numpy_basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ad9e5254",
   "metadata": {},
   "source": [
    "# NumPy Basics: Arrays and Vectorized Computation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55757383",
   "metadata": {},
   "source": [
    "One of the reasons NumPy is so important for numerical computations in Python is because it is designed for efficiency on large arrays of data. There are a number of reasons for this:\n",
    "\n",
    "- NumPy internally stores data in a contiguous block of memory, independent of other built-in Python objects. NumPy's library of algorithms written in the C language can operate on this memory without any type checking or other overhead. NumPy arrays also use much less memory than built-in Python sequences.\n",
    "\n",
    "- NumPy operations perform complex computations on entire arrays without the need for Python for loops, which can be slow for large sequences. NumPy is faster than regular Python code because its C-based algorithms avoid overhead present with regular interpreted Python code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c9a230ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "my_arr = np.arange(1_000_000)\n",
    "\n",
    "my_list = list(range(1_000_000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a516eb7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "571 µs ± 24.3 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit my_arr2 = my_arr * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a8aaa4f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.68 ms ± 21.6 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit my_list2 = my_list * 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3c72198",
   "metadata": {},
   "source": [
    "## 1. The NumPy ndarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fa6a6c2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.5, -3. , 10. ],\n",
       "       [ 0. , -0.1,  6.5]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.array([[1.5, -3, 10], [0, -0.1, 6.5]])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "98598430",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 15., -30., 100.],\n",
       "       [  0.,  -1.,  65.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data * 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d567e42f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3. , -6. , 20. ],\n",
       "       [ 0. , -0.2, 13. ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data + data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6bebf2d",
   "metadata": {},
   "source": [
    "Note: In this chapter and throughout the book, I use the standard NumPy convention of always using import numpy as np. It would be possible to put from numpy import * in your code to avoid having to write np., but I advise against making a habit of this. The numpy namespace is large and contains a number of functions whose names conflict with built-in Python functions (like min and max). Following standard conventions like these is almost always a good idea."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f5ab910",
   "metadata": {},
   "source": [
    "An ndarray is a generic multidimensional container for homogeneous data; that is, all of the elements must be the same type. Every array has a shape, a tuple indicating the size of each dimension, and a dtype, an object describing the data type of the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8920d3fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "76776e29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "52c91feb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1849faa",
   "metadata": {},
   "source": [
    "## 1.1 Creating ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fe94e613",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5ae78094",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((4,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5ab1681e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty((6,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "916c0e96",
   "metadata": {},
   "source": [
    "Caution:\n",
    "It’s not safe to assume that numpy.empty will return an array of all zeros. This function returns uninitialized memory and thus may contain nonzero \"garbage\" values. You should use this function only if you intend to populate the new array with data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2d94de8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "252ac46e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0],\n",
       "       [0, 1]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_2d_list = [[1,0],[0,1]]\n",
    "my_2d_arr = np.asarray(my_2d_list)\n",
    "my_2d_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "547abbda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [1, 1]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones_like(my_2d_arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "264c572b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0],\n",
       "       [0, 0]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros_like(my_2d_arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "52150525",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 8, 8, 8],\n",
       "       [8, 8, 8, 8],\n",
       "       [8, 8, 8, 8],\n",
       "       [8, 8, 8, 8]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full((4,4), fill_value=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e18bdae4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 5],\n",
       "       [5, 5]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full_like(my_2d_arr, fill_value=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d62e027c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8cb9aa22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.identity(7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ffc058b",
   "metadata": {},
   "source": [
    "## 1.2 Data Types for ndarrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ce2eef7",
   "metadata": {},
   "source": [
    "Data types are a source of NumPy's flexibility for interacting with data coming from other systems. In most cases they provide a mapping directly onto an underlying disk or memory representation, which makes it possible to read and write binary streams of data to disk and to connect to code written in a low-level language like C or FORTRAN. The numerical data types are named the same way: a type name, like float or int, followed by a number indicating the number of bits per element. A standard double-precision floating-point value (what’s used under the hood in Python’s float object) takes up 8 bytes or 64 bits. Thus, this type is known in NumPy as float64. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9184345a",
   "metadata": {},
   "source": [
    "<h2>Data Type Mapping</h2>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th>Type</th>\n",
    "        <th>Code</th>\n",
    "        <th>Description</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>int8, uint8</td>\n",
    "        <td>i1, u1</td>\n",
    "        <td>Signed and unsigned 8-bit (1 byte) integer types</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>int16, uint16</td>\n",
    "        <td>i2, u2</td>\n",
    "        <td>Signed and unsigned 16-bit integer types</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>int32, uint32</td>\n",
