2_NumPy_.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/YigitBCesur/Python_Essentials/blob/main/2_NumPy_.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "[![Coach Pegasus PNG- colab.png](data:image/png;base64,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)](https://yigitbravecesur.com/)\n",
        "\n",
        "### 🔗 Links\n",
        "\n",
        "\n",
        "[![linkedin](https://img.shields.io/badge/LinkedIn-0A66C2?style=for-the-badge&logo=linkedin&logoColor=white)](https://www.linkedin.com/in/yigitbcesur)\n",
        "\n",
        "[![Youtube](https://img.shields.io/badge/youtube_channel-1DA1F2?style=for-the-badge&logo=youtube&logoColor=white&color=FF0000)](https://www.youtube.com/channel/UCYLMENl4ruLkZbCqLmIKW7A)\n",
        "\n",
        "[![Twitter URL](https://img.shields.io/twitter/url/https/twitter.com/YigitBraveCesur.svg?style=social&label=Follow%20%40YigitBraveCesur)](https://twitter.com/YigitBraveCesur)"
      ],
      "metadata": {
        "id": "gg7NVNC6C-79"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KT5EMmA1iOXv"
      },
      "source": [
        "\n",
        "\n",
        "# NumPy\n",
        "\n",
        "\n",
        "1.   Numpy arrays Basics\n",
        "2.   Indexing and Slicing\n",
        "     *   Extracting with conditional selection\n",
        "3.   Shape and multiple Dimensions\n",
        "4.   Indexing and Slicing multi-dimensional arrays)\n",
        "5.   Boolean Indexing\n",
        "6.   Random Numbers\n",
        "7.   Numpy operations\n",
        "8.   Axis Logic\n",
        "9.   Summary Statistics\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yLYgMnIbiOXw"
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fnn3O8ffiOXx"
      },
      "source": [
        "##  1. NumPy Arrays Basics"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sExaMsxTiOXz",
        "outputId": "30b17331-5c50-429a-d23a-1097a3c7710a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0, 1, 2, 3]"
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ],
      "source": [
        "my_list = [0,1,2,3]\n",
        "my_list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "K3CodqiHiOX1",
        "outputId": "2f29a0e3-e018-4898-e4a8-016a08c88c33",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ],
      "source": [
        "np.array(my_list)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PzTGT6ieiOX1",
        "outputId": "dd3561ea-5477-4c8f-dfba-ffe48c601bcd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[1, 2, 3], [4, 5, 6]]"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ],
      "source": [
        "my_matrix = [[1,2,3],\n",
        "            [4,5,6]]\n",
        "my_matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yYfxxLRyiOX1",
        "outputId": "08b59b5d-647a-40cf-aa8a-bbab4ac9f66e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ],
      "source": [
        "np.array(my_matrix)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aUt50CmsiOX2",
        "outputId": "e0e53ce9-63d8-4d04-d6c5-fbbe768ba145",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ],
      "source": [
        "# Built in methods\n",
        "# np.arange() :Return evenly spaced values within a given interval.\n",
        "np.arange(0,4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "biAxkPjuiOX2",
        "outputId": "42733590-a6fc-4609-b669-a9bb6391d036",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 3, 6, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ],
      "source": [
        "np.arange(0,10,3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sn6zdlRIiOX2",
        "outputId": "e4a27de5-3bcb-4d80-d080-e6cdc3654e9b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0., 0., 0., 0., 0.])"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ],
      "source": [
        "# Zeros and ones : Generate arrays of zeros or ones\n",
        "np.zeros(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gyJmp3cfiOX3",
        "outputId": "1063f843-2627-48f8-d097-87200ab61bd5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[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.]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "np.zeros((5,5))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ye4PSeFeiOX3",
        "outputId": "69e2b883-bd60-4001-b96a-51ed0978a375",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 1., 1., 1., 1.])"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ],
      "source": [
        "np.ones(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZMlyfCCUiOX3",
        "outputId": "3ab595d1-f4da-4633-a438-261334e9d5f0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 1., 1., 1., 1.],\n",
              "       [1., 1., 1., 1., 1.],\n",
              "       [1., 1., 1., 1., 1.],\n",
              "       [1., 1., 1., 1., 1.],\n",
              "       [1., 1., 1., 1., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 80
        }
      ],
      "source": [
        "np.ones((5,5))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aQWeAK9EiOX4",
        "outputId": "3fa15b72-2f84-4164-f593-e0971f2557ca",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.,  5., 10., 15., 20.])"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ],
      "source": [
        "# linspace : Return evenly spaced numbers over a specified interval.\n",
        "np.linspace(0,20,5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "p1IM18RviOX4",
        "outputId": "9aed50b4-541a-49ef-e55c-6bf623343395",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "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.]])"
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ],
      "source": [
        "# eye: Creates identity matrix\n",
        "np.eye(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ht7BwavmiOX6",
        "outputId": "ea00787a-af89-48c3-c304-c2a78d078c22",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ],
      "source": [
        "# array methods\n",
        "\n",
        "my_array = np.arange(1,10)\n",
        "my_array\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7HmmKT53iOX6",
        "outputId": "b1dc1db3-a17f-4e43-a443-c517a512a31f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ],
      "source": [
        "# reshape\n",
        "new_array = my_array.reshape(3,3)\n",
        "new_array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nX0M74dgiOX6",
        "outputId": "d145e10c-7075-4acc-c183-62953a8b2d67",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ],
      "source": [
        "new_array.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HNShqFnRiOX7",
        "outputId": "a2832063-cc6a-4065-bcc7-0ba0ce51bde9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dtype('int64')"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "new_array.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PuBlJLeMiOX7",
        "outputId": "aae35442-324e-4ed4-fba6-15eac4a2a691",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ],
      "source": [
        "type(new_array)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kvKcv6g9iOX7",
        "outputId": "0a0a0dc6-c60d-4df9-e018-69693eafb307",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([   1,    2,    3,    4,    5,    6,    7,    8,    9,  100, -100])"
            ]
          },
          "metadata": {},
          "execution_count": 95
        }
      ],
      "source": [
        "my_array = np.append(my_array, [100,-100])\n",
        "my_array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DylQvwfEiOX7",
        "outputId": "200b3eee-d800-4637-b6c2-c734885314c9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "100"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ],
      "source": [
        "my_array.max()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NVXbkUDiiOX7",
        "outputId": "cb583bea-8c51-47c9-812c-9df3bc7e289d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "my_array.argmax()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zCxpDIwkiOX8",
        "outputId": "ccdf8cf6-2888-4859-e6b8-80569ccc383d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-100"
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ],
      "source": [
        "my_array.min()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5yElRvESiOX8",
        "outputId": "c27a3ef5-5c2f-4756-db79-3109c9f47f9e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "my_array.argmin()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "F3Ap-gnpNDrP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5dfa70fb-63ae-49e5-838f-2b8ae1cf879d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ],
      "source": [
        "a = np.arange(1,5) #create ndarray from 1 to 4 (both including)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "u-G7dCzaNDrP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "254130f3-98be-4682-81ce-3bba4255dfe4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 4, 6, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ],
      "source": [
        "a * 2 #element-wise (vectorized) operations are pretty simple with ndarrays"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SyqWWxNuNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d4950c74-a25a-4aa6-db46-9bb32bd85d98"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 4, 5, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 101
        }
