Notebooks/01-Python-Numpy/Introduction to Numpy.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "###### Notebook Template is borrowed from SBU-CE Machine Learning course - Fall 2022"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iJcNosa0ak8a"
      },
      "source": [
        "Numpy is the fundamental package for numeric computing with Python. It provides powerful ways to create,\n",
        "store, and/or manipulate data, which makes it able to seamlessly and speedily integrate with a wide variety\n",
        "of databases. This is also the foundation that Pandas is built on, which is a high-performance data-centric\n",
        "package that we will learn later in the course.\n",
        "\n",
        "In this lecture, we will talk about creating array with certain data types, manipulating array, selecting\n",
        "elements from arrays, and loading dataset into array. Such functions are useful for manipulating data and\n",
        "understanding the functionalities of other common Python data packages."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "ztpFFkYfak8d"
      },
      "outputs": [],
      "source": [
        "# You'll recall that we import a library using the `import` keyword as numpy's common abbreviation is np\n",
        "import numpy as np\n",
        "import math"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "cgmhxXTPak8e"
      },
      "source": [
        "# Array Creation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "CQoZHU9edXi6",
        "outputId": "6e0d306a-1f1f-4e59-fa2a-c2de10a7eab0"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "list1 = [1,2,3,4,5,6]\n",
        "a = np.array(list1)\n",
        "a\n",
        "type(a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nHhwKRuXak8f",
        "outputId": "cff22b3d-3a80-4f42-f80c-af91f271d753"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[1 2 3]\n",
            "1\n"
          ]
        }
      ],
      "source": [
        "# Arrays are displayed as a list or list of lists and can be created through list as well. When creating an\n",
        "# array, we pass in a list as an argument in numpy array\n",
        "a = np.array([1, 2, 3])\n",
        "print(a)\n",
        "# We can print the number of dimensions of a list using the ndim attribute\n",
        "print(a.ndim)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "axNTv7VQeGMo",
        "outputId": "1a2ae13c-33da-4205-fa41-a6e79c0ea4b9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[[1, 2, 3], [4, 5, 6], [2, [1]]]"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b = [[1,2,3],[4,5,6], [2,[1]]]\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Cvtr6sXZak8f",
        "outputId": "f833f57f-880f-4209-aed3-ed0226c95835"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# If we pass in a list of lists in numpy array, we create a multi-dimensional array, for instance, a matrix\n",
        "b = np.array([[1,2,3],[4,5,6]])\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AeopifHZak8f",
        "outputId": "f2622a89-833e-434e-fa6a-16c6a7ad28eb"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2, 3)"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# We can print out the length of each dimension by calling the shape attribute, which returns a tuple\n",
        "b.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pTzp8wEKak8g",
        "outputId": "2309874a-bf4a-499f-a1a2-a0daf8844278"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('int64')"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# We can also check the type of items in the array\n",
        "a.dtype\n",
        "b.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "Lcp1h_oxak8g",
        "outputId": "8c4979ca-cc84-4805-8bfe-6190351c86a1"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'float64'"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Besides integers, floats are also accepted in numpy arrays\n",
        "c = np.array([2.2, 5, 1.1])\n",
        "c.dtype.name"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dnn1Q8WIak8g",
        "outputId": "077cfa17-f3bc-44a8-afb8-06373f186ab2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2.2, 5. , 1.1])"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Let's look at the data in our array\n",
        "c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xiKIx76Eak8g"
      },
      "outputs": [],
      "source": [
        "# Note that numpy automatically converts integers, like 5, up to floats, since there is no loss of prescision.\n",
        "# Numpy will try and give you the best data type format possible to keep your data types homogeneous, which\n",
        "# means all the same, in the array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8DvyhK8cfjUU",
        "outputId": "75f61fbb-8851-41af-fe59-86fe1a324000"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1., 1., 1.],\n",