    "        <td>i4, u4</td>\n",
    "        <td>Signed and unsigned 32-bit integer types</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>int64, uint64</td>\n",
    "        <td>i8, u8</td>\n",
    "        <td>Signed and unsigned 64-bit integer types</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>float16</td>\n",
    "        <td>f2</td>\n",
    "        <td>Half-precision floating point</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>float32</td>\n",
    "        <td>f4 or f</td>\n",
    "        <td>Standard single-precision floating point; compatible with C float</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>float64</td>\n",
    "        <td>f8 or d</td>\n",
    "        <td>Standard double-precision floating point; compatible with C double and Python float object</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>float128</td>\n",
    "        <td>f16 or g</td>\n",
    "        <td>Extended-precision floating point</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>complex64, complex128, complex256</td>\n",
    "        <td>c8, c16, c32</td>\n",
    "        <td>Complex numbers represented by two 32, 64, or 128 floats, respectively</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>bool</td>\n",
    "        <td>?</td>\n",
    "        <td>Boolean type storing True and False values</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>object</td>\n",
    "        <td>O</td>\n",
    "        <td>Python object type; a value can be any Python object</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>string_</td>\n",
    "        <td>S</td>\n",
    "        <td>Fixed-length ASCII string type (1 byte per character); for example, to create a string data type with length 10, use 'S10'</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>unicode_</td>\n",
    "        <td>U</td>\n",
    "        <td>Fixed-length Unicode type (number of bytes platform specific); same specification semantics as string_ (e.g., 'U10')</td>\n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "da77b0e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(1,6)\n",
    "arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "0116a440",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3., 4., 5.])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "float_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "b6a0f1e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12072616, 0.54200818, 0.77124763, 0.24901243, 0.48645821])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_arr = np.random.rand(5)\n",
    "random_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b06bfdc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_arr.astype(np.int64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "6e5e0799",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.25, -9.6 , 42.  ])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_strings = np.array([\"1.25\", \"-9.6\", \"42\"], dtype=np.string_)\n",
    "\n",
    "num_strings.astype(float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04f923b0",
   "metadata": {},
   "source": [
    "<b>Caution:</b><br>\n",
    "Be cautious when using the numpy.string_ type, as string data in NumPy is fixed size and may truncate input without warning. pandas has more intuitive out-of-the-box behavior on non-numeric data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb0e4144",
   "metadata": {},
   "source": [
    "There are shorthand type code strings you can also use to refer to a dtype:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f8237caa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0], dtype=uint32)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros_uint32 = np.zeros(8, dtype=\"u4\")\n",
    "zeros_uint32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ce87fdb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([b'1', b'1', b'1', b'1', b'1', b'1', b'1', b'1'], dtype='|S1')"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones_string = np.ones(8, dtype=\"S1\")\n",
    "ones_string"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebaee672",
   "metadata": {},
   "source": [
    "## 1.3 Arithmetic with NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "374bede4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([list(range(1,4)), list(range(4,7))])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "4f49ea98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([np.arange(1,4), np.arange(4,7)])\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "8b38cc20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  4,  9],\n",
       "       [16, 25, 36]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr * arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "ba6b797a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [0, 0, 0]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr - arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "7bbf154c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.5       , 0.33333333],\n",
       "       [0.25      , 0.2       , 0.16666667]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "9e97903e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   8,  27],\n",
       "       [ 64, 125, 216]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr ** 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "4e834674",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 >= arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f994512",
   "metadata": {},
   "source": [
    "Evaluating operations between differently sized arrays is called broadcasting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ae54050",
   "metadata": {},
   "source": [
    "## 1.4 Basic Indexing and Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "881a0697",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(1,10,2)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "3d4a6361",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "5dc79e55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 7])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[2:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "ad2ffe43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3, 12, 12,  9])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[2:4] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6a288cd",
   "metadata": {},
   "source": [
    "<b>Note</b><br>\n",
    "An important first distinction from Python's built-in lists is that array slices are views on the original array. This means that the data is not copied, and any modifications to the view will be reflected in the source array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "07b17299",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice = arr[0:2]\n",
    "arr_slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "7999c558",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1, 532,  12,  12,   9])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[1] = 532\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5d6b9a19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([64, 64, 12, 12,  9])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[:] = 64\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c16a5b64",
   "metadata": {},
   "source": [
    "<b>Caution</b><br>\n",