      ],
      "source": [
        "a + 2 #addition works as well"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0KKRwZ8zNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "acbed32c-0938-430e-a030-53324655d830"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  4,  9, 16])"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ],
      "source": [
        "a**2 #all elements squared"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "abauKnK4NDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eb320c2c-c98c-4493-aaba-ecf1974bbca2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2,  4,  8, 16])"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ],
      "source": [
        "2**a #can serve as exponent as well"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6e6UDosBNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "abf6b6f9-78fc-46d4-8979-83bd0c2911b9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.        , 1.41421356, 1.73205081, 2.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ],
      "source": [
        "np.sqrt(a) #square root of all elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "D8-S9MmCNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d7b51c2f-59b0-43cc-eae5-a304b1220957"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ],
      "source": [
        "np.exp(a) #exponentiation with e"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LRfGzOVKNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8999c3d6-02cc-4864-dab6-2315cd25b53a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.        , 0.69314718, 1.09861229, 1.38629436])"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ],
      "source": [
        "np.log(a) #natural logarithm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bKBWfagZNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8fd5a9dd-c6fa-4464-9b0d-c039dc812ae6"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 107
        }
      ],
      "source": [
        "a.sum() #sum of all elements (ndarray method)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zmpew6MRNDrQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "61bd1229-3cb0-4976-c0f3-8ae00ad13c39"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 108
        }
      ],
      "source": [
        "np.sum(a) #sum of all elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "K6asntqXNDrR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "716c7922-8d68-41fc-9af3-d4f11fe6d9f8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 109
        }
      ],
      "source": [
        "sum(a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XO3YkA54NDrR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "051dc3f2-7f36-48f9-b979-c2f4f602d2a3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ],
      "source": [
        "a.size #number of elements in ndarray (ndarray attribute)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wY4IKasgNDrR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ec931391-ae4e-4a1b-df57-ffb19112cf4e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {},
          "execution_count": 111
        }
      ],
      "source": [
        "len(a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ebiUvibwNDrR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d112c77c-6d59-4385-d8f9-ba2ec1aa314a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-2. , -1. , -0.5,  0. ,  1. ,  2. ,  3.5])"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ],
      "source": [
        "b = np.array([-2, -1, -0.5, 0, 1, 2, 3.5])\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "prRjoQw-NDrR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f3aa4e70-4422-4bae-c4d9-ed4b15888282"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2. , 1. , 0.5, 0. , 1. , 2. , 3.5])"
            ]
          },
          "metadata": {},
          "execution_count": 113
        }
      ],
      "source": [
        "np.abs(b) #absolute values of all elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "q_y4JrCUNDrR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aef1ad17-5634-4580-e714-e0d39e415005"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.7, -1.5, -0.2,  0.2,  1.5,  1.7,  2. ])"
            ]
          },
          "metadata": {},
          "execution_count": 114
        }
      ],
      "source": [
        "c = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])\n",
        "c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8_KggMqhNDrS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "798d83d0-2649-45ff-dfaa-7427afea6426"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1., -1., -0.,  1.,  2.,  2.,  2.])"
            ]
          },
          "metadata": {},
          "execution_count": 115
        }
      ],
      "source": [
        "np.ceil(c) #element-wise rounding up"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WbkBw8C_NDrV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2bec4b68-2432-4496-ce6e-91db4f6154f8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-2., -2., -1.,  0.,  1.,  1.,  2.])"
            ]
          },
          "metadata": {},
          "execution_count": 116
        }
      ],
      "source": [
        "np.floor(c) #element-wise rounding down"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Q1KaTMoJNDrV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a15a7451-b570-4446-f382-d433defd94a3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-3., -1.,  1.,  3.])"
            ]
          },
          "metadata": {},
          "execution_count": 117
        }
      ],
      "source": [
        "np.around([-3.23, -0.76, 1.44, 2.65, ], decimals = 0) #evenly round all elements to the given number of decimals."
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "AfcPD95FoJz-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_BpX3etXNDrV"
      },
      "source": [
        "## 2. Indexing and Slicing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zZdAljIpNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f8e87766-6061-44a9-80e4-98e200bc49e4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  5,  9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65,\n",
              "       69, 73, 77, 81, 85, 89, 93, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ],
      "source": [
        "a = np.arange(1,100,4) #array from 1 to 100 (incl.)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Urh_Owo3NDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "584fcec7-06b1-450c-90bf-355b44111c5a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 126
        }
      ],
      "source": [
        "a[0] #first element at index position 0 (zero-based indexing!)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pSrH0uP1NDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "58980f7f-825d-4b8a-eef8-ec8db08fd88a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 127
        }
      ],
      "source": [
        "a[1] #second element (index position 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yey5m-YsNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "98556675-9874-4474-dbe0-871e590846b1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "97"
            ]
          },
          "metadata": {},
          "execution_count": 128
        }
      ],
      "source": [
        "a[-1] #last element"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "s5LkioqvNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4f21ff3d-ff23-4ef5-e82a-ab8259902523"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(0, 1),\n",
              " (1, 5),\n",
              " (2, 9),\n",
              " (3, 13),\n",
              " (4, 17),\n",
              " (5, 21),\n",
              " (6, 25),\n",
              " (7, 29),\n",
              " (8, 33),\n",
              " (9, 37),\n",
              " (10, 41),\n",
              " (11, 45),\n",
              " (12, 49),\n",
              " (13, 53),\n",
              " (14, 57),\n",
              " (15, 61),\n",
              " (16, 65),\n",
              " (17, 69),\n",
              " (18, 73),\n",
              " (19, 77),\n",
              " (20, 81),\n",
              " (21, 85),\n",
              " (22, 89),\n",
              " (23, 93),\n",
              " (24, 97)]"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ],
      "source": [
        "list(enumerate(a)) #list of index,value tuples"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XWwleRUkNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "04d250a1-7aaa-4571-ff8c-d4052faee452"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 9, 13, 17, 21])"
            ]
          },
          "metadata": {},
          "execution_count": 130
        }
      ],
      "source": [
        "a[2:6] #slicing from index position 2 (incl.) till position 6 (excl.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Oo21iXgaNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7575ac03-8e8b-4852-bffb-ff5d688ece86"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  5,  9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65,\n",
              "       69, 73, 77, 81, 85, 89, 93, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 131
        }
      ],
      "source": [
        "a[:] #all elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rQFQ9bvkNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6372373f-a97e-40ed-ecea-03f70520ff17"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  5,  9, 13, 17])"
