inference/variational_inference.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import math, random\n",
    "all_data  = pd.read_csv(\"../data/sensor_data_600.txt\", delimiter=\" \", header=None, names = (\"date\",\"time\",\"ir\",\"z\"))#lidarのセンサ値は「z」に\n",
    "data = all_data.sample(3000).sort_values(by=\"z\").reset_index()  #1000個だけサンプリングしてインデックスを振り直す\n",
    "data = pd.DataFrame(data[\"z\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "##負担率の初期化## \n",
    "\n",
    "K = 3 #クラスタ数\n",
    "n = int(math.ceil(len(data)/K)) #クラスタあたりのセンサ値の数\n",
    "for k in range(K):\n",
    "    data[k] = [1.0 if k == int(i/n) else 0.0 for i,d in data.iterrows()] #データをK個に分けて、一つのr_{i,k}を1に。他を0に。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_parameters(ds, k, mu_avg=600, zeta=1, alpha=1, beta=1, tau=1): \n",
    "    R = sum([d[k] for _, d in ds.iterrows()])\n",
    "    S = sum([d[k]*d[\"z\"] for _, d in ds.iterrows()])\n",
    "    T = sum([d[k]*(d[\"z\"]**2) for _, d in ds.iterrows()])\n",
    "    \n",
    "    hat = {}\n",
    "\n",
    "    hat[\"tau\"] = R + tau\n",
    "    hat[\"zeta\"] = R + zeta\n",
    "    hat[\"mu_avg\"] = (S + zeta*mu_avg)/hat[\"zeta\"]\n",
    "    hat[\"alpha\"] = R/2 + alpha\n",
    "    hat[\"beta\"] = (T + zeta*(mu_avg**2) - hat[\"zeta\"]*(hat[\"mu_avg\"]**2))/2 + beta\n",
    "    \n",
    "    hat[\"z_std\"] = math.sqrt(hat[\"beta\"]/hat[\"alpha\"])\n",
    "    \n",
    "    return pd.DataFrame(hat, index=[k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm, dirichlet\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def draw(ps):\n",
    "    pi = dirichlet([ps[\"tau\"][k] for k in range(K)]).rvs()[0]\n",
    "    pdfs = [ norm(loc=ps[\"mu_avg\"][k], scale=ps[\"z_std\"][k]) for k in range(K) ]\n",
    "\n",
    "    xs = np.arange(600,650,0.5)\n",
    "\n",
    "    ##p(z)の描画##\n",
    "    ys = [ sum([pdfs[k].pdf(x)*pi[k] for k in range(K)])*len(data) for x in xs] #pdfを足してデータ数をかける\n",
    "    plt.plot(xs, ys, color=\"red\")\n",
    "\n",
    "    ##各ガウス分布の描画##\n",
    "    for k in range(K):\n",
    "        ys = [pdfs[k].pdf(x)*pi[k]*len(data) for x in xs]\n",
    "        plt.plot(xs, ys, color=\"blue\")\n",
    "\n",
    "    ##元のデータのヒストグラムの描画##\n",
    "    data[\"z\"].hist(bins = max(data[\"z\"]) - min(data[\"z\"]), align='left', alpha=0.4, color=\"gray\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import digamma \n",
    "\n",
    "def responsibility(z, K, ps):\n",
    "    tau_sum = sum([ps[\"tau\"][k] for k in range(K)])\n",
    "    r = {}\n",
    "    for k in range(K):\n",
    "        log_rho = (digamma(ps[\"alpha\"][k]) - math.log(ps[\"beta\"][k]))/2 \\\n",
    "                            - (1/ps[\"zeta\"][k] + ((ps[\"mu_avg\"][k] - z)**2)*ps[\"alpha\"][k]/ps[\"beta\"][k])/2 \\\n",