    "If you want a copy of a slice of an ndarray instead of a view, you will need to explicitly copy the array—for example, <code style=\"background-color:#F6F6F6;border-radius:4;color:#9753B8\">arr[5:8].copy()</code>. As you will see, pandas works this way, too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "e7f56e24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "9b31f16e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "57c41bf6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "5c3a2353",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "898706a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "460d2c29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[32, 32, 32],\n",
       "        [32, 32, 32]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_values = arr3d[0].copy()\n",
    "\n",
    "arr3d[0] = 32\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "64cd1cb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "dce37c56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0] = old_values\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "66073627",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "df0ce951",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "7856d388",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = arr3d[1]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "943121ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "4bcc36a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "0b8224ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3], [4, 5, 6]]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list2d = [[1, 2, 3], [4, 5, 6]]\n",
    "list2d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8a6782c",
   "metadata": {},
   "source": [
    "<b>Caution</b><br>\n",
    "This multidimensional indexing syntax for NumPy arrays will <b>not</b> work with regular Python objects, such as lists of lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "57f6ac66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list2d[1][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "8df53935",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "list indices must be integers or slices, not tuple",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[103], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mlist2d\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m]\u001b[49m\n",
      "\u001b[0;31mTypeError\u001b[0m: list indices must be integers or slices, not tuple"
     ]
    }
   ],
   "source": [
    "list2d[1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "5386bfaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "144ef673",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "c838c825",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [4, 5]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "6891bbad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33cdebef",
   "metadata": {},
   "source": [
    "## 1.5 Boolean Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "285ad01f",
   "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],[-12, -4], [3, 4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "0119769d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False, False, False])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == \"Bob\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "86ab906e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 7],\n",
       "       [0, 0]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == \"Bob\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "f0f93f1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   2],\n",
       "       [-12,  -4],\n",
       "       [  3,   4]])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == \"Joe\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "4f433647",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2, -4,  4])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == \"Joe\", 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "5815c3df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2],\n",
       "       [-4],\n",
       "       [ 4]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == \"Joe\", 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "fb2a3199",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 7],\n",
       "       [0, 0]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[[ True, False, False,  True, False, False, False]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "e3435bf8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  4,   7],\n",
       "        [  0,   2],\n",
       "        [ -5,   6],\n",
       "        [  0,   0],\n",
       "        [  1,   2],\n",
       "        [-12,  -4],\n",
       "        [  3,   4]]])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[True]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "9bc0f98e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([], shape=(0, 7, 2), dtype=int64)"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[False]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cb4337e",
   "metadata": {},
   "source": [
    "The Boolean array must be of the same length as the array axis it’s indexing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "a9b70d76",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "boolean index did not match indexed array along dimension 0; dimension is 7 but corresponding boolean dimension is 2",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[120], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mdata\u001b[49m\u001b[43m[\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\n",
      "\u001b[0;31mIndexError\u001b[0m: boolean index did not match indexed array along dimension 0; dimension is 7 but corresponding boolean dimension is 2"
     ]
    }
   ],
   "source": [
    "data[[True, False]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "0545679c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   2],\n",
       "       [ -5,   6],\n",
       "       [  1,   2],\n",
       "       [-12,  -4],\n",
       "       [  3,   4]])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names != \"Bob\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "cb6d0786",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   2],\n",
       "       [ -5,   6],\n",
       "       [  1,   2],\n",
       "       [-12,  -4],\n",
       "       [  3,   4]])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[~(names == \"Bob\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "61435fc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1, -3],\n",
       "       [ 4, -7],\n",
       "       [-2, -3],\n",
       "       [11,  3],\n",
       "       [-4, -5]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "~data[~(names == \"Bob\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "83964099",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  4,   7],\n",
       "       [  0,   2],\n",
       "       [ -5,   6],\n",
       "       [  0,   0],\n",
       "       [  1,   2],\n",
       "       [-12,  -4],\n",
       "       [  3,   4]])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "01fa742f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  7],\n",
       "       [-5,  6],\n",
       "       [ 0,  0],\n",
       "       [ 1,  2]])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = (names == \"Bob\") | (names == \"Will\")\n",
