data-science-ipython-notebooks/numpy/numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy\n",
    "\n",
    "Credits: Forked from [Parallel Machine Learning with scikit-learn and IPython](https://github.com/ogrisel/parallel_ml_tutorial) by Olivier Grisel\n",
    "\n",
    "* NumPy Arrays, dtype, and shape\n",
    "* Common Array Operations\n",
    "* Reshape and Update In-Place\n",
    "* Combine Arrays\n",
    "* Create Sample Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy Arrays, dtypes, and shapes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "(3,)\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "print(a)\n",
    "print(a.shape)\n",
    "print(a.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 2 4]\n",
      " [1 3 5]]\n",
      "(2, 3)\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "b = np.array([[0, 2, 4], [1, 3, 5]])\n",
    "print(b)\n",
    "print(b.shape)\n",
    "print(b.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, 1],\n",
       "       [1, 1, 1, 1],\n",
       "       [1, 1, 1, 1]], dtype=int32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones(shape=(3, 4), dtype=np.int32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.   1.   2. ]\n",
      " [ 0.5  1.5  2.5]]\n",
      "(2, 3)\n",
      "float64\n"
     ]
    }
   ],
   "source": [
    "c = b * 0.5\n",
    "print(c)\n",
    "print(c.shape)\n",
    "print(c.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.   3.   5. ]\n",
      " [ 1.5  3.5  5.5]]\n"
     ]
    }
   ],
   "source": [
    "d = a + c\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  3.,  5.])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1. ,  1.5])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.25"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.5,   6.5,  10.5])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3. ,  3.5])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.mean(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reshape and Update In-Place"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10 11]\n"
     ]
    }
   ],
   "source": [
    "e = np.arange(12)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3]\n",
      " [ 4  5  6  7]\n",
      " [ 8  9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# f is a view of contents of e\n",
    "f = e.reshape(3, 4)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 0 0 0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# Set values of e from index 5 onwards to 0\n",
    "e[5:] = 0\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [4, 0, 0, 0],\n",
       "       [0, 0, 0, 0]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# f is also updated\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  C_CONTIGUOUS : True\n",
       "  F_CONTIGUOUS : False\n",
       "  OWNDATA : False\n",
       "  WRITEABLE : True\n",
       "  ALIGNED : True\n",
       "  UPDATEIFCOPY : False"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# OWNDATA shows f does not own its data\n",
    "f.flags"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combine Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2, 4],\n",
       "       [1, 3, 5]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  3. ,  5. ],\n",
       "       [ 1.5,  3.5,  5.5]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 1, 2, 3, 1, 2, 3])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([a, a, a])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  2. ,  3. ],\n",
       "       [ 0. ,  2. ,  4. ],\n",
       "       [ 1. ,  3. ,  5. ],\n",
       "       [ 1. ,  3. ,  5. ],\n",