              "       [1., 1., 1.]])"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.ones((2,3))\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UQ_qyeTvhcXi",
        "outputId": "3c10ae13-32f4-4b8d-c399-ec75c0ab7bf9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a= [1] * 10\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "hHvjG3XBhgJy",
        "outputId": "f72fa2b4-a63e-4099-fe61-0dd705bca08d"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'aaaaaaaaaa'"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "'a' * 10"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PJXPiXbTgzsu",
        "outputId": "a142692a-9072-4539-dd54-c87ada1b32ed"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[10, 12, 14, 16, 18, 20, 22, 24, 26, 28]"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = [b*2+10 for b in range(10)]\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3EekEnwvf9o3",
        "outputId": "d6f53f25-0763-46b6-daba-c04e73d74062"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[17, 27, 37],\n",
              "       [47, 57, 67]])"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.array([[1,2,3], [4,5,6]])\n",
        "a = a*10 + 7\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PZdKat4VhodT",
        "outputId": "e8499e3c-83d7-4bed-e9a6-cb18fb9084a9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 12, 14, 16, 18, 20, 22, 24, 26, 28])"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.array([b*2+10 for b in range(10)])\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XnLWYQ0AhxY_",
        "outputId": "dd6c1919-b2ac-4dae-8e7f-d50e9afc3d1e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 12, 14, 16, 18, 20, 22, 24, 26, 28])"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.arange(10) *2 +10\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SgwLYcfCixEi",
        "outputId": "4648bf8e-e29c-44b9-af59-020988e4310c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[1 2 3 4 5 6 7 8 9]\n",
            "[1 3 5 7 9]\n"
          ]
        }
      ],
      "source": [
        "a = np.arange(1,10)\n",
        "print(a)\n",
        "\n",
        "a = np.arange(1,10, 2)\n",
        "print(a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fdhEuiiPjDcI",
        "outputId": "56cb7e9a-12bc-4bbf-9ec2-0977cc0a803c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[ 8 10 12]\n",
            " [14 16 18]]\n",
            "[[ 7 16 27]\n",
            " [40 55 72]]\n",
            "[[0.14285714 0.25       0.33333333]\n",
            " [0.4        0.45454545 0.5       ]]\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1,2,3],[4,5,6]])\n",
        "b = np.array([[7,8,9],[10,11,12]])\n",
        "print(a+b)\n",
        "print(a*b)\n",
        "print(a/b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QWdysM59jzhS",
        "outputId": "fd4ec62d-cd86-4ede-9aa6-2a0ed78a21ab"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "210\n",
            "[[  1000   8000  27000]\n",
            " [ 64000 125000 216000]]\n",
            "10\n",
            "60\n",
            "5\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[10,20,30],[40,50,60]])\n",
        "print(a.sum())\n",
        "print(np.power(a,3))\n",
        "print(a.min())\n",
        "print(a.max())\n",
        "print(a.argmax())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y73F4pSNlgEo",
        "outputId": "5b628fba-2fed-494e-ee01-f2771fea34a0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('float64')"
            ]
          },
          "execution_count": 62,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.arange(1,10).astype(np.uint16).astype(np.float64)\n",
        "a.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nn34WD6Jl93A",
        "outputId": "248512d8-e876-42b0-8a57-7408607a909d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('float64')"
            ]
          },
          "execution_count": 64,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.zeros((2,3))\n",
        "a.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BT-x94NFmmeQ",
        "outputId": "0334f538-d33e-44b5-a7c1-648e7ba527d2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('uint16')"
            ]
          },
          "execution_count": 65,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.zeros((2,3), dtype= np.uint16)\n",
        "a.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "t8oSSIlcak8g",
        "outputId": "80019f8a-2805-4817-eddc-000c5fbe5f1f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[0. 0. 0.]\n",
            " [0. 0. 0.]]\n",
            "[[1. 1. 1.]\n",
            " [1. 1. 1.]]\n"
          ]
        }
      ],
      "source": [
        "# Sometimes we know the shape of an array that we want to create, but not what we want to be in it. numpy\n",