            ]
          },
          "metadata": {},
          "execution_count": 132
        }
      ],
      "source": [
        "a[:5] #all elements until index position 5 (excl.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KVYeXiUSNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a391ee98-9055-4e5d-c1d5-81b45fe9b2fa"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89,\n",
              "       93, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 133
        }
      ],
      "source": [
        "a[6:] #all elements from index position 6 (incl.) till the last element (incl.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "joMUUXIvNDrW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aea0631e-ea0e-4176-bb15-95d8322b8b1c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ],
      "source": [
        "a[::2] #every second element, starting from first element"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v_gAGczbNDrX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9ed01880-2ee2-4f27-c3b7-8e6e261b2512"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1, 13, 25, 37, 49, 61, 73, 85, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 135
        }
      ],
      "source": [
        "a[::3] #every third element, starting from first element"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "u5D5x_7qNDrX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "23339971-b386-4ff5-ab62-e843bcc51515"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 9, 21, 33, 45, 57, 69, 81, 93])"
            ]
          },
          "metadata": {},
          "execution_count": 136
        }
      ],
      "source": [
        "a[2::3] #every third element, starting from third element (index position 2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AmmNddMvNDrX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2bcb81c-361f-4df9-e6e6-543e5b120578"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([100,   5,   9,  13,  17,  21,  25,  29,  33,  37,  41,  45,  49,\n",
              "        53,  57,  61,  65,  69,  73,  77,  81,  85,  89,  93,  97])"
            ]
          },
          "metadata": {},
          "execution_count": 137
        }
      ],
      "source": [
        "a[0] = 100 #ndarrays are mutable, changing first element to 100\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3_-X9TMENDrX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2aec645-b40b-45d6-ad7d-b6fe1e3b6061"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([100,   5,   9,  13,  17,  21,  25,  29,  33,  37,  41,  45,  49,\n",
              "        53,  57,  61,  65,  69,  73,  77,  81,  85,  89,  93, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 138
        }
      ],
      "source": [
        "a[-1] = 101 #changing last element to 101\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-B3SWpGRNDrX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8df725be-0173-4eb1-ebf7-d1e07e338e76"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([100,   5,  50,  51,  52,  21,  25,  50,  50,  37,  41,  45,  49,\n",
              "        53,  57,  61,  65,  69,  73,  77,  81,  85,  89,  93, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 141
        }
      ],
      "source": [
        "a[7:9] = 50 #in contrast to lists, ndarrays allow braodcasting, assigning one new value to multiple elements\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xTPsmYQVNDrX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8ba19dcd-2858-449c-cb95-d5b0bbad3bfa"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([100,   5,  50,  51,  52,  21,  25,  29,  33,  37,  41,  45,  49,\n",
              "        53,  57,  61,  65,  69,  73,  77,  81,  85,  89,  93, 101])"
            ]
          },
          "metadata": {},
          "execution_count": 140
        }
      ],
      "source": [
        "a[2:5] = [50, 51, 52] #assigning multiple new values to multiple elements\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hFWGhXZDNDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "66262867-4ce3-4bd1-8717-471688f08249"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 143
        }
      ],
      "source": [
        "a = np.arange(1,11) #creating new ndarray a\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "k9Qd0cwPNDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "864eaf90-c701-450a-a00b-efe0adb29d61"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 4, 5, 6, 7, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 144
        }
      ],
      "source": [
        "b = a[2:8] # making a slice of ndarray a and assign new variable b\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xPBkMVwSNDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2f1b73b-9893-4ff8-b9f9-85bbd352dd59"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([100,   4,   5,   6,   7,   8])"
            ]
          },
          "metadata": {},
          "execution_count": 145
        }
      ],
      "source": [
        "b[0] = 100 #changing first element of ndarray b\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SISi8S7BNDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "34e63e21-8588-4405-8ee6-357904e44b2c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  1,   2, 100,   4,   5,   6,   7,   8,   9,  10])"
            ]
          },
          "metadata": {},
          "execution_count": 146
        }
      ],
      "source": [
        "a #respective element of ndarray a has changed as well!!!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nB3F1x98NDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a60b7a40-68f3-462f-d25f-d4a622a685e5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]"
            ]
          },
          "metadata": {},
          "execution_count": 147
        }
      ],
      "source": [
        "l = list(range(1,11)) #lists behave differently\n",
        "l"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4r4Kyvf1NDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8a3aab4a-680c-4d78-abb3-594f558857f1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[3, 4, 5, 6, 7, 8]"
            ]
          },
          "metadata": {},
          "execution_count": 148
        }
      ],
      "source": [
        "m = l[2:8] #here a copy of the slice of l is created\n",
        "m"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-97AQ9NtNDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eef5c32e-a7bc-4816-e522-2a618146824f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[100, 4, 5, 6, 7, 8]"
            ]
          },
          "metadata": {},
          "execution_count": 149
        }
      ],
      "source": [
        "m[0] = 100 #changing first element of slice m\n",
        "m"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_XCEsTs2NDrY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b25b0a9d-1310-4032-aed6-7bbbe271392f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]"
            ]
          },
          "metadata": {},
          "execution_count": 150
        }
      ],
      "source": [
        "l #no effect on l !!!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eNPnjS-uiOYA",
        "outputId": "af5fab2b-4566-4e68-9315-b8725029e185",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1, 2, 3, 4, 5, 6, 7, 8, 9]"
            ]
          },
          "metadata": {},
          "execution_count": 151
        }
      ],
      "source": [
        "my_list = list(range(1,10))\n",
        "my_list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-Ek-eI1QiOYB",
        "outputId": "bf9dceb3-dd0c-4fe8-831e-a1982b63413c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1, 2, 3, 4, 5]"
            ]
          },
          "metadata": {},
          "execution_count": 152
        }
      ],
      "source": [
        "my_list[0:5]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LeNaokqdiOYB",
        "outputId": "e4c3a0cc-b69f-4e17-bf9f-ad7aa6f61684",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        }
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-153-a37bc34a487d>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmy_list\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: can only assign an iterable"
          ]
        }
      ],
      "source": [
        "my_list[0:2]=100"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A8MmyAzEiOYB",
        "outputId": "ef91abe7-64ba-404a-852f-9db75dda6964",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[100, 100, 100, 3, 4, 5, 6, 7, 8, 9]"
            ]
          },
          "metadata": {},
          "execution_count": 154
        }
      ],
      "source": [
        "my_list[0:2]=[100,100,100]\n",
        "my_list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WBrWXVm6iOYB",
        "outputId": "832796bd-6ceb-45c5-b922-d2016a3a7d90",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1, 2],\n",
              "       [3, 4, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ],
      "source": [
        "# matrix: Note that matrix indexing in python is slightly different than R, Matlab or other programming languages.\n",
        "\n",
        "my_matrix= np.arange(0,6).reshape(2,3)\n",
        "my_matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FP29zZTdiOYB",