       "       [ 1.5,  3.5,  5.5]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use broadcasting when needed to do this automatically\n",
    "np.vstack([a, b, d])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0. ,  2. ,  4. ,  1. ,  3. ,  5. ],\n",
       "       [ 1. ,  3. ,  5. ,  1.5,  3.5,  5.5]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In machine learning, useful to enrich or \n",
    "# add new/concatenate features with hstack\n",
    "np.hstack([b, d])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Sample Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pylab as plt\n",
    "import seaborn\n",
    "\n",
    "seaborn.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeMAAAFVCAYAAADc5IdQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9NjDK5weEz5DGAPwjen
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bac8d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create evenly spaced numbers over the specified interval\n",
    "x = np.linspace(0, 2, 10)\n",
    "plt.plot(x, 'o-');\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create sample data, add some noise\n",
    "x = np.random.uniform(1, 100, 1000)\n",
    "y = np.log(x) + np.random.normal(0, .3, 1000)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([83.71854922, 56.42008614, 49.98694964, 93.27834525, 30.27524716,\n",
       "       41.76569611, 68.77139894, 53.85135531, 59.70938725, 47.94039486,\n",
       "       92.2794264 , 36.65789096, 34.12233513, 42.93989704, 96.31092964,\n",
       "       66.42623987, 29.29202337, 77.42591982, 23.93583307, 46.1117102 ,\n",
       "       83.87098271, 31.48546596, 37.03181147, 34.55065443, 82.69943861,\n",
       "       48.04544156, 55.28137272, 20.41569089, 34.44386826, 31.33208191,\n",
       "       68.82291735, 16.49416034, 67.52775054, 59.26870595, 34.59416856,\n",
       "       46.22618212, 43.02653129, 13.29699634, 85.87035581, 49.10256099,\n",
       "       53.80913102, 55.4370286 , 97.59276738, 76.54251692, 12.44899516,\n",
       "       24.13297416, 85.94900525, 65.19726131, 92.77112099, 61.05600087,\n",
       "       51.97623268, 74.50004466, 12.96078586,  8.45321199, 93.23475918,\n",
       "       20.50258396, 20.82425681, 63.75744397, 85.98146324,  6.58818749,\n",
       "       34.13121031,  8.77033903, 57.16966461, 55.99761995, 49.8286924 ,\n",
       "       78.83044349, 39.80510984, 30.84804662, 82.28398022,  9.93416381,\n",
       "       96.76791686, 21.62560876, 21.44950404, 44.30021138, 63.63334457,\n",
       "       83.91351217, 76.57204104,  2.85709746, 54.09131354, 98.20915521,\n",
       "       95.45205648, 52.47789366, 63.49178726, 85.79772374, 61.87730851,\n",
       "       63.6599729 , 78.42832639, 61.15016663,  9.19537288, 62.64767869,\n",
       "        9.9441762 , 30.96488801,  7.00401788, 25.45784566, 22.92861064,\n",
       "       78.9518552 , 96.70412501, 41.92897161, 88.27740138, 19.82953716,\n",
       "       19.99840143, 24.62332795, 92.57234839,  4.3085906 ,  8.39897054,\n",
       "       86.61940807, 34.73652668, 43.93647878, 87.84859818, 12.75033582,\n",
       "       14.73741943, 98.10399493, 31.25375293, 64.34812438, 19.68005629,\n",
       "       25.67171446, 60.39612831, 89.35139282, 96.57952059, 84.05577647,\n",
       "       56.69683168, 53.74545209, 48.56017275, 18.68125305,  3.72073321,\n",
       "       93.53363915, 12.02587833, 89.5376834 , 46.04924518, 77.99515893,\n",
       "       46.32252998, 81.40921193, 27.34338734, 37.47268845, 75.78202532,\n",
       "       38.29284779, 42.6343433 , 96.01020265, 97.81660871, 93.35310544,\n",