    "data[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "c81ca3a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True,  True,  True, False, False])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "6f2e6588",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False, False, False])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = (names == \"Bob\") & (names == \"Will\")\n",
    "mask"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e0750f0",
   "metadata": {},
   "source": [
    "<b>Caution</b><br>\n",
    "The Python keywords and and or do not work with Boolean arrays. Use & (and) and | (or) instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "7a12e939",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 7],\n",
       "       [0, 2],\n",
       "       [0, 6],\n",
       "       [0, 0],\n",
       "       [1, 2],\n",
       "       [0, 0],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data < 0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "6ab70f0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7, 7],\n",
       "       [0, 2],\n",
       "       [7, 7],\n",
       "       [7, 7],\n",
       "       [7, 7],\n",
       "       [0, 0],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names != \"Joe\"] = 7\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92a8fd82",
   "metadata": {},
   "source": [
    "## 1.6 Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "512cf770",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[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.],\n",
       "       [8., 8., 8., 8.]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.zeros((8, 4))\n",
    "for i in range(8):\n",
    "    arr[i] = i + 1\n",
    "    \n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85d9216e",
   "metadata": {},
   "source": [
    "To select a subset of the rows in a particular order, you can simply pass a list or ndarray of integers specifying the desired order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "5133162e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3., 3., 3., 3.],\n",
       "       [5., 5., 5., 5.],\n",
       "       [7., 7., 7., 7.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[2, 4, 6, 0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "ec663c82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3., 3., 3., 3.],\n",
       "       [6., 6., 6., 6.],\n",
       "       [8., 8., 8., 8.]])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[-6, -3, -1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "84731d70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(1, 10).reshape((3, 3))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "b7629e2e",
   "metadata": {},
   "outputs": [
    {
     "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]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6e3c36b",
   "metadata": {},
   "source": [
    "Passing multiple index arrays does something slightly different; it selects a one-dimensional array of elements corresponding to each tuple of indices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "ec03f778",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 23, 29, 10])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cdcccd9",
   "metadata": {},
   "source": [
    "In this case the first index value is an list of the rows selected but the second list determines the order of the rows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "f52a569d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  7,  5,  6],\n",
       "       [20, 23, 21, 22],\n",
       "       [28, 31, 29, 30],\n",
       "       [ 8, 11,  9, 10]])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "694f5883",
   "metadata": {},
   "source": [
    "## 1.7 Transposing Arrays and Swapping Axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "00aa9ff0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "8f894353",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  5, 10],\n",
       "       [ 1,  6, 11],\n",
       "       [ 2,  7, 12],\n",
       "       [ 3,  8, 13],\n",
       "       [ 4,  9, 14]])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "4f6eb00a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  0],\n",
       "       [ 1,  2, -2],\n",
       "       [ 6,  3,  2],\n",
       "       [-1,  0, -1],\n",
       "       [ 1,  0,  1]])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[0, 1, 0], [1, 2, -2], [6, 3, 2], [-1, 0, -1], [1, 0, 1]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "a8808a10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[39, 20, 12],\n",
       "       [20, 14,  2],\n",
       "       [12,  2, 10]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(arr.T, arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "f852c0c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[39, 20, 12],\n",
       "       [20, 14,  2],\n",
       "       [12,  2, 10]])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.T @ arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "9f2824f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  6, -1,  1],\n",
       "       [ 1,  2,  3,  0,  0],\n",
       "       [ 0, -2,  2, -1,  1]])"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.swapaxes(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1ba3d78",
   "metadata": {},
   "source": [
    "# 2. Pseudorandom Number Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "1925fb79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.40187167,  2.49914724,  0.96438334,  0.05034948],\n",
       "       [-2.84917917,  1.41504491, -0.32400285, -0.10206837],\n",
       "       [-0.6498498 ,  0.13825629, -0.55348273,  0.37200889],\n",
       "       [-0.38236299, -0.38249803, -0.70259081,  0.94609215]])"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = np.random.standard_normal(size=(4, 4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ee16ae1",
   "metadata": {},
   "source": [
    "<h2>Random Number Generation Methods</h2>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th>Method</th>\n",
    "        <th>Description</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>permutation</td>\n",
    "        <td>Return a random permutation of a sequence, or return a permuted range</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>shuffle</td>\n",
    "        <td>Randomly permute a sequence in place</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>uniform</td>\n",
    "        <td>Draw samples from a uniform distribution</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>integers</td>\n",
    "        <td>Draw random integers from a given low-to-high range</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>standard_normal</td>\n",
    "        <td>Draw samples from a normal distribution with mean 0 and standard deviation 1</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>binomial</td>\n",
    "        <td>Draw samples from a binomial distribution</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>normal</td>\n",
    "        <td>Draw samples from a normal (Gaussian) distribution</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>beta</td>\n",
    "        <td>Draw samples from a beta distribution</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>chisquare</td>\n",
    "        <td>Draw samples from a chi-square distribution</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>gamma</td>\n",
