ch04.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(12345)\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(1_000_000)\n",
    "my_list = list(range(1_000_000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%timeit my_arr2 = my_arr * 2\n",
    "%timeit my_list2 = [x * 2 for x in my_list]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "data = np.array([[1.5, -0.1, 3], [0, -3, 6.5]])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data * 10\n",
    "data + data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.shape\n",
    "data.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2.ndim\n",
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr1.dtype\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.zeros(10)\n",
    "np.zeros((3, 6))\n",
    "np.empty((2, 3, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.arange(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr1 = np.array([1, 2, 3], dtype=np.float64)\n",
    "arr2 = np.array([1, 2, 3], dtype=np.int32)\n",
    "arr1.dtype\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "arr.dtype\n",
    "float_arr = arr.astype(np.float64)\n",
    "float_arr\n",
    "float_arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])\n",
    "arr\n",
    "arr.astype(np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "numeric_strings = np.array([\"1.25\", \"-9.6\", \"42\"], dtype=np.string_)\n",
    "numeric_strings.astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "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": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "zeros_uint32 = np.zeros(8, dtype=\"u4\")\n",
    "zeros_uint32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr\n",
    "arr * arr\n",
    "arr - arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "1 / arr\n",
    "arr ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])\n",
    "arr2\n",
    "arr2 > arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "arr\n",
    "arr[5]\n",
    "arr[5:8]\n",
    "arr[5:8] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr_slice[1] = 12345\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr_slice[:] = 64\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d[0][2]\n",
    "arr2d[0, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "old_values = arr3d[0].copy()\n",
    "arr3d[0] = 42\n",
    "arr3d\n",
    "arr3d[0] = old_values\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr3d[1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = arr3d[1]\n",
    "x\n",
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr\n",
    "arr[1:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d\n",
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d[:2, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_dim_slice = arr2d[1, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_dim_slice.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d[:2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d[:, :1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d[:2, 1:] = 0\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "names = np.array([\"Bob\", \"Joe\", \"Will\", \"Bob\", \"Will\", \"Joe\", \"Joe\"])\n",
    "data = np.array([[4, 7], [0, 2], [-5, 6], [0, 0], [1, 2],\n",
    "                 [-12, -4], [3, 4]])\n",
    "names\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "names == \"Bob\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[names == \"Bob\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[names == \"Bob\", 1:]\n",
    "data[names == \"Bob\", 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "names != \"Bob\"\n",
    "~(names == \"Bob\")\n",
    "data[~(names == \"Bob\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "cond = names == \"Bob\"\n",
    "data[~cond]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = (names == \"Bob\") | (names == \"Will\")\n",
    "mask\n",
    "data[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[data < 0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[names != \"Joe\"] = 7\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.zeros((8, 4))\n",
    "for i in range(8):\n",
    "    arr[i] = i\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr[[4, 3, 0, 6]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr[[-3, -5, -7]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "arr\n",
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]\n",
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]] = 0\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr\n",
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([[0, 1, 0], [1, 2, -2], [6, 3, 2], [-1, 0, -1], [1, 0, 1]])\n",
    "arr\n",
    "np.dot(arr.T, arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr.T @ arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr\n",
    "arr.swapaxes(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.standard_normal(size=(4, 4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import normalvariate\n",
    "N = 1_000_000\n",
    "%timeit samples = [normalvariate(0, 1) for _ in range(N)]\n",
    "%timeit np.random.standard_normal(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(seed=12345)\n",
    "data = rng.standard_normal((2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "type(rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "arr\n",
    "np.sqrt(arr)\n",
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = rng.standard_normal(8)\n",
