session_13_numpy_fundamentals.ipynb

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      "name": "python"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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        "<a href=\"https://colab.research.google.com/github/singhsourav0/DSMP-2.0/blob/main/session_13_numpy_fundamentals.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "source": [
        "### What is numpy?\n",
        "\n",
        "NumPy is the fundamental package for scientific computing in Python. It is a Python library that provides a multidimensional array object, various derived objects (such as masked arrays and matrices), and an assortment of routines for fast operations on arrays, including mathematical, logical, shape manipulation, sorting, selecting, I/O, discrete Fourier transforms, basic linear algebra, basic statistical operations, random simulation and much more.\n",
        "\n",
        "\n",
        "At the core of the NumPy package, is the ndarray object. This encapsulates n-dimensional arrays of homogeneous data types"
      ],
      "metadata": {
        "id": "lFF783PD7ypT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Numpy Arrays Vs Python Sequences\n",
        "\n",
        "- NumPy arrays have a fixed size at creation, unlike Python lists (which can grow dynamically). Changing the size of an ndarray will create a new array and delete the original.\n",
        "\n",
        "- The elements in a NumPy array are all required to be of the same data type, and thus will be the same size in memory.\n",
        "\n",
        "- NumPy arrays facilitate advanced mathematical and other types of operations on large numbers of data. Typically, such operations are executed more efficiently and with less code than is possible using Python’s built-in sequences.\n",
        "\n",
        "- A growing plethora of scientific and mathematical Python-based packages are using NumPy arrays; though these typically support Python-sequence input, they convert such input to NumPy arrays prior to processing, and they often output NumPy arrays."
      ],
      "metadata": {
        "id": "HPRzhmwiZkOP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Creating Numpy Arrays"
      ],
      "metadata": {
        "id": "0PyrZ724szaG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# np.array\n",
        "import numpy as np\n",
        "\n",
        "a = np.array([1,2,3])\n",
        "print(a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V4AVNXrts3sL",
        "outputId": "5efc2800-7099-4f1a-c548-df46c157de27"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 2 3]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# 2D and 3D\n",
        "b = np.array([[1,2,3],[4,5,6]])\n",
        "print(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AAfxD1kCs6R5",
        "outputId": "e71d27eb-3106-43fd-8147-5a33b645f8b0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "c = np.array([[[1,2],[3,4]],[[5,6],[7,8]]])\n",
        "print(c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MyrHdd6J6CrF",
        "outputId": "2d7750a8-6e28-424d-bac4-7e61e7e73e9f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[[1 2]\n",
            "  [3 4]]\n",
            "\n",
            " [[5 6]\n",
            "  [7 8]]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# dtype\n",
        "np.array([1,2,3],dtype=float)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FM8AwUOdFqC7",
        "outputId": "63ee85e6-449e-4e1f-e5a3-563bfae4dc9e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 2., 3.])"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# np.arange\n",
        "np.arange(1,11,2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZY187Au_s8vm",
        "outputId": "cb13d451-a431-446f-f3a3-245315da6775"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 3, 5, 7, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# with reshape\n",
        "np.arange(16).reshape(2,2,2,2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3Gc7BaJZwl7e",
        "outputId": "c1e4173a-80d6-449b-9cbc-ae4a6fba5d20"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[[ 0,  1],\n",
              "         [ 2,  3]],\n",
              "\n",
              "        [[ 4,  5],\n",
              "         [ 6,  7]]],\n",
              "\n",
              "\n",
              "       [[[ 8,  9],\n",
              "         [10, 11]],\n",
              "\n",
              "        [[12, 13],\n",
              "         [14, 15]]]])"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# np.ones and np.zeros\n",
        "np.ones((3,4))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R2BYpYcGs-9l",
        "outputId": "992ba3c5-532b-4229-997b-b584de7d36d8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 1., 1., 1.],\n",
              "       [1., 1., 1., 1.],\n",
              "       [1., 1., 1., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.zeros((3,4))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vOjv_Euj8HGR",