    "        <td>Draw samples from a gamma distribution</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>uniform</td>\n",
    "        <td>Draw samples from a uniform [0, 1) distribution</td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47c7d7c2",
   "metadata": {},
   "source": [
    "# 3. Universal Functions: Fast Element-Wise Array Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "7c22c50d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "9e10588b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 1.        , 1.41421356, 1.73205081, 2.        ,\n",
       "       2.23606798, 2.44948974, 2.64575131, 2.82842712, 3.        ])"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "ba8efaa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 2.71828183e+00, 7.38905610e+00, 2.00855369e+01,\n",
       "       5.45981500e+01, 1.48413159e+02, 4.03428793e+02, 1.09663316e+03,\n",
       "       2.98095799e+03, 8.10308393e+03])"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "6be46d11",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(seed=12345)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "0739604a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.42382504,  1.26372846, -0.87066174, -0.25917323, -0.07534331,\n",
       "       -0.74088465, -1.3677927 ,  0.6488928 ])"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = rng.standard_normal(8)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "6001c965",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.36105811, -1.95286306,  2.34740965,  0.96849691, -0.75938718,\n",
       "        0.90219827, -0.46695317, -0.06068952])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = rng.standard_normal(8)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "0d5adeb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.36105811,  1.26372846,  2.34740965,  0.96849691, -0.07534331,\n",
       "        0.90219827, -0.46695317,  0.6488928 ])"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.maximum(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "81536a0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.06276692, -0.6891346 ,  1.47674792,  0.70932367, -0.83473049,\n",
       "        0.16131362, -1.83474588,  0.58820328])"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "9e3cb189",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.94422172, -6.28334067,  2.87928757,  6.99489497,  6.6114903 ,\n",
       "       -1.49849258,  4.51459671])"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = rng.standard_normal(7) * 5\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "e0fd20ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.94422172, -0.28334067,  0.87928757,  0.99489497,  0.6114903 ,\n",
       "       -0.49849258,  0.51459671])"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remainder, whole_part = np.modf(arr)\n",
    "remainder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "4c908360",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3., -6.,  2.,  6.,  6., -1.,  4.])"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "whole_part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "148a0c25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.94422172, -6.28334067,  2.87928757,  6.99489497,  6.6114903 ,\n",
       "       -1.49849258,  4.51459671])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "a41791cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.94422172, -5.28334067,  3.87928757,  7.99489497,  7.6114903 ,\n",
       "       -0.49849258,  5.51459671])"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_arr = np.zeros_like(arr)\n",
    "np.add(arr, 1, out=out_arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "41b773ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.94422172, -5.28334067,  3.87928757,  7.99489497,  7.6114903 ,\n",
       "       -0.49849258,  5.51459671])"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc3c63d4",
   "metadata": {},
   "source": [
    "<h2>Some unary universal functions</h2>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th>Function</th>\n",
    "        <th>Description</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>abs, fabs</code></td>\n",
    "        <td>Compute the absolute value element-wise for integer, floating-point, or complex values</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>sqrt</code></td>\n",
    "        <td>Compute the square root of each element (equivalent to arr ** 0.5)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>square</code></td>\n",
    "        <td>Compute the square of each element (equivalent to arr ** 2)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>exp</code></td>\n",
    "        <td>Compute the exponent ex of each element</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>log, log10, log2, log1p</code></td>\n",
    "        <td>Natural logarithm (base e), log base 10, log base 2, and log(1 + x), respectively</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>sign</code></td>\n",
    "        <td>Compute the sign of each element: 1 (positive), 0 (zero), or –1 (negative)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>ceil</code></td>\n",
    "        <td>Compute the ceiling of each element (i.e., the smallest integer greater than or equal to that number)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>floor</code></td>\n",
    "        <td>Compute the floor of each element (i.e., the largest integer less than or equal to each element)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>rint</code></td>\n",
    "        <td>Round elements to the nearest integer, preserving the dtype</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>modf</code></td>\n",
    "        <td>Return fractional and integral parts of array as separate arrays</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>isnan</code></td>\n",
    "        <td>Return Boolean array indicating whether each value is NaN (Not a Number)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>isfinite, isinf</code></td>\n",
    "        <td>Return Boolean array indicating whether each element is finite (non-inf, non-NaN) or infinite, respectively</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>cos, cosh, sin, sinh, tan, tanh</code></td>\n",
    "        <td>Regular and hyperbolic trigonometric functions</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>arccos, arccosh, arcsin, arcsinh, arctan, arctanh</code></td>\n",
    "        <td>Inverse trigonometric functions</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>logical_not</code></td>\n",
    "        <td>Compute truth value of not x element-wise (equivalent to ~arr)</td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0026dfa",
   "metadata": {},
   "source": [
    "<h2>Some binary universal functions</h2>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th>Function</th>\n",
    "        <th>Description</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>add</code></td>\n",
    "        <td>Add corresponding elements in arrays</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>subtract</code></td>\n",
    "        <td>Subtract elements in second array from first array</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>multiply</code></td>\n",
    "        <td>Multiply array elements</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>divide, floor_divide</code></td>\n",
