NumPy.ipynb

{
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      "source": [
        "<a href=\"https://colab.research.google.com/github/isurushanaka/AII--numpy/blob/master/NumPy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ehZ6qU1UdtDu"
      },
      "source": [
        "<img src=\"https://user-images.githubusercontent.com/7065401/39118381-910eb0c2-46e9-11e8-81f1-a5b897401c23.jpeg\"\n",
        "    style=\"width:300px; float: center; margin: 40px 40px 40px 40px;\"></img>\n",
        "\n",
        "# Numpy: Numeric computing library\n",
        "\n",
        "NumPy (Numerical Python) is one of the core packages for numerical computing in Python. Pandas, Matplotlib, Statmodels and many other Scientific libraries rely on NumPy.\n",
        "\n",
        "NumPy major contributions are:\n",
        "\n",
        "* Efficient numeric computation with C primitives\n",
        "* Efficient collections with vectorized operations\n",
        "* An integrated and natural Linear Algebra API\n",
        "* A C API for connecting NumPy with libraries written in C, C++, or FORTRAN.\n",
        "\n",
        "Let's develop on efficiency. In Python, **everything is an object**, which means that even simple ints are also objects, with all the required machinery to make object work. We call them \"Boxed Ints\". In contrast, NumPy uses primitive numeric types (floats, ints) which makes storing and computation efficient."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_nJZL3RxdtD3"
      },
      "source": [
        "<img src=\"https://docs.google.com/drawings/d/e/2PACX-1vTkDtKYMUVdpfVb3TTpr_8rrVtpal2dOknUUEOu85wJ1RitzHHf5nsJqz1O0SnTt8BwgJjxXMYXyIqs/pub?w=726&h=396\" />\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y2TDk3pOdtD4"
      },
      "source": [
        "![purple-divider](https://user-images.githubusercontent.com/7065401/52071927-c1cd7100-2562-11e9-908a-dde91ba14e59.png)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "w5gzRbludtD6"
      },
      "outputs": [],
      "source": [
        "import sys\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4sgoFI3idtD_"
      },
      "source": [
        "## Basic Numpy Arrays"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qqvTksxydtEA",
        "outputId": "d1cb6d7f-3e55-4916-defe-32638d997159"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4])"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.array([1, 2, 3, 4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_qZ7VoUAdtEC"
      },
      "outputs": [],
      "source": [
        "a = np.array([1, 2, 3, 4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gjXWYqPRdtED"
      },
      "outputs": [],
      "source": [
        "b = np.array([0, .5, 1, 1.5, 2])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mbnwRaiwdtED",
        "outputId": "256a9eec-87c9-4d74-96a2-13538944cfb9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1, 2)"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[0], a[1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-u3Tbi2idtEE",
        "outputId": "54557bf8-da9e-42e3-b2e4-ac5abd2de7c4"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4])"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[0:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xRXbIgmOdtEF",
        "outputId": "77f48a3e-293c-4a27-c0f6-ed7d99b76716"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2, 3])"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[1:3]"
      ]
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "XyfJTsjRdtEG",
        "outputId": "c25ba21f-09b8-40a6-826b-bb9142e201ba"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2, 3])"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[1:-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XOHoJsvjdtEJ",
        "outputId": "76fb1ada-6200-439d-e148-6cf1146a9bef"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 3])"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[::2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RVwHyWGBdtEL",
        "outputId": "e197e363-1e3d-4387-b295-feb17bd1e472"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0. , 0.5, 1. , 1.5, 2. ])"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "RYHXBETLdtEN",
        "outputId": "3d597212-1a36-494e-c5d9-382201dbb530"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(0.0, 1.0, 2.0)"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b[0], b[2], b[-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LWqz-ScRdtEO",
        "outputId": "585aa59f-0afb-4f72-aae9-bcac7dd246df"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0., 1., 2.])"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b[[0, 2, -1]]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LbQFYQ7EdtEP"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Array Types"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0I_Rn0u4dtEQ",
        "outputId": "b1dee419-7acb-434d-8d08-263ae7ec4ee1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4])"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "72O-nV-NdtER",
        "outputId": "7dee154e-938c-404a-f6f4-caa94ea84787"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('int64')"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_UNLoOOmdtER",
        "outputId": "1a8f0e38-00fa-4091-ab93-86c7485a8287"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0. , 0.5, 1. , 1.5, 2. ])"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wUbuqpCVdtES",
        "outputId": "4c4375e7-ef78-4a85-b5e2-33c4cbc1e7a9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('float64')"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "L4VYwgPodtET",