        "# offers several functions to create arrays with initial placeholders, such as zero's or one's.\n",
        "# Lets create two arrays, both the same shape but with different filler values\n",
        "d = np.zeros((2,3))\n",
        "print(d)\n",
        "\n",
        "e = np.ones((2,3))\n",
        "print(e)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mPekYfNDak8g",
        "outputId": "832700fa-d2f8-484f-bed8-2e216c933871"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.1078525 , 0.07789653, 0.25906896],\n",
              "       [0.90417908, 0.75385854, 0.42647088]])"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# We can also generate an array with random numbers\n",
        "np.random.rand(2,3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oNSaxGn2m_fQ",
        "outputId": "ee1feb63-a66b-498c-d480-43d5dc8a7c6d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0.031838  ,  0.40668022,  0.79471998],\n",
              "       [ 1.51620528,  0.02262842, -0.61741515]])"
            ]
          },
          "execution_count": 66,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.random.randn(2,3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mlLHYf94ak8h"
      },
      "outputs": [],
      "source": [
        "# You'll see zeros, ones, and rand used quite often to create example arrays, especially in stack overflow\n",
        "# posts and other forums."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A11qavewak8h",
        "outputId": "49aa67fe-3cf4-4c23-bc6f-689b7bb1528d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42,\n",
              "       44, 46, 48])"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# We can also create a sequence of numbers in an array with the arrange() function. The fist argument is the\n",
        "# starting bound and the second argument is the ending bound, and the third argument is the difference between\n",
        "# each consecutive numbers\n",
        "\n",
        "# Let's create an array of every even number from ten (inclusive) to fifty (exclusive)\n",
        "f = np.arange(10, 50, 2)\n",
        "f"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Wn6QqI2Nak8h",
        "outputId": "7f22187d-ee07-4803-ef77-06c78d17bb72"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.        , 0.14285714, 0.28571429, 0.42857143, 0.57142857,\n",
              "       0.71428571, 0.85714286, 1.        , 1.14285714, 1.28571429,\n",
              "       1.42857143, 1.57142857, 1.71428571, 1.85714286, 2.        ])"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# if we want to generate a sequence of floats, we can use the linspace() function. In this function the third\n",
        "# argument isn't the difference between two numbers, but the total number of items you want to generate\n",
        "np.linspace( 0, 2, 15 ) # 15 numbers from 0 (inclusive) to 2 (inclusive)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X87LHyfGnqMg",
        "outputId": "27568b72-64df-4ac0-f677-c4a4b5733f23"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]] (2, 3)\n",
            "[1 2 3 4 5 6] (6,)\n",
            "[1 2 3 4 5 6] (6,)\n",
            "[[[1 2 3]\n",
            "  [4 5 6]]] (1, 2, 3)\n",
            "[[[1 2 3]\n",
            "  [4 5 6]]] (1, 2, 3)\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1,2,3],[4,5,6]])\n",
        "print(a, a.shape)\n",
        "a= a.reshape(6)\n",
        "print(a, a.shape)\n",
        "a= a.reshape(6)\n",
        "print(a, a.shape)\n",
        "a= a.reshape((1,2,3))\n",
        "print(a, a.shape)\n",
        "a= a.reshape((1,-1,3))\n",
        "print(a, a.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 158
        },
        "id": "l-ZwB6WlomuV",
        "outputId": "e67e527c-0406-4102-b537-1770d57465fd"
      },
      "outputs": [
        {
          "ename": "ValueError",
          "evalue": "can only specify one unknown dimension",
          "output_type": "error",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-73-2ce4f71ddab4>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: can only specify one unknown dimension"
          ]
        }
      ],
      "source": [
        "a= a.reshape((1,-1,-1,3))\n",
        "print(a, a.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MjTVXDjuo1UX",
        "outputId": "e3a1e599-1b0f-49ed-d92c-331f9851fbe8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0 1 2 3 4 5]\n",
            "[False False False  True False False]\n",
            "[ True  True  True  True  True  True]\n"
          ]
        }
      ],
      "source": [
        "a = np.arange(6)\n",
        "print(a)\n",
        "print((a > 2) & (a < 4))\n",
        "print((a > 2) | (a < 4))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1yozYB40pcAa",
        "outputId": "418cbeae-1410-4fe9-f203-65a216a5ba29"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[False False False  True False False]\n"
