numpy_matplotlib.ipynb

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        "<a href=\"https://colab.research.google.com/github/aseddin/F23_ECE4715/blob/main/numpy_matplotlib.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": [
        "# [NumPy](https://numpy.org/)\n",
        "\n",
        "Short for \"Numerical Python,\" is a fundamental Python library for numerical and scientific computing. It provides support for creating and manipulating arrays of data, which are essential for tasks such as numerical calculations, data analysis, and machine learning. NumPy's key features include efficient array operations, a wide range of mathematical functions, broadcasting for element-wise operations on arrays of different shapes, and seamless integration with other scientific libraries.\n",
        "\n",
        "If you are coming from Matlab [this](https://numpy.org/doc/stable/user/numpy-for-matlab-users.html) article might be a good starting point.\n",
        "\n",
        "The following is a Numpy quickstart guide"
      ],
      "metadata": {
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    {
      "cell_type": "markdown",
      "source": [
        "## The Basics\n",
        "\n",
        "In NumPy, the primary class is `ndarray`, often simply referred to as `array`. This class is responsible for handling homogeneous N-dimensional arrays. Here are some essential attributes of the `ndarray` class:\n",
        "\n",
        "- `ndarray.ndim`: Indicates the number of dimensions (axes) of the array.\n",
        "- `ndarray.shape`: A tuple that specifies the size of the array in each dimension.\n",
        "- `ndarray.size`: Represents the total number of elements within the array, which is the product of the elements of `ndarray.shape`.\n",
        "- `ndarray.dtype`: Specifies the data type of the elements contained in the array (e.g., `numpy.int32`, `numpy.float64`, etc.).\n",
        "- `ndarray.data`: This attribute contains the actual elements of the array, but typically, you'll access these elements through slicing operations, making direct use of this attribute unnecessary."
      ],
      "metadata": {
        "id": "FgRtwpfkWnT3"
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    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np"
      ],
      "metadata": {
        "id": "ca-fLPw6p1n-"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Array Creation\n",
        "\n",
        "There are various methods for creating arrays in NumPy. You can begin by converting a standard Python sequence, such as a list or tuple, into a NumPy array. Additionally, you can generate arrays filled with ones, zeros, random numbers, or a sorted sequence of numbers."
      ],
      "metadata": {
        "id": "2buAPgB0lo0K"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Using `array`"
      ],
      "metadata": {
        "id": "1WJMaHHVtFzU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v = np.array([1, 2, 3])\n",
        "v"
      ],
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        "id": "4Sq2PCynqe3d",
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      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "type(v)"
      ],
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        },
        "id": "PRd1f0jzrCxP",
        "outputId": "13b589e4-ffb9-4d27-8a49-23503af3da60"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v.ndim"
      ],
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              "1"
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          "metadata": {},
          "execution_count": 4
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    {
      "cell_type": "code",
      "source": [
        "v.shape"
      ],
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          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v.size"
      ],
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          "base_uri": "https://localhost:8080/"
        },
        "id": "Vv0zETP3qvYJ",
        "outputId": "ad580a38-5e4a-4081-9c67-28bedaa5454b"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v.dtype"
      ],
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          "base_uri": "https://localhost:8080/"
        },
        "id": "irAvkKE6qwmg",
        "outputId": "dc42e745-254f-4909-eaaa-407d18e586d8"
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      "execution_count": 7,
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          "data": {
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              "dtype('int64')"
            ]
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          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "If the Python sequence is nested, such as a list of lists, the `array` function will transform it into a multidimensional array in NumPy."
