From 14d3ef8ed08ef8ea2c0f6ee985e08b28721d18cc Mon Sep 17 00:00:00 2001
From: Gokulakrishnan Thiagarajan <33049124+Gokulceo@users.noreply.github.com>
Date: Sun, 20 Oct 2019 13:08:56 +0530
Subject: [PATCH] Added Numpy Basics

---
 numpy/Numpy Basics.ipynb | 946 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 946 insertions(+)
 create mode 100644 numpy/Numpy Basics.ipynb

diff --git a/numpy/Numpy Basics.ipynb b/numpy/Numpy Basics.ipynb
new file mode 100644
index 00000000..91f61268
--- /dev/null
+++ b/numpy/Numpy Basics.ipynb	
@@ -0,0 +1,946 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as pp"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Creating a numpy array from Python List."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array({1, 2, 3, 4}, dtype=object)"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a = np.array({1,2,3,4})\n",
+    "a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1, 2, 3, 4])"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "b = np.array([1,2,3,4])\n",
+    "b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "dtype('int32')"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "b.dtype"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "dtype('O')"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a.dtype"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "a is created using Dicts{}, hence it took the type object. b is created by list [], so it is int type.\n",
+    "\n",
+    "To specify type manually, use it as argument."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1., 2., 3., 4.])"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "b = np.array([1,2,3,4], dtype=np.float64)\n",
+    "b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(1, (4,), 4)"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "b.ndim, b.shape, b.size"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1., 2., 3.],\n",
+       "       [4., 5., 6.]])"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c = np.array([[1,2,3],[4,5,6]], dtype=np.float64)\n",
+    "c"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(2, (2, 3), 6)"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c.ndim, c.shape, c.size"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Shape gives 2 rows 3 colomns. Dimension is 2. size is 6 elements. \n",
+    "\n",
+    "Making array of zeros. 'd' is shorthand for float64 i.e double.\n",
+    "Making empty array. It can be dangerous as it occupies more space with large digits.\n",
+    "Making array of regular spacing."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[0., 0., 0.],\n",
+       "       [0., 0., 0.],\n",
+       "       [0., 0., 0.]])"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.zeros((3,3),'d')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[0., 0., 0.],\n",
+       "       [0., 0., 0.],\n",
+       "       [0., 0., 0.]])"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.empty((3,3),'d')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 0. ,  2.5,  5. ,  7.5, 10. ])"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.linspace(0,10,5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "between 0 to 10 ,5 elements including them. Can use step a-range."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0, 2, 4, 6, 8])"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.arange(0,10,2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[-0.85105285, -0.19875055, -0.85600341, -1.4467229 ],\n",
+       "       [-1.01201233, -0.90678664, -0.86379668,  0.22333034]])"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.random.standard_normal((2,4))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Creating two arrays and making one as top of another using stack as stacking up."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = np.random.standard_gamma((2,3))\n",
+    "b = np.random.standard_gamma((2,3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1.65620786, 2.25568415],\n",
+       "       [2.0661573 , 3.8167515 ]])"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.vstack([a,b])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([2.0661573, 3.8167515])"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1.65620786, 2.25568415])"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "vstack and hstack - horizontal and vertical."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1.65620786, 2.25568415, 2.0661573 , 3.8167515 ])"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.hstack([a,b])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1.65620786, 2.25568415])"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a.transpose()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To save an array to a file and load it back."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1.65620786, 2.25568415])"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.save('examplearray.npy', a )\n",
+    "al = np.load('examplearray.npy')\n",
+    "al"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Plot here itself instead of outside."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 0.        ,  0.25641026,  0.51282051,  0.76923077,  1.02564103,\n",
+       "        1.28205128,  1.53846154,  1.79487179,  2.05128205,  2.30769231,\n",
+       "        2.56410256,  2.82051282,  3.07692308,  3.33333333,  3.58974359,\n",
