calc_distances.ipynb

{
 "cells": [
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "import glob\nimport numpy as np\nimport pandas as pd\nfrom astropy.cosmology import FlatLambdaCDM",
   "execution_count": 1,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "import healpy as hp\nfrom sklearn.neighbors import DistanceMetric",
   "execution_count": 2,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "from sklearn.neighbors import BallTree",
   "execution_count": 3,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "import matplotlib.pyplot as plt\nimport seaborn as sns\nsns.set_style('whitegrid')\nsns.set_context('paper')",
   "execution_count": 4,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "fnames  = glob.glob('sn_*MS.csv')",
   "execution_count": 5,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "ipix = np.ones(hp.nside2npix(32))*hp.UNSEEN\nhids = np.array(list((fname.split('_')[1] for fname in fnames)), dtype=np.int)\nipix[hids] = 1",
   "execution_count": 6,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "#fig, ax = plt.subplots()\nhp.mollview(ipix)",
   "execution_count": 7,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 612x388.8 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "dfs = list(pd.read_csv(fname) for fname in fnames)",
   "execution_count": 8,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "df = pd.concat(dfs)",
   "execution_count": 9,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "print('Number of healpixels used is {0} leading to a total area of {1:0.1f} sq degrees'.format(len(fnames), len(fnames) * hp.nside2pixarea(nside=32, degrees=True)))",
   "execution_count": 10,
   "outputs": [
    {
     "output_type": "stream",
     "text": "Number of healpixels used is 130 leading to a total area of 436.4 sq degrees\n",
     "name": "stdout"
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "fig, ax = plt.subplots(1, 3)\n_ = ax[0].hist(list(len(df) for df in dfs), histtype='step', density=True, lw=2, alpha=1)\n_ = ax[1].hist(list(len(df.query('z < 0.1')) for df in dfs), histtype='step', density=True, lw=2, alpha=1)\n_ = ax[2].hist(list(len(df.query('z < 0.05')) for df in dfs), histtype='step', density=True, lw=2, alpha=1)",
   "execution_count": 11,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 3 Axes>",
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "df = df[['raJ2000_gal', 'decJ2000_gal', 'snra', 'sndec', 'galaxy_id', 'z']]",
   "execution_count": 12,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "print('There are {0} and {1} SNIa at redshift below 0.05 and 0.1 respectively'.format(len(df.query('z < 0.1')),\n                                                                                      len(df.query('z < 0.05'))))",
   "execution_count": 13,
   "outputs": [
    {
     "output_type": "stream",
     "text": "There are 821 and 119 SNIa at redshift below 0.05 and 0.1 respectively\n",
     "name": "stdout"
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "df.query('z < 0.05').describe()",
   "execution_count": 14,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 14,
     "data": {
