Lab1_Tutorial.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BJrnAnEr7nu_",
        "colab_type": "text"
      },
      "source": [
        "# Getting started with Google Colab, Python, and Numpy\n",
        "This tutorial is inspired by the following online tutorials:\n",
        "\n",
        "*   https://towardsdatascience.com/getting-started-with-google-colab-f2fff97f594c\n",
        "*   http://cs231n.github.io/python-numpy-tutorial/\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-FGd6_PK8-JG",
        "colab_type": "text"
      },
      "source": [
        "##Google Colab"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4VawkdKv9DO2",
        "colab_type": "text"
      },
      "source": [
        "Google Colab is a free cloud service based on Jupyter Notebooks that supports free GPU. Not only is this a great tool for improving your coding skills, but it also allows absolutely anyone to develop deep learning applications using popular libraries such as PyTorch, TensorFlow, Keras, and OpenCV.\n",
        "\n",
        "###Setting up your drive\n",
        "If you don't already have a Gmail account, you need to create one. Then go to your [Google Drive](https://drive.google.com/drive/my-drive) and create a folder for your notebooks. You can do that by clicking “New” and then creating a new folder.\n",
        "\n",
        "![alt text](https://cdn-images-1.medium.com/max/1600/1*Rp17M-6CBfynldko2V4jmg.png)\n",
        "\n",
        "###Creating a new notebook\n",
        "If you want, while you’re already in your Google Drive you can create a new Colab notebook. Just click “New” and drop the menu down to “More” and then select “Colaboratory.”\n",
        "\n",
        "![alt text](https://cdn-images-1.medium.com/max/1600/1*SJfgGypNyhpAfNDBNA7eDg.png)\n",
        "\n",
        "Otherwise, you can always go directly to [Google Colab](https://colab.research.google.com/).\n",
        "\n",
        "You can rename your notebook by clicking on the name of the notebook and changing it or by dropping the “File” menu down to “Rename.”\n",
        "\n",
        "![alt text](https://cdn-images-1.medium.com/max/1600/1*LziarBuysU5ZpwdaWUdnBQ.png)\n",
        "\n",
        "###Set up your free GPU\n",
        "To enable GPU go to the “runtime” dropdown menu, select “change runtime type” and select GPU in the hardware accelerator drop-down menu.\n",
        "\n",
        "![alt text](https://cdn-images-1.medium.com/max/1600/1*7du2-qMemro5nvxnePNuKQ.png)\n",
        "\n",
        "###Before you proceed\n",
        "This notebook is read-only. To proceed **you must make a copy in your Google Drive**. To do this, select \"Save a copy in Drive\" in the File menu.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bioIWtxpAAu2",
        "colab_type": "text"
      },
      "source": [
        "###How to run code\n",
        "Notebooks consist of text blocks and code blocks. This is a **text block**.\n",
        "\n",
        "The block below is a **code block**. To run the code block, either click the Play button (left side) or simply press Shift-Enter."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TsrF6etMAZrV",
        "colab_type": "code",
        "outputId": "a34982ce-dd1c-495f-b3b3-82ae93ab94fa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(\"Hello world!\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Hello world!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s_pawSeaBMzf",
        "colab_type": "text"
      },
      "source": [
        "###Mounting your Google Drive folder\n",
        "At some point during the course you will want to mount your Google Drive:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bqdHYjb-BkJW",
        "colab_type": "code",
        "outputId": "ece4aaac-febe-4557-f3e7-aa16446d964c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 128
        }
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Go to this URL in a browser: https://accounts.google.com/o/oauth2/auth?client_id=947318989803-6bn6qk8qdgf4n4g3pfee6491hc0brc4i.apps.googleusercontent.com&redirect_uri=urn%3Aietf%3Awg%3Aoauth%3A2.0%3Aoob&scope=email%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fdocs.test%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fdrive%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fdrive.photos.readonly%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fpeopleapi.readonly&response_type=code\n",
            "\n",
            "Enter your authorization code:\n",
            "··········\n",
            "Mounted at /content/gdrive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hCjdk5q7Bzl_",
        "colab_type": "text"
      },
      "source": [
        "You’ll see a link. Click on that, allow access, copy the code that pops up, paste it in the box, hit enter, and you’re good to go. If you don’t see your drive in the side box on the left, just hit “refresh” and it should show up.\n",
        "\n",
        "It should look something like this:\n",
        "\n",
        "![alt text](https://cdn-images-1.medium.com/max/1600/1*VrRLOThfoTpy_2ruTzV3yg.png)\n",
        "\n",