        "outputId": "854acf0e-c214-40bc-a4b0-645aa8a95a2f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1., 2., 3., 4.])"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.array([1, 2, 3, 4], dtype=np.float)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "9o6vjGyqdtEU",
        "outputId": "295d41e8-504c-46e5-b867-4e141ecd0459"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4], dtype=int8)"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.array([1, 2, 3, 4], dtype=np.int8)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gR5WnTmbdtEU"
      },
      "outputs": [],
      "source": [
        "c = np.array(['a', 'b', 'c'])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "G3vdz2KudtEV",
        "outputId": "a59b40b9-accb-4b19-bb25-bc64c2242747"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('<U1')"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "c.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gwWN8XU_dtEV"
      },
      "outputs": [],
      "source": [
        "d = np.array([{'a': 1}, sys])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tt0CXBvEdtEW",
        "outputId": "3bb6b31f-8ed1-4067-8cca-a63dcaa28190"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('O')"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "d.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sYJZriVQdtEX"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Dimensions and shapes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ePVmOQ_mdtEX"
      },
      "outputs": [],
      "source": [
        "A = np.array([\n",
        "    [1, 2, 3],\n",
        "    [4, 5, 6]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dQneXcITdtEY",
        "outputId": "3a71b3aa-42b2-40a2-fa2c-7a9b254047d0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2, 3)"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hBUt0VmMdtEZ",
        "outputId": "d4c1cbe1-fad6-4854-c7e5-48ec469083e2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.ndim"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XwCzmyLCdtEZ",
        "outputId": "20e43dd9-a7e4-4c33-a824-b00f876b3af6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.size"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CM0i2XNEdtEa"
      },
      "outputs": [],
      "source": [
        "B = np.array([\n",
        "    [\n",
        "        [12, 11, 10],\n",
        "        [9, 8, 7],\n",
        "    ],\n",
        "    [\n",
        "        [6, 5, 4],\n",
        "        [3, 2, 1]\n",
        "    ]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Gw_QQl_odtEa",
        "outputId": "9f11770d-dcee-4528-e9f8-724458abb429"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[[12, 11, 10],\n",
              "        [ 9,  8,  7]],\n",
              "\n",
              "       [[ 6,  5,  4],\n",
              "        [ 3,  2,  1]]])"
            ]
          },
          "execution_count": 28,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iuA-x3BddtEb",
        "outputId": "7e458849-fd38-41b9-9b90-9ca954ab07d5"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2, 2, 3)"
            ]
          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "B.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9WS9JewbdtEe",
        "outputId": "64e1550a-3d2c-4620-804a-3d3340b10898"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "B.ndim"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ycQ8TkbidtEf",
        "outputId": "c1c634e6-7eaa-4929-9696-c5f538b00213"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "B.size"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FbcdHJ6zdtEg"
      },
      "source": [
        "If the shape isn't consistent, it'll just fall back to regular Python objects:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KYmbhqAwdtEh"
      },
      "outputs": [],
      "source": [
        "C = np.array([\n",
        "    [\n",
        "        [12, 11, 10],\n",
        "        [9, 8, 7],\n",
        "    ],\n",
        "    [\n",
        "        [6, 5, 4]\n",
        "    ]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wP54oEMqdtEx",
        "outputId": "d036cc14-053a-487d-c602-ddcfce550978"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('O')"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "C.dtype"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Rc1WeiEIdtEy",
        "outputId": "d626b5e1-ee42-40f6-aed1-1ac7ff098dca"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(2,)"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "C.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "N7nVa2MadtEy",
        "outputId": "afcfda25-624a-4922-bf97-5d1243445e2e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "C.size"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rn1P7H3pdtEz"
      },
      "outputs": [],
      "source": [
        "type(C[0])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y1o9MQm7dtEz"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Indexing and Slicing of Matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QDin3BZ8dtEz"
      },
      "outputs": [],
      "source": [
        "# Square matrix\n",
        "A = np.array([\n",
        "#.   0. 1. 2\n",
        "    [1, 2, 3], # 0\n",
        "    [4, 5, 6], # 1\n",
        "    [7, 8, 9]  # 2\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jSUs4TptdtE0",
        "outputId": "3c24577b-8f9a-4a8b-f2e8-7c3406a2746a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([4, 5, 6])"
            ]
          },
          "execution_count": 37,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6KmW3HNPdtE0",
