095189, 5.38516481, 5.09901951],\n",
       "       [2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424],\n",
       "       [2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425],\n",
       "       [3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ],\n",
       "       [4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595],\n",
       "       [5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563],\n",
       "       [3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189],\n",
       "       [3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ],\n",
       "       [4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069],\n",
       "       [5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128],\n",
       "       [5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766],\n",
       "       [4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481],\n",
       "       [4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595],\n",
       "       [5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128],\n",
       "       [5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712],\n",
       "       [6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798],\n",
       "       [5.09901951, 5.38516481, 5.83095189, 6.40312424, 7.07106781,\n",
       "        4.12310563, 4.47213595, 5.        , 5.65685425, 6.40312424,\n",
       "        3.16227766, 3.60555128, 4.24264069, 5.        , 5.83095189,\n",
       "        2.23606798, 2.82842712, 3.60555128, 4.47213595, 5.38516481,\n",
       "        1.41421356, 2.23606798, 3.16227766, 4.12310563, 5.09901951],\n",
       "       [5.38516481, 5.09901951, 5.38516481, 5.83095189, 6.40312424,\n",
       "        4.47213595, 4.12310563, 4.47213595, 5.        , 5.65685425,\n",
       "        3.60555128, 3.16227766, 3.60555128, 4.24264069, 5.        ,\n",
       "        2.82842712, 2.23606798, 2.82842712, 3.60555128, 4.47213595,\n",
       "        2.23606798, 1.41421356, 2.23606798, 3.16227766, 4.12310563],\n",
       "       [5.83095189, 5.38516481, 5.09901951, 5.38516481, 5.83095189,\n",
       "        5.        , 4.47213595, 4.12310563, 4.47213595, 5.        ,\n",
       "        4.24264069, 3.60555128, 3.16227766, 3.60555128, 4.24264069,\n",
       "        3.60555128, 2.82842712, 2.23606798, 2.82842712, 3.60555128,\n",
       "        3.16227766, 2.23606798, 1.41421356, 2.23606798, 3.16227766],\n",
       "       [6.40312424, 5.83095189, 5.38516481, 5.09901951, 5.38516481,\n",
       "        5.65685425, 5.        , 4.47213595, 4.12310563, 4.47213595,\n",
       "        5.        , 4.24264069, 3.60555128, 3.16227766, 3.60555128,\n",
       "        4.47213595, 3.60555128, 2.82842712, 2.23606798, 2.82842712,\n",
       "        4.12310563, 3.16227766, 2.23606798, 1.41421356, 2.23606798],\n",
       "       [7.07106781, 6.40312424, 5.83095189, 5.38516481, 5.09901951,\n",
       "        6.40312424, 5.65685425, 5.        , 4.47213595, 4.12310563,\n",
       "        5.83095189, 5.        , 4.24264069, 3.60555128, 3.16227766,\n",
       "        5.38516481, 4.47213595, 3.60555128, 2.82842712, 2.23606798,\n",
       "        5.09901951, 4.12310563, 3.16227766, 2.23606798, 1.41421356]])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.310811791889462 1.6038161458646023 0.08630509937220913\n"
     ]
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.856796996469445 1.5251169280242287 0.1025296750666597\n"
     ]
    }
   ],
   "source": [
    "cost_pmf = np.outer(pmf_cust_og,pmf_serv_og).ravel()\n",
    "weights = W.ravel()\n",
    "\n",
    "mean_cost = sum(cost_pmf*weights)\n",
    "variance_cost = sum(cost_pmf*(weights**2)) - mean_cost**2\n",
    "print(mean_cost,variance_cost, variance_cost/(mean_cost**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost M [4.3129367  3.74755445 3.66059751 3.51857837 3.41587701 3.36446695\n",
      " 3.44221268 3.33634893 3.32142489 3.2840127  3.27839178 3.26805496\n",
      " 3.26115498 3.25691954]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_rg_mwm.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, d, d, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "#average_cost_B = average_new\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M = np.average(Q_paths_M,axis = 0)\n",
    "#print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric_mw-new-jan.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, d,d,d, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B = average_new\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M_cons = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M_cons = np.average(Q_paths_M,axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.02433084  2.55877145] [0.12844861]\n",
      "[-1.24669367  0.8565793 ] [1.92073801]\n",
      "[-1.20359452  0.42830585] [0.50858386]\n",
      "[-0.84588093  0.46085391] [0.07626542]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1d1c27e7588>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM = np.log(average_cost_M[1:]-Cstar)\n",
    "yM = np.log(average_queue_M[1:])\n",
    "xM2 = np.log(average_cost_M_sc[1:10]-Cstar)\n",
    "yM2 = np.log(average_queue_M_sc[1:10])\n",
    "xB2 = np.log(average_cost_B-Cstar)\n",
    "yB2 = np.log(average_queue_B)\n",
    "xM_c = np.log(average_cost_M_cons[1:9]-Cstar)\n",
    "yM_c = np.log(average_queue_M_cons[1:9])\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM, yM, 1, full=True)\n",
    "print(p,res)\n",
    "plt.plot(xM, yM,'ro',markersize = 8)\n",
    "predict_M = np.poly1d(p)\n",
    "x  = np.array(xM)\n",
    "y = predict_M(x)\n",
    "plt.plot(x, y,'r-.')\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM_c, yM_c, 1, full=True)\n",
    "print(p,res)\n",
    "plt.plot(xM_c, yM_c,'bo',markersize = 8)\n",
    "predict_c = np.poly1d(p)\n",
    "x  = np.array(xM_c)\n",
    "y = predict_c(x)\n",
    "plt.plot(x, y,'b-.')\n",
    "\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Iterative Scaled\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Iterative MW\", str(round(predict_M[1],2))+\"x + \" + str(round(predict_M[0],2)),\n",
    "             \"Constrained MW\", str(round(predict_c[1],2))+\"x + \" + str(round(predict_c[0],2)), \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original was 1.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric_maxweight_new.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, d,d,d, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B = average_new\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M_OLD = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M_OLD = np.average(Q_paths_M,axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.02433084  2.55877145] [0.12844861]\n",
      "[-2.85208161 -4.67092336] [0.10646328]\n",
      "[-1.20359452  0.42830585] [0.50858386]\n",
      "[-1.51240752  0.10215233] [0.29445767]\n",
      "[-0.84588093  0.46085391] [0.07626542]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1d1b0b3bb70>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM = np.log(average_cost_M[:]-Cstar)\n",
    "yM = np.log(average_queue_M[9:])\n",
    "xM2 = np.log(average_cost_M_sc[1:10]-Cstar)\n",
    "yM2 = np.log(average_queue_M_sc[1:10])\n",
    "xB2 = np.log(average_cost_B-Cstar)\n",
    "yB2 = np.log(average_queue_B)\n",
    "xM_c = np.log(average_cost_M_cons[1:9]-Cstar)\n",
    "yM_c = np.log(average_queue_M_cons[1:9])\n",
    "xM_OLD = np.log(average_cost_M_OLD-Cstar)\n",
    "yM_OLD = np.log(average_queue_M_OLD)\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM, yM, 1, full=True)\n",
    "print(p,res)\n",
    "plt.plot(xM, yM,'ro',markersize = 8)\n",
    "predict_M = np.poly1d(p)\n",
    "x  = np.array(xM)\n",
    "y = predict_M(x)\n",
    "plt.plot(x, y,'r-.')\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM_c, yM_c, 1, full=True)\n",
    "print(p,res)\n",
    "plt.plot(xM_c, yM_c,'bo',markersize = 8)\n",
    "predict_c = np.poly1d(p)\n",
    "x  = np.array(xM_c)\n",
    "y = predict_c(x)\n",
    "plt.plot(x, y,'b-.')\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM_OLD, yM_OLD, 1, full=True)\n",
    "print(p,res)\n",
    "plt.plot(xM_OLD, yM_OLD,'yo',markersize = 8)\n",
    "predict_OLD = np.poly1d(p)\n",
    "x  = np.array(xM_OLD)\n",
    "y = predict_OLD(x)\n",
    "plt.plot(x, y,'y-.')\n",
    "\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Iterative Scaled\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Iterative MW\", str(round(predict_M[1],2))+\"x + \" + str(round(predict_M[0],2)),\n",
    "             \"Constrained MW\", str(round(predict_c[1],2))+\"x + \" + str(round(predict_c[0],2)), \"Maxweight\", str(round(predict_OLD[1],2))+\"x + \" + str(round(predict_OLD[0],2)),\n",
    "             \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}