        "outputId": "251e0470-dde6-4677-d00d-87fe5bc87f49",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "# Format is matrix[row][col] or matrix[row,col]\n",
        "\n",
        "# extracting the first row\n",
        "my_matrix[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yi-y5Mt_iOYB",
        "outputId": "5c2018e1-22d0-4fa0-cf45-2830bf92ec57",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ],
      "source": [
        "# extracting the first column\n",
        "my_matrix[:,0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nheDbgZIiOYB",
        "outputId": "03b6e5c4-c2a0-4bc0-b8c0-d560603d0fd5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "my_matrix[0][1] == my_matrix[0,1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hdFKQVzViOYB",
        "outputId": "e10a1c9a-2069-410d-b791-cb8289607a99",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [4, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "my_matrix[:2,1:]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9EfWgOXCiOYC"
      },
      "source": [
        "Use google image and search for \"numpy array indexing\"\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gh7e8xXiiOYC"
      },
      "source": [
        "### Extracting with conditional selection\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7yfjZZhoiOYC",
        "outputId": "e5469f17-8aa2-4289-bad7-24abe0d6a49b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 157
        }
      ],
      "source": [
        "my_arr=np.arange(1,100,6)\n",
        "my_arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KvVf03PGiOYC",
        "outputId": "5e1ed803-3f66-4bad-89b8-45d4b760a40f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False, False, False, False, False, False,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True,  True])"
            ]
          },
          "metadata": {},
          "execution_count": 159
        }
      ],
      "source": [
        "my_arr > 33"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "u66Udtb1iOYC",
        "outputId": "3b685307-5dba-4a73-ce6d-fd8377b72e89",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97])"
            ]
          },
          "metadata": {},
          "execution_count": 160
        }
      ],
      "source": [
        "my_arr[my_arr>33]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d9-eDvV9iOYC"
      },
      "source": [
        "This is another advantage of using arrays instead of lists. You cannot simply apply the comparison operators to a list. You must use filter() function instead."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ng_4s2UKiOYC",
        "outputId": "f267e062-07c4-4792-ee8d-956a48537295",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[43, 49, 55, 61, 67, 73, 79, 85, 91, 97]"
            ]
          },
          "metadata": {},
          "execution_count": 162
        }
      ],
      "source": [
        "list(filter(lambda x: x>40, my_arr))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EB7qUdDuiOYD",
        "outputId": "706814c0-12ce-4e9b-b70b-b120cd862938",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[1, 2, 3], [4, 5, 6]]"
            ]
          },
          "metadata": {},
          "execution_count": 163
        }
      ],
      "source": [
        "my_matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aNJV-xLriOYD",
        "outputId": "d0adf4ec-e6f1-4ff9-d4bc-c76873fa6219",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        }
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-164-9a636874f4e0>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmy_matrix\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: '>' not supported between instances of 'list' and 'int'"
          ]
        }
      ],
      "source": [
        "my_matrix > 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CdY4dHp0iOYD",
        "outputId": "e48f2330-9fc1-4e37-f676-68dce1a23665",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 192
        }
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-165-50294e09f3ab>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmy_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmy_matrix\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\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[0;31m# the shape is not reserved though!\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mTypeError\u001b[0m: '>' not supported between instances of 'list' and 'int'"
          ]
        }
      ],
      "source": [
        "my_matrix[my_matrix > 1]\n",
        "# the shape is not reserved though!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "uRgCr-HRNDrY"
      },
      "source": [
        "## 3. Shape and multiple Dimensions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "60ymYYMJNDrZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "97b23212-f94a-42f4-9fc9-7d0622fe6e81"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
              "       18, 19, 20])"
            ]
          },
          "metadata": {},
          "execution_count": 176
        }
      ],
      "source": [
        "a = np.arange(1,21) #creating array from 1 to 21\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yQsPW2fJNDrZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fa1e67c2-1017-4dd0-d99b-c51af0156268"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {},
          "execution_count": 177
        }
      ],
      "source": [
        "type(a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VubqvDQwNDrZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7e1c3332-c75b-4553-a959-4e1e9e930bf1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(20,)"
            ]
          },
          "metadata": {},
          "execution_count": 178
        }
      ],
      "source": [
        "a.shape #one-dimensional array, 12 elements in one dimension (vector)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qK0LQgiNNDrZ"
      },
      "outputs": [],
      "source": [
        "a = a.reshape(2,10)  #reshaping a: 2 rows / 10 columns"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cvQKmSHVNDrZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "465f7160-9ac5-46ab-e11f-f1aab41bcb5a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10],\n",
              "       [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]])"
            ]
          },
          "metadata": {},
          "execution_count": 180
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BPbO68R7NDrZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "07afee98-ee9b-44a0-d40f-0145644044db"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 10)"
            ]
          },
          "metadata": {},
          "execution_count": 181
        }
      ],
      "source": [
        "a.shape # two-dimensional array: 2 rows / 6 columns (matrix)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SB7iO-MTNDra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b3115c2f-4df4-4113-81b2-41aa2fda1c72"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2],\n",
              "       [ 3,  4],\n",
              "       [ 5,  6],\n",
              "       [ 7,  8],\n",
              "       [ 9, 10],\n",
              "       [11, 12],\n",
              "       [13, 14],\n",
              "       [15, 16],\n",
              "       [17, 18],\n",
              "       [19, 20]])"
            ]
          },
          "metadata": {},
          "execution_count": 183
        }
      ],
      "source": [
        "a = a.reshape(10,2) # two-dimensional array: 10 rows / 2 columns\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "G5KuaAlBNDra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1380ec0c-e099-4883-bbe8-11d10927f585"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 184
        }
      ],
      "source": [
        "a.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FZzcMiadNDra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "81b00adf-70f5-4ad8-f85f-ce66b021b558"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[101, 102],\n",
              "       [103, 104],\n",
              "       [105, 106],\n",
              "       [107, 108],\n",
              "       [109, 110],\n",
              "       [111, 112],\n",
              "       [113, 114],\n",
              "       [115, 116],\n",
              "       [117, 118],\n",
              "       [119, 120]])"
            ]
          },
          "metadata": {},
          "execution_count": 185
        }
      ],
      "source": [
        "a + 100 #element-wise operations still work"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jKPtkyCfNDra",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "outputId": "473a591f-91b8-4af2-9080-70b5550ac04c"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-187-74d0640de1cf>\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[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#not possible with 20 elements\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m: cannot reshape array of size 20 into shape (3,5)"
          ]
        }
      ],
      "source": [
        "a.reshape(3,5) #not possible with 20 elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sSJkhm9sNDra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "65b3553c-2e93-43e7-fcc1-34b3b129e804"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 1,  2,  3,  4,  5],\n",