        "outputId": "85fb7d62-e57f-4935-f33b-0c47a8bca4b3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0., 0.],\n",
              "       [0., 0., 0., 0.],\n",
              "       [0., 0., 0., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# np.random\n",
        "np.random.random((3,4))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fYEeYi7itCRM",
        "outputId": "6a5ead6b-3dbb-45f5-a495-b7d78c2683ba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.85721156, 0.31248316, 0.08807828, 0.35230774],\n",
              "       [0.96813914, 0.44681708, 0.56396358, 0.53020065],\n",
              "       [0.03277116, 0.28543753, 0.09521082, 0.87967034]])"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# np.linspace\n",
        "np.linspace(-10,10,10,dtype=int)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vel7WrgltE3P",
        "outputId": "21b993d2-c91c-42fa-f97c-030b87cc292a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-10,  -8,  -6,  -4,  -2,   1,   3,   5,   7,  10])"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# np.identity\n",
        "np.identity(3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ewyMuXh1tJzi",
        "outputId": "921cf302-94d7-4d44-d696-881b839ced04"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0.],\n",
              "       [0., 1., 0.],\n",
              "       [0., 0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Array Attributes"
      ],
      "metadata": {
        "id": "LphXpjZJtNyI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a1 = np.arange(10,dtype=np.int32)\n",
        "a2 = np.arange(12,dtype=float).reshape(3,4)\n",
        "a3 = np.arange(8).reshape(2,2,2)\n",
        "\n",
        "a3"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UXnB5dIEFOgD",
        "outputId": "d6261278-40ee-4caa-cf15-946552e4e7c0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0, 1],\n",
              "        [2, 3]],\n",
              "\n",
              "       [[4, 5],\n",
              "        [6, 7]]])"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ndim\n",
        "a3.ndim"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qib4oDFptRKN",
        "outputId": "b70741e8-d727-4c59-b6ed-b8fd922501b8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# shape\n",
        "print(a3.shape)\n",
        "a3"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "InUvH8KGtSRv",
        "outputId": "d567d4cb-a533-4419-e4de-677dc5dd87bb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(2, 2, 2)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0, 1],\n",
              "        [2, 3]],\n",
              "\n",
              "       [[4, 5],\n",
              "        [6, 7]]])"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# size\n",
        "print(a2.size)\n",
        "a2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9Dko5610tT-Z",
        "outputId": "5e8fdaa5-d444-4867-8ad0-3acf299c391e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.,  1.,  2.,  3.],\n",
              "       [ 4.,  5.,  6.,  7.],\n",
              "       [ 8.,  9., 10., 11.]])"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# itemsize\n",
        "a3.itemsize"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wDFdHtH3tV1Z",
        "outputId": "dd8bf2cd-bc17-4d6c-ae17-06ae052ab711"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# dtype\n",
        "print(a1.dtype)\n",
        "print(a2.dtype)\n",
        "print(a3.dtype)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Pik7FgEVtXDj",
        "outputId": "00b7b1ad-d200-4c7c-e440-ba3c05928073"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "int32\n",
            "float64\n",
            "int64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Changing Datatype"
      ],
      "metadata": {
        "id": "7Ase0eFWtcFl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# astype\n",
        "a3.astype(np.int32)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DZPEFqhotbFS",
        "outputId": "848bd55f-1d69-4443-c832-d2735f4611f3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0, 1],\n",
              "        [2, 3]],\n",
              "\n",
              "       [[4, 5],\n",
              "        [6, 7]]], dtype=int32)"
            ]
          },
          "metadata": {},
          "execution_count": 117
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Array Operations"
      ],
      "metadata": {
        "id": "k-y-aaV9u52l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a1 = np.arange(12).reshape(3,4)\n",
        "a2 = np.arange(12,24).reshape(3,4)\n",
        "\n",
        "a2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mIk8tk53HnOW",
        "outputId": "eba6d5cf-f698-494c-ea3c-c38541421cb4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[12, 13, 14, 15],\n",
              "       [16, 17, 18, 19],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "metadata": {},
          "execution_count": 119
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# scalar operations\n",
        "\n",
        "# arithmetic\n",