        "Now you can see your drive right there on the left-hand side of the screen! (You may need to hit “refresh.”) Plus, you can reach your drive any time with"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jcMfKlxYCLm0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!ls \"/content/gdrive/My Drive/\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R4ZDe2rVHKUp",
        "colab_type": "text"
      },
      "source": [
        "##Python\n",
        "Python is a high-level, dynamically typed multiparadigm programming language. Python code is often said to be almost like pseudocode, since it allows you to express very powerful ideas in very few lines of code while being very readable.\n",
        "\n",
        "There are currently two different supported versions of Python, 2 and 3. Somewhat confusingly, Python 3 introduced many backwards-incompatible changes to the language, so code written for 2 may not work under 3 and vice versa. For this class all code will use Python 3.\n",
        "\n",
        "You can check your Python version at the command line by running"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xpGIxaQnHq4f",
        "colab_type": "code",
        "outputId": "bc8d4626-899e-48a9-95fc-c8d5e558e1f8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "!python --version"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Python 3.6.8\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8oRzYDp4H1Qg",
        "colab_type": "text"
      },
      "source": [
        "###Basic data types\n",
        "Like most languages, Python has a number of basic types including integers, floats, booleans, and strings. These data types behave in ways that are familiar from other programming languages.\n",
        "\n",
        "**Numbers:** Integers and floats work as you would expect from other languages:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lnh721pNH9_v",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = 3\n",
        "print(type(x)) # Prints \"<class 'int'>\"\n",
        "print(x)       # Prints \"3\"\n",
        "print(x + 1)   # Addition; prints \"4\"\n",
        "print(x - 1)   # Subtraction; prints \"2\"\n",
        "print(x * 2)   # Multiplication; prints \"6\"\n",
        "print(x ** 2)  # Exponentiation; prints \"9\"\n",
        "x += 1\n",
        "print(x)  # Prints \"4\"\n",
        "x *= 2\n",
        "print(x)  # Prints \"8\"\n",
        "y = 2.5\n",
        "print(type(y)) # Prints \"<class 'float'>\"\n",
        "print(y, y + 1, y * 2, y ** 2) # Prints \"2.5 3.5 5.0 6.25\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VrTwnHLOIJQH",
        "colab_type": "text"
      },
      "source": [
        "Note that unlike many languages, Python does not have unary increment (x++) or decrement (x--) operators.\n",
        "\n",
        "**Booleans:** Python implements all of the usual operators for Boolean logic, but uses English words rather than symbols (&&, ||, etc.):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vn7mihFIIAgf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "t = True\n",
        "f = False\n",
        "print(type(t)) # Prints \"<class 'bool'>\"\n",
        "print(t and f) # Logical AND; prints \"False\"\n",
        "print(t or f)  # Logical OR; prints \"True\"\n",
        "print(not t)   # Logical NOT; prints \"False\"\n",
        "print(t != f)  # Logical XOR; prints \"True\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FvR2ZYHEIeeu",
        "colab_type": "text"
      },
      "source": [
        "**Strings:** Python has great support for strings:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ydLGSfMdIa1H",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "hello = 'hello'    # String literals can use single quotes\n",
        "world = \"world\"    # or double quotes; it does not matter.\n",
        "print(hello)       # Prints \"hello\"\n",
        "print(len(hello))  # String length; prints \"5\"\n",
        "hw = hello + ' ' + world  # String concatenation\n",
        "print(hw)  # prints \"hello world\"\n",
        "hw12 = '%s %s %d' % (hello, world, 12)  # sprintf style string formatting\n",
        "print(hw12)  # prints \"hello world 12\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V9Ra5oepIoJn",
        "colab_type": "text"
      },
      "source": [
        "String objects have a bunch of useful methods; for example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TIqDgbJTIjE-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "s = \"hello\"\n",
        "print(s.capitalize())  # Capitalize a string; prints \"Hello\"\n",
        "print(s.upper())       # Convert a string to uppercase; prints \"HELLO\"\n",
        "print(s.rjust(7))      # Right-justify a string, padding with spaces; prints \"  hello\"\n",
        "print(s.center(7))     # Center a string, padding with spaces; prints \" hello \"\n",
        "print(s.replace('l', '(ell)'))  # Replace all instances of one substring with another;\n",
        "                                # prints \"he(ell)(ell)o\"\n",
        "print('  world '.strip())  # Strip leading and trailing whitespace; prints \"world\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xE0VnvizIz3u",
        "colab_type": "text"
      },
      "source": [
        "###Containers\n",