      ],
      "metadata": {
        "id": "7RkJw1yFrSkm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m = np.array(\n",
        "    [[1, 2, 3],\n",
        "     [4, 5, 6]]\n",
        ")\n",
        "\n",
        "print(f\"dimensions: {m.ndim} \\nshape: {m.shape} \\nsize: {m.size}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P-teBGNuqzKy",
        "outputId": "167bc1cd-2d8d-4b07-b41d-2199d20ffa8b"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dimensions: 2 \n",
            "shape: (2, 3) \n",
            "size: 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "t = np.array(\n",
        "    [[[1, 2, 3],\n",
        "      [4, 5, 6]],\n",
        "\n",
        "     [[10, 20, 30],\n",
        "      [40, 50, 60]]\n",
        "     ]\n",
        ")\n",
        "\n",
        "print(f\"dimensions: {t.ndim} \\nshape: {t.shape} \\nsize: {t.size}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RG_9YDElsV2k",
        "outputId": "8db68fbf-1023-4f80-c962-0d846685e805"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dimensions: 3 \n",
            "shape: (2, 2, 3) \n",
            "size: 12\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Using placeholder functions\n",
        "\n",
        "Typically useful to avoid growing arrays (which are expensive)"
      ],
      "metadata": {
        "id": "03TcOQn2tKBE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "z = np.zeros((3, 4))\n",
        "\n",
        "z"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ypPWaQX4s7oS",
        "outputId": "6eb8c143-3b33-4856-c985-acb96be9eb7d"
      },
      "execution_count": 10,
      "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": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "o = np.ones((5, 6, 7))\n",
        "\n",
        "o"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5mkUUTYPtiXX",
        "outputId": "8b841ffc-182d-40e7-cec6-0bd3e3418fb0"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.]],\n",
              "\n",
              "       [[1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.]],\n",
              "\n",
              "       [[1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.]],\n",
              "\n",
              "       [[1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.]],\n",
              "\n",
              "       [[1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.],\n",
              "        [1., 1., 1., 1., 1., 1., 1.]]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "e = np.empty((2, 3))\n",
        "\n",
        "e #contains random numbers depending on the state of memory"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TzTfU5G4tqkk",
        "outputId": "a856a1ee-04b8-4b91-851d-aa70d5db2495"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.96402496e-310, 0.00000000e+000, 3.68067497e+180],\n",
              "       [2.46345036e-154, 2.65141253e+180, 3.99461109e+252]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ra = np.random.rand(3, 4) # random numbers uniformly distributed between 0 and 1\n",
        "\n",
        "ra"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D3FTHDZQu_Pa",
        "outputId": "d0496688-e061-49d2-e129-ee09b1a0c749"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.92092534, 0.80742822, 0.20777175, 0.57383635],\n",
              "       [0.2856106 , 0.08588166, 0.08228442, 0.57340077],\n",
              "       [0.52448704, 0.04978737, 0.55127754, 0.79100118]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ra = np.random.randn(3, 4) # random numbers normally distributed (mean = 0, std = 1)\n",
        "\n",
        "ra"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Jj9tlBWvvLTA",
        "outputId": "ac80272e-b3fb-42f5-e27c-94297dd497be"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.87433462,  1.06936044,  0.80861086, -1.6229711 ],\n",
              "       [ 0.27396825,  0.38308215, -0.24077186,  1.51964032],\n",
              "       [ 1.14021611, -0.39969539, -1.06648588, -0.83765346]])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ra = np.random.uniform(5, 10, (3, 4)) # random numbers uniformly distributed between 5 and 10\n",
        "\n",
        "ra"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UJB01M8JvNLs",
        "outputId": "9fac7198-5005-4b34-dd1c-1e5e184f9499"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[8.50422545, 9.7697526 , 8.25847987, 6.61942834],\n",
              "       [5.32381577, 6.32812343, 8.36525239, 9.44085673],\n",
              "       [6.96342371, 5.85749044, 9.88138638, 7.73056396]])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "i = np.eye(4)\n",
        "\n",
        "i"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "adRL3WMZuDMf",
        "outputId": "dcc6f9ae-26dd-4799-857e-12da753286dd"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0., 0.],\n",
              "       [0., 1., 0., 0.],\n",
              "       [0., 0., 1., 0.],\n",
              "       [0., 0., 0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "d = np.diag([1, 2, 3, 4])\n",
        "\n",
        "d"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JE4t3NXWuI6o",
        "outputId": "872668d6-8718-4196-f2e8-87c64c86c086"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 0, 0, 0],\n",
              "       [0, 2, 0, 0],\n",
              "       [0, 0, 3, 0],\n",
