{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XD4cDJcke_7v"
      },
      "source": [
        "# Introduction to NumPy\n",
        "\n",
        "* [Notebook](https://colab.research.google.com/drive/1qz1oLQxXZf44rjkKx3Xevngx1MEKV0yY) of this section (open in a separate tab)\n",
        "\n",
        "* [Video](https://youtu.be/z98FrHFfXaI) of this section (18 minutes)\n",
        "\n",
        "NumPy is a numerical computation library for Python."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Overview"
      ],
      "metadata": {
        "id": "kSff_moUGy1c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**NumPy***.\n",
        "- Python provides many useful modules (libraries).\n",
        "- NumPy is a module for numerical computation.\n",
        "- You can load NumPy by `import numpy`.\n",
        "- As `import numpy as np` (to read numpy as np), it is common to write `np.array()` instead of `numpy.array()`, for example\n",
        "- You can convert a list to a NumPy array with `numpy.array(list)`.\n",
        "- NumPy arrays are equivalent to vectors, matrices, and tensors.\n",
        "- Note that a list and a NumPy array look similar but are different."
      ],
      "metadata": {
        "id": "1JWWoDRFD32H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**matplotlib.pyplot***.\n",
        "- Library for drawing graphs, etc. in Python.\n",
        "- It is common to load `import matplotlib.pyplot as plt` and name it as plt\n"
      ],
      "metadata": {
        "id": "k8CEF6NiD38Y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Other Frequently Used Libraries\n",
        "\n",
        "**Pandas***.\n",
        "\n",
        " - Pandas is a library for working with two-dimensional tables like Excel\n",
        " - It is common to read `import pandas as pd` and name it `pd\n",
        "- `pd.read_csv()` used to read csv files in this course\n",
        "\n",
        "**OpenCV (cv2)**\n",
        "- Library with rich functionality for handling images\n",
        "\n",
        "**scikit-learn***\n",
        "- Module for machine learning. It has a full range of functions other than neural networks.\n",
        "\n"
      ],
      "metadata": {
        "id": "-obcXOxrD35H"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CFlQ6Wv7hROd"
      },
      "source": [
        "## Generate NumPy array\n",
        "\n",
        "np.array(list)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_b-pHtO_aLDm"
      },
      "outputs": [],
      "source": [
        "# Import NumPy and name it np.\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k-saf3S4i-p9",
        "outputId": "889df197-6652-4d50-c00b-f0724a3284b7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'numpy.ndarray'>\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = np.array([1,2,3])\n",
        "print(type(x))\n",
        "x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wSq0KoAZzWaS"
      },
      "source": [
        "`array.shape` is type as array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oaVTqCxyzVnt",
        "outputId": "26ddbf50-b74e-4264-9f52-f487b1b071c5"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qg2PYQhGj01C"
      },
      "source": [
        "where (3,) indicates that it is a 3-dimensional (three-element) vector."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VBRtfXJL3am2",
        "outputId": "6f254302-bb2f-4833-c7c0-33d05ff9e7d7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0., 0., 0.])"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.zeros(3,) # np.zeros(array type) creates an array with all 0's"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ce91xfUX3beg"
      },
      "source": [
        "matrix of $A = \\begin{bmatrix}1&2&3&4\\\\2&3&4&5\\\\3&4&5&6\\end{bmatrix}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kUJ5qTpPjAXE",
        "outputId": "629e7a46-e0d5-4c10-aff5-e1667351ad60"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(3, 4)\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3, 4],\n",
              "       [2, 3, 4, 5],\n",
              "       [3, 4, 5, 6]])"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "aa = np.array([[1,2,3,4],\n",
        "               [2,3,4,5],\n",
        "               [3,4,5,6]])\n",
        "print(aa.shape)\n",
        "aa"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gHhNjYFU0DgN"
      },
      "source": [
        "The way to refer to a value is the same as for a list.\n",
        "The following two lines refer to the same thing."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R_ktanJ-z1dI",
        "outputId": "d036d9e7-c40f-4d58-fba0-d5e965319bd9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "2\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "print(aa[0][1])\n",
        "aa[0,1]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uBAHlBDO2dyO"
      },
      "source": [
        "Unlike lists, arrays must be rectangular."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LSJafq9ZcQ8R",