       "       20.24738001, 98.46825771, 13.712137  , 33.77227359, 29.40031081,\n",
       "       54.28727788, 48.83005544,  5.6674515 , 21.1620685 , 51.63380767,\n",
       "       17.21803125,  8.61133232, 91.29855571, 87.72501975, 25.12385243,\n",
       "       69.13211569, 14.47254943,  7.38473232, 44.51243476, 38.34570006,\n",
       "       72.81345911, 38.12407287,  6.4085569 , 69.84395616,  6.73123685,\n",
       "       69.69176786, 34.52184721, 64.85272141, 88.58436437, 97.85669547,\n",
       "       50.55263643, 90.23285264, 34.54628467, 48.49646617, 89.84304147,\n",
       "       70.32288427, 54.40838621,  5.36572988, 16.77505735, 89.75713153,\n",
       "       39.20205915, 70.09879834, 72.82545558, 80.63631681, 61.18949255,\n",
       "       96.12832008, 89.86338564,  5.78167235, 62.66001616, 45.24619169,\n",
       "       68.22110483, 78.50223742, 88.518058  , 45.07746332,  5.52013397,\n",
       "       11.82882415, 60.56869955, 87.32315816, 72.04393536, 90.0505615 ,\n",
       "       73.76413058, 21.18795344, 31.72529168, 86.39558819, 65.63549891,\n",
       "       32.21931223, 16.74065236, 59.59553079,  7.52972462, 93.18470182,\n",
       "       52.96095658, 59.30359505, 64.62047666, 26.26466469,  4.81077116,\n",
       "       88.31656888, 91.61068173,  4.73609492, 81.33937848,  4.1011709 ,\n",
       "        2.57936691, 83.59191756, 17.76511103, 35.260859  ,  2.12451695,\n",
       "       92.95291768, 44.69776305, 75.06399396, 49.27140805, 70.89682392,\n",
       "       54.43181351, 71.29745173,  2.58864544, 75.63705519, 57.98533294,\n",
       "       54.09305538, 83.30654764, 76.1120146 , 14.6803717 , 49.61729746,\n",
       "       76.32994462, 94.26525748, 91.62397767, 83.37590949,  4.56719842,\n",
       "       87.78640149, 85.21532691, 55.27810805, 21.31038537, 20.02479967,\n",
       "       82.57333297, 43.6731699 , 48.80470649, 94.82564441, 69.38454334,\n",
       "       69.24588824, 23.43682139, 24.69793876, 94.56932991,  4.75665761,\n",
       "       31.26874213, 61.27296706, 38.84203184, 52.07511526, 16.74501083,\n",
       "       90.10773435, 73.63029533, 45.68134773, 74.21902068, 52.57994729,\n",
       "       36.76262087, 23.99745014,  5.97852962, 26.05342092,  7.63304941,\n",
       "       36.74485501, 25.85072155, 24.28879386, 46.38647005, 38.54809101,\n",
       "       20.08363303, 28.89598316, 65.28138835, 65.89866509, 56.21697962,\n",
       "       95.98243925, 39.6996565 ,  9.44647706, 12.53545148, 76.65801574,\n",
       "       64.16900178, 29.6652737 , 50.68757655, 85.06007367, 66.67179532,\n",
       "       73.51785038, 82.33531599, 76.30448981, 18.02927199, 34.79390567,\n",
       "       43.35736492, 42.09896227, 24.3227206 , 17.06147181, 22.26837447,\n",
       "       11.39338226,  4.0590102 , 41.72233178, 74.59919539, 70.28058278,\n",
       "       46.74347735, 50.74540797, 75.3868119 , 81.91549973, 68.66401867,\n",
       "       29.46735335, 13.16022997, 37.81641541, 95.18328584, 99.31281745,\n",
       "       93.60594966, 37.78951538,  9.58815953,  5.43466928, 29.25084117,\n",
       "       61.20781222, 73.65145942, 80.9411392 , 44.84073946, 39.15571455,\n",
       "       35.38719918, 33.18527091, 93.57087102, 82.95009024, 23.13348947,\n",
       "       99.38503438, 46.41191059, 19.78431723, 92.48274749, 94.35508113,\n",
       "       82.55464173, 24.49033533, 13.04648305,  5.33523461, 65.29334281,\n",
       "       21.76461102, 53.18091392, 37.88104412,  7.66864866, 86.43601426,\n",
       "       42.81323599, 73.73847828, 28.18782878,  9.47024692, 91.33054247,\n",
       "       19.13443638, 44.66581638, 64.54085165, 18.7005718 , 97.43973028,\n",