    "                            + digamma(ps[\"tau\"][k]) - digamma(tau_sum)\n",
    "                \n",
    "        r[k] = math.exp(log_rho)\n",
    "       \n",
    "    w = sum([ r[k] for k in range(K) ]) #正規化\n",
    "    for k in range(K): r[k] /= w\n",
    "    \n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_step(ds):\n",
    "    ##パラメータの更新##\n",
    "    params = pd.concat([update_parameters(ds, k) for k in range(K)]) \n",
    "\n",
    "    ##負担率の更新##\n",
    "    rs = [responsibility(d[\"z\"], K, params) for _, d in ds.iterrows() ]\n",
    "    for k in range(K):\n",
    "        ds[k] = [rs[i][k] for i,_ in data.iterrows()]\n",
    "        \n",
    "    return ds, params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           tau         zeta      mu_avg       alpha          beta     z_std\n",
       "0  1050.920697  1050.920697  620.737643  525.960349   5453.675418  3.220091\n",
       "1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
       "2  1951.079303  1951.079303  630.330588  976.039651  17314.305109  4.211810"
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       "      <th>beta</th>\n",
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      ],
      "text/plain": [
       "         tau       zeta      mu_avg     alpha          beta     z_std\n",
       "0  1050.9208  1050.9208  620.737643  525.9604   5453.676385  3.220091\n",
       "1     1.0000     1.0000  600.000000    1.0000      1.000000  1.000000\n",
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       "      <th>tau</th>\n",
       "      <th>zeta</th>\n",
       "      <th>mu_avg</th>\n",
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       "      <th>beta</th>\n",
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      "text/plain": [
       "           tau         zeta      mu_avg       alpha          beta     z_std\n",
       "0  1050.920861  1050.920861  620.737643  525.960431   5453.677035  3.220091\n",
       "1     1.000000     1.000000  600.000000    1.000000      1.000000  1.000000\n",
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     "metadata": {},
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   ],
   "source": [
    "params_history = {} \n",
    "for t in range(1, 10000):\n",
    "    data, params = one_step(data)\n",
    "    if t%10 ==0:              #10回ごとにパラメータを記録\n",
    "        params_history[t] = params\n",
    "        display(params)\n",
    "        \n",
    "        if len(params_history) < 2:\n",
    "            continue\n",
    "           \n",