        "outputId": "fbd2a419-2d0a-4c29-93e6-fdcc1420653f"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ]
        }
      ],
      "source": [
        "a = np.array([[1,2],[3]])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aOlkSikSvD75"
      },
      "source": [
        "## Calculating NumPy arrays\n",
        "\n",
        "Basically, it is the same as computing a matrix. For example\n",
        "$$\\begin{bmatrix}1&2&3\\\\4&5&6\\end{bmatrix}\n",
        "+\\begin{bmatrix}1&1&1\\\\2&2&2\\end{bmatrix}\n",
        "\\quad \\left(=\n",
        "\\begin{bmatrix}2&3&4\\\\6&7&8\\end{bmatrix}\\right)$$\n",
        "can be written as follows."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PIvXK9kokO2Z",
        "outputId": "85ce4711-3b58-4830-8757-b1a899242c7a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2, 3, 4],\n",
              "       [6, 7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "x = np.array([[1,2,3],\n",
        "              [4,5,6]])\n",
        "y = np.array([[1,1,1],\n",
        "              [2,2,2]])\n",
        "\n",
        "x + y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-XhUV4rzDRNo"
      },
      "source": [
        "x * y is a multiplication of the components."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6QA5AdXdDRqn",
        "outputId": "aecda757-98eb-4834-b2c0-3a5f28dd6109"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3],\n",
              "       [ 8, 10, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "x * y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ewhTiLOQv8jm"
      },
      "source": [
        "Scalar multiplication is performed using \"*\", the same as for ordinary multiplication."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aH_l03XSvura",
        "outputId": "43078dea-f464-453d-a61d-947d08c1440b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2,  4,  6],\n",
              "       [ 8, 10, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "2 * x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4LFlDHGY84xe"
      },
      "source": [
        "product of matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W4Su3Fhf85Bs",
        "outputId": "37936d1f-5082-4630-94d3-212dddd6d155"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 6, 12],\n",
              "       [15, 30]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "np.dot(x, y.T) # y.T is the transpose of y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hd3lTwfUwxVc"
      },
      "source": [
        "**Unlike what you normally learn in linear algebra**, you can also add scalars.\n",
        "The scaler is added to all the components.\n",
        "$$\\begin{bmatrix}1&2&3\\\\4&5&6\\end{bmatrix} + 2\n",
        "= \\begin{bmatrix}3&4&5\\\\6&7&8\\end{bmatrix}\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PwBCfPzNv6hd",
        "outputId": "fe56c247-8946-4700-eac7-21dbaa4cb35c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3, 4, 5],\n",
              "       [6, 7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "x + 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8rEA2UjYw658"
      },
      "source": [
        "The feature of applying a function to all elements in this way is called **Broadcast**.\n",
        "\n",
        "Broadcast can be used with many NumPy functions in addition to adding scalars. For example, `np.sin()` applies the sine function to all components."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oh_ewQGkw5xg",
        "outputId": "be390f62-ad14-447c-f0ef-2ed16b0afb6c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.84147098,  0.90929743,  0.14112001],\n",
              "       [-0.7568025 , -0.95892427, -0.2794155 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "np.sin(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GQtlncO8DVHM"
      },
      "source": [
        "Also, > and == return a boolean value (True = 1, False = 0) for each element, which can also be broadcasted."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nB3yo3ptDVzS",
        "outputId": "b70b7bcf-224b-4868-d7f6-964e940e9c0b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[False False  True]\n",
            " [ True  True  True]]\n",
            "[[False False  True]\n",
            " [False False False]]\n"
          ]
        }
      ],
      "source": [
        "print(x>2)\n",
        "print(x==3)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "37jcwiEQ9LSp"
      },
      "source": [
        "## Statistic"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rq1G4rikCofA"
      },
      "source": [
        "Maximum values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2dUQcEs59RDq",
        "outputId": "138c9d52-c07a-40e9-9532-8765a2db7685"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]]\n",
            "6\n",
            "6\n"
          ]
        }
      ],
      "source": [
        "print(x)\n",
        "\n",
        "# The following two lines both return the maximum value of the array\n",
        "print(np.max(x))\n",
        "print(x.max())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IHAIxF1H9qy-",