          ]
        }
      ],
      "source": [
        "lower_bound, upper_bound = 2, 4\n",
        "print((a > lower_bound) & (a < upper_bound))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KyOFdj8EpqCg",
        "outputId": "4b67e60e-d5d2-4074-f745-a0f61f32ecf6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0 2 4]\n"
          ]
        }
      ],
      "source": [
        "print(a[a%2==0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CAPIsucFp6L3",
        "outputId": "2c95d957-c27e-491e-a8b0-1ddc257c6367"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1\n",
            "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            "0.0\n",
            "0.0\n",
            "[[0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0.]]\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
          ]
        }
      ],
      "source": [
        "a = np.arange(6)\n",
        "print(a[1])\n",
        "\n",
        "a = np.zeros((10,20))\n",
        "print(a[1])\n",
        "print(a[1][1])\n",
        "print(a[1,1])\n",
        "print(a[1:5,7:12])\n",
        "print(a[1:5])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cXqEI7rZq1uJ",
        "outputId": "1ec806b1-b328-4116-da92-503a06bb3964"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
            ]
          },
          "execution_count": 90,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.flatten()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y3OG1YOBrBfc",
        "outputId": "40c81592-ceb3-44b6-89a5-87707b66af59"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(2, 3)\n",
            "(6,)\n"
          ]
        }
      ],
      "source": [
        "print(np.zeros((2,3)).shape)\n",
        "print(np.zeros(6).shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A-HZtMuEak8h"
      },
      "source": [
        "# Array Operations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FEnOBVjGak8h"
      },
      "outputs": [],
      "source": [
        "# We can do many things on arrays, such as mathematical manipulation (addition, subtraction, square,\n",
        "# exponents) as well as use boolean arrays, which are binary values. We can also do matrix manipulation such\n",
        "# as product, transpose, inverse, and so forth."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_bHgG9Yqak8h",
        "outputId": "162fffcc-e93b-4c33-ee7e-da6a822a5514"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[ 9 18 27 36]\n",
            "[ 10  40  90 160]\n"
          ]
        }
      ],
      "source": [
        "# Arithmetic operators on array apply elementwise.\n",
        "\n",
        "# Let's create a couple of arrays\n",
        "a = np.array([10,20,30,40])\n",
        "b = np.array([1, 2, 3,4])\n",
        "\n",
        "# Now let's look at a minus b\n",
        "c = a-b\n",
        "print(c)\n",
        "\n",
        "# And let's look at a times b\n",
        "d = a*b\n",
        "print(d)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OkB1auONovEK"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e5W1l_BKak8i",
        "outputId": "bfae2148-acdc-4fd5-d544-0771921a48d3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([-17.22222222, -22.77777778, -20.        , -25.55555556,\n",
              "       -17.22222222])"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# With arithmetic manipulation, we can convert current data to the way we want it to be. Here's a real-world\n",
        "# problem I face - I moved down to the United States about 6 years ago from Canada. In Canada we use celcius\n",
        "# for temperatures, and my wife still hasn't converted to the US system which uses farenheit. With numpy I\n",
        "# could easily convert a number of farenheit values, say the weather forecase, to ceclius\n",
        "\n",
        "# Let's create an array of typical Ann Arbor winter farenheit values\n",
        "farenheit = np.array([0,-10,-5,-15,0])\n",
        "\n",
        "# And the formula for conversion is ((°F − 32) × 5/9 = °C)\n",
        "celcius = (farenheit - 31) * (5/9)\n",
        "celcius"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "s9KbndqFak8i",
        "outputId": "883ca31b-c300-4c36-eb9f-7165f874368f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ True, False, False, False,  True])"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Another useful and important manipulation is the boolean array. We can apply an operator on an array, and a\n",
        "# boolean array will be returned for any element in the original, with True being emitted if it meets the condition and False oetherwise.\n",
        "# For instance, if we want to get a boolean array to check celcius degrees that are greater than -20 degrees\n",
        "celcius > -20"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g4I6kWI3ak8i",
