{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Random numbers\n", "Module 4 of Phys212/Biol212 class\n", "### by Ilya Nemenman, Apr 1, 2019" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#Initialization\n", "import numpy as np\n", "import numpy.random as nprnd #note the new module we will be using\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Build-in routines for random numbers generation\n", "We will first experiment with the build-in routines for generating uniform standard random numbers (floating point numbers between 0 and 1)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.18590467 0.07836866 0.88528726 0.65363238 0.72467075]\n", "[0.27348864 0.20588525 0.71587173 0.8270549 0.61474691]\n", "[0.40927548 0.1366544 0.01833716 0.23766533 0.03440748]\n", "[[0.61276945 0.92588603 0.31267497]\n", " [0.40944355 0.79352273 0.7745568 ]\n", " [0.39695436 0.07900055 0.11994983]\n", " [0.4909904 0.18042629 0.14048044]\n", " [0.15692658 0.70117428 0.50980741]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Examples of random number generation using built-in routines. The r1 variable should be pointing at an \n", "# array of 5 random numbers. We do the same calls multiple times to illustrate that the numbers are, indeed,\n", "# seeminly random (or rather pseudo-random)\n", "r1 = nprnd.random(5)\n", "print(r1)\n", "r1 = nprnd.random(5)\n", "print(r1)\n", "r1 = nprnd.random(5)\n", "print(r1)\n", "\n", "# The following command generates a 5x3 matrix of pseudo-random numbers.\n", "r2 = nprnd.random((5, 3))\n", "print(r2)\n", "\n", "# Finally, the following command generates 10^5 pseudo-random numbers and histograms them into 50 bins,\n", "# illustrating that the numbers we generate are, indeed, uniformely distributed.\n", "plt.hist(nprnd.random(int(1e5)), bins=50)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear congruential random number generator\n", "Most pseudo-random generators in use today have underneath them some version of a linear congruential generator illustrated above. They may have bells ans whistles on top, but the core remains the same. In **your work** part, experiment with the generator by using different multipliers, moduli, and increments. What happens if the multiplier has common divisers witht he modulus? Do the numbers still look reasonably random?