    "        <td>Divide or floor divide (truncating the remainder)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>power</code></td>\n",
    "        <td>Raise elements in first array to powers indicated in second array</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>maximum, fmax</code></td>\n",
    "        <td>Element-wise maximum; fmax ignores NaN</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>minimum, fmin</code></td>\n",
    "        <td>Element-wise minimum; fmin ignores NaN</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>mod</code></td>\n",
    "        <td>Element-wise modulus (remainder of division)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>copysign</code></td>\n",
    "        <td>Copy sign of values in second argument to values in first argument</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>greater, greater_equal, less, less_equal, equal, not_equal</code></td>\n",
    "        <td>Perform element-wise comparison, yielding Boolean array (equivalent to infix operators >, >=, <, <=, ==, !=)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>logical_and</code></td>\n",
    "        <td>Compute element-wise truth value of AND (&) logical operation</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>logical_or</code></td>\n",
    "        <td>Compute element-wise truth value of OR (|) logical operation</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>logical_xor</code></td>\n",
    "        <td>Compute element-wise truth value of XOR (^) logical operation</td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1902be53",
   "metadata": {},
   "source": [
    "# 4. Array-Oriented Programming with Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "0f47f575",
   "metadata": {},
   "outputs": [],
   "source": [
    "points = np.arange(-5, 5, 0.01).astype('float16')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "8165a76a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float16')"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "9783beee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],\n",
       "       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],\n",
       "       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],\n",
       "       ...,\n",
       "       [ 4.97,  4.97,  4.97, ...,  4.97,  4.97,  4.97],\n",
       "       [ 4.98,  4.98,  4.98, ...,  4.98,  4.98,  4.98],\n",
       "       [ 4.99,  4.99,  4.99, ...,  4.99,  4.99,  4.99]], dtype=float16)"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs, ys = np.meshgrid(points, points)\n",
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "26a76427",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       ...,\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99]], dtype=float16)"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "e7ded8c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.07 , 7.062, 7.06 , ..., 7.05 , 7.06 , 7.062],\n",
       "       [7.062, 7.055, 7.05 , ..., 7.04 , 7.05 , 7.055],\n",
       "       [7.06 , 7.05 , 7.043, ..., 7.035, 7.043, 7.05 ],\n",
       "       ...,\n",
       "       [7.05 , 7.04 , 7.035, ..., 7.027, 7.035, 7.04 ],\n",
       "       [7.06 , 7.05 , 7.043, ..., 7.035, 7.043, 7.05 ],\n",
       "       [7.062, 7.055, 7.05 , ..., 7.04 , 7.05 , 7.055]], dtype=float16)"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "4c60b367",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Image plot of $\\\\sqrt{x^2 + y^2}$ for a grid of values')"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\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": "markdown",
   "id": "ab146e6f",
   "metadata": {},
   "source": [
    "<b>Note</b><br>\n",
    "The term vectorization is used to describe some other computer science concepts, but in this book I use it to describe operations on whole arrays of data at once rather than going value by value using a Python for loop."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66853c55",
   "metadata": {},
   "source": [
    "## 4.1 Expressing Conditional Logic as Arrays Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c73370c3",
   "metadata": {},
   "source": [
    "Suppose we wanted to take a value from xarr whenever the corresponding value in cond is True, and otherwise take the value from yarr. A list comprehension doing this might look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "dec19d46",
   "metadata": {},
   "outputs": [],
   "source": [
    "xarr = np.random.rand(5).astype('float16')\n",
    "\n",
    "yarr = np.random.rand(5).astype('float16')\n",
    "\n",
    "cond = np.random.rand(5).astype('?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "f7e9dac4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.475, 0.715, 0.1948, 0.07355, 0.986]"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = [(x if c else y) for x, y, c in zip(xarr, yarr, cond)]\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "46f68517",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.475  , 0.715  , 0.1948 , 0.07355, 0.986  ], dtype=float16)"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.where(cond, xarr, yarr)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "27c8a9fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.62158273, -0.15818926,  0.44948393, -1.34360107],\n",
       "       [-0.08168759,  1.72473993,  2.61815943,  0.77736134],\n",
       "       [ 0.8286332 , -0.95898831, -1.20938829, -1.41229201],\n",
       "       [ 0.54154683,  0.7519394 , -0.65876032, -1.22867499]])"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = rng.standard_normal((4, 4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "808a1f03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False,  True, False],\n",
       "       [False,  True,  True,  True],\n",
       "       [ True, False, False, False],\n",
       "       [ True,  True, False, False]])"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "cf01fa9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2, -2,  2, -2],\n",
       "       [-2,  2,  2,  2],\n",
       "       [ 2, -2, -2, -2],\n",
       "       [ 2,  2, -2, -2]])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0, 2, -2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "a78d20e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.62158273, -0.15818926,  2.        , -1.34360107],\n",
       "       [-0.08168759,  2.        ,  2.        ,  2.        ],\n",
       "       [ 2.        , -0.95898831, -1.20938829, -1.41229201],\n",
       "       [ 2.        ,  2.        , -0.65876032, -1.22867499]])"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0, 2, arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e60b08a",
   "metadata": {},
   "source": [
    "## 4.2 Mathematical and Statistical Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "ca7c34d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.25755777,  0.31290292, -0.13081169,  1.26998312],\n",
       "       [-0.09296246, -0.06615089, -1.10821447,  0.13595685],\n",
       "       [ 1.34707776,  0.06114402,  0.0709146 ,  0.43365454],\n",