      "text/plain": "       raJ2000_gal  decJ2000_gal        snra       sndec     galaxy_id  \\\ncount   119.000000    119.000000  119.000000  119.000000  1.190000e+02   \nmean     60.980417    -35.217634   60.980899  -35.217006  5.193279e+09   \nstd       7.932635      5.835331    7.932196    5.834765  3.258047e+09   \nmin      48.730560    -45.596512   48.731713  -45.598373  1.000000e+09   \n25%      54.344800    -40.675013   54.347978  -40.675627  2.000003e+09   \n50%      59.808767    -34.576669   59.809307  -34.576661  5.000001e+09   \n75%      69.011253    -30.346244   69.009939  -30.343783  7.500001e+09   \nmax      75.277517    -25.391599   75.279925  -25.391758  1.400000e+10   \n\n                z  \ncount  119.000000  \nmean     0.038596  \nstd      0.009623  \nmin      0.014245  \n25%      0.030637  \n50%      0.041901  \n75%      0.046890  \nmax      0.049891  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>raJ2000_gal</th>\n      <th>decJ2000_gal</th>\n      <th>snra</th>\n      <th>sndec</th>\n      <th>galaxy_id</th>\n      <th>z</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>119.000000</td>\n      <td>119.000000</td>\n      <td>119.000000</td>\n      <td>119.000000</td>\n      <td>1.190000e+02</td>\n      <td>119.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>60.980417</td>\n      <td>-35.217634</td>\n      <td>60.980899</td>\n      <td>-35.217006</td>\n      <td>5.193279e+09</td>\n      <td>0.038596</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>7.932635</td>\n      <td>5.835331</td>\n      <td>7.932196</td>\n      <td>5.834765</td>\n      <td>3.258047e+09</td>\n      <td>0.009623</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>48.730560</td>\n      <td>-45.596512</td>\n      <td>48.731713</td>\n      <td>-45.598373</td>\n      <td>1.000000e+09</td>\n      <td>0.014245</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>54.344800</td>\n      <td>-40.675013</td>\n      <td>54.347978</td>\n      <td>-40.675627</td>\n      <td>2.000003e+09</td>\n      <td>0.030637</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>59.808767</td>\n      <td>-34.576669</td>\n      <td>59.809307</td>\n      <td>-34.576661</td>\n      <td>5.000001e+09</td>\n      <td>0.041901</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>69.011253</td>\n      <td>-30.346244</td>\n      <td>69.009939</td>\n      <td>-30.343783</td>\n      <td>7.500001e+09</td>\n      <td>0.046890</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>75.277517</td>\n      <td>-25.391599</td>\n      <td>75.279925</td>\n      <td>-25.391758</td>\n      <td>1.400000e+10</td>\n      <td>0.049891</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "df[['raJ2000_gal', 'decJ2000_gal', 'snra', 'sndec']] = df[['raJ2000_gal', 'decJ2000_gal', 'snra', 'sndec']].apply(np.radians)",
   "execution_count": 15,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "df.query('z < 0.1').z.size",
   "execution_count": 16,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 16,
     "data": {
      "text/plain": "821"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "dc2 = FlatLambdaCDM(H0=71, Om0=0.265, Ob0=0.0448)",