        "Python includes several built-in container types: lists, dictionaries, sets, and tuples.\n",
        "\n",
        "**Lists:** A list is the Python equivalent of an array, but is resizeable and can contain elements of different types:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E7B_toQGIqsX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "xs = [3, 1, 2]    # Create a list\n",
        "print(xs, xs[2])  # Prints \"[3, 1, 2] 2\"\n",
        "print(xs[-1])     # Negative indices count from the end of the list; prints \"2\"\n",
        "xs[2] = 'foo'     # Lists can contain elements of different types\n",
        "print(xs)         # Prints \"[3, 1, 'foo']\"\n",
        "xs.append('bar')  # Add a new element to the end of the list\n",
        "print(xs)         # Prints \"[3, 1, 'foo', 'bar']\"\n",
        "x = xs.pop()      # Remove and return the last element of the list\n",
        "print(x, xs)      # Prints \"bar [3, 1, 'foo']\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HHRwsD4DI9LW",
        "colab_type": "text"
      },
      "source": [
        "**Slicing:** In addition to accessing list elements one at a time, Python provides concise syntax to access sublists; this is known as slicing:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yQCkW-esI6X3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "nums = list(range(5))     # range is a built-in function that creates a list of integers\n",
        "print(nums)               # Prints \"[0, 1, 2, 3, 4]\"\n",
        "print(nums[2:4])          # Get a slice from index 2 to 4 (exclusive); prints \"[2, 3]\"\n",
        "print(nums[2:])           # Get a slice from index 2 to the end; prints \"[2, 3, 4]\"\n",
        "print(nums[:2])           # Get a slice from the start to index 2 (exclusive); prints \"[0, 1]\"\n",
        "print(nums[:])            # Get a slice of the whole list; prints \"[0, 1, 2, 3, 4]\"\n",
        "print(nums[:-1])          # Slice indices can be negative; prints \"[0, 1, 2, 3]\"\n",
        "nums[2:4] = [8, 9]        # Assign a new sublist to a slice\n",
        "print(nums)               # Prints \"[0, 1, 8, 9, 4]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8urcnDqnJGSH",
        "colab_type": "text"
      },
      "source": [
        "We will see slicing again in the context of numpy arrays.\n",
        "\n",
        "**Loops:** You can loop over the elements of a list like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8cxRTpmIJC9v",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "animals = ['cat', 'dog', 'monkey']\n",
        "for animal in animals:\n",
        "    print(animal)\n",
        "# Prints \"cat\", \"dog\", \"monkey\", each on its own line."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mEFB2Pf_JLIn",
        "colab_type": "text"
      },
      "source": [
        "**The indentation is important:** It defines blocks of code. That is, lines of code with the same indentation belong to the same block. You can use either tabs or spaces for indentation, but you cannot use both within the same block. Don't worry, you will get used to it ;-)\n",
        "\n",
        "If you want access to the index of each element within the body of a loop, use the built-in enumerate function:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8B2xz1_5JIuX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "animals = ['cat', 'dog', 'monkey']\n",
        "for idx, animal in enumerate(animals):\n",
        "    print('#%d: %s' % (idx + 1, animal))\n",
        "# Prints \"#1: cat\", \"#2: dog\", \"#3: monkey\", each on its own line"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MU1_TlNOlcH6",
        "colab_type": "text"
      },
      "source": [
        "There is of course also the good old-fashioned way:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RiAtErgIll9D",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "animals = ['cat', 'dog', 'monkey']\n",
        "for idx in range(len(animals)):\n",
        "    animal = animals[idx]  \n",
        "    print('#%d: %s' % (idx + 1, animal))\n",
        "# Prints \"#1: cat\", \"#2: dog\", \"#3: monkey\", each on its own line"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B7gPBFLGJPw9",
        "colab_type": "text"
      },
      "source": [
        "**List comprehensions:** When programming, frequently we want to transform one type of data into another. As a simple example, consider the following code that computes square numbers:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tVD2kYDsJNQR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "squares = []\n",
        "for x in nums:\n",
        "    squares.append(x ** 2)\n",
        "print(squares)   # Prints [0, 1, 4, 9, 16]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qt053rYGJWwt",
        "colab_type": "text"
      },
      "source": [
        "You can make this code simpler using a **list comprehension**:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5tH-3pZXJVgv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "squares = [x ** 2 for x in nums]\n",
        "print(squares)   # Prints [0, 1, 4, 9, 16]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ff-eXek_Jc8m",
        "colab_type": "text"
      },
      "source": [