              "       [0, 0, 0, 4]])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# arange generates a range (start, stop, step). Typically difficult to know for sure the number of elements\n",
        "r = np.arange(10, 20, 0.5)\n",
        "\n",
        "r"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h12B5XhDuN9x",
        "outputId": "15077983-7866-4d7e-d114-353f16ab5ae7"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([10. , 10.5, 11. , 11.5, 12. , 12.5, 13. , 13.5, 14. , 14.5, 15. ,\n",
              "       15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# if you want a specific number of elements use linspace\n",
        "\n",
        "l = np.linspace(10, 20, 23)\n",
        "\n",
        "l"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jflrw3zTunPD",
        "outputId": "82b27199-44da-4625-a43c-616b992e18ff"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([10.        , 10.45454545, 10.90909091, 11.36363636, 11.81818182,\n",
              "       12.27272727, 12.72727273, 13.18181818, 13.63636364, 14.09090909,\n",
              "       14.54545455, 15.        , 15.45454545, 15.90909091, 16.36363636,\n",
              "       16.81818182, 17.27272727, 17.72727273, 18.18181818, 18.63636364,\n",
              "       19.09090909, 19.54545455, 20.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "l.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ml60-Y46u0mH",
        "outputId": "fdf29627-4c5d-4eb8-f4e2-0a5c251e1fcc"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(23,)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Why use NumPy arrays?\n",
        "\n",
        "Although you can use Python lists for computation, they tend to be considerably slower. NumPy arrays are specifically designed for faster and more efficient computations, often eliminating the need for explicit loops. To appreciate the performance difference, examine the timing of the code cells below to compare the two approaches."
      ],
      "metadata": {
        "id": "dMqRyh8-wtIg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(42)\n",
        "\n",
        "np_x = np.random.rand(100_000_000)\n",
        "list_x = list(np_x)\n",
        "\n",
        "result1 = np.empty(np_x.shape)\n",
        "result2 = np.empty(np_x.shape)\n",
        "result3 = []"
      ],
      "metadata": {
        "id": "_TMspb72xNno"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "type(np_x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fPaBPVaSxNlI",
        "outputId": "2fc59dd5-38e5-4866-b2e4-3efdc5996043"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "type(list_x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1nbutqRhxNij",
        "outputId": "b894b2bc-30eb-44ea-f305-9beea29b087d"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "list"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i, x in enumerate(np_x):\n",
        "  result1[i] = x ** 3"
      ],
      "metadata": {
        "id": "4veVeti3xNdU"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# no need for loops\n",
        "result2 = np_x ** 3"
      ],
      "metadata": {
        "id": "R3HX8r9axfDR"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.array_equal(result1, result2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YzVXic5uxfAt",
        "outputId": "40837baf-e324-4db7-e193-d9e69b583e69"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i, x in enumerate(list_x):\n",
        "  result3.append(x ** 3)"
      ],
      "metadata": {
        "id": "0BDL_getxe-T"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# clear the memory by releasing result1, result2, result3\n",
        "del result1, result2, result3"
      ],
      "metadata": {
        "id": "I3UPmgh6SX2n"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Basic Operations\n",
        "\n",
        "The default mode in numpy is _elementwise_ operations.\n",
        "\n",
        "Some operators are: (`+`, `-`, `*`, `/`, `//`, `**`, `<`, `==`, etc.)\n",
        "\n"
      ],
      "metadata": {
        "id": "dwVINwpClw3T"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v1 = np.array([1 ,2])\n",
        "v2 = np.array([3, 4])"
      ],
      "metadata": {
        "id": "AtT40_8v0HBR"
      },
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "v1 + v2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FUVxVfXh0W9h",
        "outputId": "9d8564e6-bb88-4379-b4a8-9d737f80875c"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v1 - v2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "POCtjVeL0cdG",
        "outputId": "c0f9e8a8-774d-412a-86a7-db679367ff59"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-2, -2])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v1 * v2 # elementwise multiplication"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FQK5N7HA0cXs",
        "outputId": "d4e847d1-7737-4cad-abb5-bbc3c3452dfc"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v1 * 2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6GdaGfms0cQ2",
        "outputId": "388e89e5-fed0-410a-99c9-84572638f9f7"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v1 ** 2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zLLpLBfA0n4s",
        "outputId": "66f8c7fe-f8ee-4761-982c-eea1d21dfd58"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The `*` operators elementwise (not matrix multiplication). Matrix multiplication is typically using `@` operator or the `dot` function."