       "       [ 0.27748366,  0.53025239,  0.53672097,  0.61835001]])"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = rng.standard_normal((4, 4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "aa78c43f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27836619417849834"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "98dc4089",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.453859106855973"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "b64f07bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27836619417849834"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "730a0a8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.453859106855973"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "a33d2fda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.42740803, -0.28284274,  0.47819773,  0.49070176])"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "68ed52ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.44728918,  0.20953711, -0.15784765,  0.61448613])"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "3136cb98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.70963212, -1.13137096,  1.91279092,  1.96280703])"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "ee1e182c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.78915673,  0.83814844, -0.63139059,  2.45794452])"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "f9a08c3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(9).reshape((3, 3))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "300b6f72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  3,  6, 10, 15, 21, 28, 36])"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "235e6f8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  3],\n",
       "       [ 3,  7, 12],\n",
       "       [ 6, 13, 21]])"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "dfee3906",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  5,  7],\n",
       "       [ 9, 12, 15]])"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9001ea6",
   "metadata": {},
   "source": [
    "## 4.3 Methods for Boolean Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "1b5e7b75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = rng.standard_normal(100)\n",
    "\n",
    "(arr > 0).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "id": "370b4eaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(arr <= 0).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "27761985",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False,  True, False, False,  True, False,  True,\n",
       "       False, False,  True, False,  True, False, False, False,  True,\n",
       "        True, False, False,  True, False, False,  True, False, False,\n",
       "       False,  True, False,  True, False,  True,  True,  True, False,\n",
       "        True,  True,  True,  True, False, False, False, False,  True,\n",
       "       False, False, False,  True, False, False, False,  True,  True,\n",
       "       False,  True,  True, False,  True,  True,  True,  True,  True,\n",
       "        True, False, False, False,  True,  True,  True,  True,  True,\n",
       "        True, False, False, False, False,  True, False, False, False,\n",
       "        True, False,  True,  True, False,  True, False, False,  True,\n",
       "        True,  True, False, False, False,  True,  True, False,  True,\n",
       "        True])"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "32e292cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools = np.array([False, True, True, False, True])\n",
    "\n",
    "bools.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "ab6c0a55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools.all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16bc040b",
   "metadata": {},
   "source": [
    "## 4.4 Sorting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "0bce7b42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.75539067, -1.15912585,  2.15031011],\n",
       "       [-0.15027022, -0.16116428, -1.07944248],\n",
       "       [ 0.87796618,  0.22446741, -0.59159345],\n",
       "       [ 0.2262628 ,  0.68618251,  1.21500461],\n",
       "       [ 0.21605944, -0.96482356, -0.5566078 ]])"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = rng.standard_normal((5, 3))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "id": "74fc9fc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.15027022, -1.15912585, -1.07944248],\n",
       "       [ 0.21605944, -0.96482356, -0.59159345],\n",
       "       [ 0.2262628 , -0.16116428, -0.5566078 ],\n",
       "       [ 0.75539067,  0.22446741,  1.21500461],\n",
       "       [ 0.87796618,  0.68618251,  2.15031011]])"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort(axis=0)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "id": "470c4245",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.15912585, -1.07944248, -0.15027022],\n",
       "       [-0.96482356, -0.59159345,  0.21605944],\n",
       "       [-0.5566078 , -0.16116428,  0.2262628 ],\n",
       "       [ 0.22446741,  0.75539067,  1.21500461],\n",
       "       [ 0.68618251,  0.87796618,  2.15031011]])"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort(axis=1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eb36bb8",
   "metadata": {},
   "source": [
    "<code>np.sort()</code> returns a copy for passed sorted array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "id": "238ed1f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.29838764, -0.73208213,  0.7364691 ],\n",
       "       [-0.34143629, -0.10787605,  0.46571672],\n",
       "       [ 0.28224121,  0.90954639,  1.58453379],\n",
       "       [-0.66937652,  0.39507157,  1.55536898],\n",
       "       [-1.23813903, -1.19617346, -0.42914951]])"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = rng.standard_normal((5, 3))\n",
    "np.sort(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "id": "802ee2cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.29838764, -0.73208213,  0.7364691 ],\n",
       "       [ 0.46571672, -0.10787605, -0.34143629],\n",
       "       [ 1.58453379,  0.28224121,  0.90954639],\n",
       "       [ 0.39507157, -0.66937652,  1.55536898],\n",
       "       [-1.23813903, -1.19617346, -0.42914951]])"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b81631dd",
   "metadata": {},
   "source": [
    "## 4.5 Unique and Other Set Logic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c0052cf",
   "metadata": {},
   "source": [
    "<code>np.unique(array)</code> returns a sorted array with the unique items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "42fd5198",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will'], dtype='<U4')"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array([\"Bob\", \"Will\", \"Joe\", \"Bob\", \"Will\", \"Joe\", \"Joe\"])\n",
    "\n",
    "np.unique(names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "54368e91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])\n",
    "\n",
    "np.unique(ints)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f2df323",
   "metadata": {},
   "source": [
    "Python alternative:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "034a2e50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Bob', 'Joe', 'Will']"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(set(names))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d3b80f4",
   "metadata": {},
   "source": [
    "In many cases, the NumPy version is faster and returns a NumPy array rather than a Python list."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "908bf379",
   "metadata": {},
   "source": [