        "outputId": "184ae0f4-c9ce-4b92-f458-1400fe645045"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([False, False,  True, False, False])"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Here's another example, we could use the modulus operator to check numbers in an array to see if they are even. Recall that modulus does division but throws away everything but the remainder (decimal) portion)\n",
        "celcius%2 == 0"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b6Y6sOI4ak8i",
        "outputId": "defe59ee-09f8-48da-c3fc-aa797879ab2b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[2 0]\n",
            " [0 4]]\n",
            "[[5 4]\n",
            " [3 4]]\n"
          ]
        }
      ],
      "source": [
        "# Besides elementwise manipulation, it is important to know that numpy supports matrix manipulation. Let's\n",
        "# look at matrix product. if we want to do elementwise product, we use the \"*\" sign\n",
        "A = np.array([[1,1],[0,1]])\n",
        "B = np.array([[2,0],[3,4]])\n",
        "print(A*B)\n",
        "\n",
        "# if we want to do matrix product, we use the \"@\" sign or use the dot function\n",
        "print(A@B)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yRcRqGpQak8i"
      },
      "outputs": [],
      "source": [
        "# You don't have to worry about complex matrix operations for this course, but it's important to know that\n",
        "# numpy is the underpinning of scientific computing libraries in python, and that it is capable of doing both\n",
        "# element-wise operations (the asterix) as well as matrix-level operations (the @ sign). There's more on this\n",
        "# in a subsequent course."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "B86_og5Xak8j",
        "outputId": "1308ee32-f8b0-4f69-92a4-bc8e2fdde0bc"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "int64\n",
            "float64\n"
          ]
        }
      ],
      "source": [
        "# When manipulating arrays of different types, the type of the resulting array will correspond to\n",
        "# the more general of the two types. This is called upcasting.\n",
        "\n",
        "# Let's create an array of integers\n",
        "array1 = np.array([[1, 2, 3], [4, 5, 6]])\n",
        "print(array1.dtype)\n",
        "\n",
        "# Now let's create an array of floats\n",
        "array2 = np.array([[7.1, 8.2, 9.1], [10.4, 11.2, 12.3]])\n",
        "print(array2.dtype)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AHiUlSarak8j"
      },
      "outputs": [],
      "source": [
        "# Now, we often think about two dimensional arrays being made up of rows and columns, but you can also think\n",
        "# of these arrays as just a giant ordered list of numbers, and the *shape* of the array, the number of rows\n",
        "# and columns, is just an abstraction that we have for a particular purpose. Actually, this is exactly how\n",
        "# basic images are stored in computer environments.\n",
        "\n",
        "# Let's take a look at an example and see how numpy comes into play."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7FdHpkswak8j",
        "outputId": "c29902eb-7e7a-42c0-ec78-8cc9e3dda0d3"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<PIL.TiffImagePlugin.TiffImageFile image mode=L size=200x200 at 0x109128EB0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# For this demonstration I'll use the python imaging library (PIL) and a function to display images in the\n",
        "# Jupyter notebook\n",
        "from PIL import Image\n",
        "from IPython.display import display\n",
        "\n",
        "# And let's just look at the image I'm talking about\n",
        "im = Image.open('images/chris.tiff')\n",
        "display(im)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9GpVAX-fak8j",
        "outputId": "b60a85ab-697e-45de-cf20-40fb85db2f07"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(200, 200)\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "array([[118, 117, 118, ..., 103, 107, 110],\n",
              "       [113, 113, 113, ..., 100, 103, 106],\n",
              "       [108, 108, 107, ...,  95,  98, 102],\n",
              "       ...,\n",
              "       [177, 181, 182, ..., 193, 198, 192],\n",
              "       [178, 182, 183, ..., 193, 201, 189],\n",
              "       [178, 182, 184, ..., 193, 201, 187]], dtype=uint8)"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Now, we can convert this PIL image to a numpy array\n",
        "array=np.array(im)\n",
        "print(array.shape)\n",
        "array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "peMb_ppEak8j",
        "outputId": "639c8f20-5af7-464e-d9b6-a3b7486d0899"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[255, 255, 255, ..., 255, 255, 255],\n",
              "       [255, 255, 255, ..., 255, 255, 255],\n",