        "a1 ** 2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vtQrWQKD87Fn",
        "outputId": "632feb6a-d00e-481f-806c-7b8589742bd2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  0,   1,   4,   9],\n",
              "       [ 16,  25,  36,  49],\n",
              "       [ 64,  81, 100, 121]])"
            ]
          },
          "metadata": {},
          "execution_count": 124
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# relational\n",
        "a2 == 15"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mCgPxTzQrtte",
        "outputId": "14a8bbd7-363d-42a7-bc28-984d37c6de07"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[False, False, False,  True],\n",
              "       [False, False, False, False],\n",
              "       [False, False, False, False]])"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# vector operations\n",
        "# arithmetic\n",
        "a1 ** a2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E2S3xDRxrt5D",
        "outputId": "2dfc1e18-65f7-4131-aed8-67bcc7b0996b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[                   0,                    1,                16384,\n",
              "                    14348907],\n",
              "       [          4294967296,         762939453125,      101559956668416,\n",
              "           11398895185373143],\n",
              "       [ 1152921504606846976, -1261475310744950487,  1864712049423024128,\n",
              "         6839173302027254275]])"
            ]
          },
          "metadata": {},
          "execution_count": 135
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Array Functions"
      ],
      "metadata": {
        "id": "AQZgntYTu8ot"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a1 = np.random.random((3,3))\n",
        "a1 = np.round(a1*100)\n",
        "a1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CHUj0a_dIP4F",
        "outputId": "a4e84b6e-e80f-4612-b9ae-9b64c87de269"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[43., 28., 71.],\n",
              "       [27., 93., 36.],\n",
              "       [31., 18.,  7.]])"
            ]
          },
          "metadata": {},
          "execution_count": 136
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# max/min/sum/prod\n",
        "# 0 -> col and 1 -> row\n",
        "np.prod(a1,axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J1EWNET29Urx",
        "outputId": "34e6d72b-35f5-4dc3-f107-289bb0396c39"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([35991., 46872., 17892.])"
            ]
          },
          "metadata": {},
          "execution_count": 148
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# mean/median/std/var\n",
        "np.var(a1,axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JAlMLFkds9KC",
        "outputId": "63636deb-3321-4714-d5a4-388445e1c492"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([317.55555556, 854.        ,  96.22222222])"
            ]
          },
          "metadata": {},
          "execution_count": 153
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# trigonomoetric functions\n",
        "np.sin(a1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vwLoQQVqs-m-",
        "outputId": "128781c4-4e3d-4748-c619-cdb874c99d9b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.83177474,  0.27090579,  0.95105465],\n",
              "       [ 0.95637593, -0.94828214, -0.99177885],\n",
              "       [-0.40403765, -0.75098725,  0.6569866 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 154
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# dot product\n",
        "a2 = np.arange(12).reshape(3,4)\n",
        "a3 = np.arange(12,24).reshape(4,3)\n",
        "\n",
        "np.dot(a2,a3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RoEtYuiytFm1",
        "outputId": "7ab0e6f1-820d-4deb-c7a3-b3301eed9ec4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[114, 120, 126],\n",
              "       [378, 400, 422],\n",
              "       [642, 680, 718]])"
            ]
          },
          "metadata": {},
          "execution_count": 157
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# log and exponents\n",
        "np.exp(a1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qd7GmrgEtH6i",
        "outputId": "85a52de0-68b1-4838-c462-f28a7e00d4db"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.72783947e+18, 1.44625706e+12, 6.83767123e+30],\n",
              "       [5.32048241e+11, 2.45124554e+40, 4.31123155e+15],\n",
              "       [2.90488497e+13, 6.56599691e+07, 1.09663316e+03]])"
            ]
          },
          "metadata": {},
          "execution_count": 160
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# round/floor/ceil\n",
        "\n",
        "np.ceil(np.random.random((2,3))*100)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EOXnVCZhtKk1",
        "outputId": "3be37070-696a-46e9-b5e7-6298bf2cdbb9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[48.,  4.,  6.],\n",
              "       [ 3., 18., 82.]])"