        "outputId": "20c9f31c-f8f8-49a9-9465-b5a532ad3457"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "execution_count": 38,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[1][0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wrqWp75BdtE0"
      },
      "outputs": [],
      "source": [
        "# A[d1, d2, d3, d4]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QRnPBYb3dtE1",
        "outputId": "c71b7e98-d5b8-438c-c00c-8fd535e33387"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[1, 0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "n9OU5G7sdtE1",
        "outputId": "c83c9818-fd5d-4727-e7c4-86b08bdbddbe"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "execution_count": 40,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[0:2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "l6oPLRCndtE2",
        "outputId": "1084f81e-8133-4c09-f7cd-eab0a74f8d6b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [4, 5],\n",
              "       [7, 8]])"
            ]
          },
          "execution_count": 41,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[:, :2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "K2ICUwpjdtE2",
        "outputId": "c17a0436-2b64-4347-c153-37cb796c9468"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [4, 5]])"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[:2, :2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BJUEvgDxdtE2",
        "outputId": "7e08078b-9154-484c-ecd8-adc62cb84fa9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[3],\n",
              "       [6]])"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[:2, 2:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oE74tsrvdtE6",
        "outputId": "05277c90-8557-4a0c-a511-17c9a623a345"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9]])"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ojJVQxSydtE7"
      },
      "outputs": [],
      "source": [
        "A[1] = np.array([10, 10, 10])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wpmGsXsudtE7",
        "outputId": "f1e549e7-35b4-4f35-fb36-b8948c5e7d57"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3],\n",
              "       [10, 10, 10],\n",
              "       [ 7,  8,  9]])"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "25zirPr8dtE8"
      },
      "outputs": [],
      "source": [
        "A[2] = 99"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iIjzMZ6udtE8",
        "outputId": "89df9666-a721-43a0-9ce1-cdc60ba0267b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3],\n",
              "       [10, 10, 10],\n",
              "       [99, 99, 99]])"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o28EN5NbdtE9"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Summary statistics"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vcvqjgepdtE-"
      },
      "outputs": [],
      "source": [
        "a = np.array([1, 2, 3, 4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1WaQZ8IUdtE_",
        "outputId": "95ecaea2-6c77-42f2-a342-d9e353b36c81"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.sum()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MXIdXdSYdtFA",
        "outputId": "d92fc5cb-ac6c-45ae-8359-a6e8c395013c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2.5"
            ]
          },
          "execution_count": 51,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-dGQl4N1dtFB",
        "outputId": "4ea95428-77ad-4b1e-8c77-559beb69bfd1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.118033988749895"
            ]
          },
          "execution_count": 52,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.std()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A7yZSOn8dtFD",
        "outputId": "faa49f5c-3c31-457e-9399-c3ce296dd7b7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.25"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.var()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Nl_JuTlndtFE"
      },
      "outputs": [],
      "source": [
        "A = np.array([\n",
        "    [1, 2, 3],\n",
        "    [4, 5, 6],\n",
        "    [7, 8, 9]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eBL_FHZ4dtFE",
        "outputId": "39e021b3-6a63-4809-e787-72ed9278c85c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "45"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.sum()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j_-VuHn0dtFF",
        "outputId": "cba21c73-e298-4e9d-86ba-58a74977fb81"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5.0"
            ]
          },
          "execution_count": 56,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6aI0pEdzdtFF",
        "outputId": "ab9c0695-f425-4315-b7be-1714136312fe"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2.581988897471611"
            ]
          },
          "execution_count": 57,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.std()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zMae83M6dtFG",
        "outputId": "d1a44a0b-814d-4d8c-f7ab-f15bab7e86ef"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([12, 15, 18])"
            ]
          },
          "execution_count": 58,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.sum(axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8dZ1GXXidtFG",
        "outputId": "fa9db6c7-5ab0-4773-a7b6-5f541558dd86"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 6, 15, 24])"
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.sum(axis=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "7huqoz5BdtFH",
        "outputId": "485be068-c31c-4288-e5b0-c7994109625f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([4., 5., 6.])"