              "       [255, 255, 255, ..., 255, 255, 255],\n",
              "       ...,\n",
              "       [255, 255, 255, ..., 255, 255, 255],\n",
              "       [255, 255, 255, ..., 255, 255, 255],\n",
              "       [255, 255, 255, ..., 255, 255, 255]])"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Here we see that we have a 200x200 array and that the values are all uint8. The uint means that they are\n",
        "# unsigned integers (so no negative numbers) and the 8 means 8 bits per byte. This means that each value can\n",
        "# be up to 2*2*2*2*2*2*2*2=256 in size (well, actually 255, because we start at zero). For black and white\n",
        "# images black is stored as 0 and white is stored as 255. So if we just wanted to invert this image we could\n",
        "# use the numpy array to do so\n",
        "\n",
        "# Let's create an array the same shape\n",
        "mask=np.full(array.shape,255)\n",
        "mask"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ydjHfWCqak8j",
        "outputId": "e5cd2037-7e83-4aa6-b9d5-6f5942091a24"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[137, 138, 137, ..., 152, 148, 145],\n",
              "       [142, 142, 142, ..., 155, 152, 149],\n",
              "       [147, 147, 148, ..., 160, 157, 153],\n",
              "       ...,\n",
              "       [ 78,  74,  73, ...,  62,  57,  63],\n",
              "       [ 77,  73,  72, ...,  62,  54,  66],\n",
              "       [ 77,  73,  71, ...,  62,  54,  68]], dtype=uint8)"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Now let's subtract that from the modified array\n",
        "modified_array=array-mask\n",
        "\n",
        "# And lets convert all of the negative values to positive values\n",
        "modified_array=modified_array*-1\n",
        "\n",
        "# And as a last step, let's tell numpy to set the value of the datatype correctly\n",
        "modified_array=modified_array.astype(np.uint8)\n",
        "modified_array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RNzm-DwFak8j",
        "outputId": "b7a9b31b-2a54-475c-d393-69cb16374e3e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<PIL.Image.Image image mode=L size=200x200 at 0x1044988E0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# And lastly, lets display this new array. We do this by using the fromarray() function in the python\n",
        "# imaging library to convert the numpy array into an object jupyter can render\n",
        "display(Image.fromarray(modified_array))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Om5Boyfwak8j"
      },
      "source": [
        "# Indexing, Slicing and Iterating"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9zvFIQzvak8k"
      },
      "outputs": [],
      "source": [
        "# Indexing, slicing and iterating are extremely important for data manipulation and analysis because these\n",
        "# techinques allow us to select data based on conditions, and copy or update data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1HDKCk5iak8k"
      },
      "source": [
        "## Indexing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wVqCIxBWak8k",
        "outputId": "1716c043-62b4-476f-eea9-5b5c03579953"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# First we are going to look at integer indexing. A one-dimensional array, works in similar ways as a list -\n",
        "# To get an element in a one-dimensional array, we simply use the offset index.\n",
        "a = np.array([1,3,5,7])\n",
        "a[2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ubL_w0Kpak8k",
        "outputId": "e9712ee5-8e3a-4a80-9eab-5129eb910ce6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [3, 4],\n",
              "       [5, 6]])"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# For multidimensional array, we need to use integer array indexing, let's create a new multidimensional array\n",
        "a = np.array([[1,2], [3, 4], [5, 6]])\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GpIh_PCSak8k",
        "outputId": "ca76815c-f0ef-41fd-b164-14188fdcad7b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# if we want to select one certain element, we can do so by entering the index, which is comprised of two\n",
        "# integers the first being the row, and the second the column\n",
        "a[1,1] # remember in python we start at 0!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BoZDlqQgak8k"
      },
      "source": [
        "## Boolean Indexing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "obXakfH3ak8k",
        "outputId": "8b498008-1cd6-4ac5-e1e8-a8c5018bdde5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[False False]\n",
            " [False False]\n",
            " [False  True]]\n"
          ]
        }
      ],
      "source": [