            ]
          },
          "metadata": {},
          "execution_count": 165
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Indexing and Slicing"
      ],
      "metadata": {
        "id": "2pYZJMrAuvuv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a1 = np.arange(10)\n",
        "a2 = np.arange(12).reshape(3,4)\n",
        "a3 = np.arange(8).reshape(2,2,2)\n",
        "\n",
        "a3"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v1LynzX9u2R-",
        "outputId": "38bb09f7-c353-4da7-8f65-29126e81e742"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0, 1],\n",
              "        [2, 3]],\n",
              "\n",
              "       [[4, 5],\n",
              "        [6, 7]]])"
            ]
          },
          "metadata": {},
          "execution_count": 168
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qyFbwR9Ku2YE",
        "outputId": "ee0795d0-a9e0-4494-dcf1-25278cdd3ef6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 169
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q2IbBdEXu2a5",
        "outputId": "27f37180-6151-4b88-a4a7-b6b943a1a79f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 172
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[1,0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GIR5YhVzu2dc",
        "outputId": "5827789b-c94c-4343-f4bf-c37c0e55ae7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {},
          "execution_count": 175
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IbM-KNY3HP9-",
        "outputId": "b1ef95eb-dba8-4a19-f8d2-28505beffbff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0, 1],\n",
              "        [2, 3]],\n",
              "\n",
              "       [[4, 5],\n",
              "        [6, 7]]])"
            ]
          },
          "metadata": {},
          "execution_count": 176
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3[1,0,1]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xG7HU0RgHQD-",
        "outputId": "c0c15e95-2b15-4167-aeea-a2e9751aedb8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 177
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3[1,1,0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3EhcikSWHQKO",
        "outputId": "1a3fe02e-8b8f-4182-9a6d-0bb023be5b8c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {},
          "execution_count": 179
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_cgU2A52HQO0",
        "outputId": "eed00cc5-cefc-48de-bdc4-f28946b3131e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 180
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a1[2:5:2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HnFM0Wa5IMw2",
        "outputId": "312df828-b754-46e8-e47c-b6f3f2d11ad8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 182
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SDWOK56EIM3n",
        "outputId": "682830f3-6c21-43c3-9b05-df473541570c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 183
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[0:2,1::2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q55x6VoiKmpX",
        "outputId": "9b758dd3-e64b-46c0-e4e3-3c342660d19d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 3],\n",
              "       [5, 7]])"
            ]
          },
          "metadata": {},
          "execution_count": 193
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[::2,1::2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t2hA9ZJNJOBW",
        "outputId": "e6740d01-e110-4b16-cb76-f5f7471eab2d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  3],\n",
              "       [ 9, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 189
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[1,::3]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hubSAa0eKSCt",
        "outputId": "fd7f2aef-9c08-4621-9bb7-0877dc98fb8d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4, 7])"
            ]
          },
          "metadata": {},
          "execution_count": 190
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[0,:]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mi2B5NN9IM-B",
        "outputId": "673febf9-b6ed-4fb7-d12d-32e9b3a9938a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 184
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[:,2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u7dQcPKpINDS",
        "outputId": "dd032bf5-8e11-4f23-9ec7-5e1807fda319"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2,  6, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 185
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2[1:,1:3]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GYjyXNKnINTA",
        "outputId": "d1214ff7-d55d-43e4-94bb-8a6153a07a8a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 5,  6],\n",
              "       [ 9, 10]])"
            ]
          },
          "metadata": {},
          "execution_count": 186
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3 = np.arange(27).reshape(3,3,3)\n",
        "a3"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z-24y62tK7KO",
        "outputId": "41eb67f0-d6f2-4c25-e64f-0482607c4d27"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 0,  1,  2],\n",
              "        [ 3,  4,  5],\n",
              "        [ 6,  7,  8]],\n",
              "\n",
              "       [[ 9, 10, 11],\n",
              "        [12, 13, 14],\n",
              "        [15, 16, 17]],\n",
              "\n",
              "       [[18, 19, 20],\n",
              "        [21, 22, 23],\n",
              "        [24, 25, 26]]])"
            ]
          },
          "metadata": {},
          "execution_count": 195
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3[::2,0,::2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DB1bM8NCMTub",
        "outputId": "9d8f91b7-3074-4788-e464-5529082cf4ba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  2],\n",
              "       [18, 20]])"
            ]
          },
          "metadata": {},
          "execution_count": 201