      ],
      "metadata": {
        "id": "Nuq8Tkb7063z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.eye(2)\n",
        "b = np.array([\n",
        "    [3, 7],\n",
        "    [0, 5]\n",
        "])\n"
      ],
      "metadata": {
        "id": "r0iE0DcJ0n2s"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8HvO6hRN0n0e",
        "outputId": "d71ce2ee-f367-4026-b16b-aadb6bf4b96c"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0.],\n",
              "       [0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# elementwise product\n",
        "a * b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VAfT9_fa0nuG",
        "outputId": "5fe5a006-a810-481c-b4d1-d477d4a7f212"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3., 0.],\n",
              "       [0., 5.]])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# matrix product\n",
        "a @ b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zUVgTlht1SmS",
        "outputId": "59d50fb8-73f6-4e05-c88e-9f6bccbfa876"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3., 7.],\n",
              "       [0., 5.]])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# matrix product using procedural function dot\n",
        "np.dot(a, b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ltYdvBvM1SkI",
        "outputId": "4da42c52-18ca-4664-cbad-3135d56c745e"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3., 7.],\n",
              "       [0., 5.]])"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# matrix product using OOP method dot\n",
        "\n",
        "a.dot(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "75_3ZtDG1e6f",
        "outputId": "5f7629f9-432d-4d3e-fdc3-1934c087867a"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3., 7.],\n",
              "       [0., 5.]])"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "m = np.random.randint(0, 100, (4, 5))\n",
        "m"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wRK2ZMQL1_sc",
        "outputId": "53fefc1c-bdab-4630-fdee-82c1f947928b"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25, 29, 56, 83, 72],\n",
              "       [71, 45, 62, 48,  3],\n",
              "       [69, 30, 84, 95, 15],\n",
              "       [ 6, 50, 46,  5, 36]])"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# logical operators\n",
        "m > 50"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pYFQWM9d2JNn",
        "outputId": "4c041532-8b17-4961-c67b-58196a2b05e9"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[False, False,  True,  True,  True],\n",
              "       [ True, False,  True, False, False],\n",
              "       [ True, False,  True,  True, False],\n",
              "       [False, False, False, False, False]])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Unary operations**\n"
      ],
      "metadata": {
        "id": "cN_ujJam2p_2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.random.randint(0, 10, (4, 3))\n",
        "a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5xOxdOk_2pbB",
        "outputId": "9226b193-6cfe-4373-fddc-733bdd18d664"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[7, 9, 5],\n",
              "       [4, 5, 4],\n",
              "       [1, 4, 6],\n",
              "       [7, 4, 3]])"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "72CtW6a328iA",
        "outputId": "2fef3bc3-7014-4d71-82f9-cce6c5d0e058"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "59"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.sum(axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M7N9u6n928f6",
        "outputId": "fea298e7-9a85-4f38-a627-2b2ee4cb9c94"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([19, 22, 18])"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.sum(axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mcZ6zfrD28do",
        "outputId": "320cfc11-debf-4233-9445-f73b59a4357d"
      },
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([21, 13, 11, 14])"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.max()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BFHjglmg3NCl",
        "outputId": "6e11ea6e-7752-4031-b8dd-a669a296b2a6"
      },
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.max(axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mEkPq-vl3NAn",
        "outputId": "84231dde-f669-4382-ca31-9fe50918e4d3"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([7, 9, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.min(axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wDSB89gc3M-v",
        "outputId": "bb18fa69-76fb-471b-f489-83b24c178c8f"
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5, 4, 1, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.cumsum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TA4zgQ2d3iS3",