+       "        3.84615385,  4.1025641 ,  4.35897436,  4.61538462,  4.87179487,\n",
+       "        5.12820513,  5.38461538,  5.64102564,  5.8974359 ,  6.15384615,\n",
+       "        6.41025641,  6.66666667,  6.92307692,  7.17948718,  7.43589744,\n",
+       "        7.69230769,  7.94871795,  8.20512821,  8.46153846,  8.71794872,\n",
+       "        8.97435897,  9.23076923,  9.48717949,  9.74358974, 10.        ])"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x = np. linspace(0,10,40) \n",
+    "x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 0.        ,  0.25360981,  0.49063689,  0.69558279,  0.85504677,\n",
+       "        0.95860198,  0.99947728,  0.97499996,  0.88677052,  0.740558  ,\n",
+       "        0.54592277,  0.31559139,  0.06462451, -0.19056796, -0.43329981,\n",
+       "       -0.64769957, -0.81974833, -0.93819637, -0.99529876, -0.98732176,\n",
+       "       -0.91478695, -0.78243716, -0.59892631, -0.37625358, -0.12897884,\n",
+       "        0.12672941,  0.37415123,  0.5971085 ,  0.78102277,  0.91386845,\n",
+       "        0.98695921,  0.99551587,  0.93897894,  0.82104518,  0.64942592,\n",
+       "        0.43534277,  0.19279396, -0.06236104, -0.31343844, -0.54402111])"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sinx = np.sin(x)\n",
+    "sinx"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x256138e6a90>]"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pp.plot(x,sinx)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x25613951518>]"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "cosx = np.cos(x)\n",
+    "pp.plot(x,cosx)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x2561396de48>]"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pp.plot(x,cosx)\n",
+    "pp.plot(x,sinx)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x256139cb198>]"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pp.plot(x,cosx,'x')\n",
+    "pp.plot(x,sinx,'o')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x256137a7b00>"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "y = sinx * cosx\n",
+    "z= sinx**2 - cosx**2\n",
+    "pp.plot(x,y)\n",
+    "pp.plot(x,z)\n",
+    "pp.legend(['sinx * cosx','sinx**2 - cosx**2'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To do linear algebra, eg: multilpy elemnt by element and take whole sum"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.7926526973869159"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.dot(sinx,cosx)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 0.        ,  0.        ,  0.        , ..., -0.        ,\n",
+       "        -0.        , -0.        ],\n",
+       "       [ 0.25360981,  0.24531844,  0.22098649, ..., -0.2531162 ,\n",
+       "        -0.24083004, -0.21279677],\n",
+       "       [ 0.49063689,  0.4745963 ,  0.42752338, ..., -0.48968194,\n",
+       "        -0.46591297, -0.41167944],\n",
+       "       ...,\n",
+       "       [-0.06236104, -0.06032224, -0.05433917, ...,  0.06223966,\n",
+       "         0.05921857,  0.05232537],\n",
+       "       [-0.31343844, -0.30319107, -0.27311901, ...,  0.31282838,\n",
+       "         0.29764381,  0.26299727],\n",
+       "       [-0.54402111, -0.52623521, -0.47404048, ...,  0.54296226,\n",
+       "         0.51660708,  0.45647263]])"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.outer(sinx,cosx)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 0. ,  2.5,  5. ,  7.5, 10. ])"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v= np.linspace(0,10,5)\n",
+    "v"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 1. ,  3.5,  6. ,  8.5, 11. ])"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v+1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It added + 1 to all elements. In case of 2D,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[  0.  ,   0.  ,   0.  ,   0.  ,   0.  ],\n",
+       "       [  0.  ,   6.25,  12.5 ,  18.75,  25.  ],\n",
+       "       [  0.  ,  12.5 ,  25.  ,  37.5 ,  50.  ],\n",
+       "       [  0.  ,  18.75,  37.5 ,  56.25,  75.  ],\n",
+       "       [  0.  ,  25.  ,  50.  ,  75.  , 100.  ]])"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "vv= np.outer(v,v)\n",
+    "vv"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 0. ,  2.5,  5. ,  7.5, 10. ])"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[  0.  ,   2.5 ,   5.  ,   7.5 ,  10.  ],\n",
+       "       [  0.  ,   8.75,  17.5 ,  26.25,  35.  ],\n",
+       "       [  0.  ,  15.  ,  30.  ,  45.  ,  60.  ],\n",
+       "       [  0.  ,  21.25,  42.5 ,  63.75,  85.  ],\n",
+       "       [  0.  ,  27.5 ,  55.  ,  82.5 , 110.  ]])"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "vv+v"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here it added v to every row. To add to every colomn, newaxis is used."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[  0.  ,   0.  ,   0.  ,   0.  ,   0.  ],\n",
+       "       [  2.5 ,   8.75,  15.  ,  21.25,  27.5 ],\n",
+       "       [  5.  ,  17.5 ,  30.  ,  42.5 ,  55.  ],\n",
+       "       [  7.5 ,  26.25,  45.  ,  63.75,  82.5 ],\n",
+       "       [ 10.  ,  35.  ,  60.  ,  85.  , 110.  ]])"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "vv + v[:,np.newaxis]"
+   ]
+  },
+  {
+   "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}