    "y = rng.standard_normal(8)\n",
    "x\n",
    "y\n",
    "np.maximum(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = rng.standard_normal(7) * 5\n",
    "arr\n",
    "remainder, whole_part = np.modf(arr)\n",
    "remainder\n",
    "whole_part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr\n",
    "out = np.zeros_like(arr)\n",
    "np.add(arr, 1)\n",
    "np.add(arr, 1, out=out)\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = np.arange(-5, 5, 0.01) # 100 equally spaced points\n",
    "xs, ys = np.meshgrid(points, points)\n",
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(z, cmap=plt.cm.gray, extent=[-5, 5, -5, 5])\n",
    "plt.colorbar()\n",
    "plt.title(\"Image plot of $\\sqrt{x^2 + y^2}$ for a grid of values\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.close(\"all\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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])\n",
    "cond = np.array([True, False, True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = [(x if c else y)\n",
    "          for x, y, c in zip(xarr, yarr, cond)]\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = np.where(cond, xarr, yarr)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = rng.standard_normal((4, 4))\n",
    "arr\n",
    "arr > 0\n",
    "np.where(arr > 0, 2, -2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.where(arr > 0, 2, arr) # set only positive values to 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = rng.standard_normal((5, 4))\n",
    "arr\n",
    "arr.mean()\n",
    "np.mean(arr)\n",
    "arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr.mean(axis=1)\n",
    "arr.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([0, 1, 2, 3, 4, 5, 6, 7])\n",
    "arr.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr.cumsum(axis=0)\n",
    "arr.cumsum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = rng.standard_normal(100)\n",
    "(arr > 0).sum() # Number of positive values\n",
    "(arr <= 0).sum() # Number of non-positive values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "bools = np.array([False, False, True, False])\n",
    "bools.any()\n",
    "bools.all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = rng.standard_normal(6)\n",
    "arr\n",
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = rng.standard_normal((5, 3))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr.sort(axis=0)\n",
    "arr\n",
    "arr.sort(axis=1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2 = np.array([5, -10, 7, 1, 0, -3])\n",
    "sorted_arr2 = np.sort(arr2)\n",
    "sorted_arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "names = np.array([\"Bob\", \"Will\", \"Joe\", \"Bob\", \"Will\", \"Joe\", \"Joe\"])\n",
    "np.unique(names)\n",
    "ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])\n",
    "np.unique(ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "sorted(set(names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "values = np.array([6, 0, 0, 3, 2, 5, 6])\n",
    "np.in1d(values, [2, 3, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "np.save(\"some_array\", arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.load(\"some_array.npy\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez(\"array_archive.npz\", a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "arch = np.load(\"array_archive.npz\")\n",
    "arch[\"b\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez_compressed(\"arrays_compressed.npz\", a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "!rm some_array.npy\n",
    "!rm array_archive.npz\n",
    "!rm arrays_compressed.npz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "y = np.array([[6., 23.], [-1, 7], [8, 9]])\n",
    "x\n",
    "y\n",
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "x @ np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv, qr\n",
    "X = rng.standard_normal((5, 5))\n",
    "mat = X.T @ X\n",
    "inv(mat)\n",
    "mat @ inv(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "position = 0\n",
    "walk = [position]\n",
    "nsteps = 1000\n",
    "for _ in range(nsteps):\n",
    "    step = 1 if random.randint(0, 1) else -1\n",
    "    position += step\n",
    "    walk.append(position)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(walk[:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsteps = 1000\n",
    "rng = np.random.default_rng(seed=12345)  # fresh random generator\n",
    "draws = rng.integers(0, 2, size=nsteps)\n",
    "steps = np.where(draws == 0, 1, -1)\n",
    "walk = steps.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "walk.min()\n",
    "walk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "draws = rng.integers(0, 2, size=(nwalks, nsteps)) # 0 or 1\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walks = steps.cumsum(axis=1)\n",
    "walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "walks.max()\n",
    "walks.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(axis=1)\n",
    "hits30\n",
    "hits30.sum() # Number that hit 30 or -30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax(axis=1)\n",
    "crossing_times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "crossing_times.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "draws = 0.25 * rng.standard_normal((nwalks, nsteps))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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