        "**Dictionaries:** A dictionary stores (key, value) pairs, similar to a Map in Java or an object in Javascript. You can use it like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zl3sSbxXJbQO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "d = {'cat': 'cute', 'dog': 'furry'}  # Create a new dictionary with some data\n",
        "print(d['cat'])       # Get an entry from a dictionary; prints \"cute\"\n",
        "print('cat' in d)     # Check if a dictionary has a given key; prints \"True\"\n",
        "d['fish'] = 'wet'     # Set an entry in a dictionary\n",
        "print(d['fish'])      # Prints \"wet\"\n",
        "# print(d['monkey'])  # KeyError: 'monkey' not a key of d\n",
        "print(d.get('monkey', 'N/A'))  # Get an element with a default; prints \"N/A\"\n",
        "print(d.get('fish', 'N/A'))    # Get an element with a default; prints \"wet\"\n",
        "del d['fish']         # Remove an element from a dictionary\n",
        "print(d.get('fish', 'N/A')) # \"fish\" is no longer a key; prints \"N/A\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ds3RtELlJnKH",
        "colab_type": "text"
      },
      "source": [
        "**Loops:** It is easy to iterate over the keys in a dictionary:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zTKmnBWJJkPw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "d = {'person': 2, 'cat': 4, 'spider': 8}\n",
        "for animal in d:\n",
        "    legs = d[animal]\n",
        "    print('A %s has %d legs' % (animal, legs))\n",
        "# Prints \"A person has 2 legs\", \"A cat has 4 legs\", \"A spider has 8 legs\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "boDZUymqJuOm",
        "colab_type": "text"
      },
      "source": [
        "If you want access to keys and their corresponding values, use the items method:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b9gKsgs8Jran",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "even_num_to_square = {x: x ** 2 for x in nums if x % 2 == 0}\n",
        "print(even_num_to_square)  # Prints \"{0: 0, 2: 4, 4: 16}\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1KRIDdGSJ36W",
        "colab_type": "text"
      },
      "source": [
        "**Tuples:** A tuple is an (immutable) ordered list of values. A tuple is in many ways similar to a list; one of the most important differences is that tuples can be used as keys in dictionaries and as elements of sets, while lists cannot. Here is a trivial example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HsOsWs21JyK3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "d = {(x, x + 1): x for x in range(10)}  # Create a dictionary with tuple keys\n",
        "t = (5, 6)        # Create a tuple\n",
        "print(type(t))    # Prints \"<class 'tuple'>\"\n",
        "print(d[t])       # Prints \"5\"\n",
        "print(d[(1, 2)])  # Prints \"1\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O2XE6JYNKdgH",
        "colab_type": "text"
      },
      "source": [
        "###Functions\n",
        "Python functions are defined using the def keyword. For example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PVzN64-gJ60v",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sign(x):\n",
        "    if x > 0:\n",
        "        return 'positive'\n",
        "    elif x < 0:\n",
        "        return 'negative'\n",
        "    else:\n",
        "        return 'zero'\n",
        "\n",
        "for x in [-1, 0, 1]:\n",
        "    print(sign(x))\n",
        "# Prints \"negative\", \"zero\", \"positive\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7txkZNgeKn5F",
        "colab_type": "text"
      },
      "source": [
        "We will often define functions to take optional keyword arguments, like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CHIli5aDKmRY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def hello(name, loud=False):\n",
        "    if loud:\n",
        "        print('HELLO, %s!' % name.upper())\n",
        "    else:\n",
        "        print('Hello, %s' % name)\n",
        "\n",
        "hello('Bob') # Prints \"Hello, Bob\"\n",
        "hello('Fred', loud=True)  # Prints \"HELLO, FRED!\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0k7NUMeRKzZ9",
        "colab_type": "text"
      },
      "source": [
        "###Classes\n",
        "The syntax for defining classes in Python is straightforward:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sgzDbYBuKu0e",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Greeter(object):\n",
        "\n",
        "    # Constructor\n",
        "    def __init__(self, name):\n",
        "        self.name = name  # Create an instance variable\n",
        "\n",
        "    # Instance method\n",
        "    def greet(self, loud=False):\n",
        "        if loud:\n",
        "            print('HELLO, %s!' % self.name.upper())\n",
        "        else:\n",
        "            print('Hello, %s' % self.name)\n",
        "\n",
        "g = Greeter('Fred')  # Construct an instance of the Greeter class\n",
        "g.greet()            # Call an instance method; prints \"Hello, Fred\"\n",
        "g.greet(loud=True)   # Call an instance method; prints \"HELLO, FRED!\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2IyWpwOOLF89",