              "        [ 6,  7,  8,  9, 10]],\n",
              "\n",
              "       [[11, 12, 13, 14, 15],\n",
              "        [16, 17, 18, 19, 20]]])"
            ]
          },
          "metadata": {},
          "execution_count": 189
        }
      ],
      "source": [
        "a = a.reshape(2,2,5) #creating a three-dimensional array\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1GTYhJeRNDra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fe832fe6-e6e6-4d25-bb01-124ccb755612"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 2, 5)"
            ]
          },
          "metadata": {},
          "execution_count": 190
        }
      ],
      "source": [
        "a.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gqAN9phhNDra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "acbcefb0-cd4e-44ad-e240-125edce32c2e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  1,   2,   3,   4],\n",
              "       [  5,   6,   7,   8],\n",
              "       [  9,  10,  11,  12],\n",
              "       [ 13,  14,  15,  16],\n",
              "       [ 17,  18,  19,  20],\n",
              "       [ 21,  22,  23,  24],\n",
              "       [ 25,  26,  27,  28],\n",
              "       [ 29,  30,  31,  32],\n",
              "       [ 33,  34,  35,  36],\n",
              "       [ 37,  38,  39,  40],\n",
              "       [ 41,  42,  43,  44],\n",
              "       [ 45,  46,  47,  48],\n",
              "       [ 49,  50,  51,  52],\n",
              "       [ 53,  54,  55,  56],\n",
              "       [ 57,  58,  59,  60],\n",
              "       [ 61,  62,  63,  64],\n",
              "       [ 65,  66,  67,  68],\n",
              "       [ 69,  70,  71,  72],\n",
              "       [ 73,  74,  75,  76],\n",
              "       [ 77,  78,  79,  80],\n",
              "       [ 81,  82,  83,  84],\n",
              "       [ 85,  86,  87,  88],\n",
              "       [ 89,  90,  91,  92],\n",
              "       [ 93,  94,  95,  96],\n",
              "       [ 97,  98,  99, 100]])"
            ]
          },
          "metadata": {},
          "execution_count": 191
        }
      ],
      "source": [
        "b = np.arange(1,101).reshape(25,4) #creating 2-dim ndarray with one line of code\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "wT8B18Sboo_J"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eo38vSJWNDra"
      },
      "source": [
        "## 4. Indexing and Slicing multi-dimensional arrays"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jrSasUcHNDrb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "39b419db-9516-4dbd-c375-5f76593f01ed"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81,\n",
              "       86, 91, 96])"
            ]
          },
          "metadata": {},
          "execution_count": 194
        }
      ],
      "source": [
        "a = np.arange(1,100,5)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "len(a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nsQKEsAOsvu6",
        "outputId": "42e4ea2a-5a82-4731-ab58-95a9a0a266ba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20"
            ]
          },
          "metadata": {},
          "execution_count": 195
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OhRCrAzhNDrb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9988f5be-9bd8-4f7b-c66d-6f9bf2e99083"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  6, 11, 16, 21],\n",
              "       [26, 31, 36, 41, 46],\n",
              "       [51, 56, 61, 66, 71],\n",
              "       [76, 81, 86, 91, 96]])"
            ]
          },
          "metadata": {},
          "execution_count": 197
        }
      ],
      "source": [
        "a = a.reshape(4,5, order = \"C\")     #creating matrix with 4 rows and 5 columns\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bi7wJoyxNDrb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9f6d3c3c-94c7-4cf5-fe07-e0d64160ecf9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  6, 11, 16, 21])"
            ]
          },
          "metadata": {},
          "execution_count": 198
        }
      ],
      "source": [
        "a[0] #first row (index position 0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ICsGeUUYNDrb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b75ff609-53ad-47c4-9c4f-27bea03a9d5a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([26, 31, 36, 41, 46])"
            ]
          },
          "metadata": {},
          "execution_count": 199
        }
      ],
      "source": [
        "a[1] #second row (index position 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6E1Lo0JvNDrb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6da1090b-c502-406f-e92b-3f0633c50772"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([51, 56, 61, 66, 71])"
            ]
          },
          "metadata": {},
          "execution_count": 200
        }
      ],
      "source": [
        "a[2] #third row (index position 2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "elHB-4VXNDrb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0f3c642c-3c84-4f84-aa18-b9d462330f18"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([76, 81, 86, 91, 96])"
            ]
          },
          "metadata": {},
          "execution_count": 201
        }
      ],
      "source": [
        "a[-1] #last row (index position -1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f11PxTuvNDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9fa0caaa-b9ad-4b67-bf9d-69ee935236bc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "31"
            ]
          },
          "metadata": {},
          "execution_count": 202
        }
      ],
      "source": [
        "a[1][1] #second row, second column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SF_b3WJxNDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1df72425-a7c1-4633-dee9-cbd1a8fe5993"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "31"
            ]
          },
          "metadata": {},
          "execution_count": 203
        }
      ],
      "source": [
        "a[1,1] #more convenient in one square bracket"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ki5a9ouiNDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b3f112c8-f3f7-421c-fd82-d3a499e7774a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "71"
            ]
          },
          "metadata": {},
          "execution_count": 204
        }
      ],
      "source": [
        "a[2,-1] #third row, last column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fBoReVw2NDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "73c8284e-7882-49d5-ac54-292705986260"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1, 26, 51, 76])"
            ]
          },
          "metadata": {},
          "execution_count": 205
        }
      ],
      "source": [
        "a[:,0] #all rows, first column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6tA4mBdONDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "43cc116f-298b-4254-c306-7b1f0c63c895"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 6, 31, 56, 81])"
            ]
          },
          "metadata": {},
          "execution_count": 206
        }
      ],
      "source": [
        "a[:,1] #all rows, second column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9JOimSAyNDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4fe671ec-91b2-4c20-f314-b4fdf1193971"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([21, 46, 71, 96])"
            ]
          },
          "metadata": {},
          "execution_count": 207
        }
      ],
      "source": [
        "a[:,-1] #all rows, last column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FZ-Happ3NDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4abe0746-d324-4af2-cd02-0cc54c7a235b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 6, 11],\n",
              "       [31, 36]])"
            ]
          },
          "metadata": {},
          "execution_count": 208
        }
      ],
      "source": [
        "a[:2,1:3] #first two rows, column two and three"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uIF04hcmNDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fc8857f8-31ed-43d7-deab-237f9c1bd714"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  6, 11, 16, 21],\n",
              "       [26, 31, 36, 41, 46],\n",
              "       [51, 56, 61, 66, 71],\n",
              "       [76, 81, 86, 91, 96]])"
            ]
          },
          "metadata": {},
          "execution_count": 209
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iGUcdHReNDrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c1073fe3-d27a-4aee-bbe1-c84568c34977"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1, 26, 51, 76],\n",
              "       [ 6, 31, 56, 81],\n",
              "       [11, 36, 61, 86],\n",
              "       [16, 41, 66, 91],\n",
              "       [21, 46, 71, 96]])"
            ]
          },
          "metadata": {},
          "execution_count": 210
        }
      ],
      "source": [
        "a.T #Transpose: switching axes (attribute)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ifkaff3jNDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0e405b5e-3ebe-42d5-c1a3-1f9c7df20cd7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1, 26, 51, 76],\n",