    "        if all([ abs(params_history[t-10][\"tau\"][k] - params_history[t][\"tau\"][k]) < 10e-5 for k in range(K)]):\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4YecPOuH2mkz0WutbtNYdtdZ+WusuWuv3tda3aa0Haa0Ha62v0lrn1ln/Wa11T611H631D44NX7RK//ynuWH6t99CWJjVm+VfcQUHnn+e4F276D19OoYCO0zKnZsLDzwAY8Zw8vrrz3t569YQysoMJCcX2n4sGyVcWIMJP3bMkWaWrY30jBUeJejIEfMV9B//CLGxzd6+IDWVfa++SuDhw/SePh3ffBvnbL3vPigvN49SWc+N3oyMMHx8NAkJJbYdxw76XhNNIOVkrHbAPQrh1iTRC4/S/aOPICjoN2PINFfxqFHmZJ+dbU72p061bEczZ8K8eeZvGH361LtKeno4ffuWERbm+hpM/1BfRkVsY82hXq4ORTiZJHrh1jIzM88+dnzxBe1XrCD3xhvJzM62ab/FSUnsfe01/HNy6HP33QQeONC8HXz5JUyfbr4Z/NBD9a5SVubDtm0hJCXZ8X6AjUYPOs6Oqj4U7Djt6lCEE0miFx6j09tvUxUSgvG22+yyv5LERPa+9RaG8nL63nknEatXW7fhokVw663mIQ7mzGnwZnBWVijV1YoRI9xnjJnhl/sDsGWe6+8ZCOeRRC88QtCuXUSuXs2B66+nOjzcbvstHTyYnR9/TEXXrvR88EE6vf02PiUN1KebTPD++3D99TB4MHz/vXnS7wZs3BiOv38NQ4a4vn6+VuyFUUSrPDakR7g6FOFEkuiFR4ieP5+agAAOX3653fdd1aEDu997j/zLLqPj++8z6Ior6PTWW7B/Pxw7Zp4xZO5cc3POe+4xDz28eDFENJ4sN24MY/DgEgID3Wd2Jx+DYkyH7azOHYiurnF1OMJJJNELt6fOnKHtkiUUpKRgctD4JzowkENPP83OWbMoTkqiw4cfQq9e0KWLeRD5yZPNnbLmzYO1a6Fdu0b3V1BgYM+eYBIT3afaptbIxEJydQd2fLvH1aEIJ5EZpoTbi1i1Ct+iIvKcMDVTWf/+HHjxRQIOHWJgfj7U1Jh7vrZvD1dd1XTnLIuMDHP7/qQk90v0Q64Jhe9hxRe5DLi+r6vDEU4giV64vagFCzjTvj3FI0ZAXp5TjlkZF2eui2+h9PRwQkKq6d+/1H5B2Un7IRF0M2STtj6A+1wdjHAKSfTCrfnm5RGxfj3Hp04Fg3kOG61h+/ZgTp8Gf38ICTFXmzdjYEqHy8gIY/jwYmu/ADjd6E57WH50CDWmGnx83egPJxxC3mHh1qIWLUJVV3PKchNWa3j77U7ccUc/Lr7YPDpxYiLccou5UYw7OH7cjyNHAt2qWeW5EhJKyNPR7Ji/19WhCCeQRC/cl9ZELVhAyeDBVMbFoTV89FEfPvigI1dfncfq1bB8OTz1FHz1Fdx1l7lK3dUyM8318+54I7bWwCvNMaZ9kdvEmsIbuOkXSyGAzEyCDhzg8JNPojW89lpn5szpwOTJJ3jkkWxGjIgG4MILwc8P/v53CAw0D0/vypEis7LCCA830atXueuCaEL7IRHE+h6VevpWQhK9cF/z5qENBk5PmMDy5ZF8+mkHrrjiEI8+egqlfjs708SJcPBgJ959tyPBwTHcdpuxkR07VlZWKEOHlrjVPYP6pMQdYuH+vlJP3wrIuyvc1/ffUzxsGJXB4bz9dmd69Chn2rQdDV6t//GPOSQnF/LRRx0oKXHNqX3ihB/Z2YEMH+6+1Ta1UlKU1NO3EtZMPPKBUuqEUmpbnWUvKaV2KaW2KqW+UUpFWpbHKaXKlVKbLY93HBm88GIHD8K2bRSOHcsPP0Rx+HAg06fn1Da8qZdSMH16DoWFvsye3d55sdaRlWXu0OUOwxI3JeV28zDPUk/v/aypuvkIeAOYVWfZj8DjWmuTUuoF4HHgUctr+7XWQ+0apWh9vv8egJPJKbz7l47061dKamoBJ040vln//mWMG1fAZ5/FcNNNJ20aHrihibsbm1Q7MzOMkJBqevd2/1mc4sZ0kXr6VsKaGaZWAfnnLFuqta5tzPYz5knAhbCf776Dfv34KmMoOTkB/PGPOVbfYJ02LYfiYl8+/9z5V/VZWWEMHVrS6DcPd5ISd4iVufHUmNyguZJwGHtUZN4F1J0ysLtSapNSaqVSaqwd9i9am8JCWLmSsonX8/77HRg6tJjRo60f071v33JSU0/z+ecxFBY6L+Pm5fly+HAgCQnuXz9f62w9/Xf7XB2KcCCbWt0opZ4ETMBnlkW5QDet9SmlVALwrVJqgNb6vP9SpdQ0YBpATEwMaWlpLY6jpKTEpu09kTeXud1PPzHAZOK53FTy8vx56KEsTpwwf6k0mUwYjU23qJk8uYwVK8bywQfB/O539k1iDf3d09LMwyfHxR3GaLTfeO/Wlrm50tLSCBtk/lD66rUt5LXNsfsxWsqbz+/GOKrcLU70Sqk7gCuACVprDaC1rgQqLc8zlVL7gd5Axrnba61nAjMBEhMTdUpKSktDIS0tDVu290ReXeZ334XoaFZmpxIbW8FFF/mhVAwARqORmJiYJncREwMjRxaxYkUsf/1rsV3b1TdUR//WWycIDq4mOTkQX99Aux3P2jI3V0JCAno8dH3wGLsPdOZ/U5LtfoyW8urzuxGOKneLqm6UUpcBjwBXaa3L6ixvp5QyWJ73AOKBZs7RJlq1qipYtIiD4+9g9RrF5ZefanGSnjTpFDk5AWzZEmLfGBuQmRnGkCElbju+zbkyMzPJyspkZMxuVh3rScbGjAZvQAvP1uQpqZT6AkgBopVSR4F/YG5lEwD8qMz/hT9rracD44D/VUpVATXAdK11fr07FqI+a9dCQQGf+t0JwMSJLT99UlMLeO65ahYtimLoUPuNIllfMiwoMHDgwFCb4nWVYUOKmZMTg3HDZjqMjnZ1OMIBmkz0Wutb6ln