        "outputId": "649d26b4-497d-4908-ae75-093374ab3eb0"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 7, 16, 21, 25, 30, 34, 35, 39, 45, 52, 56, 59])"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.cumsum(axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "18s6r9Po3Y1p",
        "outputId": "ff0fbc54-09f1-491e-cae8-e788cab5a70c"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 7,  9,  5],\n",
              "       [11, 14,  9],\n",
              "       [12, 18, 15],\n",
              "       [19, 22, 18]])"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.transpose()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D8qGwnlj34qy",
        "outputId": "d8488049-c597-4e70-aac4-3cea7b4f8c7b"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[7, 4, 1, 7],\n",
              "       [9, 5, 4, 4],\n",
              "       [5, 4, 6, 3]])"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a.flatten()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nxo5AEXt4BJk",
        "outputId": "a56a688a-a6ba-49ee-8bbe-1f5f7c8a0e82"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([7, 9, 5, 4, 5, 4, 1, 4, 6, 7, 4, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Indexing and Slicing\n",
        "\n",
        "Very similar to standard lists"
      ],
      "metadata": {
        "id": "obAaePGdlwuO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = np.arange(1, 10, 2) ** 2\n",
        "print(n)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MAjZ1MOCWk-o",
        "outputId": "980c7957-655b-4046-b857-5a3b6b00b828"
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1  9 25 49 81]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_CJ4DNP6Wzbq",
        "outputId": "b60804b9-ccf9-4939-da11-58801b36b736"
      },
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[-3:]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m1Xpj5HpW2fL",
        "outputId": "50c560b4-249d-41fe-ece4-029396a3329e"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25, 49, 81])"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n = np.random.randint(1, 100, (3, 5))\n",
        "n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KOkv5bFUYA70",
        "outputId": "fb5690ca-98b9-4380-f9ba-985ddc56b9ff"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[31, 53, 39, 26, 41],\n",
              "       [84, 61, 85, 29, 16],\n",
              "       [53, 80, 21, 30, 48]])"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[0, 1]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8nHpxcRMYKXm",
        "outputId": "cf1de4b8-f53e-46af-90d1-64dfa0af616e"
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "53"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[0][1]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a5ubfPuPYPgy",
        "outputId": "970831f2-a52b-4a5e-cf8c-f0d0165c6509"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "53"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[1:3, 1:3]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oD_xPU4GYUcQ",
        "outputId": "ed5511d9-5d30-4817-f366-6a8388b30457"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[61, 85],\n",
              "       [80, 21]])"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[:, 2] # all rows in the third column"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DAOOwBD-LtzD",
        "outputId": "e598441d-6c6a-4662-d504-8836b92deb39"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([39, 85, 21])"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n > 50"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gU7E-7hfZXGn",
        "outputId": "a1398649-e118-48da-ac73-a29ff12cc322"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[False,  True, False, False, False],\n",
              "       [ True,  True,  True, False, False],\n",
              "       [ True,  True, False, False, False]])"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n[n > 50]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6qhIwv0TZdY9",
        "outputId": "ff0cc81f-b1c8-4d7f-fbe2-0da0fb1811d7"
      },
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([53, 84, 61, 85, 53, 80])"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Shape Manipulation"
      ],
      "metadata": {
        "id": "TJ3-m-Vdlwk2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = np.random.randint(1, 100, (3, 8))\n",
        "n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Vo_tTwQFZqt1",
        "outputId": "5033ee8e-0b24-4717-9895-dd570882aa65"
      },
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[44, 94, 18,  6, 24,  3, 72, 71],\n",
              "       [73, 39, 70, 27, 86, 35, 22, 72],\n",
              "       [17, 15, 99, 11, 82, 99, 39, 89]])"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GFW2kggAZzxM",