        "outputId": "1870287e-7951-47e5-edd4-2d6007ce3d8c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[4 5 6]\n",
            "[3 6]\n"
          ]
        }
      ],
      "source": [
        "#maximum value for the 0th index\n",
        "print(np.max(x, axis =0))\n",
        "\n",
        "#maximum value for the first index\n",
        "print(x.max(axis =1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jupOcqJ0-_Rm"
      },
      "source": [
        "Index that takes the maximum value"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LfJ24Y_C_DwP",
        "outputId": "8c8165a8-da48-40d9-cbb6-5254f16d2f0e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "5\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "array([1, 1, 1])"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "print(x.argmax()) # Returns the index of the entire as a first order array.\n",
        "x.argmax(axis = 0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zYS87z3G-JXh"
      },
      "source": [
        "sum"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sp30I7TX-JXs",
        "outputId": "607c74f3-8760-449a-b75a-bc21b12d22a5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "21\n",
            "21\n"
          ]
        }
      ],
      "source": [
        "# The following two lines both return the sum of the array components\n",
        "print(np.sum(x))\n",
        "print(x.sum())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6sKI7pQt-JX3",
        "outputId": "122d003d-4f0d-44ac-9fad-46caab061f08"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[5 7 9]\n",
            "[ 6 15]\n"
          ]
        }
      ],
      "source": [
        "# 第0インデックスに関する和\n",
        "print(np.sum(x, axis =0))\n",
        "\n",
        "#第1インデックスに関する和\n",
        "print(x.sum(axis =1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8RVQCM5K-gY4"
      },
      "source": [
        "Mean, variance, and standard deviation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ExkggfxP-lrO",
        "outputId": "e2d7a526-b244-47b0-c911-c038b5bf47ef"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[2.5 3.5 4.5]\n",
            "[2.25 2.25 2.25]\n",
            "[1.5 1.5 1.5]\n"
          ]
        }
      ],
      "source": [
        "print( x.mean(axis = 0) )\n",
        "print( x.var(axis = 0) )\n",
        "print( x.std(axis = 0) )"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EJtmM2ujHIY7"
      },
      "source": [
        "## Matplotlib\n",
        "\n",
        "Matplotlib is a Python library for drawing, and pyplot is a module (i.e., a subset of the library) of Matplotlib for drawing graphs.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 684
        },
        "id": "khWGY7kU_AaH",
        "outputId": "f14b3432-876a-43b9-f636-318e326138f8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x =  [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.  1.1 1.2 1.3 1.4 1.5 1.6 1.7\n",
            " 1.8 1.9 2.  2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.  3.1 3.2 3.3 3.4 3.5\n",
            " 3.6 3.7 3.8 3.9 4.  4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.  5.1 5.2 5.3\n",
            " 5.4 5.5 5.6 5.7 5.8 5.9]\n",
            "y =  [ 0.          0.09983342  0.19866933  0.29552021  0.38941834  0.47942554\n",
            "  0.56464247  0.64421769  0.71735609  0.78332691  0.84147098  0.89120736\n",
            "  0.93203909  0.96355819  0.98544973  0.99749499  0.9995736   0.99166481\n",
            "  0.97384763  0.94630009  0.90929743  0.86320937  0.8084964   0.74570521\n",
            "  0.67546318  0.59847214  0.51550137  0.42737988  0.33498815  0.23924933\n",
            "  0.14112001  0.04158066 -0.05837414 -0.15774569 -0.2555411  -0.35078323\n",
            " -0.44252044 -0.52983614 -0.61185789 -0.68776616 -0.7568025  -0.81827711\n",
            " -0.87157577 -0.91616594 -0.95160207 -0.97753012 -0.993691   -0.99992326\n",
            " -0.99616461 -0.98245261 -0.95892427 -0.92581468 -0.88345466 -0.83226744\n",
            " -0.77276449 -0.70554033 -0.63126664 -0.55068554 -0.46460218 -0.37387666]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x = np.arange(0, 6, 0.1) # Generate array of 0.1 increments from 0 to 6\n",
        "y = np.sin(x) # Broadcast sin() to all components of array x\n",
        "\n",
        "print('x = ',x)\n",
        "print('y = ',y)\n",
        "\n",
        "plt.plot(x,y)\n",
        "\n",
        "plt.show()# instruction to display (works without, but also displays extra information)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "DzoZoQalItua",
        "outputId": "ac73aa53-ca5d-474f-cb9e-7ce6d17566e6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "y1 = np.sin(x)\n",
        "y2 = np.cos(x)\n",
        "\n",
        "plt.plot(x,y1, label='sin')\n",
        "plt.plot(x,y2, label='cos', linestyle= '--')\n",
        "plt.legend() # Display descriptions for graphs\n",
        "\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.8.8"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}