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3[2,1:,1:]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gPOgRWfNLxPF",
        "outputId": "ecbe6944-ed2f-4036-8deb-edc9880285a2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[22, 23],\n",
              "       [25, 26]])"
            ]
          },
          "metadata": {},
          "execution_count": 200
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3[0,1,:]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S3OJJAMXK7RV",
        "outputId": "b6630bc9-6ffd-4258-fe8f-bc7f988d39fc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 4, 5])"
            ]
          },
          "metadata": {},
          "execution_count": 198
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "av7DbeP5K7Xf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "MTLPaOobK7dc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "0StTG7ycK7kQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "mkUuhK9UK7pA"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "JyonJsQVK7tm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Iterating"
      ],
      "metadata": {
        "id": "dUv9qM1yuIKJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a1\n",
        "\n",
        "for i in a1:\n",
        "  print(i)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lNgaCad6uKhm",
        "outputId": "b841e6c6-2d41-4a11-c9c1-7af7bb5dc72c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0\n",
            "1\n",
            "2\n",
            "3\n",
            "4\n",
            "5\n",
            "6\n",
            "7\n",
            "8\n",
            "9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jNIsE0YFM6ZN",
        "outputId": "54433740-b3db-4467-a002-c447b8e8ebd7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 203
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in a2:\n",
        "  print(i)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B2Hk-zAONHTY",
        "outputId": "793c2607-7b52-4556-cda0-fd82e60905c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 1 2 3]\n",
            "[4 5 6 7]\n",
            "[ 8  9 10 11]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a3"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8hfuC98qM-hC",
        "outputId": "0fb1ef2e-f8fd-4701-ba34-28c54527e2ce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 0,  1,  2],\n",
              "        [ 3,  4,  5],\n",
              "        [ 6,  7,  8]],\n",
              "\n",
              "       [[ 9, 10, 11],\n",
              "        [12, 13, 14],\n",
              "        [15, 16, 17]],\n",
              "\n",
              "       [[18, 19, 20],\n",
              "        [21, 22, 23],\n",
              "        [24, 25, 26]]])"
            ]
          },
          "metadata": {},
          "execution_count": 204
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in a3:\n",
        "  print(i)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DsYEnw2ONOIy",
        "outputId": "e1b309f4-0101-4991-8663-06e5f60597a1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0 1 2]\n",
            " [3 4 5]\n",
            " [6 7 8]]\n",
            "[[ 9 10 11]\n",
            " [12 13 14]\n",
            " [15 16 17]]\n",
            "[[18 19 20]\n",
            " [21 22 23]\n",
            " [24 25 26]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in np.nditer(a3):\n",
        "  print(i)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IuRJ1QiRNZRM",
        "outputId": "438cbd63-6e58-49a8-b8c7-313e40addfce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0\n",
            "1\n",
            "2\n",
            "3\n",
            "4\n",
            "5\n",
            "6\n",
            "7\n",
            "8\n",
            "9\n",
            "10\n",
            "11\n",
            "12\n",
            "13\n",
            "14\n",
            "15\n",
            "16\n",
            "17\n",
            "18\n",
            "19\n",
            "20\n",
            "21\n",
            "22\n",
            "23\n",
            "24\n",
            "25\n",
            "26\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Reshaping"
      ],
      "metadata": {
        "id": "ZSS6AF_luNc-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# reshape"
      ],
      "metadata": {
        "id": "NeXLsnBb9ko7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Transpose\n",
        "np.transpose(a2)\n",
        "a2.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DBIaUE8duQDz",
        "outputId": "ea99f6b4-b3ef-4cd7-dfee-63f1bcb3f6a3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  4,  8],\n",
              "       [ 1,  5,  9],\n",
              "       [ 2,  6, 10],\n",
              "       [ 3,  7, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 212
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ravel\n",
        "a3.ravel()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IULUNn5OuQMT",
        "outputId": "0588ea26-7e91-4f04-c291-e650892551da"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
              "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26])"
            ]
          },
          "metadata": {},
          "execution_count": 216
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Stacking"
      ],
      "metadata": {
        "id": "ouKcJQ5EuUQC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# horizontal stacking\n",
        "a4 = np.arange(12).reshape(3,4)\n",
        "a5 = np.arange(12,24).reshape(3,4)\n",
        "a5"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HHSY1njTuXLi",
        "outputId": "a059eb6d-0f0c-48a3-c992-f513cbeabc70"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[12, 13, 14, 15],\n",
              "       [16, 17, 18, 19],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "metadata": {},
          "execution_count": 218
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.hstack((a4,a5))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ne9uXt3yPKez",
        "outputId": "a7a04092-8889-4628-9966-85b7ef7f5b99"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3, 12, 13, 14, 15],\n",