        "outputId": "7bdfa0a9-7343-4481-c248-13df9532d78f"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 8)"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# flatten the array\n",
        "n.ravel()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aLcuzamkZ2a4",
        "outputId": "642865ce-c8c4-481a-fe89-38886b3d3cce"
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([44, 94, 18,  6, 24,  3, 72, 71, 73, 39, 70, 27, 86, 35, 22, 72, 17,\n",
              "       15, 99, 11, 82, 99, 39, 89])"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ravel returns a new array but keeps the original unchanged\n",
        "n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fQ7dg_C2Nw6h",
        "outputId": "c5c04a98-50e8-4760-9781-8f456169c0a1"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[44, 94, 18,  6, 24,  3, 72, 71],\n",
              "       [73, 39, 70, 27, 86, 35, 22, 72],\n",
              "       [17, 15, 99, 11, 82, 99, 39, 89]])"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n.flatten() # similar to ravel"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9wGIn6FkZ6rd",
        "outputId": "2ecb0c3d-3df1-4165-b84d-894c409d348b"
      },
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([44, 94, 18,  6, 24,  3, 72, 71, 73, 39, 70, 27, 86, 35, 22, 72, 17,\n",
              "       15, 99, 11, 82, 99, 39, 89])"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n.reshape(2, 12) # returns a new array but keep original unchanged"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "khj7kY_EZ-IB",
        "outputId": "0d7f67ef-5aec-4c84-ff97-3ac86bf7d05f"
      },
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[44, 94, 18,  6, 24,  3, 72, 71, 73, 39, 70, 27],\n",
              "       [86, 35, 22, 72, 17, 15, 99, 11, 82, 99, 39, 89]])"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n.reshape(2, -1) # -1 automatically calculated"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IQbwTP5paMwd",
        "outputId": "bd26207a-4c60-44d2-c478-acf0b7e2c6ba"
      },
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[44, 94, 18,  6, 24,  3, 72, 71, 73, 39, 70, 27],\n",
              "       [86, 35, 22, 72, 17, 15, 99, 11, 82, 99, 39, 89]])"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QAYoMETnOlMq",
        "outputId": "fffb03a1-d9bf-4243-e86d-a8052fc994b5"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[44, 94, 18,  6, 24,  3, 72, 71],\n",
              "       [73, 39, 70, 27, 86, 35, 22, 72],\n",
              "       [17, 15, 99, 11, 82, 99, 39, 89]])"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n.resize(2, 12) # reshape modifies the array itself"
      ],
      "metadata": {
        "id": "6B5hTjhUan8k"
      },
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9aFj1vT8OnAI",
        "outputId": "02941a92-da49-4307-e74e-b1c7f06242f0"
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[44, 94, 18,  6, 24,  3, 72, 71, 73, 39, 70, 27],\n",
              "       [86, 35, 22, 72, 17, 15, 99, 11, 82, 99, 39, 89]])"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5JRMNhPkavSS",
        "outputId": "d1a2bb3f-27ac-4042-f4dd-df45e8707dee"
      },
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 12)"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# `matplotlib`\n",
        "\n",
        "A library that allows you to generate graphs. Its interface is very similar to Matlab.\n",
        "\n",
        "The following shows basic plotting examples. If you want something else or more complicated, check this [gallery](https://matplotlib.org/stable/gallery/index.html), look for what might be close to what you want, copy its code, play around with it and adapt it to your needs."
      ],
      "metadata": {
        "id": "W5aOewSkV2xq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "x = np.linspace(-100, 100, 50)\n",
        "y = x ** 2\n",
        "\n",
        "plt.plot(x, y, 'g--', linewidth=2)\n",
        "plt.xlabel('$x$', fontsize=20)\n",
        "plt.ylabel('$y = x^2$', fontsize=20)\n",
        "plt.title('Plot')\n",
        "plt.grid('on')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        },
        "id": "XXe1oCaPV3GR",
        "outputId": "62780a6f-80e2-4101-dddf-dde3c2f844a8"
      },
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.linspace(-1.5, 1.3, 50)\n",
        "plt.plot(x, x, 'b--', x, x**2, 'g:', x, x**3, 'm^', linewidth=2)\n",
        "plt.grid('on')\n",
        "plt.xlabel('$x$', fontsize=14)\n",
        "plt.legend(['$x$', '$x^2$', '$x^3$'], loc='lower center', fontsize=14)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "d-KpkRCTV4Rw",
        "outputId": "96d171dd-1274-470b-e9ea-0f16e0a3bfa3"
      },
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7c05a2f762c0>"
            ]
          },
          "metadata": {},
          "execution_count": 76
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}