       "       27.37321214, 46.5371998 , 70.13804771, 94.12044806,  9.59499349,\n",
       "       91.77590893, 23.85416154, 24.81854893, 10.16994817, 61.65265823,\n",
       "       30.80094459, 99.88974271, 51.48970062, 64.00534117, 28.32498996,\n",
       "       95.96330362, 78.57156869, 11.26172063,  5.12727213, 83.23240357,\n",
       "       63.42265511,  7.90992072, 77.6435666 , 41.32153067, 87.12421958,\n",
       "        4.58744694, 21.34868307, 38.36679011,  1.11168295, 34.81460997,\n",
       "       23.7319703 , 55.55322603, 48.93390941, 66.01891832, 71.46395879,\n",
       "       62.992747  , 30.26651591, 28.89364795, 13.02103718, 88.40437453,\n",
       "       49.46881189, 56.98669103, 65.94627196, 73.44799534,  7.07694658,\n",
       "       57.50564017, 86.69127084, 51.97069366, 40.02469257, 61.93274575,\n",
       "        1.58154704, 93.39278209, 82.09048206, 99.30157407, 71.37967429,\n",
       "       99.65860368, 26.9048574 , 88.00957877, 63.99884793, 10.28088743,\n",
       "       18.48922532, 22.36531754, 72.60527259, 88.6110272 , 28.01144336,\n",
       "       17.52897011, 85.50803706, 14.10783113, 62.39177242, 76.29680583,\n",
       "       74.94812139,  4.76563935, 88.05763191, 13.73016167, 47.9184943 ,\n",
       "       30.94590316, 44.76643412, 54.71164969, 96.50874683,  6.4070926 ,\n",
       "       92.91869417,  2.33965435, 24.31750859, 45.16218788, 62.55255338,\n",
       "        3.60786013, 77.53976478, 98.73528801,  1.64118966, 35.96948083,\n",
       "       63.82340742, 29.28053425, 71.02014774, 28.73677381, 15.76749613,\n",
       "       32.00299167, 74.98351357, 19.09729316, 75.85201677, 97.38180446,\n",
       "       40.2195637 , 92.80691414, 88.18935951, 47.08953732, 99.64806564,\n",
       "       11.97679595, 13.6471891 , 13.29711511, 81.0494752 , 44.25642235,\n",
       "       85.61065761, 26.32544564, 99.8654296 , 61.32416734, 75.46948802,\n",
       "       73.42675464, 86.08518275, 30.78745229, 92.39237228,  4.69877434,\n",
       "        1.78078896, 65.81981226,  4.17379548, 82.92842122,  5.49215947,\n",
       "       69.63154521, 85.77172747, 95.26456345, 69.26493585,  8.31519357,\n",
       "       14.43209414, 62.24093408,  3.86016656, 58.90288874, 72.78974919,\n",
       "       86.08114266, 28.85912804, 42.74809433, 62.12023518, 37.06068036,\n",
       "       33.67501142, 72.67099543, 25.8959871 , 19.35368386, 77.86678593,\n",
       "       98.17072223, 91.9655844 , 37.40524565, 66.06172207, 21.42105259,\n",
       "       12.07382067, 24.46328008, 22.8252266 , 90.31364028, 71.45629137,\n",
       "       34.32928778, 49.90021701, 57.82790169, 90.18307693, 52.71020508,\n",
       "        4.37248993, 99.19034421, 43.49641918, 91.43200285, 38.88519619,\n",
       "       87.31336992, 85.27853155, 38.59268811, 21.38292392, 28.89497952,\n",
       "       63.97828694,  9.32114043, 94.2860323 , 67.32812315, 11.59505624,\n",
       "       89.60322313, 65.29211118, 28.35101787, 53.15742267, 97.06572541,\n",
       "       90.20759753, 99.72005092, 30.54779196, 99.87712067, 51.44041505,\n",
       "       77.06212412, 58.00468992, 89.70375746, 11.54967882, 65.99904723,\n",
       "        3.54165483, 39.59921523, 18.42266877, 41.91468144, 78.72957495,\n",
       "       37.74087603, 46.42494793, 45.51476976,  6.6295963 , 55.56110509,\n",
       "       41.70129659, 62.79875187, 43.5800473 , 71.13001042, 66.58592771,\n",
       "       34.88457248, 66.36602253, 70.42746458, 28.81987688, 23.82952431,\n",
       "       55.54583673, 18.86600223, 71.99843093, 69.58836276,  7.40583417,\n",