            ]
          },
          "execution_count": 60,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.mean(axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xL2vXYBpdtFH",
        "outputId": "a246a643-5624-4de8-827f-bcd9083143cd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2., 5., 8.])"
            ]
          },
          "execution_count": 61,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.mean(axis=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GfQaGfGudtFI",
        "outputId": "2879af50-6cc8-4c36-fdfa-df5c03654779"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2.44948974, 2.44948974, 2.44948974])"
            ]
          },
          "execution_count": 62,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.std(axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "fqakrYDGdtFI",
        "outputId": "5a97b0e4-b52b-4687-9685-3060f220f251"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.81649658, 0.81649658, 0.81649658])"
            ]
          },
          "execution_count": 63,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.std(axis=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n-2uO-4MdtFJ"
      },
      "source": [
        "And [many more](https://docs.scipy.org/doc/numpy-1.13.0/reference/arrays.ndarray.html#array-methods)..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kq_4gMoSdtFJ"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Broadcasting and Vectorized operations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WSA7pNP2dtFK"
      },
      "outputs": [],
      "source": [
        "a = np.arange(4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DFjYpklndtFK",
        "outputId": "f3dfafc1-d5e2-4a2a-b046-9bb0f3beee45"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "execution_count": 67,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oasPuhfpdtFK",
        "outputId": "587303a3-84fe-4114-f162-152e8433ea73"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 11, 12, 13])"
            ]
          },
          "execution_count": 68,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a + 10"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "D1yXD_3JdtFL",
        "outputId": "8941a03e-9261-4f00-cc8e-ea010efb5977"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0, 10, 20, 30])"
            ]
          },
          "execution_count": 69,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a * 10"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TM68uYo2dtFL",
        "outputId": "fcc1f1b3-3019-4f92-8161-137dc5ba65f6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "execution_count": 70,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TkloBcUJdtFM"
      },
      "outputs": [],
      "source": [
        "a += 100"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ptsvl96NdtFM",
        "outputId": "fe8164a1-8aa8-45a2-f6d1-d9abbc53c0cd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([100, 101, 102, 103])"
            ]
          },
          "execution_count": 73,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dNTRYscTdtFN"
      },
      "outputs": [],
      "source": [
        "l = [0, 1, 2, 3]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wyPuS_wDdtFO",
        "outputId": "c6273adb-9c9c-413f-b842-b025e1477feb"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[0, 10, 20, 30]"
            ]
          },
          "execution_count": 75,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "[i * 10 for i in l]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sahTqwtBdtFP"
      },
      "outputs": [],
      "source": [
        "a = np.arange(4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RrJ_fY_ndtFP",
        "outputId": "023c8d08-fa27-43f1-8152-04ec2d7228b7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "execution_count": 77,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oD6AvXsBdtFQ"
      },
      "outputs": [],
      "source": [
        "b = np.array([10, 10, 10, 10])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bBwsbHhudtFQ",
        "outputId": "455f9824-c89f-419b-e039-70f64a9a7f6e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 10, 10, 10])"
            ]
          },
          "execution_count": 79,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zBjtvu6ZdtFR",
        "outputId": "b136ee65-3eb8-45ac-e8f0-ac1b91606114"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 11, 12, 13])"
            ]
          },
          "execution_count": 80,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a + b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Z14UKNZadtFS",
        "outputId": "e186de29-97b0-4a17-caf0-e9cccd9b2116"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0, 10, 20, 30])"
            ]
          },
          "execution_count": 81,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a * b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nG2WsFJVdtFS"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Boolean arrays\n",
        "_(Also called masks)_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Rajil-BkdtFT"
      },
      "outputs": [],
      "source": [
        "a = np.arange(4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "a4tChcfzdtFU",