        "# Boolean indexing allows us to select arbitrary elements based on conditions. For example, in the matrix we\n",
        "# just talked about we want to find elements that are greater than 5 so we set up a conditon a > 5\n",
        "print(a >5)\n",
        "# This returns a boolean array showing that if the value at the corresponding index is greater than 5"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SVdNKxIQak8k",
        "outputId": "8b7ba53d-acd6-4a41-ad7b-41bf100b61c0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[6]\n"
          ]
        }
      ],
      "source": [
        "# We can then place this array of booleans like a mask over the original array to return a one-dimensional\n",
        "# array relating to the true values.\n",
        "print(a[a>5])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-tvnFS-Dak8l"
      },
      "outputs": [],
      "source": [
        "# As we will see, this functionality is essential in the pandas toolkit which is the bulk of this course"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "08t-K-WWak8l"
      },
      "source": [
        "## Slicing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WHR1JYEgak8l",
        "outputId": "2d9097a1-475c-4cdc-f466-882006838966"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0 1 2]\n"
          ]
        }
      ],
      "source": [
        "# Slicing is a way to create a sub-array based on the original array. For one-dimensional arrays, slicing\n",
        "# works in similar ways to a list. To slice, we use the : sign. For instance, if we put :3 in the indexing\n",
        "# brackets, we get elements from index 0 to index 3 (excluding index 3)\n",
        "a = np.array([0,1,2,3,4,5])\n",
        "print(a[:3])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "10UmhEZyak8l",
        "outputId": "a2f4437f-8cab-4df6-f516-93850e9f280a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[2 3]\n"
          ]
        }
      ],
      "source": [
        "# By putting 2:4 in the bracket, we get elements from index 2 to index 4 (excluding index 4)\n",
        "print(a[2:4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yj-ZtwCPak8m",
        "outputId": "c74577fc-ce01-4b4b-be67-4c33fe65b633"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [ 5,  6,  7,  8],\n",
              "       [ 9, 10, 11, 12]])"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# For multi-dimensional arrays, it works similarly, lets see an example\n",
        "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1CYGYoyvak8m",
        "outputId": "2570218d-fade-40a0-8bdb-a7560ccdd4e4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3, 4],\n",
              "       [5, 6, 7, 8]])"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# First, if we put one argument in the array, for example a[:2] then we would get all the elements from the\n",
        "# first (0th) and second row (1th)\n",
        "a[:2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "haf_mmDQak8m",
        "outputId": "a4b63514-d063-4b45-cc02-331c46f18968"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[2, 3],\n",
              "       [6, 7]])"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# If we add another argument to the array, for example a[:2, 1:3], we get the first two rows but then the\n",
        "# second and third column values only\n",
        "a[:2, 1:3]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pUFTB8Dzak8m"
      },
      "outputs": [],
      "source": [
        "# So, in multidimensional arrays, the first argument is for selecting rows, and the second argument is for\n",
        "# selecting columns"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lBzE5xYDak8m",
        "outputId": "c5650596-6ccc-41ba-db75-44fa4d714abc"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "sub array index [0,0] value before change: 2\n",
            "sub array index [0,0] value after change: 50\n",
            "original array index [0,1] value after change: 50\n"
          ]
        }
      ],
      "source": [
        "# It is important to realize that a slice of an array is a view into the same data. This is called passing by\n",
        "# reference. So modifying the sub array will consequently modify the original array\n",
        "\n",
        "# Here I'll change the element at position [0, 0], which is 2, to 50, then we can see that the value in the\n",
        "# original array is changed to 50 as well\n",
        "\n",
        "sub_array = a[:2, 1:3]\n",
        "print(\"sub array index [0,0] value before change:\", sub_array[0,0])\n",
        "sub_array[0,0] = 50\n",
        "print(\"sub array index [0,0] value after change:\", sub_array[0,0])\n",
        "print(\"original array index [0,1] value after change:\", a[0,1])"
      ]
    }
  ],
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