ch4_numpy_v01.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# chapter 4. Numpy basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.random.seed(12345)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('figure', figsize=(10, 6))\n",
    "np.set_printoptions(precision=4, suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "my_arr = np.arange(1000000)\n",
    "my_list = list(range(1000000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 14.6 ms, sys: 6.73 ms, total: 21.4 ms\nWall time: 25 ms\nCPU times: user 707 ms, sys: 223 ms, total: 930 ms\nWall time: 979 ms\n"
    }
   ],
   "source": [
    "# print CPU times\n",
    "%time for _ in range(10): my_arr2 = my_arr * 2\n",
    "%time for _ in range(10): my_list2 = [x * 2 for x in my_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 4.1 numpy ndarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.2047,  0.4789, -0.5194],\n       [-0.5557,  1.9658,  1.3934]])"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "data = np.random.randn(2, 3)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-2.0471,  4.7894, -5.1944],\n       [-5.5573, 19.6578, 13.9341]])"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "data * 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.4094,  0.9579, -1.0389],\n       [-1.1115,  3.9316,  2.7868]])"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "data + data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(2, 3)"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "dtype('float64')"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "data.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "### creating ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([6. , 7.5, 8. , 0. , 1. ])"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "arr1.dtype"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(5,)"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "arr1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "5"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "arr1.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "len(arr1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1, 2, 3, 4],\n       [5, 6, 7, 8]])"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(2, 4)"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "arr2.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "4"
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "arr2.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "dtype('int64')"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2"
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "# use .ndim attrib to check the number of dimensions of an array\n",
    "arr2.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "source": [
    "np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
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HetUtSZ5WVacleU2Sm7r74e7+ZpKbcuhwAwAco47UMyWnJ7l/Znv/1LZR++NU1a6qWq6q5ZWVlR9ZoQDA0XGkQkmt09aHaH98Y/fu7l7q7qWdO3cutDgA4Og7UqFkf5IzZ7bPSHLgEO0AwHHmSIWSPUneOH0L5+VJvtXdDyS5Mcmrq+rk6QHXV09tAMBxZsciDlJVH0nyiiSnVtX+rH6j5klJ0t3vTbI3yeuS7Evy3SRvmvoerqq3J7l1OtQ13X2oB2YBgGPUQkJJd1+2SX8n+ZUN+q5Lct0i6gAAti9vdAUAhiCUAABDEEoAgCEIJQDAEIQSAGAIQgkAMAShBAAYglACAAxBKAEAhiCUAABDEEoAgCEIJQDAEIQSAGAIQgkAMAShBAAYglACAAxBKAEAhiCUAABDEEoAgCEIJQDAEIQSAGAIQgkAMAShBAAYglACAAxBKAEAhiCUAABDEEoAgCEIJQDAEIQSAGAIQgkAMAShBAAYglACAAxhIaGkqq6rqger6s4N+v9RVd0+LZ+vqp+Y6ftaVd1RVbdV1fIi6gEAtp9FXSn5YJKLDtH/1SQ/3d0vTvL2JLvX9P9Md5/X3UsLqgcA2GZ2LOIg3f25qnrOIfo/P7N5S5IzFvG5AMCx42g8U/LmJJ+c2e4k/72q/ryqdm20U1XtqqrlqlpeWVn5kRcJABxZC7lSslVV9TNZDSV/f6b5gu4+UFXPSHJTVf3v7v7c2n27e3em2z5LS0t9RAoGAI6YI3alpKpenOT9SS7p7ocea+/uA9PfB5N8PMn5R6omAGAcRySUVNVZSf4kyS9295dn2p9SVT/22HqSVydZ9xs8AMCxbSG3b6rqI0lekeTUqtqf5G1JnpQk3f3eJG9N8vQkv1tVSXJw+qbNM5N8fGrbkeQ/dfd/W0RNAMD2sqhv31y2Sf+VSa5cp/2+JD/x+D0AgOONN7oCAEMQSgCAIQglAMAQhBIAYAhCCQAwBKEEABiCUAIADEEoAQCGIJQAAEMQSgCAIQglAMAQhBIAYAhCCQAwBKEEABiCUAIADEEoAQCGIJQAAEMQSgCAIQglAMAQhBIAYAhCCQAwBKEEABiCUAIADEEoAQCGIJQAAEMQSgCAIQglAMAQhBIAYAhCCQAwBKEEABiCUAIADGEhoaSqrquqB6vqzg36X1FV36qq26blrTN9F1XVPVW1r6quXkQ9AMD2s6grJR9MctEmY/5Hd583LdckSVWdkOQ9SV6b5Nwkl1XVuQuqCQDYRhYSSrr7c0kefgK7np9kX3ff193fT3JDkksWURMAsL0cyWdKfrKqvlhVn6yqF05tpye5f2bM/qkNADjO7DhCn/MXSZ7d3d+pqtcl+c9JzklS64zt9Q5QVbuS7Jo2H9no+RW27NQk3zjaRRwDzOP8zOFimMfFMI/ze94T3fGIhJLu/vbM+t6q+t2qOjWrV0bOnBl6RpIDGxxjd5LdSVJVy9299CMs+ZhnDhfDPM7PHC6GeVwM8zi/qlp+ovsekds3VfWsqqpp/fzpcx9KcmuSc6rq7Ko6McmlSfYciZoAgLEs5EpJVX0kySuSnFpV+5O8LcmTkqS735vkDUl+uaoOJvlekku7u5McrKqrktyY5IQk13X3XYuoCQDYXhYSSrr7sk36353k3Rv07U2y9zA/cvdhjufxzOFimMf5mcPFMI+LYR7n94TnsFYvWAAAHF1eMw8ADGFbhJKqOqWqbqqqe6e/J28w7tGZV9l7YDabv8a/qk6qqo9O/V+oqucc+SrHt4V5vKKqVmbOvyuPRp0j28LPUVRV/c40x7dX1UuPdI2jm+cnPVhVVWdW1Weq6ktVdVdV/bN1xjgXN7HFeTz887G7h1+S/FaSq6f1q5O8c4Nx3znatY60ZPXh4a8keW6SE5N8Mcm5a8b8kyTvndYvTfLRo133aMsW5/GKJO8+2rWOvCT5qSQvTXLnBv2vS/LJrL6/6OVJvnC0ax5t2cIcviLJfznadY68JDktyUun9R9L8uV1/j07Fxczj4d9Pm6LKyVZffX89dP69UlefxRr2U628hr/2bn9WJJXPvb1bX7IzyEsQG/+cxSXJPlQr7olydOq6rQjU932sIU5ZBPd/UB3/8W0/n+SfCmPf5O4c3ETW5zHw7ZdQskzu/uBZHUikjxjg3FPrqrlqrqlqgSXrb3G/4djuvtgkm8lefoRqW772OrPIfzcdKn3Y1V15jr9HJqfnViM9X7Sg3VMt6tfkuQLa7qci4fhEPOYHOb5eKReM7+pqvpUkmet0/WWwzjMWd19oKqem+Tmqrqju7+ymAq3pa28xn/Lr/o/jm1ljv40yUe6+5Gq+qWsXn362R95ZccW5+L8NvpJD9aoqqcm+eMk/7xn3jr+WPc6uzgX17HJPB72+TjMlZLuflV3/511lk8k+fpjl86mvw9ucIwD09/7knw2q8nteLaV1/j/cExV7Ujy43F5eK1N57G7H+ruR6bN30vysiNU27Fkyz87wfq6+9vd/Z1pfW+SJ00/6cGMqnpSVv9H+gfd/SfrDHEubsFm8/hEzsdhQskm9iS5fFq/PMkn1g6oqpOr6qRp/dQkFyS5+4hVOKatvMZ/dm7fkOTmnp5Q4oc2ncc195svzur9VQ7PniRvnL758PIk33rsti1bc4if9GAyzc8Hknypu//9BsOci5vYyjw+kfNxmNs3m7g2yR9W1ZuT/GWSn0+SqlpK8kvdfWWSFyR5X1X9IKv/4dd293EdSrp73df4V9U1SZa7e09WT6oPV9W+rF4hufToVTymLc7jr1bVxUkOZnUerzhqBQ+qNv85ir1Z/dbDviTfTfKmo1PpuLYwhxv9pAf/3wVJfjHJHVV129T2r5OclTgXD8NW5vGwz0dvdAUAhrBdbt8AAMc4oQQAGIJQAgAMQSgBAIYglAAAQxBKAIAhCCUAwBCEEgBgCP8PRxMCJ3Kl8KUAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "zeros_arr = np.zeros((2, 3))\n",
    "print(zeros_arr, '\\n')\n",
    "\n",
    "plt.imshow(zeros_arr, cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[0., 0., 0.],\n        [0., 0., 0.],\n        [0., 0., 0.],\n        [0., 0., 0.]],\n\n       [[0., 0., 0.],\n        [0., 0., 0.],\n        [0., 0., 0.],\n        [0., 0., 0.]]])"