              "       [ 6, 31, 56, 81],\n",
              "       [11, 36, 61, 86],\n",
              "       [16, 41, 66, 91],\n",
              "       [21, 46, 71, 96]])"
            ]
          },
          "metadata": {},
          "execution_count": 211
        }
      ],
      "source": [
        "a.transpose() #same (method)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kbzhSaqINDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0e378a23-d8d7-4f36-938f-6815a508097b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  6, 11, 16, 21],\n",
              "       [26, 31, 36, 41, 46],\n",
              "       [51, 56, 61, 66, 71],\n",
              "       [76, 81, 86, 91, 96]])"
            ]
          },
          "metadata": {},
          "execution_count": 212
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bfD1utIzNDrd"
      },
      "outputs": [],
      "source": [
        "a[:,-1] = a[:,-1] /4 #changing slice inplace"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "i5oDrqE4NDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "efa3ec99-2816-4fde-b236-4fb803e57272"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  6, 11, 16,  5],\n",
              "       [26, 31, 36, 41, 11],\n",
              "       [51, 56, 61, 66, 17],\n",
              "       [76, 81, 86, 91, 24]])"
            ]
          },
          "metadata": {},
          "execution_count": 214
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vP1kJBMVNDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7a0977b7-9e23-4d0f-e72a-a0a0949a9c21"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2],\n",
              "       [ 3,  4],\n",
              "       [ 5,  6],\n",
              "       [ 7,  8],\n",
              "       [ 9, 10]])"
            ]
          },
          "metadata": {},
          "execution_count": 217
        }
      ],
      "source": [
        "a = np.arange(1,11).reshape(5,2) #creating a 5x2 matrix\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xYJ1MCFGNDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "969d9273-d781-4eaf-963f-a63f78a95e1f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "55"
            ]
          },
          "metadata": {},
          "execution_count": 218
        }
      ],
      "source": [
        "a.sum() #sum over all elements in matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "y1RZcQmyNDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0570f407-c54a-4cd9-b8f1-6abdf493cfd9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25, 30])"
            ]
          },
          "metadata": {},
          "execution_count": 219
        }
      ],
      "source": [
        "a.sum(axis = 0) #sum of each column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kURGXEAfNDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "78bc3483-3432-47df-d983-7b4e99e30f56"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 3,  7, 11, 15, 19])"
            ]
          },
          "metadata": {},
          "execution_count": 220
        }
      ],
      "source": [
        "a.sum(axis = 1) #sum of each row"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JQl9vIrbNDrd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ac2e3217-9fca-41e8-88d3-b691ec8cc42b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  3,  6, 10, 15, 21, 28, 36, 45, 55])"
            ]
          },
          "metadata": {},
          "execution_count": 221
        }
      ],
      "source": [
        "a.cumsum() #cumulative sum of all elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WOGFPb2INDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c6ab7567-b2d4-4901-f7d2-ed7f002c575c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2],\n",
              "       [ 4,  6],\n",
              "       [ 9, 12],\n",
              "       [16, 20],\n",
              "       [25, 30]])"
            ]
          },
          "metadata": {},
          "execution_count": 222
        }
      ],
      "source": [
        "a.cumsum(axis = 0) #cumulative sum for each column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VGu_LeTeNDre",
        "outputId": "d91e6e24-e0bc-48b4-e934-67fbd12bbe6e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  3],\n",
              "       [ 3,  7],\n",
              "       [ 5, 11],\n",
              "       [ 7, 15],\n",
              "       [ 9, 19]])"
            ]
          },
          "metadata": {},
          "execution_count": 223
        }
      ],
      "source": [
        "a.cumsum(axis = 1) #cumulative sum for each row"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jeIqxIXKNDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8d84019a-55a5-42a2-f55c-f264e57c1a7d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2],\n",
              "       [ 3,  4],\n",
              "       [ 5,  6],\n",
              "       [ 7,  8],\n",
              "       [ 9, 10]])"
            ]
          },
          "metadata": {},
          "execution_count": 224
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "diNCv2c_NDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "771e096f-7586-4002-d1d9-96991ffcfaaf"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3628800"
            ]
          },
          "metadata": {},
          "execution_count": 225
        }
      ],
      "source": [
        "a.prod() #product over all elements"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Jj5bXB0lNDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b0e7a166-3676-4601-b5fc-dd1b2b90581d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 945, 3840])"
            ]
          },
          "metadata": {},
          "execution_count": 226
        }
      ],
      "source": [
        "a.prod(axis = 0) #product over all elements in each column"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "I9UX0m4lNDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e7f4ebc2-8456-4e44-add8-b002e24d1cf3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2, 12, 30, 56, 90])"
            ]
          },
          "metadata": {},
          "execution_count": 227
        }
      ],
      "source": [
        "a.prod(axis = 1) #product over all elements in each row"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LtPeq99KNDre"
      },
      "source": [
        "## 5. Boolean Indexing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lHtL4OIHNDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1cb70068-dce2-4cae-dd6a-ba567f7c4327"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 228
        }
      ],
      "source": [
        "a = np.arange(1,11) #array from 1 to 10\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FrNlu63_NDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "33a0b79c-3e8e-4b0e-aedd-2b73bdb51c93"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False, False, False, False, False,  True,  True,  True,  True,\n",
              "        True])"
            ]
          },
          "metadata": {},
          "execution_count": 229
        }
      ],
      "source": [
        "mask1 = a > 5 #element-wise check if greater than 5\n",
        "mask1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RDMlDa12NDre",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e3bf79ba-f9be-4f80-b9c0-dbf3bdb223ba"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True,  True,  True,  True,  True,  True,  True, False, False,\n",
              "       False])"
            ]
          },
          "metadata": {},
          "execution_count": 230
        }
      ],
      "source": [
        "mask2 = a < 8 #element-wise check if smaller than 8\n",
        "mask2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-CN1St7iNDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "75b4c8e5-2530-44c0-9f36-650a904c2702"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False, False, False, False, False,  True,  True, False, False,\n",
              "       False])"
            ]
          },
          "metadata": {},
          "execution_count": 231
        }
      ],
      "source": [
        "mask3 = (a > 5) & (a < 8) #element-wise check if greater 5 and smaller 8 (logical and)\n",
        "mask3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FGzBa4hjNDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9bd25198-bc67-410e-bfb9-aace2fa7b20a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True])"
            ]
          },
          "metadata": {},
          "execution_count": 232
        }
      ],
      "source": [
        "mask4 = (a > 5) | (a < 8) #element-wise check if greater 5 or smaller 8 (logical or)\n",
        "mask4"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KHXQM7DfNDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7e8eef38-0368-4e7d-ed61-b25ded9e0c43"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True,  True,  True,  True,  True, False, False,  True,  True,\n",
              "        True])"
            ]
          },
          "metadata": {},
          "execution_count": 233
        }
      ],
      "source": [
        "mask5 = ~((a > 5) & (a < 8)) #the opposite of mask3\n",
        "mask5"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "27WgUhACNDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "df92f530-0867-4b29-df03-8b85a8c652bf"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 6,  7,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 234