        "outputId": "429cb860-6e39-44e9-c93b-7d7504a7337b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "execution_count": 83,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y9NzwbFYdtFU",
        "outputId": "b123a8bb-e46b-47db-b828-7d7bf08655a6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(0, 3)"
            ]
          },
          "execution_count": 85,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[0], a[-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vAicCQSzdtFU",
        "outputId": "8cefa855-6f6e-4a31-b787-7c1c23ea4bb0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 3])"
            ]
          },
          "execution_count": 84,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[[0, -1]]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3r9MO8i7dtFV",
        "outputId": "4fb996d8-80db-42ed-c274-885e0ab59a76"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 3])"
            ]
          },
          "execution_count": 86,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[[True, False, False, True]]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AfngTREMdtFV",
        "outputId": "67170d89-8838-4b3c-fdad-1c8b8bb064e8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3])"
            ]
          },
          "execution_count": 89,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-pRtlXF2dtFW",
        "outputId": "d7ec9319-0eed-46e0-ed3b-6cc6c8f95971"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([False, False,  True,  True])"
            ]
          },
          "execution_count": 88,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a >= 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GG7VGnGUdtFW",
        "outputId": "f3c04254-a43f-4daf-8d2c-f17b8cebf769"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2, 3])"
            ]
          },
          "execution_count": 90,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[a >= 2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "12iBrYEldtFW",
        "outputId": "07059d7f-7c50-4312-fb03-747337b924e4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.5"
            ]
          },
          "execution_count": 91,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "0ly9Ud-PdtFX",
        "outputId": "f11c1123-51b5-484a-e55c-55ab801b94d2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2, 3])"
            ]
          },
          "execution_count": 92,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[a > a.mean()]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b8igODZedtFX",
        "outputId": "c2e54956-a06b-459c-d041-8c280b5524fb"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1])"
            ]
          },
          "execution_count": 93,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[~(a > a.mean())]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rcz05A6ddtFY",
        "outputId": "4c025453-c4fb-4c06-c388-ea55d7f6c731"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 1])"
            ]
          },
          "execution_count": 94,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[(a == 0) | (a == 1)]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hhFBPI4PdtFY",
        "outputId": "cf2f8e6a-2b89-4c4f-8bac-829170090574"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 2])"
            ]
          },
          "execution_count": 95,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a[(a <= 2) & (a % 2 == 0)]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Myceg5vCdtFZ"
      },
      "outputs": [],
      "source": [
        "A = np.random.randint(100, size=(3, 3))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "p9KKUQJVdtFZ",
        "outputId": "d41ba061-fde9-4909-fe5b-2dbc528e950d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[71,  6, 42],\n",
              "       [40, 94, 24],\n",
              "       [ 2, 85, 36]])"
            ]
          },
          "execution_count": 97,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e29MOq4xdtFa",
        "outputId": "817efa9c-8ac7-4ac2-f214-1181444bfeb2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([71, 42, 94,  2, 36])"
            ]
          },
          "execution_count": 98,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[np.array([\n",
        "    [True, False, True],\n",
        "    [False, True, False],\n",
        "    [True, False, True]\n",
        "])]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YcLbQGbUdtFa",
        "outputId": "ec495eab-a7ee-4f7a-dd93-0afb5416edef"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ True, False,  True],\n",
              "       [ True,  True, False],\n",
              "       [False,  True,  True]])"
            ]
          },
          "execution_count": 99,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A > 30"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "siMFiGjwdtFb",
        "outputId": "5517395b-ed7d-48a7-f1e4-cf06c1529618"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([71, 42, 40, 94, 85, 36])"
            ]
          },
          "execution_count": 100,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A[A > 30]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-rYxBrFzdtFb"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Linear Algebra"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZasxfEb4dtFc"
      },
      "outputs": [],
      "source": [