    "<h2>Array Set Operations</h2>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th><code>Method</code></th>\n",
    "        <th>Description</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>unique(x)</code></td>\n",
    "        <td>Compute the sorted, unique elements in x</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>intersect1d(x, y)</code></td>\n",
    "        <td>Compute the sorted, common elements in x and y</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>union1d(x, y)</code></td>\n",
    "        <td>Compute the sorted union of elements</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>in1d(x, y)</code></td>\n",
    "        <td>Compute a Boolean array indicating whether each element of x is contained in y</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>setdiff1d(x, y)</code></td>\n",
    "        <td>Set difference, elements in x that are not in y</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>setxor1d(x, y)</code></td>\n",
    "        <td>Set symmetric differences; elements that are in either of the arrays, but not both</td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7a7ed61",
   "metadata": {},
   "source": [
    "# 5. File Input and Output with Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c53dd17c",
   "metadata": {},
   "source": [
    "<code>numpy.save</code> and <code>numpy.load</code> are the two workhorse functions for efficiently saving and loading array data on disk. Arrays are saved by default in an uncompressed raw binary format with file extension .npy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "3c29e740",
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "\n",
    "np.save(\"some_array\", arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "8d9580d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.load(\"some_array.npy\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "e93ece06",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez(\"array_archive.npz\", a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "id": "320dcbb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch = np.load(\"array_archive.npz\")\n",
    "\n",
    "arch[\"b\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "f27cd7a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NpzFile 'array_archive.npz' with keys: a, b"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dee8fc2a",
   "metadata": {},
   "source": [
    "# 6. Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "id": "34df9f94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3],\n",
       "       [4, 5]])"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(6).reshape((3, 2))\n",
    "y = np.arange(8).reshape((2, 4))\n",
    "\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "id": "ec677187",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [4, 5, 6, 7]])"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "id": "6dbf2344",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6,  7],\n",
       "       [12, 17, 22, 27],\n",
       "       [20, 29, 38, 47]])"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "id": "80b6a648",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6,  7],\n",
       "       [12, 17, 22, 27],\n",
       "       [20, 29, 38, 47]])"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "id": "edf706b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5,  6,  7],\n",
       "       [12, 17, 22, 27],\n",
       "       [20, 29, 38, 47]])"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "id": "45afbb29",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv, qr\n",
    "\n",
    "X = rng.standard_normal((5, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "id": "683a06ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = X.T @ X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "id": "575c4f60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  5.4755939 ,   4.82719485,  14.00262023, -16.92859212,\n",
       "         17.18430654],\n",
       "       [  4.82719485,   5.18449275,  13.02261242, -15.92387568,\n",
       "         15.9811525 ],\n",
       "       [ 14.00262023,  13.02261242,  37.27115446, -44.93508608,\n",
       "         45.48194869],\n",
       "       [-16.92859212, -15.92387568, -44.93508608,  54.65071429,\n",
       "        -55.06163996],\n",
       "       [ 17.18430654,  15.9811525 ,  45.48194869, -55.06163996,\n",
       "         55.77310104]])"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inv(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "id": "bc233825",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.09227484,  0.91698401,  0.36633341, -0.25999821, -2.69526818],\n",
       "       [ 0.91698401,  2.03338355,  0.3377165 ,  0.94640951, -0.20624085],\n",
       "       [ 0.36633341,  0.3377165 ,  5.69339976,  0.77485925, -4.0875292 ],\n",
       "       [-0.25999821,  0.94640951,  0.77485925,  4.02813473,  3.15379218],\n",
       "       [-2.69526818, -0.20624085, -4.0875292 ,  3.15379218,  7.35433455]])"
      ]
     },
     "execution_count": 268,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "id": "2c4e2881",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 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.]], dtype=float16)"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "(mat @ inv(mat)).astype('float16')"
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   "source": [
    "<h2>Commonly used <code>numpy.linalg</code> functions</h2>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th><code>Function</code></th>\n",
    "        <th>Description</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>diag</code></td>\n",
    "        <td>Return the diagonal (or off-diagonal) elements of a square matrix as a 1D array, or convert a 1D array into a square matrix with zeros on the off-diagonal</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>dot</code></td>\n",
    "        <td>Matrix multiplication</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>trace</code></td>\n",
    "        <td>Compute the sum of the diagonal elements</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>det</code></td>\n",
    "        <td>Compute the matrix determinant</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>eig</code></td>\n",
    "        <td>Compute the eigenvalues and eigenvectors of a square matrix</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>inv</code></td>\n",
    "        <td>Compute the inverse of a square matrix</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>pinv</code></td>\n",
    "        <td>Compute the Moore-Penrose pseudoinverse of a matrix</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>qr</code></td>\n",
    "        <td>Compute the QR decomposition</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>svd</code></td>\n",
    "        <td>Compute the singular value decomposition (SVD)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>solve</code></td>\n",
    "        <td>Solve the linear system Ax = b for x, where A is a square matrix</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><code>lstsq</code></td>\n",
    "        <td>Compute the least-squares solution to Ax = b</td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7fc954c0",
   "metadata": {},
   "outputs": [],
   "source": []
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