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# simple linear congruential random number generator\n", "# similar to the one that is built-in\n", "seed = 10\n", "multiplier = 7**5\n", "modulus = 2**31-1\n", "increment = 0\n", "\n", "n_rands = 10000 # we will generate these many numbers\n", "\n", "rand_flt = np.zeros(n_rands) # allocate memory for our pseudo-random numbers\n", "rand_flt[0] = seed # seed\n", "\n", "for i in np.arange(1, n_rands): # generate the pseudo-random integres\n", " rand_flt[i] = np.mod(rand_flt[i-1] * multiplier + increment, modulus)\n", "\n", "rand_flt = rand_flt / modulus # transform the pseudo-random integers into pseudo-random standard uniform numbers\n", "plt.hist(rand_flt, 50) # show the resulting histogram of random numbers\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Examples of using the standard uniform pseudo-random number to generate other types of pseudo-random numbers\n", "Make sure to run each cell multiple times to convince yourself that the generated numbers indeed change." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating integer randoms 1...4\n", "rand4 = np.floor(nprnd.random(1000)*4)\n", "plt.hist(rand4)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating integer 1...6 with nonuniform probabilities \n", "p1 = .2\n", "p2 = .3\n", "p3 = .1\n", "p4 = .15\n", "p5 = .1\n", "p6 = 1 - p1 - p2 - p3 - p4 - p5\n", "\n", "rand6 = nprnd.random(1000)\n", "\n", "for i in np.arange(1000):\n", " if rand6[i] < p1:\n", " rand6[i] = 1\n", " elif rand6[i] < p1 + p2:\n", " rand6[i] = 2\n", " elif rand6[i] < p1 + p2 + p3:\n", " rand6[i] = 3\n", " elif rand6[i] < p1 + p2 + p3 + p4:\n", " rand6[i] = 4\n", " elif rand6[i] < p1 + p2 + p3 + p4 + p5:\n", " rand6[i] = 5\n", " else:\n", " rand6[i] = 6\n", "\n", "plt.hist(rand6)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAEUVJREFUeJzt3W+MnWd55/HvDwdoC7ub0EyiYJudbNfdEpBIkBXSjbRiSZs4CVqn0mblSEtdFMm8SHahQqoMWild2kiuVGBBgkiBeDG7LGnEH8UiVlNvSoX6ghAnpAHHjTINbjLYjadNCLCo0KTXvji3y8EZz5yZOTPHnvv7kY7O81znfs65btma3zz/zqSqkCT15xWTbkCSNBkGgCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlT50y6gYWcf/75NT09Pek2JOms8vDDD/9tVU0tNu6MDoDp6WkOHTo06TYk6ayS5K9HGechIEnqlAEgSZ0yACSpUwaAJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6tQZfSfwSk3vvm+kcUf3XL/KnUjSmcc9AEnqlAEgSZ0yACSpU4sGQJKfS/KNJH+R5HCS/97qFyd5MMmTSf4oyata/dVtfaa9Pj30Xh9o9SeSXLNak5IkLW6UPYAfA++oqrcAlwLbklwB/AHw0araAjwP3NzG3ww8X1X/GvhoG0eSS4AdwJuAbcAnk2wY52QkSaNbNABq4Idt9ZXtUcA7gC+0+j7ghra8va3TXr8qSVr97qr6cVV9B5gBLh/LLCRJSzbSOYAkG5I8CpwADgJ/BXyvql5sQ2aBjW15I/AMQHv9BeAXh+vzbCNJWmMjBUBVvVRVlwKbGPzW/sb5hrXnnOa109V/RpJdSQ4lOTQ3NzdKe5KkZVjSVUBV9T3gz4ArgHOTnLyRbBNwrC3PApsB2uv/AnhuuD7PNsOfcWdVba2qrVNTi/5JS0nSMo1yFdBUknPb8