       "       55.9290922 , 63.88481835, 40.49188544, 81.76814657, 23.91812497,\n",
       "       97.12356037, 87.72888049, 23.5467403 ,  9.91766421, 54.49355654,\n",
       "       94.80589326, 85.0925874 , 42.9035636 , 35.4074615 , 85.74094001,\n",
       "       85.29724961, 78.69422009, 93.88531889,  1.91114894,  8.35013631,\n",
       "       81.35857237, 96.58928956, 14.96986652,  4.51965273, 18.76465261,\n",
       "       48.20441099, 11.01367646, 32.5464884 , 83.91009799, 43.05660662,\n",
       "       55.58054646, 85.6051006 , 37.27065264, 29.23600466, 61.98880438,\n",
       "       23.40683658,  8.73572281, 12.5780708 , 61.97662   , 75.39708566,\n",
       "       30.86608386, 28.23203191, 80.31505372,  9.9430856 , 65.7743332 ,\n",
       "       80.53733201, 90.75376285, 50.19607544, 67.80631336,  7.65902916,\n",
       "       25.52639161, 32.78467178, 58.53780351, 66.21926794, 32.82406798,\n",
       "       48.56459098, 31.916896  , 22.19556823, 87.98891375, 33.93848311,\n",
       "       89.87015706, 43.46471924, 78.99058464, 74.8917485 , 53.49389516,\n",
       "       34.16920218,  8.36695026, 35.05523802, 36.44041851, 67.32627207,\n",
       "       20.68761506, 75.28144536, 81.84296375, 75.05291647, 25.89441905,\n",
       "       41.71943856, 60.32045188, 67.49597781,  8.59341878, 16.35732665,\n",
       "       82.27752258, 84.0430634 , 21.89443452, 57.84318896, 76.33390719,\n",
       "        5.03865717, 32.87868733, 39.98074345, 58.72895018, 53.89488776,\n",
       "       16.84976396, 76.37786876, 88.30790222, 95.18498538, 88.43881969,\n",
       "       10.74906256, 64.96716397,  6.38143823, 71.6895052 , 17.87446043,\n",
       "       57.62254779, 70.70280433, 13.58816799, 21.27095675, 73.02813501,\n",
       "       14.54336889, 81.12768622, 36.43237455, 98.33159296, 77.1175084 ,\n",
       "       56.32993189, 37.77787235, 86.15033356, 95.1657446 , 56.1391928 ,\n",
       "        3.33269156, 87.51147207, 12.48020131, 37.38358574, 51.82399254,\n",
       "       85.17045198, 10.06535465,  4.38184052, 88.72640384, 56.32410384,\n",
       "        5.68598327, 36.82194916, 92.78379779, 33.39425213, 54.95334915,\n",
       "       85.94358896, 83.63198392, 31.14138104, 25.76465325, 40.10815033,\n",
       "       29.93102743, 87.82450043, 87.0613059 , 98.5794072 , 55.842131  ,\n",
       "       79.01925454,  7.70400408, 52.11817952, 30.8189784 ,  2.91965406,\n",
       "       13.6781815 , 15.12406058, 56.79443758, 26.53000083, 30.88338582,\n",
       "       65.50542143,  6.82709354, 54.19720068, 45.04461585, 87.87798472,\n",
       "       73.27065288, 54.22309175, 96.22197906, 23.35058715, 37.97415674,\n",
       "       72.42933878, 20.0757852 , 95.37401501, 85.05327666, 61.81980442,\n",
       "       69.05262958,  2.47239674, 32.78089927, 18.97786073, 14.66373124,\n",
       "       64.38037433, 14.06439643,  7.88521442, 34.27349917, 91.30270012,\n",
       "       50.77830259, 39.92756108, 64.42967576, 54.25245251, 18.46216324,\n",
       "       16.3073457 ,  3.21559196, 90.83863994, 82.88699709, 96.34412644,\n",
       "       64.48614797, 79.30412286, 69.83996183, 47.19306815, 31.05912063,\n",
       "       91.19304615, 79.1326671 , 20.91611598, 53.23337673, 40.79977915,\n",
       "       75.96391179, 91.31188341,  4.60932064, 60.02520109, 80.06573205,\n",
       "       28.56731442, 10.91341691, 89.2289396 , 33.27688809, 88.98493405,\n",
       "       22.49696371, 27.43148086, 64.56889446, 47.91786999, 83.40675052,\n",
       "       94.32205803, 74.6907083 , 69.04350503, 82.47487169, 28.93519227,\n",