   "execution_count": 17,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "##  Translate comoving distances to angular distances"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "we are doing two bins (z = `[0, 0.05)` and z = `[0.05, 0.1)`). Bin midpoints are taken at 0.025 and 0.075 rather than weighting by volume. We need to translate "
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "# comoving transverse distance : Comoving distance between two objects at the same redshift apart by a radian.\nradians_0p025 = 1/ (dc2.comoving_transverse_distance(z=0.025).value / np.arange(5, 100., 5.))\ndc2_0p025 = dc2.comoving_transverse_distance(z=0.025) * radians_0p025",
   "execution_count": 20,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "# comoving transverse distance : Comoving distance between two objects at the same redshift apart by a radian.\nradians_0p075 = 1/ (dc2.comoving_transverse_distance(z=0.075).value / np.arange(5, 100., 5.))\ndc2_0p075 = dc2.comoving_transverse_distance(z=0.075) * radians_0p075",
   "execution_count": 21,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "def get_num_pairs(X, radians):\n    edges = (radians[: -1] + radians[1:] )/ 2.0\n    dm = DistanceMetric.get_metric('haversine')\n    masks = list(np.array(dm.pairwise(X)  < edge, dtype=np.int) for edge in edges)\n    nums = np.array(list((mask.sum() - len(mask)) / 2.0 for mask in masks))\n    return nums",
   "execution_count": 22,
   "outputs": []
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### Calculation for z < 0.05  bin"
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "X = df.query('z < 0.05')[['snra', 'sndec']].values",
   "execution_count": 23,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "#tree = BallTree(df.query('z < 0.05')[['snra', 'sndec']].values, metric='haversine')",
   "execution_count": 24,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "len(df.query('z < 0.05')[['snra', 'sndec']].values)",
   "execution_count": 25,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 25,
     "data": {
      "text/plain": "119"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "fig, ax = plt.subplots(1, 2, sharey=True)\nax[0].plot(radians_0p025[:-1], get_num_pairs(X, radians_0p025), 'o')\nax[0].set_xlabel('radians')\nax[1].plot(dc2_0p025.value[:-1], get_num_pairs(X, radians_0p025), 'o')\nax[1].set_xlabel('comoving distance')\nfig.savefig('NumberPairsatDistanceLessThan_z0p25.png')",
   "execution_count": 26,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": "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\n"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "fig, ax = plt.subplots(1, 2, sharey=True)\ny = get_num_pairs(X, radians_0p025) \n\nax[0].plot(radians_0p025[:-2], y[1:] - y[:-1], 'o')\nax[0].set_xlabel('radians')\nax[1].plot(dc2_0p025.value[:-2], y[1:] - y[:-1], 'o')\nax[1].set_xlabel('comoving distance')\nfig.savefig('NumberPairsatDistance_z0p25.png')",
   "execution_count": 27,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": "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\n"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### Calculation for z > 0.05 bin"