        }
      ],
      "source": [
        "a[a>5] #slicing all elements that are greater 5 (fulfill condition of mask1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A1L9tCV-NDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7c6fbaa2-ec9e-4cc5-cb8f-e8f7dbf3cbe7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 6,  7,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 235
        }
      ],
      "source": [
        "a[mask1] #slicing all elements that fulfill condition of mask1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WM9-d8ojNDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "daa0a950-2c4e-4eb3-a6cc-5cad3a504a1a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6, 7])"
            ]
          },
          "metadata": {},
          "execution_count": 236
        }
      ],
      "source": [
        "a[mask2] #slicing all elements that fulfill condition of mask2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kka5hr06NDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "be70fe99-002c-4856-ae96-f0af0b4032b8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([6, 7])"
            ]
          },
          "metadata": {},
          "execution_count": 239
        }
      ],
      "source": [
        "a[mask3] #slicing all elements that fulfill condition of mask3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ngh4hoSUNDrf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f3fcd9d0-6b9b-4791-8cb9-77a955814806"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 238
        }
      ],
      "source": [
        "a[mask4] #slicing all elements that fulfill condition of mask4"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KJHN5JpWNDrg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ac243381-35c2-4ce6-a2ce-ce1384779d30"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 237
        }
      ],
      "source": [
        "a[mask5] #slicing all elements that fulfill condition of mask5"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a2HpXT-5NDrg"
      },
      "source": [
        "## 6. Random Numbers"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IWaIr_oRiOX5",
        "outputId": "4d278f42-f52d-4890-fc10-cd724cb0ef43",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ],
      "source": [
        "# randint(a,b) : create random sample of integers from a (including a) to b (excluding b)\n",
        "np.random.randint(1,5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Wp_kpcyBiOX5",
        "outputId": "205e5674-e28a-4dc7-d953-bfc5da0ebd02",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 1, 3, 4, 4, 3, 4, 3, 2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 88
        }
      ],
      "source": [
        "np.random.randint(1,5,20)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6N5pZeeWiOX6",
        "outputId": "8c7babb2-72db-4fd9-908b-c53c7e020926",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.74976547,  0.3426804 ,  1.1530358 , -0.25243604,  0.98132079])"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ],
      "source": [
        "# seed is used to fix the random state.\n",
        "np.random.seed(100)\n",
        "np.random.randn(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uxUgKxFSiOX6",
        "outputId": "dc2f4465-13bb-4bd2-ea42-1b3d61c6c537",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.74976547,  0.3426804 ,  1.1530358 , -0.25243604])"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ],
      "source": [
        "np.random.seed(100)\n",
        "np.random.randn(4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f6rlNku9NDrg"
      },
      "outputs": [],
      "source": [
        "a = np.random.randint(1,101,10) #creating 10 random integers between 1 (incl.) and 101 (excl.)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1GlNZOA_NDrg"
      },
      "outputs": [],
      "source": [
        "np.random.seed(123) #setting a seed enables reproducibility\n",
        "a = np.random.randint(1,101,10)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VSPxxfxPNDrh"
      },
      "outputs": [],
      "source": [
        "np.random.normal(5, 2,10) #creating 10 normal disctributed numbers with mean 5 and std 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "h9juFw0vNDrh"
      },
      "outputs": [],
      "source": [
        "b = np.arange(1,101) #creating array b from 1 to 100\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6wOhjHkvNDrh"
      },
      "outputs": [],
      "source": [
        "np.random.shuffle(b) #randomly shuffle ndarray b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LDrvCJqSNDrh"
      },
      "outputs": [],
      "source": [
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tgSFSvLkNDrh"
      },
      "outputs": [],
      "source": [
        "b.sort() #sorting ndarray b again"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Q6yyW2QBNDrh"
      },
      "outputs": [],
      "source": [
        "b[::-1] #sorting in reverse order"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gbZo0JI_NDrh"
      },
      "outputs": [],
      "source": [
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "apII1qV_NDrh"
      },
      "outputs": [],
      "source": [
        "np.random.seed(123)\n",
        "b1 = np.random.choice(b, 100, replace = True) #randomly creating a 100 elements sample of ndarray b with/without replacement\n",
        "b1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "udvlBu8mNDrh"
      },
      "outputs": [],
      "source": [
        "b1.sort() #sorting b1\n",
        "b1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZMVNsx5CNDri"
      },
      "outputs": [],
      "source": [
        "np.unique(b1) #unique elements of b1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kmiPOyzMNDri"
      },
      "outputs": [],
      "source": [
        "np.array(list(set(b1))) #same"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e5-ONo2ZNDri"
      },
      "outputs": [],
      "source": [
        "np.unique(b1).size #how many unique elements?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "S04sY689NDri"
      },
      "outputs": [],
      "source": [
        "np.unique(b1, return_index= True, return_counts=True) #.unique()-method is quite informative"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tkQyzNEPNDri"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jgKHw-XEiOYD"
      },
      "source": [
        "## 7. Numpy operations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ATwkkHqIiOYD",
        "outputId": "1aab57cc-d2c6-4489-cbf0-78b3cd9d7a16",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "arr = np.arange(0,5)\n",
        "arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "E2LuJ3BWiOYE",
        "outputId": "61f8385e-0164-4334-fe91-f47d0acd289b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 2, 4, 6, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ],
      "source": [
        "arr + arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "O-z0FEyCiOYE",
        "outputId": "6c4e98f9-3fbc-4928-c372-ab7f84f1ba2c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  1,   1,   4,  27, 256])"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "arr ** arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0b7eCH0giOYE",
        "outputId": "1543ab72-3fd6-4232-c6e4-2750a25ce592",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-55-50b4ced5627e>:1: RuntimeWarning: invalid value encountered in divide\n",
            "  arr/arr\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([nan,  1.,  1.,  1.,  1.])"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ],
      "source": [
        "arr/arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6ho_Es-iiOYE",
        "outputId": "1f20b8f7-72e9-411f-9dc4-2899a56e9bb0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-56-016353831300>:1: RuntimeWarning: divide by zero encountered in divide\n",
            "  1/arr\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([       inf, 1.        , 0.5       , 0.33333333, 0.25      ])"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ],
      "source": [
        "1/arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5pxQRSociOYE",
        "outputId": "e886a044-7b97-4668-b2a4-7fbe595b925d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.        , 1.        , 1.41421356, 1.73205081, 2.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ],
      "source": [
        "# Square Roots\n",
        "np.sqrt(arr)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uP3DIiWXiOYF",
        "outputId": "fc4a86a8-241a-48c9-be5d-51c083a4c30d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.        ,  2.71828183,  7.3890561 , 20.08553692, 54.59815003])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ],
      "source": [
        "# Exponential\n",
        "np.exp(arr)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pAIC1TD_iOYF",
        "outputId": "99038dab-695d-413b-d0ea-64119ce34635",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-59-ec65176af587>:2: RuntimeWarning: divide by zero encountered in log\n",
            "  np.log(arr)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([      -inf, 0.        , 0.69314718, 1.09861229, 1.38629436])"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ],
      "source": [
        "# Natural Logarithm\n",