       "       46.39544481, 78.34537786, 12.09724051, 14.53354392, 82.302103  ,\n",
       "       17.19395458, 29.60479998, 69.93440739, 92.85866959, 61.61931256,\n",
       "        5.80564087, 50.15101646, 81.28072275, 36.94549342,  4.36878219,\n",
       "        5.87871949, 94.00096934, 65.22752929, 60.66694428, 88.27438076,\n",
       "       40.56594596, 23.74457297, 79.11077282, 34.30046574, 24.68386668,\n",
       "       99.08402707, 12.97650105, 78.91590839, 85.80182735, 95.04699804,\n",
       "       71.64920897, 13.5941554 , 80.01214555, 80.58090451, 64.91685865,\n",
       "       48.60988235, 11.78744087, 76.5527322 , 46.72406034, 88.70228966,\n",
       "       17.0732701 , 51.73385222, 41.25930885, 24.11436322, 47.46343385,\n",
       "       27.79711887, 64.86774917, 74.91027445, 60.12828689, 69.29063747,\n",
       "       46.42082819, 77.06172463, 28.75769098, 25.38818924, 62.86101569,\n",
       "       62.17339483, 60.23323666, 28.43954838, 11.10739197, 55.77612286,\n",
       "       12.67580226, 95.40992531, 62.42992154, 56.06482565, 46.12781689,\n",
       "       12.03525238,  9.89705202, 52.74351118, 94.65177242, 56.47294124,\n",
       "       15.82019626, 20.38215606,  2.38069139, 56.81831224, 80.84914494,\n",
       "       14.53097875, 88.48943365, 92.97658183, 92.57013978, 49.40256786,\n",
       "       56.06991209, 81.67945331, 97.11608435,  4.92776729,  1.3771565 ,\n",
       "       91.31110986, 90.80864324, 15.9037535 , 85.81519919, 79.76466967,\n",
       "       53.39190823, 40.88215654, 35.98198293, 91.2566525 , 69.75144119,\n",
       "       21.32552851, 48.98342546, 30.83134303,  3.02042083,  8.62269438,\n",
       "       31.47233402, 90.3420669 ,  1.00491528, 41.7978035 , 21.63776208,\n",
       "       46.70208863, 59.92869295, 21.55388203, 62.98701444,  4.45183257,\n",
       "       88.13512421, 30.57894217, 67.18211241,  7.1852894 , 63.32296695,\n",
       "       40.47106611, 82.46440949, 55.99998777, 65.94642036, 17.88883329,\n",
       "       84.37839975, 70.25555238, 50.43084756, 37.37166596, 15.05648505,\n",
       "       76.20628745, 70.10005939, 52.17012073, 71.61366057, 67.03226755,\n",
       "       40.21254478,  8.80774537, 90.83517444, 85.03965457, 18.85223271,\n",
       "       77.42658886, 12.59288102, 52.47095802, 20.41637383, 85.87626666,\n",
       "       27.87167901, 59.44302695, 18.20788808, 10.44638281, 56.79568224,\n",
       "       37.6338477 , 52.92135026, 68.42349055, 34.1362987 , 52.95759166,\n",
       "       92.21537018,  1.66060537, 88.44675783, 80.98066845,  3.28514697,\n",
       "       54.01542978, 13.65847397, 16.99730425,  7.76964967,  3.88317039,\n",
       "       93.86374579, 36.13225968, 60.96492413, 29.45753097, 88.3003696 ,\n",
       "       97.0733586 , 27.05594121, 24.92214054, 93.61527649, 11.9576937 ,\n",
       "       99.84326102,  1.267823  , 46.33099186, 75.86836483, 70.78338433,\n",
       "       74.47149114, 88.04387566,  7.42541445, 17.97614452, 27.59771801,\n",
       "       23.26554208, 41.1571498 , 59.49604902, 65.47981923, 74.44316543,\n",
       "       20.58415102, 84.83878697, 46.34912541, 42.00300668, 15.54338058,\n",
       "       89.30469477, 94.97632108, 15.11922228, 26.02091974, 50.66762452,\n",
       "       41.08850685,  5.11189478, 91.92108523, 67.04864043, 14.66461341,\n",
       "       97.22322874, 76.70158353, 96.63558981, 52.79773946, 66.26472366,\n",
       "       17.74787387, 19.5352013 , 74.25434184, 12.53154567, 64.76064791])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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