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "source": [
    "a_3d_arr = np.zeros((2, 4, 3))\n",
    "a_3d_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[[ 0.0929  0.2817  0.769   1.2464]\n  [ 1.0072 -1.2962  0.275   0.2289]\n  [ 1.3529  0.8864 -2.0016 -0.3718]]\n\n [[ 1.669  -0.4386 -0.5397  0.477 ]\n  [ 3.2489 -1.0212 -0.5771  0.1241]\n  [ 0.3026  0.5238  0.0009  1.3438]]] \n\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 720x432 with 1 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"361.037344pt\" version=\"1.1\" viewBox=\"0 0 488.514375 361.037344\" width=\"488.514375pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 361.037344 \nL 488.514375 361.037344 \nL 488.514375 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 38.482813 337.159219 \nL 473.362813 337.159219 \nL 473.362813 10.999219 \nL 38.482813 10.999219 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g clip-path=\"url(#p3444ba5315)\">\n    <image height=\"327\" 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "a_random_3d_arr = np.random.randn(2, 3, 4)\n",
    "print(a_random_3d_arr, '\\n')\n",
    "\n",
    "extent = (a_random_3d_arr[0])\n",
    "for _ in a_random_3d_arr:\n",
    "    plt.imshow(_, cmap='binary')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "source": [
    "a_1d_range_arr = np.arange(10)\n",
    "a_1d_range_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[[1. 0. 0. 0. 0.]\n [0. 1. 0. 0. 0.]\n [0. 0. 1. 0. 0.]\n [0. 0. 0. 1. 0.]\n [0. 0. 0. 0. 1.]]\n"
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "eye_arr = np.eye(5)\n",
    "print(eye_arr)\n",
    "plt.imshow(eye_arr, cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data types for ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "dtype('float64')"
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "source": [
    "arr1 = np.array([1, 2, 3], dtype=np.float64)\n",
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "dtype('int32')"
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "source": [
    "arr2 = np.array([1, 2, 3], dtype=np.int32)\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "dtype('int64')"
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "dtype('float64')"
     },
     "metadata": {},
     "execution_count": 29
    }
   ],
   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "float_arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 3.7, -1.2, -2.6,  0.5, 12.9, 10.1])"
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "source": [
    "arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 3, -1, -2,  0, 12, 10], dtype=int32)"
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "source": [
    "arr.astype(np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([  1.23,  -9.4 , 223.  ])"
     },
     "metadata": {},
     "execution_count": 32
    }
   ],
   "source": [
    "numerical_str = np.array(['1.23', '-9.4', '223'], dtype=np.string_)\n",
    "numerical_str.astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
     },
     "metadata": {},
     "execution_count": 33
    }
   ],
   "source": [
    "# cast the data type to that of another array\n",
    "int_array = np.arange(10)\n",
    "calibers = np.array([.22, .270, .357, .380, .44, .50], dtype=np.float64)\n",
    "int_array.astype(calibers.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([3435973856, 1075629260, 1305670058, 1081004130, 1717986928,\n       1076569702,  652835029, 1081083953], dtype=uint32)"
     },
     "metadata": {},
     "execution_count": 34
    }
   ],
   "source": [
    "empty_unit32 = np.empty(8, dtype='u4')\n",
    "empty_unit32"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# arithmetic with numpy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1., 2., 3.],\n       [4., 5., 6.]])"
     },
     "metadata": {},
     "execution_count": 35
    }
   ],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 1.,  4.,  9.],\n       [16., 25., 36.]])"
     },
     "metadata": {},
     "execution_count": 36
    }
   ],
   "source": [
    "arr * arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0., 0., 0.],\n       [0., 0., 0.]])"
     },
     "metadata": {},
     "execution_count": 37
    }
   ],
   "source": [
    "arr - arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1.    , 0.5   , 0.3333],\n       [0.25  , 0.2   , 0.1667]])"
     },
     "metadata": {},
     "execution_count": 38
    }
   ],
   "source": [
    "1 / arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1.    , 1.4142, 1.7321],\n       [2.    , 2.2361, 2.4495]])"
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "source": [
    "arr ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.,  4.,  1.],\n       [ 7.,  2., 12.]])"
     },
     "metadata": {},
     "execution_count": 40
    }
   ],
   "source": [
    "arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[False,  True, False],\n       [ True, False,  True]])"
     },
     "metadata": {},
     "execution_count": 41
    }
   ],
   "source": [
    "arr2 > arr"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# basic indexing and slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 42
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "5"
     },
     "metadata": {},
     "execution_count": 43
    }
   ],
   "source": [
    "arr[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([5, 6, 7])"
     },
     "metadata": {},
     "execution_count": 44
    }
   ],
   "source": [
    "arr[5:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[5 6 7]\n"
    }
   ],
   "source": [
    "print(arr[5:8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 0,  1,  2,  3,  4, 99, 99, 99,  8,  9])"
     },
     "metadata": {},
     "execution_count": 46
    }
   ],
   "source": [
    "arr[5:8] = 99\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([99, 99, 99])"
     },
     "metadata": {},
     "execution_count": 47
    }
   ],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "* !!! array slices are **_views_** on the **_source array_**, i.e., the data in the source is not copied to the slice.\n",
    "* !!! any modifications to the **_view(slice)_** will be reflected in the source array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "6"
     },
     "metadata": {},
     "execution_count": 48
    }
   ],
   "source": [
    "# get a slice of an array\n",
    "arr = np.arange(10)\n",
    "arr_slice = arr[5:8]\n",
    "arr_slice[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[  5 999   7]\n"
    }
   ],
   "source": [
    "# modify the slice\n",
    "arr_slice[1] =  999\n",
    "print(arr_slice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[  0   1   2   3   4   5 999   7   8   9]\n"
    }
   ],
   "source": [
    "# note that the change to the slice is reflected in the source array\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[ 0  1  2  3  4 64 64 64  8  9]\n"
    }
   ],
   "source": [
    "arr_slice[:] = 64\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "* to make a copy of the data from the source array to a slice, the **_.copy()_** method must be used explicitly when \"cutting\" the slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[64 64 64]\n"
    }
   ],
   "source": [
    "# explicitly copy data from source array\n",
    "arr_slice_copied = arr[5:8].copy()\n",
    "print(arr_slice_copied)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "[999 999 999]\n[ 0  1  2  3  4 64 64 64  8  9]\n"
    }
   ],
   "source": [
    "# now, changing the slice will not affect the source array\n",
    "arr_slice_copied[:] = 999\n",
    "print(arr_slice_copied)\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1, 2, 4],\n       [3, 4, 6],\n       [4, 6, 9]])"
     },
     "metadata": {},
     "execution_count": 54
    }
   ],
   "source": [
    "arr2d = np.array([[1, 2, 4], [3, 4, 6], [4, 6, 9]])\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([3, 4, 6])"
     },
     "metadata": {},
     "execution_count": 55
    }
   ],
   "source": [
    "arr2d[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "6"
     },
     "metadata": {},
     "execution_count": 56
    }
   ],
   "source": [
    "arr2d[1][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "6"
     },
     "metadata": {},
     "execution_count": 57
    }
   ],
   "source": [
    "arr2d[1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[ 1,  2,  3],\n        [ 4,  5,  6]],\n\n       [[ 7,  8,  9],\n        [10, 11, 12]]])"
     },
     "metadata": {},
     "execution_count": 58
    }
   ],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1, 2, 3],\n       [4, 5, 6]])"
     },
     "metadata": {},
     "execution_count": 59
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([4, 5, 6])"
     },
     "metadata": {},
     "execution_count": 60
    }
   ],
   "source": [
    "arr3d[0, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1, 2, 3],\n       [4, 5, 6]])"
     },
     "metadata": {},
     "execution_count": 61
    }
   ],
   "source": [
    "old_values = arr3d[0].copy()\n",
    "old_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[42, 42, 42],\n       [42, 42, 42]])"
     },
     "metadata": {},
     "execution_count": 62
    }
   ],
   "source": [
    "arr3d[0] = 42\n",
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[ 1,  2,  3],\n        [ 4,  5,  6]],\n\n       [[ 7,  8,  9],\n        [10, 11, 12]]])"
     },
     "metadata": {},
     "execution_count": 63
    }
   ],
   "source": [
    "arr3d[0] = old_values\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 64
    }
   ],
   "source": [
    "arr3d[1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 65
    }
   ],
   "source": [
    "# the above code is the same as the following\n",
    "x = arr3d[1][0]\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# indexing with slices\n",
    "\n",
    "* Note that slicing with labels in Pandas is different from normal Python slicing in that **_the endpoint is INCLUSIVE_**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "b    1.0\nc    2.0\ndtype: float64"
     },
     "metadata": {},
     "execution_count": 66
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "obj = pd.Series(np.arange(4.0), index=['a', 'b', 'c', 'd'])\n",
    "obj['b':'c']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "a    0.0\nb    5.0\nc    5.0\nd    3.0\ndtype: float64"
     },
     "metadata": {},
     "execution_count": 67
    }
   ],
   "source": [
    "obj['b':'c'] = 5\n",
    "obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "          one  two  three  four\nOhio        0    1      2     3\nColorado    4    5      6     7\nUtah        8    9     10    11\nNY         12   13     14    15",
      "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>one</th>\n      <th>two</th>\n      <th>three</th>\n      <th>four</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Ohio</th>\n      <td>0</td>\n      <td>1</td>\n      <td>2</td>\n      <td>3</td>\n    </tr>\n    <tr>\n      <th>Colorado</th>\n      <td>4</td>\n      <td>5</td>\n      <td>6</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>Utah</th>\n      <td>8</td>\n      <td>9</td>\n      <td>10</td>\n      <td>11</td>\n    </tr>\n    <tr>\n      <th>NY</th>\n      <td>12</td>\n      <td>13</td>\n      <td>14</td>\n      <td>15</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 68
    }
   ],
   "source": [
    "data = pd.DataFrame(np.arange(16).reshape((4,4)), index=['Ohio', 'Colorado', 'Utah', 'NY'], columns=['one', 'two', 'three', 'four'])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "report one column by its index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Ohio         1\nColorado     5\nUtah         9\nNY          13\nName: two, dtype: int64"
     },
     "metadata": {},
     "execution_count": 69
    }
   ],
   "source": [
    "data['two']"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "report multiple columns by passing a one list of \"a list of column index\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "          three  one\nOhio          2    0\nColorado      6    4\nUtah         10    8\nNY           14   12",
      "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>three</th>\n      <th>one</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Ohio</th>\n      <td>2</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>Colorado</th>\n      <td>6</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>Utah</th>\n      <td>10</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>NY</th>\n      <td>14</td>\n      <td>12</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 70
    }
   ],
   "source": [
    "data[['three', 'one']]"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## boolean indexing\n",
    "\n",
    "use a boolean DataFrame for indexing, such as one produced by a scalar comparison:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "            one    two  three   four\nOhio       True   True   True   True\nColorado   True  False  False  False\nUtah      False  False  False  False\nNY        False  False  False  False",
      "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>one</th>\n      <th>two</th>\n      <th>three</th>\n      <th>four</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Ohio</th>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>Colorado</th>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>Utah</th>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>NY</th>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 71
    }
   ],
   "source": [
    "data < 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "          one  two  three  four\nOhio        0    0      0     0\nColorado    0    5      6     7\nUtah        8    9     10    11\nNY         12   13     14    15",
      "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>one</th>\n      <th>two</th>\n      <th>three</th>\n      <th>four</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Ohio</th>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>Colorado</th>\n      <td>0</td>\n      <td>5</td>\n      <td>6</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>Utah</th>\n      <td>8</td>\n      <td>9</td>\n      <td>10</td>\n      <td>11</td>\n    </tr>\n    <tr>\n      <th>NY</th>\n      <td>12</td>\n      <td>13</td>\n      <td>14</td>\n      <td>15</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 72
    }
   ],
   "source": [
    "# assign zero to all cells with value < 5\n",
    "data[data < 5] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "<class 'pandas.core.frame.DataFrame'>\n"
    }
   ],
   "source": [
    "print(type(data<5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "<class 'pandas.core.frame.DataFrame'>\n"
    }
   ],
   "source": [
    "print(type(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "names = np.array(['Bob', 'Joe','Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "data = np.random.randn(7, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')"
     },
     "metadata": {},
     "execution_count": 76
    }
   ],
   "source": [
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.7135, -0.8312, -2.3702, -1.8608],\n       [-0.8608,  0.5601, -1.2659,  0.1198],\n       [-1.0635,  0.3329, -2.3594, -0.1995],\n       [-1.542 , -0.9707, -1.307 ,  0.2863],\n       [ 0.378 , -0.7539,  0.3313,  1.3497],\n       [ 0.0699,  0.2467, -0.0119,  1.0048],\n       [ 1.3272, -0.9193, -1.5491,  0.0222]])"
     },
     "metadata": {},
     "execution_count": 77
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ True, False, False,  True, False, False, False])"
     },
     "metadata": {},
     "execution_count": 78
    }
   ],
   "source": [
    "names == \"Bob\""
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "The boolean values in the array obtained above can be used to filter \"rows\" in the same order,\n",
    "\n",
    "... i.e., row #N will be kept if the Nth boolean value in the array derived from the evaluation **_names==\"Bob\"_** is **_True_**, which is highlighted below:\n",
    "\n",
    "|           |  col_0  |  col_1  |  col_2  |  col_3  |\n",
    "| --------- |--------:|--------:|--------:|--------:|\n",
    "|**_row_0 Bob _**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |\n",
    "| row_1 Joe     | -  | - | -  | -   |\n",
    "| row_2 Will    | -  | - | -  | -   |\n",
    "|**_row_3 Bob_**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |\n",
    "| row_4 Will    | -  | - | -  | -   |\n",
    "| row_5 Joe    | -  | - | -  | -   |\n",
    "| row_6 Joe    | -  | - | -  | -   |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.7135, -0.8312, -2.3702, -1.8608],\n       [-1.542 , -0.9707, -1.307 ,  0.2863]])"
     },
     "metadata": {},
     "execution_count": 79
    }
   ],
   "source": [
    "data[names == \"Bob\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get the rows whose index correspond to a boolean value of True\n",
    "\n",
    "... based on the evaluation **_names=='Bob'_**, i.e., only row 0 and 3\n",
    "\n",
    "..., and get only the columns from the 2nd one (inlusive) onward for these filtered rows\n",
    "\n",
    "... which are highlighted below: (Note that it returns a 2-d array)\n",
    "\n",
    "|           |  col_0  |  col_1  | _col_2_ | _col_3_ |\n",
    "| --------- |--------:|--------:|--------:|--------:|\n",
    "|**_row_0 Bob_**| -  | - |**_XXX_**|**_XXX_**|\n",
    "| row_1 Joe    | -  | - | -  | - |\n",
    "| row_2 Will    | -  | - | -  | -  |\n",
    "|**_row_3 Bob_**| - | - |**_XXX_**|**_XXX_**|\n",
    "| row_4 Will    | -  | - | -  | - |\n",
    "| row_5 Joe    | -  | - | -  | - |\n",
    "| row_6 Joe    | -  | - | -  | - |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-2.3702, -1.8608],\n       [-1.307 ,  0.2863]])"
     },
     "metadata": {},
     "execution_count": 80
    }
   ],
   "source": [
    "data[names == 'Bob', 2:]"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get the rows 1, 4, 5 whose index correspond to a boolean value of True\n",
    "\n",
    "... based on the evaluation **_names=='Joe'_**,\n",
    "\n",
    "..., and get only column 3\n",
    "\n",
    "... which are highlighted below: (Note that it returns a 1-d array)\n",
    "\n",
    "|           |  col_0  |  col_1  | _col_2_ | _col_3_ |\n",
    "| --------- |--------:|--------:|--------:|--------:|\n",
    "| row_0 Bob    | - | - | - | - |\n",
    "|**_row_1 Joe_**| - | - | - |**_XXX_**|\n",
    "| row_2 Will    | - | - | - | - |\n",
    "| row_3 Bob    | - | - | - | - |\n",
    "| row_4 Will| - | - | - | - |\n",
    "|**_row_5 Joe_**| - | - | - |**_XXX_**|\n",
    "|**_row_6 Joe_**| - | - | - |**_XXX_**|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.1198, 1.0048, 0.0222])"
     },
     "metadata": {},
     "execution_count": 81
    }
   ],
   "source": [
    "data[names == \"Joe\", 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([False,  True,  True, False,  True,  True,  True])"
     },
     "metadata": {},
     "execution_count": 82
    }
   ],
   "source": [
    "names != 'Bob'"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Get the rows whose index that **DO NOT** corespond to **_True_**\n",
    "\n",
    "... based on evaluation **_names == 'Bob'_**\n",
    "\n",
    "... i.e., row 1, 2, 4, 5, 6\n",
    "\n",
    "|           |  col_0  |  col_1  |  col_2  |  col_3  |\n",
    "| --------- |--------:|--------:|--------:|--------:|\n",
    "| row_0 Bob    | -  | - | -  | -   |\n",
    "|**_row_1 Joe_**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |\n",
    "|**_row_2 Will_**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |\n",
    "| row_3 Bob    | -  | - | -  | -   |\n",
    "|**_row_4 Will_**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |\n",
    "|**_row_5 Joe_**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |\n",
    "|**_row_6 Joe_**| **_XXX_**  | **_XXX_** | **_XXX_** | **_XXX_** |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.8608,  0.5601, -1.2659,  0.1198],\n       [-1.0635,  0.3329, -2.3594, -0.1995],\n       [ 0.378 , -0.7539,  0.3313,  1.3497],\n       [ 0.0699,  0.2467, -0.0119,  1.0048],\n       [ 1.3272, -0.9193, -1.5491,  0.0222]])"
     },
     "metadata": {},
     "execution_count": 83
    }
   ],
   "source": [
    "data[~(names == 'Bob')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.8608,  0.5601, -1.2659,  0.1198],\n       [-1.0635,  0.3329, -2.3594, -0.1995],\n       [ 0.378 , -0.7539,  0.3313,  1.3497],\n       [ 0.0699,  0.2467, -0.0119,  1.0048],\n       [ 1.3272, -0.9193, -1.5491,  0.0222]])"
     },
     "metadata": {},
     "execution_count": 84
    }
   ],
   "source": [
    "cond = names == 'Bob'\n",
    "data[~cond]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ True, False,  True,  True,  True, False, False])"
     },
     "metadata": {},
     "execution_count": 85
    }
   ],
   "source": [
    "mask = (names == 'Bob') | (names == 'Will')\n",
    "mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.7135, -0.8312, -2.3702, -1.8608],\n       [-1.0635,  0.3329, -2.3594, -0.1995],\n       [-1.542 , -0.9707, -1.307 ,  0.2863],\n       [ 0.378 , -0.7539,  0.3313,  1.3497]])"
     },
     "metadata": {},
     "execution_count": 86
    }
   ],
   "source": [
    "data[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0.    , 0.    , 0.    , 0.    ],\n       [0.    , 0.5601, 0.    , 0.1198],\n       [0.    , 0.3329, 0.    , 0.    ],\n       [0.    , 0.    , 0.    , 0.2863],\n       [0.378 , 0.    , 0.3313, 1.3497],\n       [0.0699, 0.2467, 0.    , 1.0048],\n       [1.3272, 0.    , 0.    , 0.0222]])"
     },
     "metadata": {},
     "execution_count": 87
    }
   ],
   "source": [
    "# assign value zero to those cells < 0\n",
    "data[data < 0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "assign value 7 to cells whose row index correspond to \"NOT Joe\"'\n",
    "\n",
    "... i.e. row 0, 2, 3, 4.\n",
    "\n",
    "|           |  col_0  |  col_1  |  col_2  |  col_3  |\n",
    "| --------- |--------:|--------:|--------:|--------:|\n",
    "| row_0     | 7 | 7 | 7 | 7 |\n",
    "| row_1     | -  | - | - | - |\n",
    "| row_2     | 7 | 7 | 7 | 7 |\n",
    "| row_3     | 7 | 7 | 7 | 7 |\n",
    "| row_4     | 7 | 7 | 7 | 7 |\n",
    "| row_5     | -  | - | - | - |\n",
    "| row_6     | -  | - | - | - |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[7.    , 7.    , 7.    , 7.    ],\n       [0.    , 0.5601, 0.    , 0.1198],\n       [7.    , 7.    , 7.    , 7.    ],\n       [7.    , 7.    , 7.    , 7.    ],\n       [7.    , 7.    , 7.    , 7.    ],\n       [0.0699, 0.2467, 0.    , 1.0048],\n       [1.3272, 0.    , 0.    , 0.0222]])"
     },
     "metadata": {},
     "execution_count": 88
    }
   ],
   "source": [
    "data[names != 'Joe'] = 7\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[37.7969, 64.3125, 12.8906, 25.3906],\n       [37.7969, 25.3906,  0.    ,  0.    ],\n       [35.2031, 72.9062, 47.6094, 72.9062],\n       [47.6094, 25.3906, 58.0156, 25.3906],\n       [58.0156, 17.1875, 47.6094, 17.1875],\n       [47.6094,  0.    , 37.7969,  0.    ],\n       [37.7969, 17.1875,  4.8906, 17.1875],\n       [ 4.8906, 26.7031,  0.    ,  0.    ]])"
     },
     "metadata": {},
     "execution_count": 89
    }
   ],
   "source": [
    "arr_8_4 = np.empty((8, 4))\n",
    "arr_8_4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0., 0., 0., 0.],\n       [1., 1., 1., 1.],\n       [2., 2., 2., 2.],\n       [3., 3., 3., 3.],\n       [4., 4., 4., 4.],\n       [5., 5., 5., 5.],\n       [6., 6., 6., 6.],\n       [7., 7., 7., 7.]])"
     },
     "metadata": {},
     "execution_count": 90
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    arr_8_4[i] = i\n",
    "\n",
    "arr_8_4"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "**_arr\\[\\[4, 3, 0\\]\\]_** filters row 4, 3, 0, in this order, for all columns:\n",
    "\n",
    "|             | _col_0_ | _col_1_ | _col_2_ | _col_3_ |\n",
    "|   -         | :-:    | :-:    | :-:    | :-:    |\n",
    "| **_row_0_** (plaeced at 3rd row) | 0. | 0. | 0. | 0. |\n",
    "| row_1 | -     | -     | -     | -     |\n",
    "| row_2 | -     | -     | -     | -     |\n",
    "| **_row_3_** (plaeced at 2nd row)| 3. | 3. | 3. | 3. |\n",
    "| **_row_4_** (plaeced at 1st row) | 4. | 4. | 4. | 4. |\n",
    "| row_5 | -     | -     | -     | -     |\n",
    "| row_6 | -     | -     | -     | -     |\n",
    "| row_7 | -     | -     | -     | -     |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[4., 4., 4., 4.],\n       [3., 3., 3., 3.],\n       [0., 0., 0., 0.]])"
     },
     "metadata": {},
     "execution_count": 91
    }
   ],
   "source": [
    "arr_8_4[[4, 3, 0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "**_arr\\[\\[-3, -5, -1]\\]_** filters row 5 (-1), 3 (-5), 7 (-1), in this order, for all columns:\n",
    "\n",
    "|             | _col_0_ | _col_1_ | _col_2_ | _col_3_ |\n",
    "|   -         | :-:    | :-:    | :-:    | :-:    |\n",
    "| row_0 | -     | -     | -     | -     |\n",
    "| row_1 | -     | -     | -     | -     |\n",
    "| row_2 | -     | -     | -     | -     |\n",
    "| **_row_3_** (row -5, placed at the 2nd row) | 3. | 3. | 3. | 3. |\n",
    "| row_4 | -     | -     | -     | -     |\n",
    "| **_row_5_** (row -3, placed at the 1st row)  | 5. | 5. | 5. | 5. |\n",
    "| row_6 | -     | -     | -     | -     |\n",
    "| **_row_7_** (row -1, placed at the 3rd row) | 7. | 7. | 7. | 7. |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[5., 5., 5., 5.],\n       [3., 3., 3., 3.],\n       [7., 7., 7., 7.]])"
     },
     "metadata": {},
     "execution_count": 92
    }
   ],
   "source": [
    "# using negative indices selects rows from the end\n",
    "arr_8_4[[-3, -5, -1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0,  1,  2,  3],\n       [ 4,  5,  6,  7],\n       [ 8,  9, 10, 11],\n       [12, 13, 14, 15],\n       [16, 17, 18, 19],\n       [20, 21, 22, 23],\n       [24, 25, 26, 27],\n       [28, 29, 30, 31]])"
     },
     "metadata": {},
     "execution_count": 93
    }
   ],
   "source": [
    "arr_8_4_new = np.arange(32).reshape(8, 4)\n",
    "arr_8_4_new"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "**_arr\\[\\[1, 5, 7\\], \\[0, 3, 1\\]\\]_** produces:\n",
    "\n",
    "|             | **_col_0_** | **_col_1_** | col_2 | **_col_3_** |\n",
    "|   -         | :-:    | :-:    | :-:    | :-:    |\n",
    "| row_0       | -     | -     | -     | -     |\n",
    "| **_row_1_** | 4\\[1,0\\]| -     | -     | -     |\n",
    "| row_2       | -     | -     | -     | -     |\n",
    "| row_3       | -     | -     | -     | -     |\n",
    "| row_4       | -     | -     | -     | -     |\n",
    "| **_row_5_** | -     | -     | -     |23\\[5,3\\]|\n",
    "| row_6       | -     | -     | -     | -     |\n",
    "| **_row_7_** | -     |29\\[7,1\\]| -     | -     |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 4, 23, 29])"
     },
     "metadata": {},
     "execution_count": 94
    }
   ],
   "source": [
    "arr_8_4_new[[1, 5, 7], [0, 3, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "To produces this:\n",
    "\n",
    "|             | **_col_0_** | **_col_1_** | col_2 | **_col_3_** |\n",
    "|   -         | :-:    | :-:    | :-:    | :-:    |\n",
    "| row_0       | -     | -     | -     | -     |\n",
    "| **_row_1_** | 4\\[1,0\\]| 5\\[1,1\\]| - | 7\\[1,3\\] |\n",
    "| row_2       | -     | -     | -     | -     |\n",
    "| row_3       | -     | -     | -     | -     |\n",
    "| row_4       | -     | -     | -     | -     |\n",
    "| **_row_5_** | 20\\[5,0\\] | 21\\[5,1\\] | -     |23\\[5,3\\]|\n",
    "| row_6       | -     | -     | -     | -     |\n",
    "| **_row_7_** | 28\\[7,0\\] | 29\\[7,1\\]| -     | 31\\[7,3\\] |\n",
    "\n",
    "... the code is the following, i.e. get rows 1, 5, 7 first and then get columns 0, 3, 1, in this order, for these rows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 4,  7,  5],\n       [20, 23, 21],\n       [28, 31, 29]])"
     },
     "metadata": {},
     "execution_count": 95
    }
   ],
   "source": [
    "arr_8_4_new[[1, 5, 7]][: , [0, 3, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## transposing arrays and swapping axes"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0,  1,  2,  3,  4],\n       [ 5,  6,  7,  8,  9],\n       [10, 11, 12, 13, 14]])"
     },
     "metadata": {},
     "execution_count": 96
    }
   ],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0,  5, 10],\n       [ 1,  6, 11],\n       [ 2,  7, 12],\n       [ 3,  8, 13],\n       [ 4,  9, 14]])"
     },
     "metadata": {},
     "execution_count": 97
    }
   ],
   "source": [
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.7584, -0.6605,  0.8626],\n       [-0.01  ,  0.05  ,  0.6702],\n       [ 0.853 , -0.9559, -0.0235],\n       [-2.3042, -0.6525, -1.2183],\n       [-1.3326,  1.0746,  0.7236],\n       [ 0.69  ,  1.0015, -0.5031]])"
     },
     "metadata": {},
     "execution_count": 98
    }
   ],
   "source": [
    "arr = np.random.randn(6, 3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 8.8642, -0.5543,  2.1232],\n       [-0.5543,  3.9361,  0.5549],\n       [ 2.1232,  0.5549,  3.4548]])"
     },
     "metadata": {},
     "execution_count": 99
    }
   ],
   "source": [
    "np.dot(arr.T, arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[ 0,  1,  2,  3],\n        [ 4,  5,  6,  7]],\n\n       [[ 8,  9, 10, 11],\n        [12, 13, 14, 15]]])"
     },
     "metadata": {},
     "execution_count": 100
    }
   ],
   "source": [
    "arr = np.arange(16).reshape((2, 2, 4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[ 0,  1,  2,  3],\n        [ 8,  9, 10, 11]],\n\n       [[ 4,  5,  6,  7],\n        [12, 13, 14, 15]]])"
     },
     "metadata": {},
     "execution_count": 101
    }
   ],
   "source": [
    "arr.transpose((1, 0, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[ 0,  1,  2,  3],\n        [ 4,  5,  6,  7]],\n\n       [[ 8,  9, 10, 11],\n        [12, 13, 14, 15]]])"
     },
     "metadata": {},
     "execution_count": 102
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[[ 0,  4],\n        [ 1,  5],\n        [ 2,  6],\n        [ 3,  7]],\n\n       [[ 8, 12],\n        [ 9, 13],\n        [10, 14],\n        [11, 15]]])"
     },
     "metadata": {},
     "execution_count": 103
    }
   ],
   "source": [
    "arr.swapaxes(1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## universal functions"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 104
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.    , 1.    , 1.4142, 1.7321, 2.    , 2.2361, 2.4495, 2.6458,\n       2.8284, 3.    ])"
     },
     "metadata": {},
     "execution_count": 105
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([   1.    ,    2.7183,    7.3891,   20.0855,   54.5982,  148.4132,\n        403.4288, 1096.6332, 2980.958 , 8103.0839])"
     },
     "metadata": {},
     "execution_count": 106
    }
   ],
   "source": [
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.randn(8)\n",
    "y = np.random.randn(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-0.6223, -0.9212, -0.7262,  0.2229,  0.0513, -1.1577,  0.8167,\n        0.4336])"
     },
     "metadata": {},
     "execution_count": 108
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 1.0107,  1.8249, -0.9975,  0.8506, -0.1316,  0.9124,  0.1882,\n        2.1695])"
     },
     "metadata": {},
     "execution_count": 109
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 1.0107,  1.8249, -0.7262,  0.8506,  0.0513,  0.9124,  0.8167,\n        2.1695])"
     },
     "metadata": {},
     "execution_count": 110
    }
   ],
   "source": [
    "np.maximum(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-0.5746, 10.0185,  0.1481,  3.9763,  0.5905, -3.7427,  2.9248])"
     },
     "metadata": {},
     "execution_count": 111
    }
   ],
   "source": [
    "arr = np.random.randn(7) *5\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "remainder, whole_part = np.modf(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-0.5746,  0.0185,  0.1481,  0.9763,  0.5905, -0.7427,  0.9248])"
     },
     "metadata": {},
     "execution_count": 113
    }
   ],
   "source": [
    "remainder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-0., 10.,  0.,  3.,  0., -3.,  2.])"
     },
     "metadata": {},
     "execution_count": 114
    }
   ],
   "source": [
    "whole_part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-0.5746, 10.0185,  0.1481,  3.9763,  0.5905, -3.7427,  2.9248])"
     },
     "metadata": {},
     "execution_count": 115
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([   nan, 3.1652, 0.3848, 1.9941, 0.7685,    nan, 1.7102])"
     },
     "metadata": {},
     "execution_count": 116
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([   nan, 3.1652, 0.3848, 1.9941, 0.7685,    nan, 1.7102])"
     },
     "metadata": {},
     "execution_count": 117
    }
   ],
   "source": [
    "np.sqrt(arr, arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 arrary-oriented programming with arrays"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.random.seed(42)\n",
    "points_x = np.sin(np.arange(-5, 5, 0.01))\n",
    "# np.random.seed(41)\n",
    "points_y = np.cos(np.arange(-5, 5, 0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs, ys = np.meshgrid(points_x, points_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.9589,  0.9617,  0.9644, ..., -0.967 , -0.9644, -0.9617],\n       [ 0.9589,  0.9617,  0.9644, ..., -0.967 , -0.9644, -0.9617],\n       [ 0.9589,  0.9617,  0.9644, ..., -0.967 , -0.9644, -0.9617],\n       ...,\n       [ 0.9589,  0.9617,  0.9644, ..., -0.967 , -0.9644, -0.9617],\n       [ 0.9589,  0.9617,  0.9644, ..., -0.967 , -0.9644, -0.9617],\n       [ 0.9589,  0.9617,  0.9644, ..., -0.967 , -0.9644, -0.9617]])"
     },
     "metadata": {},
     "execution_count": 120
    }
   ],
   "source": [
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0.2837, 0.2837, 0.2837, ..., 0.2837, 0.2837, 0.2837],\n       [0.2741, 0.2741, 0.2741, ..., 0.2741, 0.2741, 0.2741],\n       [0.2644, 0.2644, 0.2644, ..., 0.2644, 0.2644, 0.2644],\n       ...,\n       [0.2548, 0.2548, 0.2548, ..., 0.2548, 0.2548, 0.2548],\n       [0.2644, 0.2644, 0.2644, ..., 0.2644, 0.2644, 0.2644],\n       [0.2741, 0.2741, 0.2741, ..., 0.2741, 0.2741, 0.2741]])"
     },
     "metadata": {},
     "execution_count": 121
    }
   ],
   "source": [
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1.    , 1.0027, 1.0053, ..., 1.0077, 1.0053, 1.0027],\n       [0.9973, 1.    , 1.0026, ..., 1.0051, 1.0026, 1.    ],\n       [0.9947, 0.9974, 1.    , ..., 1.0025, 1.    , 0.9974],\n       ...,\n       [0.9922, 0.9949, 0.9975, ..., 1.    , 0.9975, 0.9949],\n       [0.9947, 0.9974, 1.    , ..., 1.0025, 1.    , 0.9974],\n       [0.9973, 1.    , 1.0026, ..., 1.0051, 1.0026, 1.    ]])"
     },
     "metadata": {},
     "execution_count": 122
    }
   ],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 720x432 with 2 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.imshow(z, cmap=plt.cm.gray)\n",
    "plt.colorbar()\n",
    "plt.title(\"image plot of $\\sqrt{x^2 + y^2}$ for a grid of values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## expressing conditional logic as array operations"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])\n",
    "yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "cond = np.array([True, False, True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 43 µs, sys: 0 ns, total: 43 µs\nWall time: 49.1 µs\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[1.1, 2.2, 1.3, 1.4, 2.5]"
     },
     "metadata": {},
     "execution_count": 126
    }
   ],
   "source": [
    "%%time\n",
    "results = [(x if c else y)\n",
    "           for x, y, c in zip(xarr, yarr, cond)]\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 45 µs, sys: 1e+03 ns, total: 46 µs\nWall time: 50.1 µs\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1.1, 2.2, 1.3, 1.4, 2.5])"
     },
     "metadata": {},
     "execution_count": 127
    }
   ],
   "source": [
    "%%time\n",
    "results = np.where(cond, xarr, yarr)\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.1527, -1.5657, -0.5625, -0.0327],\n       [-0.929 , -0.4826, -0.0363,  1.0954],\n       [ 0.9809, -0.5895,  1.5817, -0.5287],\n       [ 0.457 ,  0.93  , -1.5693, -1.0225]])"
     },
     "metadata": {},
     "execution_count": 128
    }
   ],
   "source": [
    "arr = np.random.randn(4, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ True, False, False, False],\n       [False, False, False,  True],\n       [ True, False,  True, False],\n       [ True,  True, False, False]])"
     },
     "metadata": {},
     "execution_count": 129
    }
   ],
   "source": [
    "arr > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 2, -2, -2, -2],\n       [-2, -2, -2,  2],\n       [ 2, -2,  2, -2],\n       [ 2,  2, -2, -2]])"
     },
     "metadata": {},
     "execution_count": 130
    }
   ],
   "source": [
    "np.where(arr>0, 2, -2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[999.    ,  -1.5657,  -0.5625,  -0.0327],\n       [ -0.929 ,  -0.4826,  -0.0363, 999.    ],\n       [999.    ,  -0.5895, 999.    ,  -0.5287],\n       [999.    , 999.    ,  -1.5693,  -1.0225]])"
     },
     "metadata": {},
     "execution_count": 131
    }
   ],
   "source": [
    "np.where(arr > 0, 999, arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## mathematical and statistical methods"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.4028,  0.2205, -0.1934,  0.6692],\n       [-1.649 , -2.2528, -1.1668,  0.3536],\n       [ 0.7021, -0.2746, -0.1391,  0.1077],\n       [-0.6065, -0.4171, -0.017 , -1.2241],\n       [-1.8008,  1.6347,  0.989 ,  0.4579]])"
     },
     "metadata": {},
     "execution_count": 132
    }
   ],
   "source": [
    "arr = np.random.randn(5, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-0.25047255656175255"
     },
     "metadata": {},
     "execution_count": 133
    }
   ],
   "source": [
    "arr.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-0.25047255656175255"
     },
     "metadata": {},
     "execution_count": 134
    }
   ],
   "source": [
    "np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-5.009451131235051"
     },
     "metadata": {},
     "execution_count": 135
    }
   ],
   "source": [
    "arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 0.0734, -1.1788,  0.099 , -0.5662,  0.3202])"
     },
     "metadata": {},
     "execution_count": 136
    }
   ],
   "source": [
    "arr.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-0.7514, -0.2178, -0.1055,  0.0728])"
     },
     "metadata": {},
     "execution_count": 137
    }
   ],
   "source": [
    "arr.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 0,  1,  3,  6, 10, 15, 21, 28, 36, 45])"
     },
     "metadata": {},
     "execution_count": 139
    }
   ],
   "source": [
    "arr.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0, 1, 2],\n       [3, 4, 5],\n       [6, 7, 8]])"
     },
     "metadata": {},
     "execution_count": 140
    }
   ],
   "source": [
    "arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0,  1,  2],\n       [ 3,  5,  7],\n       [ 9, 12, 15]])"
     },
     "metadata": {},
     "execution_count": 141
    }
   ],
   "source": [
    "arr.cumsum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0,  1,  3],\n       [ 3,  7, 12],\n       [ 6, 13, 21]])"
     },
     "metadata": {},
     "execution_count": 142
    }
   ],
   "source": [
    "arr.cumsum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## methods for boolean arrays"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "44"
     },
     "metadata": {},
     "execution_count": 144
    }
   ],
   "source": [
    "(arr > 0).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "bools = np.array([False, False, True, False, True])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "True"
     },
     "metadata": {},
     "execution_count": 146
    }
   ],
   "source": [
    "bools.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "False"
     },
     "metadata": {},
     "execution_count": 147
    }
   ],
   "source": [
    "bools.all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sorting"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-2.4203, -1.0623,  0.2374,  0.001 ,  0.0653, -1.3675])"
     },
     "metadata": {},
     "execution_count": 148
    }
   ],
   "source": [
    "arr = np.random.randn(6)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([-2.4203, -1.3675, -1.0623,  0.001 ,  0.0653,  0.2374])"
     },
     "metadata": {},
     "execution_count": 149
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.0303,  0.9405, -0.6424,  1.0402, -1.0829],\n       [ 0.4292, -0.2362,  0.6418, -0.3317,  1.3941],\n       [-1.0767, -0.1925, -0.8712,  0.4209, -1.2114]])"
     },
     "metadata": {},
     "execution_count": 150
    }
   ],
   "source": [
    "arr = np.random.randn(3, 5)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0x1204db4d0>"
     },
     "metadata": {},
     "execution_count": 151
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(arr, cmap=plt.cm.gray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-1.0767, -0.2362, -0.8712, -0.3317, -1.2114],\n       [-0.0303, -0.1925, -0.6424,  0.4209, -1.0829],\n       [ 0.4292,  0.9405,  0.6418,  1.0402,  1.3941]])"
     },
     "metadata": {},
     "execution_count": 152
    }
   ],
   "source": [
    "arr.sort(0)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0x11b08a690>"
     },
     "metadata": {},
     "execution_count": 153
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 720x432 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(arr, cmap=plt.cm.gray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-1.2114, -1.0767, -0.8712, -0.3317, -0.2362],\n       [-1.0829, -0.6424, -0.1925, -0.0303,  0.4209],\n       [ 0.4292,  0.6418,  0.9405,  1.0402,  1.3941]])"
     },
     "metadata": {},
     "execution_count": 154
    }
   ],
   "source": [
    "arr.sort(1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0x11bfb2cd0>"
     },
     "metadata": {},
     "execution_count": 155
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(arr, cmap=plt.cm.gray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "large_arr = np.random.randn(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "large_arr.sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-1.5308984278773312"
     },
     "metadata": {},
     "execution_count": 158
    }
   ],
   "source": [
    "large_arr[int(0.05 * len(large_arr))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## unique and other set logic"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "names = np.array(['bob', 'joe', 'will', 'bob', 'will', 'joe', 'joe'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array(['bob', 'joe', 'will'], dtype='<U4')"
     },
     "metadata": {},
     "execution_count": 160
    }
   ],
   "source": [
    "np.unique(names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "['bob', 'joe', 'will']"
     },
     "metadata": {},
     "execution_count": 161
    }
   ],
   "source": [
    "sorted(set(names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "ints = np.array([3, 3, 3, 2, 2, 1, 4, 4, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1, 2, 3, 4])"
     },
     "metadata": {},
     "execution_count": 163
    }
   ],
   "source": [
    "np.unique(ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "values = np.array([6, 0, 0, 3, 2, 5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ True, False, False,  True,  True, False,  True])"
     },
     "metadata": {},
     "execution_count": 165
    }
   ],
   "source": [
    "np.in1d(values, [2, 3, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.4 file input and output with arrays"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 166
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('some_array', arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "metadata": {},
     "execution_count": 168
    }
   ],
   "source": [
    "np.load('some_array.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.5 linear algebra"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "y = np.array([[6., 23.], [-1, 7], [8, 9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[1., 2., 3.],\n       [4., 5., 6.]])"
     },
     "metadata": {},
     "execution_count": 170
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 6., 23.],\n       [-1.,  7.],\n       [ 8.,  9.]])"
     },
     "metadata": {},
     "execution_count": 171
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 28.,  64.],\n       [ 67., 181.]])"
     },
     "metadata": {},
     "execution_count": 172
    }
   ],
   "source": [
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 28.,  64.],\n       [ 67., 181.]])"
     },
     "metadata": {},
     "execution_count": 173
    }
   ],
   "source": [
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 6., 15.])"
     },
     "metadata": {},
     "execution_count": 174
    }
   ],
   "source": [
    "np.dot(x, np.ones(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 6., 15.])"
     },
     "metadata": {},
     "execution_count": 175
    }
   ],
   "source": [
    "x @ np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-6.3093,  1.2618,  4.3678, -2.2306, -2.3985],\n       [ 0.    , -1.77  ,  1.4984,  4.7179,  1.776 ],\n       [ 0.    ,  0.    , -3.6373,  3.813 , -1.3294],\n       [ 0.    ,  0.    ,  0.    , -5.2192, -2.3222],\n       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.0826]])"
     },
     "metadata": {},
     "execution_count": 176
    }
   ],
   "source": [
    "from numpy.linalg import inv, qr\n",
    "X = np.random.randn(5, 5)\n",
    "mat = X.T.dot(X)\n",
    "inv(mat)\n",
    "mat.dot(inv(mat))\n",
    "q, r = qr(mat)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.4459,  0.5732,  0.1933,  0.4429,  1.2796],\n       [ 0.575 ,  0.4339, -0.7658, -1.237 , -0.5367],\n       [ 1.8545, -0.92  , -0.1082,  0.1525,  0.9435],\n       [-1.0953, -0.144 ,  1.9562, -0.2912,  0.1048],\n       [ 0.1396, -0.2841, -0.7082,  2.4632,  0.2175]])"
     },
     "metadata": {},
     "execution_count": 177
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 5.1879, -1.083 , -2.7963,  0.4317,  1.9273],\n       [-1.083 ,  1.4647, -0.2026, -1.081 , -0.4443],\n       [-2.7963, -0.2026,  4.9639, -1.2976,  0.6072],\n       [ 0.4317, -1.081 , -1.2976,  7.902 ,  1.8797],\n       [ 1.9273, -0.4443,  0.6072,  1.8797,  2.8739]])"
     },
     "metadata": {},
     "execution_count": 178
    }
   ],
   "source": [
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.4459,  0.575 ,  1.8545, -1.0953,  0.1396],\n       [ 0.5732,  0.4339, -0.92  , -0.144 , -0.2841],\n       [ 0.1933, -0.7658, -0.1082,  1.9562, -0.7082],\n       [ 0.4429, -1.237 ,  0.1525, -0.2912,  2.4632],\n       [ 1.2796, -0.5367,  0.9435,  0.1048,  0.2175]])"
     },
     "metadata": {},
     "execution_count": 179
    }
   ],
   "source": [
    "X.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pseudorandom number generation"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.0106, -0.006 ,  0.4901, -0.2772],\n       [-0.7072, -0.5601,  2.7355,  0.9273],\n       [ 1.5139,  0.5386,  1.2738,  0.6679],\n       [-0.9692,  1.6761, -0.8176,  0.0502]])"
     },
     "metadata": {},
     "execution_count": 180
    }
   ],
   "source": [
    "samples = np.random.normal(size=(4,4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "886 ms ± 66 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n26.9 ms ± 389 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
    }
   ],
   "source": [
    "from random import normalvariate\n",
    "N = 1000000\n",
    "%timeit samples = [normalvariate(0,1) for _ in range(N)]\n",
    "%timeit np.random.normal(size=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ 0.4714, -1.191 ,  1.4327, -0.3127, -0.7206,  0.8872,  0.8596,\n       -0.6365,  0.0157, -2.2427])"
     },
     "metadata": {},
     "execution_count": 183
    }
   ],
   "source": [
    "rng = np.random.RandomState(1234)\n",
    "rng.randn(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.7 example: random walks"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "position = 0\n",
    "walk = [position]\n",
    "steps = 1000\n",
    "for i in range(steps):\n",
    "    step = 1 if random.randint(0, 1) else -1\n",
    "    position += step\n",
    "    walk.append(position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x11c3ab650>]"
     },
     "metadata": {},
     "execution_count": 185
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(walk[:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(12345)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=nsteps)\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walk = steps.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-3"
     },
     "metadata": {},
     "execution_count": 188
    }
   ],
   "source": [
    "walk.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "31"
     },
     "metadata": {},
     "execution_count": 189
    }
   ],
   "source": [
    "walk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "37"
     },
     "metadata": {},
     "execution_count": 190
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## simulating many random walks at once"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ -1,   0,  -1, ...,  24,  23,  22],\n       [ -1,   0,  -1, ..., -36, -37, -36],\n       [  1,   2,   3, ..., -42, -41, -40],\n       ...,\n       [  1,   0,  -1, ...,  48,  49,  50],\n       [ -1,  -2,  -3, ..., -38, -39, -40],\n       [ -1,   0,   1, ..., -48, -47, -48]])"
     },
     "metadata": {},
     "execution_count": 192
    }
   ],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=(nwalks, nsteps))\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walks = steps.cumsum(1)\n",
    "walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "130"
     },
     "metadata": {},
     "execution_count": 193
    }
   ],
   "source": [
    "walks.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-117"
     },
     "metadata": {},
     "execution_count": 194
    }
   ],
   "source": [
    "walks.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([ True,  True,  True, ...,  True,  True,  True])"
     },
     "metadata": {},
     "execution_count": 195
    }
   ],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)\n",
    "hits30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "3412"
     },
     "metadata": {},
     "execution_count": 196
    }
   ],
   "source": [
    "hits30.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "497.04103165298943"
     },
     "metadata": {},
     "execution_count": 197
    }
   ],
   "source": [
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)\n",
    "crossing_times.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = np.random.normal(loc=0, scale=0.25, size=(nwalks, nsteps))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}