        "A = np.array([\n",
        "    [1, 2, 3],\n",
        "    [4, 5, 6],\n",
        "    [7, 8, 9]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "05TOmIFzdtFc"
      },
      "outputs": [],
      "source": [
        "B = np.array([\n",
        "    [6, 5],\n",
        "    [4, 3],\n",
        "    [2, 1]\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lLkGYcpWdtFd",
        "outputId": "2112522b-bf59-4d08-e22c-a16261d959f6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[20, 14],\n",
              "       [56, 41],\n",
              "       [92, 68]])"
            ]
          },
          "execution_count": 103,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.dot(B)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "No7LBnkLdtFd",
        "outputId": "6533d687-04d5-4dd9-90a0-e26162f95802"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[20, 14],\n",
              "       [56, 41],\n",
              "       [92, 68]])"
            ]
          },
          "execution_count": 104,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A @ B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Mt2ppsRTdtFd",
        "outputId": "bff35a34-3fd8-40b2-b7b1-b11c3b5a8e63"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[6, 4, 2],\n",
              "       [5, 3, 1]])"
            ]
          },
          "execution_count": 105,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "B.T"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OZNDo3bYdtFh",
        "outputId": "1e4a8fc1-75b0-49cb-ab66-e20adfc69f8e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9]])"
            ]
          },
          "execution_count": 106,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "4G0tA-oYdtFi",
        "outputId": "15e801d4-9738-4f32-fd88-866717e4b1b2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[36, 48, 60],\n",
              "       [24, 33, 42]])"
            ]
          },
          "execution_count": 107,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "B.T @ A"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kWaQ_g6OdtFj"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Size of objects in Memory"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4u7O33HMdtFj"
      },
      "source": [
        "### Int, floats"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gzk0QfeJdtFk",
        "outputId": "f5fe8280-42a8-4a32-ab04-a4b6cfe6bee8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "28"
            ]
          },
          "execution_count": 108,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# An integer in Python is > 24bytes\n",
        "sys.getsizeof(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "NoS6nylCdtFk",
        "outputId": "11273989-33b6-46bb-9836-32e04f16c556"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "72"
            ]
          },
          "execution_count": 109,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Longs are even larger\n",
        "sys.getsizeof(10**100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "VlNvZe_jdtFl",
        "outputId": "b205e8f6-0c44-44f0-cbad-ae8356f27c0a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "execution_count": 110,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Numpy size is much smaller\n",
        "np.dtype(int).itemsize"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "BVdd9N5OdtFl",
        "outputId": "a3eb1d6a-15c8-4e03-a077-ca4de96040c5"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 112,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Numpy size is much smaller\n",
        "np.dtype(np.int8).itemsize"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "hrQCpovwdtFm",
        "outputId": "b5b31471-7a17-442f-e043-e0fb71bfec13"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "execution_count": 111,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.dtype(float).itemsize"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r0uT5jHXdtFm"
      },
      "source": [
        "### Lists are even larger"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NEDoZQ0TdtFn"
      },
      "outputs": [],
      "source": [
        "# A one-element list\n",
        "sys.getsizeof([1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "IiT-hWNjdtFn"
      },
      "outputs": [],
      "source": [
        "# An array of one element in numpy\n",
        "np.array([1]).nbytes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hwfrwazrdtFn"
      },
      "source": [
        "### And performance is also important"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dEFGQuGRdtFo"
      },
      "outputs": [],
      "source": [
        "l = list(range(100000))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "88b0FEm0dtFp"
      },
      "outputs": [],
      "source": [
        "a = np.arange(100000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "B_RyMb2bdtFq",
        "outputId": "606dc439-749c-4966-ddf2-ed96318ad412"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "CPU times: user 1.06 ms, sys: 279 µs, total: 1.34 ms\n",
            "Wall time: 701 µs\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "333328333350000"
            ]
          },
          "execution_count": 119,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "%time np.sum(a ** 2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "Q9j31C2FdtFr",