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "X = df.query('z > 0.05 and z < 0.1')[['snra', 'sndec']].values",
   "execution_count": 28,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "#dists = tree.query_radius(df.query('z < 0.05')[['snra', 'sndec']].values, r=radians_0p025[0], \n#                  count_only=True)",
   "execution_count": 40,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "fig, ax = plt.subplots(1, 2, sharey=True)\nax[0].plot(radians_0p075[:-1], get_num_pairs(X, radians_0p075), 'o')\nax[0].set_xlabel('radians')\nax[1].plot(dc2_0p075.value[:-1], get_num_pairs(X, radians_0p075), 'o')\nax[1].set_xlabel('comoving distance')\nfig.savefig('NumberPairsatDistanceLessThan_z0p075.png')",
   "execution_count": 29,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": "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\n"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "fig, ax = plt.subplots(1, 2, sharey=True)\ny = get_num_pairs(X, radians_0p075) \n\nax[0].plot(radians_0p025[:-2], y[1:] - y[:-1], 'o')\nax[0].set_xlabel('radians')\nax[1].plot(dc2_0p075.value[:-2], y[1:] - y[:-1], 'o')\nax[1].set_xlabel('comoving distance')\nfig.savefig('NumberPairsatDistance_z0p075.png')",
   "execution_count": 30,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": 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9yN0HgDnV/SiSBrG385VsynpeFx0aSn7ct5vZsmTSDGAouX2YMETUmhSGwmmFs+0wMFrwurL09/dX8rKqGxkZSU0skM54eG2EE6OjJ00fHR2l5bVf0N9f0dc/6ZjSNI/GamRsaZo3qY+lAXldz3lSyc7iIcIPff7/AcKPfF4ncJCwbyDvTMLWR2fBtBOlvmFXV1cFYVZff39/amKBdMZz3ZIunnm1/aSx1FVL5/GbK97ZsJgmmke9vb11jOZUjfz+0pQ/aY+lq4u65/Vk50k5uV1JIegh7AvYAqwgDBntTbYYeoBFgAODyU7kQ8B0d3/ezGaY2XTgLOBABe8tTUCtqiWLspzXlRSCu4GHzOxW4FF3f9HM1hMKQidwl7sfNbM1hKOLzgDWJK9dCzxG2Dq4cbLBS3qpVbVkUVbzuuRC4O5rC+5ePeaxAcLWQeG0pwg7kgunbQe2lxukiIjUjs4sFhGJnAqBiEjkVAhERCKnQiAiEjkVAhGRyKkQiIhEToVARCRyuh6BNERW+7qLNGNuqxBI3WW5r7vErVlzW0NDUldZ7+su8Wrm3FYhkLrKel93iVcz57YKgdTVgrM6yOVOnpbLwflndzQmIJEqaebcViGQulq6YBbXL53LtPY2Os5oY1p7G6uWzmuanWoip9PMua2dxVJ3We7rLnFr1txWIZCGyGpfd5FmzG0NDYmIRE6FQEQkcioEIiKRUyEQEYmcCoGISORUCEREIqdCICISuaY9j6AZW72KlEK5LfXWlIWgWVu9ihSj3JZGaLqhoWZu9SoyEeW2NErTFYJmbvUq5ekZGORbvfH8ECq345G23G66oaFmbvUqpYtxiES5HYc05nbTbRE0c6tXKU2sQyTK7exLa2433RYBNG+rVynNREMkWf+uldvZltbcbspCAM3Z6lVKE/sQiXI7u9Ka2003NCTZpyESyaq05nbTbhFItmmIRLIqjbmtQiCppSESyaq05XZFhcDMpgLfAmYCvcAXga1AJ7DN3TeY2Txgc/Ied7r7FjNbDGwEcsBqd985+Y8gIiKTUek+gquAPnd/D3AecCvwILAcuMLMzgVWA7cBlwM3m9lbgPXAKuBq4I7JhS4iItVQ6dDQPwLLzawFmEb4sf8Ld8+Z2S5gGbAEuCmZ1gcsBGa7+wsAZnbEzN7q7q8Ue7P+/v4Kw6yukZGR1MQCiqcUaYypUCNjS9O8USyNjaPSQnCMsFb/IcCTaUPJ/4cJQ0St7p4bM63wCNr8tKKFoKurq8Iwq6u/vz81sYDiKUWxmHp7e+sYzakaOb/S9H0plurHUU5uVzo0dAuwwd0N+AlwMeFHneT/g8BowfPz0wqPoD0TOFTh+4uISJVUukUwRPhhB9gPfJUwPLQFWAFsAvaa2TKgB1hE2HIYTHYiHwKmu/tBRESkoSrdIvg68Htm9gSwkvDDf4OZ7QZ2ufuLhB3DXwV+DNzj7keBNYSji3agncUiIqlQ0RaBuw8CHxwz+eoxzxkgbB0UTnuKsCNZRERSQieUSVPTZR0li3oGBnny2SGGOwbrktcqBNK00tjXXWSy8nmdy42ycfdgXfJaTeekKaW1r7vIZBTm9cjrubrltQqBNCVd1lGyqFF5rUIgTSmtfd1FJqNRea1CIE0prX3dRSajMK+nTmmpW15rZ7E0rTT2dReZrHxe/+jpZ7l00QU6akikmLT1dRephu75s+gYnk5XnXJbQ0MiIpFTIRARiZwKgYhI5FQIREQip0IgIhI5FQIRkcipEIiIRE6FQEQkcioEIiKRUyEQEYmcWkxIpvW9NELf8D71IpLMqebV+VQIJLNuf3QvD+/5OW2t+3UFM8mUal+dT0NDkkn5Kz0dfT2nK5hJptTi6nwqBJJJuoKZZFUtcluFQDJJVzCTrKpFbqsQSCblr/Q0dUqLrmAmmVKLq/NpZ7Fk1rqVF7Jo5nFynbN11JBkSrWvzqdCIJm28JypdHXNbXQYIlVXzavzaWhIRCRyKgQiIpFTIRARiZwKgYhI5FQIREQi15Ibe2ZCyvT29qY7QGl63d3dLcWfVX3Kbam1UnM79YVARERqS0NDIiKRUyEQEYmcCoGISORUCEREIqdCICISORUCEZHIqRCIiERObajHYWZTgM3AHGC3u3+u4LH/CnwYyAGfdffeRsaTPH4G0A/8mru/1sh4zOzXgbWE3Lrd3b9X63hKiOkm4PeBw8DvuPu+esSUNmY2A3gY6AB+AXwKeAToBLa5+4Y6x/MB4Ebgt5ggv2scQwvwZ8ASYAT4KHB3g2KZCnwLmAn0Al8EtlKH70dbBOP7TeBpd18OzDSziwDM7JeBq9x9GfA7wB2NjKfAfwRm1ymW08ZjZm2EInAl8OvAgkbHlLgZWAb8CfDZOsaUNjcC/8vdLyesOHwaeBBYDlxhZufWKxAzayXkSgvF87uWPggcdff3AP8D+GQDY7kK6EtiOQ+4lTp9PyoE47sEeDy5/RjwnuT2AeC65PYU4FiD48HMzgYuAp6qUywTxWOENc1vEtY0f5CCmAD+AZhGWLMaqmNMaXMP8FByewrwBeBxd88BuwjFsl4+CeS3Fif67mrtMiBnZj8A/j1wbgNj+UdgSrKVMg24nDp9PyoE45vBmz8Yhwk/ILj76+4+aGbTCAvV1xoZT+J2YH2d4igWzyzCJvaNhLWZ/5mCmEim9yXxPFzHmFLF3Q+5+1EzuxhYQVh5ON08qxkzmw78BrAlmTTRd1drs4Bp7n4FcAS4toGxHAOuBv4fcCKZVpdYVAjGN8SbM70TOJh/wMw6ge8A33D3HzcyHjPrAtrd/ek6xTFhPMArwN+7+6vuvpewdtXQmMxsEWFL5VeAS4G/qGNMqWNmlwJ3Af+BCfK8xr4A/HfCfjYaGAeEnN2R3N4B/G0DY7kF2ODuBvwEuLhesagQjK+HsFkG8D5gd8FjW4GN7r5l7IsaEM8VwBIz2wksBh5ocDw/A843s+lmtgAYrFM8E8X0GnDY3Y8n8ZxZx5hSxcx+FfhT4Dfc/V85eZ6tIOygrIdLgT8mbJ2tIPwY5+MYu7zV2u7kPSEMse5uYCxDvPljvx/4KnX6ftR9dBzJUTgPAm8HfkrYhH0X8AzwXd78Qtzdb2xUPO5+V8FzdgIfqtNRQ6eNx8yuI6zxjQKfdve67LsoEtNqwlBEDviiu/+wHjGljZndRxjzfjGZ9HXgD4GzgEfd/ct1jmcBYQf+b1Pw3bn7p+sYwxTCVuI7CPPlY4QVqkbEMoswHzqBQ8AfAX9OHb4fFQIRkchpaEhEJHIqBCIikVMhEBGJnAqBiEjkVAhERCKnpnNNzszWAgPAvwHnuvv9jYxHpBxm9rC7f7QKf2ctRZYDM5sHLHT37ZN9v6xRIcgId//fjY5BpFzVKAJj/t5Ey8H7CY0QVQjG0HkEKWRmvwd8glCo9xPOhn0r8Nfu/hUzWwFsIJyR2QZsSl66APgycC+hvcPZwNfdfZOZ9RBOhPs1wokyN5rZzcDvEoYIv+nu36jPJ5Q0StqnbALeRjj57rcJuXEvIc9eJbTzXgR8ntAP5zxCy4prCCdl/aG7P2Fmnwc+kvzpPwO+D3zP3fOdan9IaDy3090XnCY/3528Nn/G7bcL1/SLLAebgfuTGF8mtLr+KTCVsGy9jdCGewqhUeJ1wJcIrUh+mdAK+nrgXwgndb0reY8bCVse9xF6JL0GfNLdXypzdqeK9hGk188JLXIfd/crCV0S/yB57GvAR9z9A4SFs9A84PvJa64lnJ0IoSjcTehgeFnS0vbjhIVxOfB6DT+LNIdPA//g7u8m/Ch2E878Xe/uK4BvA2uS584m/Ph/jfCDei3hjPLfSvo7XUXItRWEopED9pnZO83sPCDn7gMF7z1efv4JsMrd30v4wR1rouXgSuAJ4L2EM4VnEVo23O/uOwhnDl+ZtJueAXQlr/tFsuz8NeHaBB8GWt39EsKychFwG/BXSVx3E9ppNzUVgvRyQvIvMLMHCGs+7clj57j788ntH4153cuEBWkTIWHbCx57Jmlp+yJhzehTyXO+T1gYJG4XkPTWcfcfuvs2wg/kk8nj/xd4Z3K7z91HCWPynuTVK4S8egfwE3cfdfcRQmuWCwhr0R9L/uXX3guNzc9z3P1nBe891kTLwV8StgYeI1zvYOyKzgHgATP7JuEiNPnl5Jnk/39JYiicJ0+7+z3JPLg5aeuymvo2V6wJFYL0GiX0Rz/H3W8gFIJ8J8KDZvbvktvdY173+8BL7v5xwtWOWvIPJAtZoU8RtjLeC3w2GRqQeP0TYY0XM3ufmX2RsELy7uTx5cCzye2JxpQduNjMWpOrbi0BniNcf2AFIa//6pQXnZqfg2Z2fnL7knHeZ6Ll4BrgiWSt/WeEYZ4c0GJmM4H/Rhj6uoXwO5hfTsbGUDhPftXM7kk+31eSC/x8Dvib8WZCM9HO4nTbDXzJzP6O0ITq35Je7h8HtpjZQeDomNfsAB42s/cCLwHtydWgxtOfvMcBwpWrat6wTlLtHmBTsqabI8kz4Btmtg4YBm7gzWGUcbn7T5MLvTxJWNP+U3ffD5Dk8kx3Hy4hnlsIufwa4Yd67Fr9RMvB3wMPmtmXkrg/QVjzv42Q83sI+ySGCcvJ204Tw7eBq8zs/xAKxh8B+4B7zexzwFsIQ2pNTTuLRSSVkoMZNrv7q2Z2P2F8f2djo8ombRGISFodAJ4ws0OEK8ztanA8maUtAhGRyGlnsYhI5FQIREQip0IgIhI5FQIRkcipEIiIRO7/A5URJVpO9hHpAAAAAElFTkSuQmCC\n"
     },
     "metadata": {}
    }
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3",
   "language": "python"
  },
  "language_info": {
   "name": "python",
   "version": "3.6.5",
   "mimetype": "text/x-python",
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}