              "       [ 4,  5,  6,  7, 16, 17, 18, 19],\n",
              "       [ 8,  9, 10, 11, 20, 21, 22, 23]])"
            ]
          },
          "metadata": {},
          "execution_count": 223
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Vertical stacking\n",
        "np.vstack((a4,a5))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F6bFFNKuuZW5",
        "outputId": "14145606-ead6-417d-ae7f-f9ff5ec78394"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11],\n",
              "       [12, 13, 14, 15],\n",
              "       [16, 17, 18, 19],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "metadata": {},
          "execution_count": 222
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Splitting"
      ],
      "metadata": {
        "id": "kaY006uXucF5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# horizontal splitting\n",
        "a4"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kgbl6wkD9ll6",
        "outputId": "cb3ca012-8b56-426f-b3c8-eb919a4b89d8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 224
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.hsplit(a4,5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        },
        "id": "FIfZM5BsQE5l",
        "outputId": "5d220f04-bf07-480c-9f51-d360c77f3635"
      },
      "execution_count": null,
      "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-227-59485ca7f23c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhsplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mhsplit\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/numpy/lib/shape_base.py\u001b[0m in \u001b[0;36mhsplit\u001b[0;34m(ary, indices_or_sections)\u001b[0m\n\u001b[1;32m    938\u001b[0m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'hsplit only works on arrays of 1 or more dimensions'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    939\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mary\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\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[0;32m--> 940\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindices_or_sections\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    941\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    942\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindices_or_sections\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36msplit\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/numpy/lib/shape_base.py\u001b[0m in \u001b[0;36msplit\u001b[0;34m(ary, indices_or_sections, axis)\u001b[0m\n\u001b[1;32m    870\u001b[0m         \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mary\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    871\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mN\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0msections\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 872\u001b[0;31m             raise ValueError(\n\u001b[0m\u001b[1;32m    873\u001b[0m                 'array split does not result in an equal division') from None\n\u001b[1;32m    874\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0marray_split\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindices_or_sections\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: array split does not result in an equal division"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# vertical splitting"
      ],
      "metadata": {
        "id": "nfhKoruOuhK-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a5"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qJ2xEBFUuieB",
        "outputId": "d8395819-f098-4caa-9501-281d0722d593"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[12, 13, 14, 15],\n",
              "       [16, 17, 18, 19],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "metadata": {},
          "execution_count": 228
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.vsplit(a5,2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        },
        "id": "1wxcLLR_QWVu",
        "outputId": "29ed6135-282d-4ed2-ddde-24c3b7fe750b"
      },
      "execution_count": null,
      "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-230-5b73f701499e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvsplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mvsplit\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/numpy/lib/shape_base.py\u001b[0m in \u001b[0;36mvsplit\u001b[0;34m(ary, indices_or_sections)\u001b[0m\n\u001b[1;32m    989\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0m_nx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    990\u001b[0m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'vsplit only works on arrays of 2 or more dimensions'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 991\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindices_or_sections\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\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    992\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    993\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36msplit\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/numpy/lib/shape_base.py\u001b[0m in \u001b[0;36msplit\u001b[0;34m(ary, indices_or_sections, axis)\u001b[0m\n\u001b[1;32m    870\u001b[0m         \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mary\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    871\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mN\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0msections\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 872\u001b[0;31m             raise ValueError(\n\u001b[0m\u001b[1;32m    873\u001b[0m                 'array split does not result in an equal division') from None\n\u001b[1;32m    874\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0marray_split\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindices_or_sections\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: array split does not result in an equal division"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "E_EVrYA7QadG"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}