8fgPrzgXm2hqUaMWWLEEbfJmV3peUFOjY8UyLdxUcXENqagHLlrXh4Yez8fd33ExPmzaZx44ZNsxzbsTWGnhpEPwA2xaX0WG0q6MRjiA9Y4V7Wb6cDQPuYt8BH6ZOtX13kyblU1Tky9q1jp0jNSsrlICAGgYMcP/28+fqlNyWaJXHps1hrg5FOIgkeuEWMjMz2bxiBTojg7dNtxAQUEOPHpts3u+IEUVERVWxaFFbO0TZsE2bQhk0qAQ/P/eZH9ZaykcxKnonPx/v7epQhINIohduIywjgzPaj/mHRpOSUkBoqO2deHx94dJL81mzJsJhbepLSnzYsyeYYcPcf9iDhiQMzOdwdTdObTnt6lCEA0iiF24jbONGFvpfQ2FZAJdffspu+5006RRVVT4sW9bGbvusa+vWUGpqlEcn+kEX+QOwfZHn3WMQTZNEL9xG+IYNzI2cSliYiaQk63vCNqVPn3Li4spZvtwxiX7TplAMBs2gQe43P6y1uqZGEU4hmzKd0xRVOJckeuEW/I4fx/9INkuKx5GcXGTXtuhKwbhxhWRlhTpk+OKsrDD69SslKMhzx4sx+BsY2WYH6Ud7uDoU4QCS6IVbCN+4kY2M4FR5GGPHFth9/2PGFGIy+bBhQ7hd91tRodixw7Pr52sl9jvJblMvTmxrYohQ4XEk0Qu3EJaezvzAGzAYdLMGMLPW4MElhIWZWLPGvs0st28PoarKh+HDPT/RD0o136xe9aEMcOZtJNEL19Oa8PR0Fvhdw5AhJUREtHwM+Yb4+kJychFr10bYdQLxTZtCUUozZIjnJ/rul7UjiDJWL295JzXhniTRC9fbsYPjp4L4pbgXY8bYb9THc40ZU0h+vh87dgTbbZ+bNoXRq1c54eH2/3ByNr8gA4lhO1i1p4OrQxF2JoleuN7y5SzkcgDGjnVcoh89uhAfH2236huTCbZuDfGK+vlaI+Jz2VLem8LD9r9PIlzHQ8bZE15t5Uq+C5hO5+hK4uIqHHaYyMhqBg0qZc2aCKZPt32e1F27gikvN3hVoh88DnSWD2s/3MOkGUm/ea0lUysK9yBX9MK1tKZs5UZWVI1j3LgCu44bX5+xYwvYtSuEEyf8bN7X5s3micA9cSCzhvS6Ihpfqli12PPG7BENk0QvXGvnTn46NZiKmgCH1s/Xqj2GPQY5y8wMo1u3CqKjTU2v7CECI/1JDN3N6h2OHRtIOJckeuFaq1axmMsICjQ5pYliz54VdOxYaXM9fU2N+Yrem6ptao0bkMfG4r6U5clVvbewKtErpT5QSp1QSm2rs6ytUupHpdRey882luVKKfUfpdQ+pdRWpdRwRwUvvMDKlSwzXMbwBOeM/KgUjBpVREZGGCYbLsT37w+iuNiX4cO9p9qm1rjLQqjCnw2zdrs6FGEn1l7RfwRcds6yx4DlWut4YLnld4CJmKcQjMc8+ffbtocpvJLWHF2xl93VvUhKcl7CTEoqprTUwM6dLR/XJSvLXD/vDR2lznXBnb1R1LD6e2l54y2sSvRa61XAuXOkXQ18bHn+MXBNneWztNnPQKRSqqM9ghVeZv9+lhsHADg10Scmmo+Vnt7yiTY2bQqlQ4dKm2bAcleRsREMCdrDqi32HS5CuI4tdfQxWuvaNmrHgdpp6jsD2XXWO2pZJsRvrVrFMi6ifZSJnj3LnXbYNm1M9O5dRnp6yxKZ1uaOUt5YP19rbG8j60/3parU+z7IWiO7tKPXWmulVLMqWJVS0zBX7RATE0NaWlqLj19SUmLT9p7IG8rc58uvWKY+YuCQU5w8abRqG5PJhNFo3bqNGTCgDd9/H8vhwycJDGzemAjHjoVw6pQfvXrl2CWWptirzNZKS0sjrvcJyraE8PmMOcRebp4wvKys/puzjjgPveH8bglHlduWRG9USnXUWudaqmZqh7w7BnSts14Xy7Lf0FrPBGYCJCYm6pSUlBYHkpaWhi3beyJvKPP2Kf/iuO7As1PMH/bWMBqNVq/bmNTUar75xkBubg9GjWpetdH69VEAjB+v7BJLU+xVZmslJCTQL/okD30Nxu3R3P5SCuDcDlPecH63hKPKbUvVzXfA7ZbntwPz6yyfaml9MwoorFPFI4TZkSMsz+kLwEUXOf/ww4aV4Otb06Lqm6ysMNq2rSI2ttIBkbmHmIHt6ON/gFUZ9hsXSLiOtc0rvwDWA32UUkeVUncDzwMXK6X2AhdZfgdYBBwA9gHvAn+ye9TC81nq5+O7VdCtm/MPHxRUw+DBpS26Ibtpk7n9vKN78bpaSs+jrD7Zh+pK7+kQ1lpZ2+rmFq11R621n9a6i9b6fa31Ka31BK11vNb6Iq11vmVdrbW+V2vdU2s9SGud4dgiCE+SmZlJZmYmOXPmk0YKgxMLG6wScLSkpCJ27w6moMD6ScNzc/3JzQ3wqmEPGjJ+gi9FRLD5qz2uDkXYSHrGCpfYna4pJpykka5ruTJiRDFaKzIyrL+qr20/780tbmqNv9M8reDKr2XGKU8niV44naGggNW5/VHUnG3T7goDBpQSElLdrHr6rKwwwsNNxMc7rzmoq3Qa3oF4v4OkpQe5OhRhI0n0wulCN28mjRT6dct3yGxS1vL1heHDi9m40for+owMc/t5n1bynzO+RzarT/Sh+oznT6zSmrWS01W4E7+MbawjmWHJru+Mk5BQTHZ2oFXDFh8/7sexYwEu/RbibONTDRToSH6Zt9fVoQgbSKIXTrdzfQ2VBJI40vWjI9Ym7czMpq/qa9dJSGhFid5ST5/2pfM6bAn7k0QvnMqnvJz1R3rio2oYOtT1NzTj48sJCzORmRna5LqZmeb6+V69vL9+vlbXpI708D3Myg0Brg5F2EASvXCqkF9+YaUeR/8uJwkLc329r8FgbkFj7RX98OHFraZ+vtb47tmsOt6bGlPzhooQ7qOVnbLC1Qwbt7Ge0W5RP1+rtp7eaGy4nr62fj4hwfXfQpwtJQXydVuOpuW5OhTRQpLohVPtXFfDGQJIGO24ScCby5p6+tq29q2pfr7W+NvjANi61HuHfPB2kuiF81RV8fO+rm5TP18rPr6c8HBTo4k+MzOMiIjWVT9fK/aCLsT5ZpOxNcrVoYgWkkQvnGfTJlZVj2Fg5+OEhrpPfa+Pj7k9fWM9ZLOyWmf9fK0Lexxibd5AaU/voVrpaStcoWz5en5mFMNGuV8VQEJCCceOBXD8+Pn19Lm5/pb6+dZXbVNrwkU+nKYNR5ZkjwMlAAAfPklEQVRJPb0nkkQvnGb9glNU4c+wMe43GmJtEq+v+qa26WVrvBFbK/X3vQDYvKTKxZGIlpBEL5yjpoYVWREYVLVb1c/X6tWrnIgIU73VNxs3hhMR4dzpDt1Nx6Ex9PPbw4bt7V0dimgBSfTCOXbsIK1iJAM75bpV/Xyt2nr6c6/otYaNG8NISipqtfXztUbHHmBdwWBMZe73jUw0rpWfusJZSpetJ50kEka671VxQkIxOTkB5Ob6n112+HAAJ074k5TUeuvnayWOqaSMEPYtPOnqUEQztTjRK6X6KKU213kUKaX+qpSaoZQ6Vmf5JHsGLDzTuvknqcKfoeObNYe8U/3anv7X4RA2bDAPYZyUVOSSmNzJgGvb4kM1m5a573so6tfiRK+13q21Hqq1HgokAGXAN5aXX619TWu9yB6BCg+mNWkZoeb6+WGlro6mQT16VJxXT5+eHk7nzpV07uw+PXldJaRzMEMDd/Lz7k6uDkU0k72qbiYA+7XWh+20P+FNDhxgRUkiI+JOEhzsfvXztXx8zNU3tfX0JpO5R6xczf9qdM/DpJcMojLf/ZrIiobZK9HfDHxR5/f7lFJblVIfKKXa2OkYwkOVLF3HRkaQepGvq0NpUmJiMbm5ARw75s/OnSGUlhqkfr6O4SnVVOHPrvnSnt6T2Pyfp5TyB64CHrcseht4GtCWn/8G7qpnu2nANICYmBjS0tJaHENJSYlN23siTypz7vu7MOFHm15HMRptG9fcZDLZvI/GxMWVAt346SdNfr4CIDZ2P0aj69qPO7rM52rovCorKyMqWeP35hk2/FhDh0nGRte3hSed3/bkqHLb4xJrIpCltTYC1P4EUEq9CyyobyOt9UxgJkBiYqJOSUlpcQBpaWnYsr0n8qQyP75/F77KxJ/uHcquXbZ1oTcajcTExNgpsvO1bw9t2lSxd29njEZ/+vQpo3fvtg47njUcXeZzJSQk1Ls8MzMTYmBk6FY2HI5nWkxFo+vbwpPOb3tyVLntUXVzC3WqbZRSHeu8di2wzQ7HEJ7q2DHSCoaQFHuCkBBXB9M0pcz19BkZYWzdGiL18/UYMzCHLZUDKNwnVVqewqZEr5QKAS4G5tVZ/KJS6hel1FYgFXjAlmMIz1a8dL25fv5C5epQrJaYWMyJE/5UVfkwcqQk+nMlXG6uCNj81WkXRyKsZVPVjda6FIg6Z9ltNkUkvMraucepxpeUGz2n63ztmDYGg3bL4RpcLfbidrR/6gTrf45gvKuDEVZx/2YQwiNlZmYC8ONqX/xUFUGhv5CZ6RkdbeLiKjAYNJGRVQQGekbMzuTj68P4jttYkTuYR0wHXR2OsIIkeuEwvnl5rCpKYFinwx6VMI1GP6qrFRUVPmhtrrcXvzV6dBFfz43m8NJ0fHwz613HETdpRcvIWDfCYWpWbyOTBEaMdN/esPVZuzYCgNJSXw4dCnRxNO5p6I2RAGQslAHOPIEkeuEwm380ofFh2MSGJ912R+vWRdC+vXnIg/T0hmedas3Ce4YxNGA7q7d1cXUowgqS6IXD/Ly9I6GGMgYOdt8RK8915owiPT2MceMK6Ny5kvT0cFeH5LbG9TlIeukgyoye8/62VpLohUP4HT9OWulIkrodwteD7gRt3hxKebmB5OQikpKKyMgIwyS1E/UacYnGhB/bv5LhENydJHrhEMXL97CHPiSOqXB1KM2ydm0Efn41jBhRTFJSMaWlBnbu9ICeXi4Qf00MYRSxflWQq0MRTZBELxwi6ydzU5XhE/2bWNO9rFsXzvDhJQQF1TBihLmzlNTT18830MD4dpv56fBAdI3ntKpqjSTRC/vTmvW7u9DO7zQ94z1nONucHH8OHgwiObkQgMjIanr3LpN6+kaMvyCfozWdObTkhKtDEY2QRC/sTu8/wIqKCxjd67BHtUFft86c0C+4oPDsspEji9i6NYSKCg8qiBMlTGmDD9Ws/8a2weqEY0miF3a347NNHKcjCSme9c+/enUknTtXEhv767eQpKRiqqp82Lw5tJEtW6/w7qGMDNnCsu09XR2KaIQkemF3y74rA2DYZZ7Tfr6kxIf09DDGjy/4zbeQoUNL8POrOTt3rDjfhUOz2VrZn7ytBa4ORTRAEr2wr5oalm2LoXtwDp06u26yjuZaty6CqiofUlN/m6yCgmoYNKhU6ukbMepmc6ub9M9l2GJ3JYle2FXlhs38dGYMyQNyXB1Ks6xYEUmbNlUMHnz+aJVJSUXs3h1Mfr4HdQhwoo6jo+jtu58V6R2bXlm4hCR6YVerZu6ijBBGXmlwdShWO3NGsW5dBOPHF2CoJ+wxY8w3Z9evl6v6hlzUexdrioZRelx6ybojmxO9UuqQZaKRzUqpDMuytkqpH5VSey0/ZYLwVuKHpQYCVCXDUl0difU2bgyjtNRASkr9dcy9e5cTFVXFmjURTo7McyRfqanCny2fSS9Zd2SvK/pUrfVQrXWi5ffHgOVa63hgueV34e0KCliUM4Tx3Y8QFFTj6mislpYWSUhINUlJ9dcx+/hAcnIhP/8cLsMhNCD+6vZEqzxWpsmHoTtyVNXN1cDHlucfA9c46DjCxTIzM88+Vjz3JbvpS0LSKVeHZbXqali5MpLk5EL8/Rvu3XnBBYUUF/uybZsMh1Afg7+BS7puYmluAmeKzrg6HHEOeyR6DSxVSmUqpaZZlsVorXMtz48DzpvCXrjMhiXmdokjrvOcMdx/+SWE/Hy/81rbnGvUqCIMBn12rHpxvglXllNMOJtnSS9Zd2OPZgRjtNbHlFLtgR+VUrvqvqi11kqp8y6VLB8K0wBiYmJIS0trcQAlJSU2be+J3KXMZWXmNvNozcqdccQFHiUgJAej0THHM5lMGO2484UL++LrW018/D6MxsbrZfr370ZaWgiTJzuocA2wd5mb0tB5dfa9bkD7i3yIfiuPxQtDib3BKP/TLeCoctuc6LXWxyw/TyilvgGSAKNSqqPWOlcp1RE47yNeaz0TmAmQmJioU1JSWhxDWloatmzvidylzLVzw6pdh1h5JpWbErcQE+O4L3BGo9Fu+6+pgXXrujB6dDHdu0c1uX5KSjmvvx6FUl1o3955fQTsWWZrNDQFYO173ZjL4zL5+uAYHvXbQnJKcotjcJfz29kcVW6bqm6UUiFKqbDa58AlwDbgO+B2y2q3A/NtOY5wfzvmnKScYEZc4TnNKrOyQjEa/bnssnyr1q8dA6d2TBxxvgnXnaGMEDI+kOobd2JrHX0MsEYptQVIBxZqrRcDzwMXK6X2AhdZfhdebO36NgSqCoZc5DmdihYvbktwcDXjx1vXdb9nzwpiYs5IPX0j+lwfQyefXJYua/obknAem/4rtdYHgCH1LD8FTLBl38JzqOISlhoTSe60m8BAzxiX/MwZxfLlbUhJKbA6ZqXMV/WLF7elqkrh5+cZZXUmg7+By3ttZtaeVAqPFBLRTT4U3YH0jBU2y5mzlwP0ZPzF5w8f4K7Wro2guNiXiROtq7apNXZsIWVlBjZulMlIGnLhjTVUEsj8Z35xdSjCQhK9sFnawgB8qCb5d8GuDsVqixa1JSqq6uwsUtYaObKIkJBqli+Xzt4N6XVVDN0M2cz+NsDVoQgLSfTCJqqigkWHExndbidtojyjN2xxsYE1ayK45JL8Zk9c7u+vGTu2gLS0SOkl2wDlo7h6wBaWnhxGTtZxV4cjkEQvbHRi/h526n5MSPGc3rDLl0dSVeVjdWubc02YUEBhoS9ZWVJ905BLp/lTjS8fP76r6ZWFw0miFzZZNd98STx6quckvUWLoujWrYL+/RvvANSQ0aMLCQqS6pvGdBgVRUrkJt7/qTs1Js/4pufNJNGLlquqYuG+ISS12UG7jp7RAuXQoQCyssK46qq8Fs9nGxioueCCQlasiKTas2ZLdKp7biljvymWlf/Z4upQWj1J9KLF9n+RztaawVw01rlDAthi7tx2+PrWcNVVtlU1TZhQQH6+H1u2yFyyDbnumeFEqgLe+0/LvjkJ+5FEL1ps7jvm3o/JHlJtU1GhWLAgigkTCmjb1rY7qRdcUEhAQI1U3zQiqG0Qtw7cwtzDCeTvP+3qcFo1SfSiZaqrmZsRy7CwXXSIa2EdiJMtWdKW4mJfrr/+pM37Cg6uYfToQn76KZIaqYKuV2ZmJqm/K6OSQF6ftvLscNbC+STRixbZ9cE60quGc+k4z2k+N3duO3r0KGfYMPt07LrootOcPOnPpk1SfdOQ2IvbMzxwG1+v6Yeu8Yz7ON5IEr1okY9eyceAidTpnpHkduwIZseOEK6//mSLb8KeKyWlgJCQar7/XsZ1acyNE/ay/Uwftn/qWRPGexPPGYFKuA1TXgGzdo1gUtxOojp6RrXNnDntCAys5vLL7dfePzBQc8kl+fzwQ1sefjib0FCpw6nPuIc6ELPIyKez2vH81IaHO25oeGRhO7miF822ZMZ6cunEXfcFuToUq+Tl+bJ4cVsmTsy3ezK++uo8KioMLFsmN2Ub4h/uz+0jNrCsYDTZK2y/PyKaTxK9aLYPvwigneEUl9/f09WhWOXzz2MwmRS33Wb/ZqADBpTRo0c5330Xbfd9e5OJj0YQTClf/kcqEVxBEr1olryf9/Fd/hhuTT6In7/7V9sUFhqYM6cdF110mm7dKu2+f6Xgqqvy2Lo1lIMHPWeuXGcLiw3llvhVzM0eR/6OQleH0+pIohfN8vnfd1KFP3fOiHV1KFb56qv2lJUZuPNOx7UOmjgxH4NB8913clO2Mdc/5Es1Br57sdzVobQ6LU70SqmuSqkVSqkdSqntSqm/WJbPUEodU0pttjwm2S9c4Ur6TBUfrOxBQsReBl3YztXhNKmszIfZs9szdmwB8fGOSy5RUSbGji1g4cIoGdGyEe0T23Jl+zV8su0CSo9Jb1lnsuWK3gQ8pLXuD4wC7lVK9be89qrWeqjlscjmKIVbWPXMSrZUDeD3v/OMf9J586IpLPTl7rtzHX6sq68+RX6+Hz/9JDdlG3P7g2UUEc7XTzZvHgBhmxYneq11rtY6y/K8GNgJdLZXYMLNaM2LrwXSznCKqS8NcnU0TSor8+GTTzqQlFTEwIGO/2BKTi6kW7cKZs2KQUu/oAZ1u6g9N3RewXvbLiR/u9TVO4vSdjgrlVJxwCpgIPAgcAdQBGRgvuo/b6ALpdQ0YBpATExMwuzZs1t8/JKSEkJDPaPjjr04u8x5i45ww0tT+XPyYq599tebjmVlzr26N5lM+FoxW8gnn8Qze3Y8L7+8jn79rJv821aLF3fl9dcH8cwzGxg2zH7t9a0ts70EB9c/U5i93uvC7aXc8chVXNf5J26b+Wv+qXvc1vg/Dc0vd2pqaqbWOrGp9WxO9EqpUGAl8KzWep5SKgbIAzTwNNBRa31XY/tITEzUGRkZLY4hLS2NlJSUFm/viZxd5ju6LOPrY8kcOepDVOdfE72zxy4xGo3ExMQ0uk5urj+TJw8gNfU0zzxzyDmBAZWViquuGkSvXuW8+eZeu+3XmjLbU0Mdl+z5Xs+cYuS93ZfyzavL6Dw2+rzjtsb/aWh+uZVSViV6m1rdKKX8gLnAZ1rreQBaa6PWulprXQO8CyTZcgzhekeX7+bzY+O4e+S23yR5d/X66+YaxPvuO+bU4wYEaG65xciGDeHs2uUZnclc5eZ/hRJCKTOf9Zx5hj2ZLa1uFPA+sFNr/Uqd5R3rrHYtsK3l4Ql38NpfD1KNgQfeind1KE3asiWEpUvbMnXqcTp0qHL68a+/Po+QkGo+/riD04/tScJjQ/hjUhoL88ay5UPnfiC3RrZU/F0A3Ab8opTabFn2BHCLUmoo5qqbQ8AfbIpQuFRe1hH+uy2ZK7v+TL4OJN+NR5mtroZ//7sr7dqdYepU10yGEhZWzXXXneSzz2LIzs6ha1f7d9LyFtc8345vL9nPP98ZxudXHnF1OF7NllY3a7TWSms9uG5TSq31bVrrQZblV2mtHd+2TTjMjJt2UkYwUx93/znzPv00hh07QvjLX44SFOS6AcamTDHi71/DG29II7TG+If784+HdpBd3ZmP/yzNLR1JesaKBm3/dBPv7JvA9BGZxCaFuDqcRu3dG8Q773QiNfU0l17q2tmMoqNN3HHHcZYvb0NGRutrOdIcfW7oxJ09l/LenktZP/MXV4fjtSTRi3rp6hoevLeSMFXCjK8HujqcRp05o/j73+MID6/myScP2228eVvcequRjh0r+fe/u8oE4k24840wuvjkcPf9wVQUVLg6HK8kiV7Ua9Fjq1haNIp/3LyH6Fj3vpp/551O7NsXzN//fojISPfIqoGBmr/85Sh79wbz7bcysmVjgtoFMmN6FjvP9ORPSRtlJioHkEQvzlN5qoSH/q8LvQMO86cPmmyi61KrVkXwyScxXHPNScaMca963gkTChg+vJi33upMUZHB1eG4tSF3debvY9P4cO9Y3pmy2tXheB1J9OI8j49by25TL157tgT/QPc9RXbtCuLJJ7vTr18ZDz+c7epwzqMUPPxwNsXFBl54oZsMjdCEGT+NY1K7jfxl9igOzM9zdThexX3/i4VLLHg4jVd3XMr9ST9z2UMDXB1Og06c8OPBB3sRHl7NK6/sIzDQPbNo797l/OEPOSxZ0pb582UY48b4+Prw2cbexPrl8ORrYziyXtrX24skenHWsbWHuOOVQQwN2cOLy923yqakxIcHH+xJSYmB//u/fURHu/fYwHfccZykpCJeeqkb+/a5f89iV4qMjeCbL6so14GkjKsme4NMKG4PkugFAKbSSqZMPEWFDmD296EEhrrnlG+Fhf784Q992Ls3mH/964BDx5m3F4MBnn76IKGh1Tz+eA/Ky+XfrjEDr43ntUeWc8oUQeqYKo5ulK44tpIzrhXKzMz8zSN93Qam9FzJyuIE3rp/F31SO7k6xHoZjX488sgoDh0K5JVX9rndzdfGREWZeOaZgxw6FMijj/bgzBk3aAPqxmInRrH0vWxOmNqQekElh9YcdXVIHk0SfStXU1XN6zfm85XxEv429gem/sc9q2x27w7innv6kJ8fwBtv7OWCCzwnydcaMaKYJ588zLp1ETz6aA+qqiTZ11X34qOsrAzfoZX894lVnKyKJHFcEMtezHJ1iB5LEn0rpqtrePuWk3x6bCJ/SVrMTa+2d3VI59EavvqqHXfe2ReTSfGvf21g2LASV4fVYtdcc4rHHjvM6tWRPPZYD5l6sAm9r+vIZ2+kE+N/mksfHcK/r0yTdvYtIIm+lSrNLmHGZWV8eOhy/jh4Cbe+6X5zwObl+fK3v/XgxRe7kZRUxBdf7CA+3vOu5M81eXIef/vbEVaujOTee3uTl+ee90PcRYdRUfz3WyOXt1vLwwtSuLBNOgvfXOr0uRA8mST6Vujg/GPcPjmOJaeT+Z8JC7nrvSi3GDagVmWl4sMPO3DddQNZsyaCBx7I5tVX97tNr1d7uOmmk8yYcZDt24O55Zb+/PxzmKtDcmtB7QJ5amEwT1/8LVlFfbn+vnHMnn6M8nz3vxnvDiTRtyIFB0/zxKjlTHn6Ukz4MmvGcq55oQPKxz2yfHm5D3PmRDN58gDefLMzI0YU89VXO5gy5YRbfRDZyxVX5DNr1i7atDFx//3xvPBCV06dkqv7higfxcTnujL3sywu77CelzOuonu7Yp6/LI3CIzL/bGPkrPJitV9tK/MrWPL0Cd5YPZ58JjC5cxr3vulLWBfXV9doDfv3B7JgQRTz50dTXOxL//6lPPXUYUaMKHZ1eA7Xo0cFs2bt5LXXujBvXjsWLIji1luNTJliJDTUdUMtu7M2fcJ5YgFc88X3fPJhJx5fksLzsYXcNmglt/4liqQ7B7jNxYu7cFiiV0pdBrwGGID3tNbPO+pY4nw1phr2fHWMhbMD+e7IKIoJ58LIDfzx0QK6X+zaQbYqKhTbt4ewfn04P/3UhiNHAjEYNBdeeJqbbz7B4MGlXnkF35DAQM2jj2Zz000