        "outputId": "c39fb74e-cdae-42ce-b186-838bc44d357c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "CPU times: user 36.1 ms, sys: 0 ns, total: 36.1 ms\n",
            "Wall time: 35.5 ms\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "333328333350000"
            ]
          },
          "execution_count": 120,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "%time sum([x ** 2 for x in l])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rbJgIt-8dtFt"
      },
      "source": [
        "![green-divider](https://user-images.githubusercontent.com/7065401/52071924-c003ad80-2562-11e9-8297-1c6595f8a7ff.png)\n",
        "\n",
        "## Useful Numpy functions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WruIjgIVdtFt"
      },
      "source": [
        "### `random` "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FCaGcM3ldtFu"
      },
      "outputs": [],
      "source": [
        "np.random.random(size=2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yWnFrNNsdtFu"
      },
      "outputs": [],
      "source": [
        "np.random.normal(size=2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tMVEAu9kdtFu"
      },
      "outputs": [],
      "source": [
        "np.random.rand(2, 4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k4NjhAcodtFx"
      },
      "source": [
        "---\n",
        "### `arange`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cb9nNEgPdtFz"
      },
      "outputs": [],
      "source": [
        "np.arange(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gHxkdasLdtF0"
      },
      "outputs": [],
      "source": [
        "np.arange(5, 10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QLO2J0APdtF1"
      },
      "outputs": [],
      "source": [
        "np.arange(0, 1, .1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kbRqO4hzdtF2"
      },
      "source": [
        "---\n",
        "### `reshape`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3oWdnm98dtF2"
      },
      "outputs": [],
      "source": [
        "np.arange(10).reshape(2, 5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GS0bxzYKdtF3"
      },
      "outputs": [],
      "source": [
        "np.arange(10).reshape(5, 2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KMWBLEXwdtF3"
      },
      "source": [
        "---\n",
        "### `linspace`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cue-GzOsdtF3"
      },
      "outputs": [],
      "source": [
        "np.linspace(0, 1, 5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f0WklMzZdtF4"
      },
      "outputs": [],
      "source": [
        "np.linspace(0, 1, 20)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "ZxkJo0bBdtF4"
      },
      "outputs": [],
      "source": [
        "np.linspace(0, 1, 20, False)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aUk4wUC_dtF4"
      },
      "source": [
        "---\n",
        "### `zeros`, `ones`, `empty`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "esMmRUW4dtF5"
      },
      "outputs": [],
      "source": [
        "np.zeros(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "YIxnbCHidtF5"
      },
      "outputs": [],
      "source": [
        "np.zeros((3, 3))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "w2X21Je-dtF5"
      },
      "outputs": [],
      "source": [
        "np.zeros((3, 3), dtype=np.int)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "G09CrdDOdtF6"
      },
      "outputs": [],
      "source": [
        "np.ones(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xsDAYSOudtF6"
      },
      "outputs": [],
      "source": [
        "np.ones((3, 3))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SlAlVrxYdtF6"
      },
      "outputs": [],
      "source": [
        "np.empty(5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "nljjwQ0edtF6"
      },
      "outputs": [],
      "source": [
        "np.empty((2, 2))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JbNtA7d2dtF7"
      },
      "source": [
        "---\n",
        "### `identity` and `eye`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vzl39dqhdtF7"
      },
      "outputs": [],
      "source": [
        "np.identity(3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oil-x8NCdtF7"
      },
      "outputs": [],
      "source": [
        "np.eye(3, 3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YtEiMeNadtF8"
      },
      "outputs": [],
      "source": [
        "np.eye(8, 4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "91MIxaUJdtF8"
      },
      "outputs": [],
      "source": [
        "np.eye(8, 4, k=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Zi7A-KzgdtF8"
      },
      "outputs": [],
      "source": [
        "np.eye(8, 4, k=-3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": true,
        "id": "7T0hrcpzdtF9"
      },
      "outputs": [],
      "source": [
        "\"Hello World\"[6]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DWNkiNOcdtF9"
      },
      "source": [
        "![purple-divider](https://user-images.githubusercontent.com/7065401/52071927-c1cd7100-2562-11e9-908a-dde91ba14e59.png)"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.8"
    },
    "colab": {
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}