        "np.log(arr)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3KdJaB4ZiOYF",
        "outputId": "e9e6298d-8e69-4731-d297-aff3262fc48e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ],
      "source": [
        "# summary statistics on arrays\n",
        "arr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hUr4clTpiOYF",
        "outputId": "1328ec6f-d6ae-4618-d201-97fd2866cdda",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ],
      "source": [
        "arr.sum()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2hWsM9ZMiOYF",
        "outputId": "78e92be4-26e0-492e-c8b6-de4c1430adad",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.0"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ],
      "source": [
        "arr.mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v6R68wB8iOYF",
        "outputId": "d19bde7a-c456-486a-d873-902b96ddbdd4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.0"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ],
      "source": [
        "arr.var()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "87XeldlBiOYG",
        "outputId": "2e24fbf1-1464-4434-f533-6c1ed29bed2e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.4142135623730951"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ],
      "source": [
        "arr.std()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0cPMM6QTiOYG"
      },
      "source": [
        "## 8. Axis Logic\n",
        "When working with 2-dimensional arrays (matrices) we have to consider rows and columns. This becomes very important when we get to the section on pandas. In array terms, axis 0 is the vertical axis (elements on the rows), and axis 1 is the horizonal axis (elements on the columns). These values (0,1) correspond to the order in which <tt>arr.shape</tt> values are returned.\n",
        "\n",
        "Let's see how this affects our summary statistic calculations from above."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "17d9oE6JiOYG",
        "outputId": "dea00c52-50c3-444e-a9f8-6e3d7d8d04d4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1, 2],\n",
              "       [3, 4, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ],
      "source": [
        "my_matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rz3fM_KliOYG",
        "outputId": "a7116a5c-81ce-4eae-d013-d177572cec69",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 5, 7])"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ],
      "source": [
        "# axis 0 (zero) is doing a vertical operation, and axis 1 a horizonal one.\n",
        "# again, note that the logic is different from R, Matlab or etc\n",
        "my_matrix.sum(axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FtYT5fMiiOYG",
        "outputId": "3ff6bb5d-f972-46a2-8edb-3f0379398163",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 3, 12])"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ],
      "source": [
        "my_matrix.sum(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "15o-RZjhiOYG",
        "outputId": "716c67a2-cb42-419c-8385-efcee0634d74",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  4],\n",
              "       [ 9, 16, 25]])"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ],
      "source": [
        "my_matrix * my_matrix  # note that this is not a matrix multiplication"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "X-vpr-5FiOYG",
        "outputId": "c9970855-6418-4275-90d7-7c1b1e81abe1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 5, 14],\n",
              "       [14, 50]])"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ],
      "source": [
        "# To do a matrix multiplication use np.dot (equivalent to %*% in R)\n",
        "np.dot(my_matrix,my_matrix.T)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JiMHcM-ziOYG",
        "outputId": "ad95579e-34da-474d-fd1b-817e4c0e8cbb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [3, 4]])"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ],
      "source": [
        "# inverse of a matrix\n",
        "A = np.array([[1,2],[3,4]])\n",
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SQInjto_iOYH",
        "outputId": "d0efd237-3ed0-4b88-c607-14ba0ac45c3e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-2. ,  1. ],\n",
              "       [ 1.5, -0.5]])"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ],
      "source": [
        "A_inv = np.linalg.inv(A)\n",
        "A_inv"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "eeirvMQSNDrl"
      },
      "source": [
        "## 9. Summary Statistics"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9ped98VxiOX5",
        "outputId": "caa307dc-d568-47a0-9311-e569174790fb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.88973148, -0.88179839,  0.01863895,  0.23784462,  0.01354855])"
            ]
          },
          "metadata": {},
          "execution_count": 243
        }
      ],
      "source": [
        "# randn : create random samples from standard normal distribution\n",
        "norm=np.random.randn(5)\n",
        "norm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YRz3C0NBiOX5",
        "outputId": "7a9c1cdc-57f9-41f2-8c31-16092b311e1c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.6355294 , -1.04420988,  0.61303888,  0.73620521,  1.02692144,\n",
              "        -1.43219061, -1.8411883 ,  0.36609323],\n",
              "       [-0.33177714, -0.68921798,  2.03460756, -0.55071441,  0.75045333,\n",
              "        -1.30699234,  0.58057334, -1.10452309],\n",
              "       [ 0.69012147,  0.68689007, -1.56668753,  0.90497412,  0.7788224 ,\n",
              "         0.42823287,  0.10887199,  0.02828363],\n",
              "       [-0.57882582, -1.1994512 , -1.70595201,  0.36916396,  1.87657343,\n",
              "        -0.37690335,  1.83193608,  0.00301743],\n",
              "       [-0.07602347,  0.00395759, -0.18501411, -2.48715154, -1.70465121,\n",
              "        -1.13626101, -2.97331547,  0.03331728],\n",
              "       [-0.24888867, -0.45017644,  0.1324278 ,  0.02221393,  0.31736798,\n",
              "        -0.75241418, -1.29639181,  0.09513944]])"
            ]
          },
          "metadata": {},
          "execution_count": 244
        }
      ],
      "source": [
        "norm1=np.random.randn(6,8)\n",
        "norm1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f2rhcpIFNDrm"
      },
      "outputs": [],
      "source": [
        "np.random.seed(123)\n",
        "a = np.random.randint(1,101, 11) #creating an array with 11 random integers between 1 and 100\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9yK4KzyENDrm"
      },
      "outputs": [],
      "source": [
        "a.sort()\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_exH5tTONDrn"
      },
      "outputs": [],
      "source": [
        "a.max() #maximum"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1VOimxX6NDrn"
      },
      "outputs": [],
      "source": [
        "np.max(a) #maximum"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "x5JJ7UcuNDrn"
      },
      "outputs": [],
      "source": [
        "max(a) #maximum"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "y8EiXt3pNDrn"
      },
      "outputs": [],
      "source": [
        "a.min() #minimum"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "saTxORXYNDrn"
      },
      "outputs": [],
      "source": [
        "np.mean(a) #mean"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LuSPoTr2NDrn"
      },
      "outputs": [],
      "source": [
        "a.mean() #mean"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hfw83ZVgNDro"
      },
      "outputs": [],
      "source": [
        "np.median(a) #median"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "i_pfDXWFNDro"
      },
      "outputs": [],
      "source": [
        "np.std(a) #standard deviation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J7_QucB2NDro"
      },
      "outputs": [],
      "source": [
        "np.var(a) #variance"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5PnglQInNDro"
      },
      "outputs": [],
      "source": [
        "np.percentile(a, 10) #10th percentile"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KKNL6PeJNDro"
      },
      "outputs": [],
      "source": [
        "np.percentile(a, 90) #90th percentile"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fYOd3UHRNDro"
      },
      "outputs": [],
      "source": [
        "np.random.seed(123)\n",
        "a = np.random.randint(1,101, 11) #creating an array a with 11 random integers between 1 and 100\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RJpaHuaqNDro"
      },
      "outputs": [],
      "source": [
        "np.random.seed(111) #different seed!!!\n",
        "b = np.random.randint(1,101, 11) #creating an array b with 11 random integers between 1 and 100\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7FhCqUSRNDro"
      },
      "outputs": [],
      "source": [
        "np.cov(a,b) #covariance matrix"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8rC3TEOONDro"
      },
      "outputs": [],
      "source": [
        "np.corrcoef(a,b) #correlation matrix"
      ]
    }
  ],
  "metadata": {
    "anaconda-cloud": {},
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.7"
    },
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}