s8DvwYcAb4K/Mc2bCdwb1ve39Zpr/9pVVWr72hXCV0MbAG+Ma6JSJKWZpSvgrgI2Neu2HkFcE9VfSXJ48DdSX4f+CZwVxt/F/C/ksww+M1/B0BVHU5yD/A48CJwS1W9NN7pSJJGtWgAVNVjwGXz1J9inqt4qurvgRtP8163A7cvvU1J0rh5J7AkdcoAkKROGQCS1CkDQJI6ZQBIUqcMAEnqlAEgSZ0yACSpUwaAJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6pQBIEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTiwZAks1JvprkSJLDSd7b6r+b5LtJHm2P64a2+UCSmSRPJLlmqL6t1WaS7F6dKUmSRnHOCGNeBN5fVY8k+WfAw0kOttc+WlV/ODw4ySXADuBNwOuB/5vkl9vLnwB+HZgFHkqyv6oeH8dEJElLs2gAVNVx4Hhb/kGSI8DGBTbZDtxdVT8GvpNkBri8vTZTVU8BJLm7jTUAJGkClnQOIMk0cBnwYCvdmuSxJHuTnNdqG4FnhjabbbXT1SVJEzByACR5LfBF4H1V9X3gDuCXgEsZ7CF8+OTQeTavBeqnfs6uJIeSHJqbmxu1PUnSEo0UAEleyeCH/+eq6ksAVfVsVb1UVf8IfIqfHuaZBTYPbb4JOLZA/WdU1Z1VtbWqtk5NTS11PpKkEY1yFVCAu4AjVfWRofpFQ8N+A/h2W94P7Ejy6iQXA1uAbwAPAVuSXJzkVQxOFO8fzzQkSUs1ylVAVwLvAr6V5NFW+yBwU5JLGRzGOQq8B6CqDie5h8HJ3ReBW6rqJYAktwL3AxuAvVV1eIxzkSQtwShXAf058x+/P7DANrcDt89TP7DQdpKkteOdwJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkdcoAkKROGQCS1CkDQJI6ZQBIUqcMAEnqlAEgSZ0yACSpUwaAJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6pQBIEmdOmfSDZwJpnffN9K4o3uuX+VOJGntuAcgSZ0yACSpU4sGQJLNSb6a5EiSw0ne2+qvS3IwyZPt+bxWT5KPJ5lJ8liStw691842/skkO1dvWpKkxYyyB/Ai8P6qeiNwBXBLkkuA3cADVbUFeKCtA1wLbGmPXcAdMAgM4DbgbcDlwG0nQ0OStPYWDYCqOl5Vj7TlHwBHgI3AdmBfG7YPuKEtbwc+WwNfB85NchFwDXCwqp6rqueBg8C2sc5GkjSyJZ0DSDINXAY8CFxYVcdhEBLABW3YRuCZoc1mW+10dUnSBIwcAEleC3wReF9VfX+hofPUaoH6qZ+zK8mhJIfm5uZGbU+StEQjBUCSVzL44f+5qvpSKz/bDu3Qnk+0+iyweWjzTcCxBeo/o6rurKqtVbV1ampqKXORJC3BKFcBBbgLOFJVHxl6aT9w8kqencC9Q/XfbFcDXQG80A4R3Q9cneS8dvL36laTJE3AKHcCXwm8C/hWkkdb7YPAHuCeJDcDTwM3ttcOANcBM8CPgHcDVNVzSX4PeKiN+1BVPTeWWUiSlmzRAKiqP2f+4/cAV80zvoBbTvNee4G9S2lQkrQ6vBNYkjplAEhSpwwASeqUASBJnTIAJKlTBoAkdcoAkKROGQCS1CkDQJI6ZQBIUqcMAEnqlAEgSZ0yACSpUwaAJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6pQBIEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjq1aAAk2ZvkRJJvD9V+N8l3kzzaHtcNvfaBJDNJnkhyzVB9W6vNJNk9/qlIkpZilD2AzwDb5ql/tKoubY8DAEkuAXYAb2rbfDLJhiQbgE8A1wKXADe1sZKkCTlnsQFV9bUk0yO+33bg7qr6MfCdJDPA5e21map6CiDJ3W3s40vuWJI0Fis5B3BrksfaIaLzWm0j8MzQmNlWO139ZZLsSnIoyaG5ubkVtCdJWshyA+AO4JeAS4HjwIdbPfOMrQXqLy9W3VlVW6tq69TU1DLbkyQtZtFDQPOpqmdPLif5FPCVtjoLbB4augk41pZPV5ckTcCy9gCSXDS0+hvAySuE9gM7krw6ycXAFuAbwEPAliQXJ3kVgxPF+5fftiRppRbdA0jyeeDtwPlJZoHbgLcnuZTBYZyjwHsAqupwknsYnNx9Ebilql5q73MrcD+wAdhbVYfHPhtJ0shGuQropnnKdy0w/nbg9nnqB4ADS+pOkrRqvBNYkjq1rJPAvZrefd9I447uuX6VO5GklXMPQJI6ZQBIUqcMAEnqlAEgSZ0yACSpUwaAJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6pQBIEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkdeqcxQYk2Qu8EzhRVW9utdcBfwRMA0eB/1RVzycJ8DHgOuBHwG9V1SNtm53Af2tv+/tVtW+8UzlzTO++b6RxR/dcv8qdSNLpjbIH8Blg2ym13cADVbUFeKCtA1wLbGmPXcAd8E+BcRvwNuBy4LYk5620eUnS8i0aAFX1NeC5U8rbgZO/we8Dbhiqf7YGvg6cm+Qi4BrgYFU9V1XPAwd5eahIktbQcs8BXFhVxwHa8wWtvhF4ZmjcbKudrv4ySXYlOZTk0Nzc3DLbkyQtZtwngTNPrRaov7xYdWdVba2qrVNTU2NtTpL0U8sNgGfboR3a84lWnwU2D43bBBxboC5JmpDlBsB+YGdb3gncO1T/zQxcAbzQDhHdD1yd5Lx28vfqVpMkTcgol4F+Hng7cH6SWQZX8+wB7klyM/A0cGMbfoDBJaAzDC4DfTdAVT2X5PeAh9q4D1XVqSeWJUlraNEAqKqbTvPSVfOMLeCW07zPXmDvkrqTJK0a7wSWpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkdcoAkKROGQCS1CkDQJI6ZQBIUqcMAEnq1KLfBqrVM737vpHGHd1z/Sp3IqlH7gFIUqcMAEnqlAEgSZ0yACSpUwaAJHXKAJCkThkAktQpA0CSOmUASFKnDABJ6tSKAiDJ0STfSvJokkOt9rokB5M82Z7Pa/Uk+XiSmSSPJXnrOCYgSVqecewB/PuqurSqtrb13cADVbUFeKCtA1wLbGmPXcAdY/hsSdIyrcYhoO3Avra8D7hhqP7ZGvg6cG6Si1bh8yVJI1hpABTwJ0keTrKr1S6squMA7fmCVt8IPDO07WyrSZImYKVfB31lVR1LcgFwMMlfLjA289TqZYMGQbIL4A1veMMK25Mknc6K9gCq6lh7PgF8GbgcePbkoZ32fKINnwU2D22+CTg2z3veWVVbq2rr1NTUStqTJC1g2XsASV4DvKKqftCWrwY+BOwHdgJ72vO9bZP9wK1J7gbeBrxw8lCRFjbqH44B/3iMpNGt5BDQhcCXk5x8n/9TVX+c5CHgniQ3A08DN7bxB4DrgBngR8C7V/DZkqQVWnYAVNVTwFvmqf8dcNU89QJuWe7nSZLGyzuBJalTBoAkdcoAkKROGQCS1CkDQJI6tdI7gXWGGfWeAe8XkOQegCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASeqUl4F2ystFJbkHIEmdMgAkqVMeAtKCPFQkrV/uAUhSpwwASeqUASBJnTIAJKlTngTWWHiyWDr7uAcgSZ1yD0Bryj0F6czhHoAkdWrN9wCSbAM+BmwAPl1Ve9a6B5353FOQVt+aBkCSDcAngF8HZoGHkuyvqsfXsg+tH6MGBRgW0qnWeg/gcmCmqp4CSHI3sB0wALTqlhIWozBQdLZb6wDYCDwztD4LvG2Ne5DGYtyBMkmGWZ/WOgAyT61+ZkCyC9jVVn+Y5IkVfN75wN+uYPszmXM7O52Rc8sfjOVtzsi5jcnZNrd/OcqgtQ6AWWDz0Pom4NjwgKq6E7hzHB+W5FBVbR3He51pnNvZybmdndbr3Nb6MtCHgC1JLk7yKmAHsH+Ne5AkscZ7AFX1YpJbgfsZXAa6t6oOr2UPkqSBNb8PoKoOAAfW6OPGcijpDOXczk7O7ey0LueWqlp8lCRp3fGrICSpU+syAJJsS/JEkpkkuyfdz7gk2Zzkq0mOJDmc5L2T7mnckmxI8s0kX5l0L+OW5NwkX0jyl+3f8Fcn3dO4JPnt9n/y20k+n+TnJt3TciXZm+REkm8P1V6X5GCSJ9vzeZPscVzWXQAMfd3EtcAlwE1JLplsV2PzIvD+qnojcAVwyzqa20nvBY5MuolV8jHgj6vqV4C3sE7mmWQj8F+BrVX1ZgYXeOyYbFcr8hlg2ym13cADVbUFeKCtn/XWXQAw9HUTVfUT4OTXTZz1qup4VT3Sln/A4AfIxsl2NT5JNgHXA5+edC/jluSfA/8OuAugqn5SVd+bbFdjdQ7w80nOAX6BU+7vOZtU1deA504pbwf2teV9wA1r2tQqWY8BMN/XTaybH5InJZkGLgMenGwnY/U/gN8B/nHSjayCfwXMAf+zHeL6dJLXTLqpcaiq7wJ/CDwNHAdeqKo/mWxXY3dhVR2HwS9iwAUT7mcs1mMALPp1E2e7JK8Fvgi8r6q+P+l+xiHJO4ETVfXwpHtZJecAbwXuqKrLgP/HOjmM0I6HbwcuBl4PvCbJf55sVxrFegyARb9u4myW5JUMfvh/rqq+NOl+xuhK4D8kOcrgsN07kvzvybY0VrPAbFWd3GP7AoNAWA9+DfhOVc1V1T8AXwL+7YR7Grdnk1wE0J5PTLifsViPAbBuv24iSRgcQz5SVR+ZdD/jVFUfqKpNVTXN4N/sT6tq3fwWWVV/AzyT5N+00lWsn69Bfxq4IskvtP+jV7FOTnAP2Q/sbMs7gXsn2MvYrLu/CbzOv27iSuBdwLeSPNpqH2x3V+vM91+Az7VfTJ4C3j3hfsaiqh5M8gXgEQZXqn2Ts/jO2SSfB94OnJ9kFrgN2APck+RmBoF34+Q6HB/vBJakTq3HQ0CSpBEYAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkder/Aw6SpDycvRHlAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating exponential random numbers using built-in function\n", "plt.hist(nprnd.exponential(size=n_rands), 30)\n", "plt.show()\n", "# and comparing built-in to our own generator\n", "plt.hist([nprnd.exponential(size=n_rands), -np.log(nprnd.random(10000))], 30,log=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Your work: different (some wrong) attempts to generate a random number in a circle\n", "Run all of them and figure out which one is correct and why. Also modify the code to check which way of gheneration is faster." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = 2*nprnd.random(int(1e3)) - 1 # generate random x\n", "y = 2*nprnd.random(int(1e3)) - 1 # generate random y\n", "r = np.sqrt(x**2+y**2) # calculate radius \n", "# the line below -- we should check that r>0, but we don't now\n", "scale = nprnd.random(int(1e3)) # generating random distance from the center\n", "x = x/r*scale # keeping the angle and moving to the distance\n", "y = y/r*scale\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n", "\n", "r = nprnd.random(int(1e3)) # generate random radius\n", "phi = 2*np.pi*nprnd.random(int(1e3)) # generate random angle\n", "x = r*np.cos(phi)\n", "y = r*np.sin(phi)\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n", "r2 = nprnd.random(int(1e3)) # generate random radius squared\n", "phi = 2*np.pi*nprnd.random(int(1e3)) # generate random angle\n", "x = np.sqrt(r2)*np.cos(phi)\n", "y = np.sqrt(r2)*np.sin(phi)\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n", "# rejection method\n", "x = 2*nprnd.random(int(1e3)) - 1 # generate random x\n", "y = 2*nprnd.random(int(1e3)) - 1 # generate random y\n", "ind = (x**2+y**2 < 1) # which points fall in the circle?\n", "x = x[ind]\n", "y = y[ind] # note that we generated fewer than 10^3 data points\n", "plt.plot(x, y, 'o')\n", "plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating gaussian random numbers using built-in function\n", "plt.hist(nprnd.randn(n_rands), 30)\n", "plt.show()\n", "# and comparing built-in to our own generator\n", "phi = 2 * np.pi * nprnd.random(n_rands)\n", "r = np.sqrt(2 * nprnd.exponential(size=n_rands))\n", "rand_norm = r * np.cos(phi)\n", "plt.hist([nprnd.randn(n_rands), rand_norm], 30)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }