Estudos em Python for Data Science - Numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "88b36a12",
   "metadata": {},
   "source": [
    "##  Data Manipulation with Pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ef4f2eb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2394f9e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12.,  2.,  3.,  4.,  5.], dtype=float32)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Array of float numbers\n",
    "np.array([12,2,3,4,5], dtype='float32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f7d11d0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [4, 5, 6],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# nested lists result in multi-dimensional arrays\n",
    "np.array([range(i, i + 3) for i in [2, 4, 6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "70344302",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a length-10 integer array filled with zeros\n",
    "np.zeros(10, dtype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "92e96180",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a 3x5 floating-point array filled with ones\n",
    "np.ones((3,5), dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cffe74f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create an array filled with a linear sequence\n",
    "# Starting at 0, ending at 20, stepping by 2\n",
    "# (this is similar to the built-in range() function)\n",
    "\n",
    "np.arange(0, 20, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aa428207",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Etc with basic arrays functions in NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9443236",
   "metadata": {},
   "source": [
    "## NumPy Array Attributes\n",
    "\n",
    "### The Basics of NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "50733f1f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x3 ndim:  3\n",
      "x3 shape: (3, 4, 5)\n",
      "x3 size:  60\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0) # seed for reproducibility\n",
    "\n",
    "x1 = np.random.randint(10, size=6)  # One-dimensional array\n",
    "x2 = np.random.randint(10, size=(3, 4))  # Two-dimensional array\n",
    "x3 = np.random.randint(10, size=(3, 4, 5))  # Three-dimensional array\n",
    "\n",
    "print(\"x3 ndim: \", x3.ndim)\n",
    "print(\"x3 shape:\", x3.shape)\n",
    "print(\"x3 size: \", x3.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "319ac749",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dtype: int32\n"
     ]
    }
   ],
   "source": [
    "print(\"dtype:\", x3.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f848549c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itemsize: 4 bytes\n",
      "nbytes: 240 bytes\n"
     ]
    }
   ],
   "source": [
    "print(\"itemsize:\", x3.itemsize, \"bytes\")\n",
    "print(\"nbytes:\", x3.nbytes, \"bytes\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b34eb1b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 3, 3, 7, 9])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2dc23619",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1a6e3929",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [1, 6, 7, 7]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c4308ba7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[8, 1, 5, 9, 8],\n",
       "        [9, 4, 3, 0, 3],\n",
       "        [5, 0, 2, 3, 8],\n",
       "        [1, 3, 3, 3, 7]],\n",
       "\n",
       "       [[0, 1, 9, 9, 0],\n",
       "        [4, 7, 3, 2, 7],\n",
       "        [2, 0, 0, 4, 5],\n",
       "        [5, 6, 8, 4, 1]],\n",
       "\n",
       "       [[4, 9, 8, 1, 1],\n",
       "        [7, 9, 9, 3, 6],\n",
       "        [7, 2, 0, 3, 5],\n",
       "        [9, 4, 4, 6, 4]]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fb0b0551",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(10)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "698c8246",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "87d54643",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7e835b7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [1, 6, 7, 7]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5806fbda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2],\n",
       "       [7, 6, 8]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[:2, :3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b0db0f5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 5]\n",
      " [7 6]]\n"
     ]
    }
   ],
   "source": [
    "x2_sub_copy = x2[:2, :2].copy()\n",
    "print(x2_sub_copy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "dc1a52bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[42  5]\n",
      " [ 7  6]]\n"
     ]
    }
   ],
   "source": [
    "x2_sub_copy[0, 0] = 42\n",
    "print(x2_sub_copy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "96ba4427",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "grid = np.arange(1, 10).reshape((3, 3))\n",
    "print(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "462a9e36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1, 2, 3])\n",
    "\n",
    "# row vector via reshape\n",
    "x.reshape((1, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "df2b5713",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# row vector via newaxis\n",
    "x[np.newaxis, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2b1af236",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# column vector via reshape\n",
    "x.reshape((3, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0884bce0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 3, 2, 1])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1, 2, 3])\n",
    "y = np.array([3, 2, 1])\n",
    "np.concatenate([x, y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "790e14ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  3  2  1 99 99 99]\n"
     ]
    }
   ],
   "source": [
    "z = [99, 99, 99]\n",
    "print(np.concatenate([x, y, z]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c9dadb6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = np.array([[1, 2, 3],\n",
    "                 [4, 5, 6]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bdd152f",
   "metadata": {},
   "source": [
    "### NumPy Universal Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cddb7dfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16666667, 1.        , 0.25      , 0.25      , 0.125     ])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "\n",
    "def compute_reciprocals(values):\n",
    "    output = np.empty(len(values))\n",
    "    for i in range(len(values)):\n",
    "        output[i] = 1.0 / values[i]\n",
    "    return output\n",
    "\n",
    "values = np.random.randint(1, 10, size=5)\n",
    "compute_reciprocals(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "891814d3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.71 s ± 43.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "big_array = np.random.randint(1, 100, size=1000000)\n",
    "%timeit compute_reciprocals(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "fc6c99e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.16666667 1.         0.25       0.25       0.125     ]\n",
      "[0.16666667 1.         0.25       0.25       0.125     ]\n"
     ]
    }
   ],
   "source": [
    "print(compute_reciprocals(values))\n",
    "print(1.0 / values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0611ec89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.54 ms ± 61.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit (1.0 / big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cbf13ec9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.5       , 0.66666667, 0.75      , 0.8       ])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(5) / np.arange(1, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b85693ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   2,   4],\n",
       "       [  8,  16,  32],\n",
       "       [ 64, 128, 256]], dtype=int32)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(9).reshape((3, 3))\n",
    "2 ** x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5bd353ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x     = [0 1 2 3]\n",
      "x + 5 = [5 6 7 8]\n",
      "x - 5 = [-5 -4 -3 -2]\n",
      "x * 2 = [0 2 4 6]\n",
      "x / 2 = [0.  0.5 1.  1.5]\n",
      "x // 2 = [0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(4)\n",
    "print(\"x     =\", x)\n",
    "print(\"x + 5 =\", x + 5)\n",
    "print(\"x - 5 =\", x - 5)\n",
    "print(\"x * 2 =\", x * 2)\n",
    "print(\"x / 2 =\", x / 2)\n",
    "print(\"x // 2 =\", x // 2)  # floor division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "3a7c6941",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-x     =  [ 0 -1 -2 -3]\n",
      "x ** 2 =  [0 1 4 9]\n",
      "x % 2  =  [0 1 0 1]\n"
     ]
    }
   ],
   "source": [
    "print(\"-x     = \", -x)\n",
    "print(\"x ** 2 = \", x ** 2)\n",
    "print(\"x % 2  = \", x % 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f0189234",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4, 5])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(x, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "db44d1cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta      =  [0.         1.57079633 3.14159265]\n",
      "sin(theta) =  [0.0000000e+00 1.0000000e+00 1.2246468e-16]\n",
      "cos(theta) =  [ 1.000000e+00  6.123234e-17 -1.000000e+00]\n",
      "tan(theta) =  [ 0.00000000e+00  1.63312394e+16 -1.22464680e-16]\n"
     ]
    }
   ],
   "source": [
    "theta = np.linspace(0, np.pi, 3)\n",
    "\n",
    "print(\"theta      = \", theta)\n",
    "print(\"sin(theta) = \", np.sin(theta))\n",
    "print(\"cos(theta) = \", np.cos(theta))\n",
    "print(\"tan(theta) = \", np.tan(theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ad579a5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1,6)\n",
    "np.add.reduce(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "492e577a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 2,  4,  6,  8, 10],\n",
       "       [ 3,  6,  9, 12, 15],\n",
       "       [ 4,  8, 12, 16, 20],\n",
       "       [ 5, 10, 15, 20, 25]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 6)\n",
    "np.multiply.outer(x, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1302f8bb",
   "metadata": {},
   "source": [
    "## Aggregations: Min, Max, and Everything In Between"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "8677d588",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.461758453195614"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = np.random.random(100)\n",
    "sum(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "2e5b5f2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "92.7 ms ± 1.47 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "1.22 ms ± 14.3 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "big_array = np.random.rand(1000000)\n",
    "%timeit sum(big_array)\n",
    "%timeit np.sum(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "2e7c3402",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7.071203171893359e-07, 0.9999997207656334)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(big_array), max(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "5232168d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7.071203171893359e-07, 0.9999997207656334)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(big_array), np.max(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "67a86237",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64.6 ms ± 1.69 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "\n",
      "570 µs ± 11.9 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit min(big_array)\n",
    "print(\"\")\n",
    "%timeit np.min(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f2e541a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.071203171893359e-07 0.9999997207656334 500216.8034810001\n"
     ]
    }
   ],
   "source": [
    "print(big_array.min(), big_array.max(), big_array.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "01c5794c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.79832448 0.44923861 0.95274259 0.03193135]\n",
      " [0.18441813 0.71417358 0.76371195 0.11957117]\n",
      " [0.37578601 0.11936151 0.37497044 0.22944653]]\n"
     ]
    }
   ],
   "source": [
    "M = np.random.random((3, 4))\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "437c5d92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.18441813, 0.11936151, 0.37497044, 0.03193135])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.min(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caf7a364",
   "metadata": {},
   "source": [
    "### Computation on Arrays: Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "7ea1bb31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 1, 2])\n",
    "b = np.array([5, 5, 5])\n",
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "344a4a03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "7f300068",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.ones((3, 3))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "a3212a89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [1., 2., 3.],\n",
       "       [1., 2., 3.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "b235fb30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2]\n",
      "[[0]\n",
      " [1]\n",
      " [2]]\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(3)\n",
    "b = np.arange(3)[:, np.newaxis]\n",
    "\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "f4109834",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = np.ones((2,3))\n",
    "a = np.arange(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "a78dc0b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [1., 2., 3.]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "43631bc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.random((10,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "fd97708e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.49831076, 0.50193438, 0.46752888])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xmean = X.mean(0)\n",
    "Xmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "53fa710f",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_centered = X - Xmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "fbb0b9ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.44089210e-17,  3.33066907e-17, -9.43689571e-17])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_centered.mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "7ef558ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# x and y have 50 steps from 0 to 5\n",
    "x = np.linspace(0, 5, 50)\n",
    "y = np.linspace(0, 5, 50)[:, np.newaxis]\n",
    "\n",
    "z = np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "4ab44138",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "587989e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(z, origin='lower', extent=[0, 5, 0, 5], cmap='viridis')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56fb69ed",
   "metadata": {},
   "source": [
    "### Comparisons, Masks, and Boolean Logic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c53ee54f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b493436",
   "metadata": {},
   "source": [
    "### Comparison Operators as ufuncs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "822ecc58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True  True False False False]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.array([1, 2, 3, 4, 5])\n",
    "print(x < 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "ef5a47b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False, False, False])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2 * x) == (x ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "836038b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3, 3],\n",
       "       [7, 9, 3, 5],\n",
       "       [2, 4, 7, 6]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "x = rng.randint(10, size=(3, 4))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "e3656978",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True,  True],\n",
       "       [False, False,  True,  True],\n",
       "       [ True,  True, False, False]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "6cafa4e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5 0 3 3]\n",
      " [7 9 3 5]\n",
      " [2 4 7 6]]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "a6eab318",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(x < 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "f7d7f97e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(x < 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "12feb7d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True,  True,  True],\n",
       "       [False, False,  True, False],\n",
       "       [ True,  True, False, False]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "f39e4058",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 3, 3, 2, 4])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[x < 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "7ab71331",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b101010'"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "0ddb141a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b101010'"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(42 & 59)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bdad958",
   "metadata": {},
   "source": [
    "### Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "23f8b984",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[51 92 14 71 60 20 82 86 74 74]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "rand = np.random.RandomState(42)\n",
    "\n",
    "x = rand.randint(100, size=10)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "a2b93468",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[71, 86, 14]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x[3], x[7], x[2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "0e87284e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([71, 86, 14])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind = [3, 7, 2]\n",
    "x[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "e4ed75d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.arange(12).reshape((3, 4))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "d994bd64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  5, 11])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row = np.array([0, 1, 2])\n",
    "col = np.array([2, 1, 3])\n",
    "X[row, col]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "cd1eedc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  1,  3],\n",
       "       [ 6,  5,  7],\n",
       "       [10,  9, 11]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row[:, np.newaxis], col]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "43607614",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = [0, 0]\n",
    "cov = [[1, 2],\n",
    "       [2, 5]]\n",
    "X = rand.multivariate_normal(mean, cov, 100)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "55ddfce8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set()  # for plot styling\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "1b8ad578",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22, 34, 30, 40, 27, 12, 65,  5, 54, 74, 78, 96, 70, 18, 72, 89, 29,\n",
       "       45, 36, 88])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices = np.random.choice(X.shape[0], 20, replace=False)\n",
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "d2353cd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 2)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection = X[indices]  # fancy indexing here\n",
    "selection.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "3e99ad39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.3)\n",
    "plt.scatter(selection[:, 0], selection[:, 1],\n",
    "            facecolor='none', s=200);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "5d34a703",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0 99 99  3 99  5  6  7 99  9]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(10)\n",
    "i = np.array([2, 1, 8, 4])\n",
    "x[i] = 99\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "a07e0f50",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0 89 89  3 89  5  6  7 89  9]\n"
     ]
    }
   ],
   "source": [
    "x[i] -= 10\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "5c1af85d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "x = np.zeros(10)\n",
    "x[[0, 0]] = [4, 6]\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "02019659",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 1. 1. 0. 1. 0. 0. 0. 1. 0.]\n"
     ]
    }
   ],
   "source": [
    "x = np.zeros(10)\n",
    "np.add.at(x, i, 1)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c06ca7d9",
   "metadata": {},
   "source": [
    "### Structured Data: Sorting Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "a0de3a8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def selection_sort(x):\n",
    "    for i in range(len(x)):\n",
    "        swap = i + np.argmin(x[i:])\n",
    "        (x[i], x[swap]) = (x[swap], x[i])\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "4eeb2dd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 1, 4, 3, 5])\n",
    "selection_sort(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "cd1bb617",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bogosort(x):\n",
    "    while np.any(x[:-1] > x[1:]):\n",
    "        np.random.shuffle(x)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "001837a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 1, 3, 4, 5])\n",
    "bogosort(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "b7a9172f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 1, 4, 3, 5])\n",
    "np.sort(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "35ef25c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 3 2 4]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([2, 1, 4, 3, 5])\n",
    "i = np.argsort(x)\n",
    "print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "d9a3542f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "ee097ab3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6 3 7 4 6 9]\n",
      " [2 6 7 4 3 7]\n",
      " [7 2 5 4 1 7]\n",
      " [5 1 4 0 9 5]]\n"
     ]
    }
   ],
   "source": [
    "rand = np.random.RandomState(42)\n",
    "X = rand.randint(0, 10, (4, 6))\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "e506f867",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 4, 0, 1, 5],\n",
       "       [5, 2, 5, 4, 3, 7],\n",
       "       [6, 3, 7, 4, 6, 7],\n",
       "       [7, 6, 7, 4, 9, 9]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sort each column of X\n",
    "np.sort(X, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "9a55c241",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 6, 6, 7, 9],\n",
       "       [2, 3, 4, 6, 7, 7],\n",
       "       [1, 2, 4, 5, 7, 7],\n",
       "       [0, 1, 4, 5, 5, 9]])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sort each row of X\n",
    "np.sort(X, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "8ba38dec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 3, 4, 6, 5, 7])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([7, 2, 3, 1, 6, 5, 4])\n",
    "np.partition(x, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "5eec27d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 6, 7, 6, 9],\n",
       "       [2, 3, 4, 7, 6, 7],\n",
       "       [1, 2, 4, 5, 7, 7],\n",
       "       [0, 1, 4, 5, 9, 5]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.partition(X, 2, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "72f9c5cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = rand.rand(10, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "c8414f94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set() # Plot styling\n",
    "plt.scatter(X[:, 0], X[:, 1], s=100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "5c8016e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_sq = np.sum((X[:, np.newaxis, :] - X[np.newaxis, :, :]) ** 2, axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "61ea2403",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10, 2)"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for each pair of points, compute differences in their coordinates\n",
    "differences = X[:, np.newaxis, :] - X[np.newaxis, :, :]\n",
    "differences.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "2984bf0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10, 2)"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# square the coordinate differences\n",
    "sq_differences = differences ** 2\n",
    "sq_differences.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "85f3bcbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum the coordinate differences to get the squared distance\n",
    "dist_sq = sq_differences.sum(-1)\n",
    "dist_sq.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "5c93644a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_sq.diagonal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "9d1523ab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 3 9 7 1 4 2 5 6 8]\n",
      " [1 4 7 9 3 6 8 5 0 2]\n",
      " [2 1 4 6 3 0 8 9 7 5]\n",
      " [3 9 7 0 1 4 5 8 6 2]\n",
      " [4 1 8 5 6 7 9 3 0 2]\n",
      " [5 8 6 4 1 7 9 3 2 0]\n",
      " [6 8 5 4 1 7 9 3 2 0]\n",
      " [7 9 3 1 4 0 5 8 6 2]\n",
      " [8 5 6 4 1 7 9 3 2 0]\n",
      " [9 7 3 0 1 4 5 8 6 2]]\n"
     ]
    }
   ],
   "source": [
    "nearest = np.argsort(dist_sq, axis=1)\n",
    "print(nearest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "3bd0b28c",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 2\n",
    "nearest_partition = np.argpartition(dist_sq, K + 1, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "f3384105",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100)\n",
    "\n",
    "# draw lines from each point to its two nearest neighbors\n",
    "K = 2\n",
    "\n",
    "for i in range(X.shape[0]):\n",
    "    for j in nearest_partition[i, :K+1]:\n",
    "        # plot a line from X[i] to X[j]\n",
    "        # use some zip magic to make it happen:\n",
    "        plt.plot(*zip(X[j], X[i]), color='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42797131",
   "metadata": {},
   "source": [
    "### Structured Data: NumPy's Structured Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "ae4a336a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.zeros(4, dtype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "149e4131",
   "metadata": {},
   "outputs": [],
   "source": [
    "name = ['Alice', 'Bob', 'Cathy', 'Doug']\n",
    "age = [25, 45, 37, 19]\n",
    "weight = [55.0, 85.5, 68.0, 61.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "24bfe5bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('name', '<U10'), ('age', '<i4'), ('weight', '<f8')]\n"
     ]
    }
   ],
   "source": [
    "# Use a compound data type for structured arrays\n",
    "data = np.zeros(4, dtype={'names':('name', 'age', 'weight'),\n",
    "                          'formats':('U10', 'i4', 'f8')})\n",
    "print(data.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "0f4b3348",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('Alice', 25, 55. ) ('Bob', 45, 85.5) ('Cathy', 37, 68. )\n",
      " ('Doug', 19, 61.5)]\n"
     ]
    }
   ],
   "source": [
    "data['name'] = name\n",
    "data['age'] = age\n",
    "data['weight'] = weight\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "3aaa798a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Alice', 'Bob', 'Cathy', 'Doug'], dtype='<U10')"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get all names\n",
    "data['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "1022686b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Alice', 25, 55.)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get first row of data\n",
    "data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "345f99b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Doug'"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the name from the last row\n",
    "data[-1]['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "621598e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Alice', 'Doug'], dtype='<U10')"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get names where age is under 30\n",
    "data[data['age'] < 30]['name']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cf361eb",
   "metadata": {},
   "source": [
    "### Creating Structured Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "07ae4d5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype([('name', '<U10'), ('age', '<i4'), ('weight', '<f8')])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dtype({'names':('name', 'age', 'weight'),\n",
    "          'formats':('U10', 'i4', 'f8')})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "3d59d2b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype([('name', '<U10'), ('age', '<i4'), ('weight', '<f4')])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dtype({'names':('name', 'age', 'weight'),\n",
    "          'formats':((np.str_, 10), int, np.float32)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "beb05d04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int8')"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dtype('b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "238288cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dtype('V') == np.void"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "7bead934",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]])\n",
      "[[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "tp = np.dtype([('id', 'i8'), ('mat', 'f8', (3, 3))])\n",
    "X = np.zeros(1, dtype=tp)\n",
    "print(X[0])\n",
    "print(X['mat'][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "a81d591d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 45, 37, 19])"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['age']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "695f6f6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 45, 37, 19])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_rec = data.view(np.recarray)\n",
    "data_rec.age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bdc647a3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c36237aa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90139f8c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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