neOedTrz7bidmzepAauppLr88n9hY10yi4u7639KJpS8nkPnpTl564jTv/jKSN+4JpOf0w1w79CATrg5l7LR+hLR370H5nMEhiV4pZQDeBC4GjgIblVLfaa13OOJ4AkpPlLJryWHSF55kxRo/VuT0Jk9fRQglXNl1A1dMqaDv5A6A85K81lBYaODIkUD27w9i//5AduwIYceOYEwmHwwGTUJCMb/7nZGUlAK37+HqaHFxlTz//EF27TrOt99Gs3RpWxYvjiI0NJaEhDISEooZPLiE7t0rCAmRq/1aCbf2Y/atUHikkHkzNvL5/GD+kzGalzMC8Pv7GYaFbGNYt3yGDYOBYyLpeUEHYga2a1VX/Y66ok8C9mmtDwAopWYDVwN2TfSFRwr5+ZO9HDpyEjZvxuCrCAjxJSDEl8AwPwLC/AkM9ycgzB//ED/8gs0Pd3uDdY2m+kw1pgoTpgoTVeUmzpRWcaa0ivKCSkrzKykrOEPhiUpOG89w+qSJPbsLmFW+mqP5wewviuagqSua/gB0MeQwscduhgxdy6hp7QiMimw6Bm2eiq+y0vyzuhpMJvOjqgqOHfOnqkpRVeVDRYX5UV7uQ1mZD8XFvpSUGCgsNJCf78fp074Yjf7k5vpTXv7rqI1BQdXEx5fzu9+dYNiwEoYMKSE83HtusNpL377lPPZYNg8+eJTVqyNYvtyfnTvbsXLlr+9jTMwZYmMraNeuivbtzxAVVUVYWDXh4dWEhlYTFFRNYGANgYE1+Plp/Pw0vr4ag6H2gdd9a4roFsGdH4zlTqAsr4w172ay/Nti0vdE8OWuwfx3ZyR8bl43mFJi/Y/TMaSQjhHlxERV0SYS2kYrIqN8CY30JbStP8ERfgSGWR7h/vgFGvAL8sUv2A/fAAO+gb4Y/A0Y/A34+Pq4XW6ppbQDhtRTSk0GLtNa32P5/TZgpNb6vvrWT0xM1BkZGc0+zj9/n82M97q2IEJ3aofb0hPDnmWw18mpUYo6D332p4/Pr8ttOoLWKG/LUE2oLbPWUFOjqKkx/9Sasw/7nkcN7cud/m9qWVtua2K33/9Bc4T6VlBcFQRAWloaKSkpVm+rlMrUWjfZy9FlN2OVUtOAaZZfS5RSu23YXTTQ2sY1dcsy/5p4HMYty+1gUmYvVmL6zQVQc8sda81Kjkr0x4C6l9pdLMvO0lrPBGba42BKqQxrPtW8SWssM7TOckuZWw9HldtR7eg3AvFKqe5KKX/gZuA7Bx1LCCFEIxxyRa+1Niml7gOWYG5e+YHWersjjiWEEKJxDquj11ovAhY5av/nsEsVkIdpjWWG1lluKXPr4ZByO6TVjRBCCPchY90IIYSX84hEr5SKVErNUUrtUkrtVEqNVkq1VUr9qJTaa/nZxrKuUkr9Rym1Tym1VSk13NXxt0QDZb5BKbVdKVWjlEo8Z/3HLWXerZS61FVx26qBcr9k+X2rUuobpVRknfU9vtwNlPlpS3k3K6WWKqU6Wdb1ivMb6i93ndceUkpppVS05XevKHcD7/UMpdQxy3u9WSk1qc769jm/tdZu/wA+Bu6xPPcHIoEXgccsyx4DXrA8nwT8gLn3wyhgg6vjt2OZ+wF9gDQgsc66/YEtQADQHdgPGFxdBjuW+xLA17LshTrvtVeUu4Eyh9d5/c/AO5bnXnF+N1Ruy/OumBtyHAaivancDbzXM4CH61nXbue321/RK6UigHHA+wBa6zNa6wLMQyp8bFntY+Aay/OrgVna7GcgUinV0clh26ShMmutd2qt6+tYdjUwW2tdqbU+COzDPAyFR2mk3Eu11rUD4fyMuV8GeEG5Gylz3RlWQvi1u6XHn9/Q6P81wKvAI/y2i6nHl7uJMtfHbue32yd6zJ9kJ4EPlVKblFLvKaVCgBitde308MeBGMvzzkB2ne2PWpZ5kobK3BBvKDNYV+67MF/ZgXeUu8EyK6WeVUplA1OApyzre0OZoYFyK6WuBo5prbecs743lLux8/s+S5XUB7XV0NixzJ6Q6H2B4cDbWuthQCnmqpqztPl7jjc1H2qyzF6q0XIrpZ4ETMBnrgnPIRoss9b6Sa11V8zlrXecKA9WX7lnAE/w64eat2novX4b6AkMBXKBf9v7wJ6Q6I8CR7XWGyy/z8H8xzLWfnWz/Dxheb3J4Rc8QENlbog3lBkaKbdS6g7gCmCK5YMdvKPc1rzXnwHXW557Q5mh4XJ3B7YopQ5hLluWUqoD3lHuesustTZqrau11jXAu/xaPWO3Mrt9otdaHweylVJ9LIsmYB7u+Dvgdsuy24H5luffAVMtd+lHAYV1qng8QiNlbsh3wM1KqQClVHcgHkh3cJh211C5lXkSm0eAq7TWZXU28fhyN1Lm+DqrXQ3ssjz3+PMbGix3lta6vdY6TmsdhzkxDres6/HlbuS9rnuv4Vpgm+W5/c5vV9+FtuaB+StNBrAV+BZoA0QBy4G9wDKgrWVdhXnSk/3AL9RpneJJjwbKfC3mk78SMAJL6qz/pKXMu4GJro7fzuXeh7mucrPl8Y43lbuBMs+1/MNvBb4HOlvW9Yrzu6Fyn/P6IX5tdeMV5W7gvf7EUqatmJN7xzrr2+X8lp6xQgjh5dy+6kYIIYRtJNELIYSXk0QvhBBeThK9EEJ4OUn0Qgjh5STRCyGEl5NEL4QQXk4SvRBCeLn/B7x8VtaEvVrdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(params) "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}