        "colab_type": "text"
      },
      "source": [
        "##Numpy\n",
        "Numpy is the core library for scientific computing in Python. It provides a high-performance multidimensional array object, and tools for working with these arrays.\n",
        "\n",
        "###Arrays\n",
        "A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers. The number of dimensions is the rank of the array; the shape of an array is a tuple of integers giving the size of the array along each dimension.\n",
        "\n",
        "We can initialize numpy arrays from nested Python lists, and access elements using square brackets:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s9o1RorzK2Y_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "a = np.array([1, 2, 3])   # Create a rank 1 array\n",
        "print(type(a))            # Prints \"<class 'numpy.ndarray'>\"\n",
        "print(a.shape)            # Prints \"(3,)\"\n",
        "print(a[0], a[1], a[2])   # Prints \"1 2 3\"\n",
        "a[0] = 5                  # Change an element of the array\n",
        "print(a)                  # Prints \"[5, 2, 3]\"\n",
        "\n",
        "b = np.array([[1,2,3],[4,5,6]])    # Create a rank 2 array\n",
        "print(b.shape)                     # Prints \"(2, 3)\"\n",
        "print(b[0, 0], b[0, 1], b[1, 0])   # Prints \"1 2 4\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L2z4JCPtLWKu",
        "colab_type": "text"
      },
      "source": [
        "Numpy also provides many functions to create arrays:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XYI9NP6JLTlb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a = np.zeros((2,2))   # Create an array of all zeros\n",
        "print(a)              # Prints \"[[ 0.  0.]\n",
        "                      #          [ 0.  0.]]\"\n",
        "\n",
        "b = np.ones((1,2))    # Create an array of all ones\n",
        "print(b)              # Prints \"[[ 1.  1.]]\"\n",
        "\n",
        "c = np.full((2,2), 7)  # Create a constant array\n",
        "print(c)               # Prints \"[[ 7.  7.]\n",
        "                       #          [ 7.  7.]]\"\n",
        "\n",
        "d = np.eye(2)         # Create a 2x2 identity matrix\n",
        "print(d)              # Prints \"[[ 1.  0.]\n",
        "                      #          [ 0.  1.]]\"\n",
        "\n",
        "e = np.random.random((2,2))  # Create an array filled with random values\n",
        "print(e)                     # Might print \"[[ 0.91940167  0.08143941]\n",
        "                             #               [ 0.68744134  0.87236687]]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FeZINNwbLdou",
        "colab_type": "text"
      },
      "source": [
        "###Array indexing\n",
        "Numpy offers several ways to index into arrays.\n",
        "\n",
        "**Slicing:** Similar to Python lists, numpy arrays can be sliced. Since arrays may be multidimensional, you must specify a slice for each dimension of the array:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fvl9FwslLZcv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Create the following rank 2 array with shape (3, 4)\n",
        "# [[ 1  2  3  4]\n",
        "#  [ 5  6  7  8]\n",
        "#  [ 9 10 11 12]]\n",
        "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
        "\n",
        "# Use slicing to pull out the subarray consisting of the first 2 rows\n",
        "# and columns 1 and 2; b is the following array of shape (2, 2):\n",
        "# [[2 3]\n",
        "#  [6 7]]\n",
        "b = a[:2, 1:3]\n",
        "\n",
        "# A slice of an array is a view into the same data, so modifying it\n",
        "# will modify the original array.\n",
        "print(a[0, 1])   # Prints \"2\"\n",
        "b[0, 0] = 77     # b[0, 0] is the same piece of data as a[0, 1]\n",
        "print(a[0, 1])   # Prints \"77\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPHBRKLWLpoG",
        "colab_type": "text"
      },
      "source": [
        "You can also mix integer indexing with slice indexing. However, doing so will yield an array of lower rank than the original array:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_r3eWleMLjy3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Create the following rank 2 array with shape (3, 4)\n",
        "# [[ 1  2  3  4]\n",
        "#  [ 5  6  7  8]\n",
        "#  [ 9 10 11 12]]\n",
        "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
        "\n",
        "# Two ways of accessing the data in the middle row of the array.\n",
        "# Mixing integer indexing with slices yields an array of lower rank,\n",
        "# while using only slices yields an array of the same rank as the\n",
        "# original array:\n",
        "row_r1 = a[1, :]    # Rank 1 view of the second row of a\n",
        "row_r2 = a[1:2, :]  # Rank 2 view of the second row of a\n",
        "print(row_r1, row_r1.shape)  # Prints \"[5 6 7 8] (4,)\"\n",
        "print(row_r2, row_r2.shape)  # Prints \"[[5 6 7 8]] (1, 4)\"\n",
        "\n",
        "# We can make the same distinction when accessing columns of an array:\n",
        "col_r1 = a[:, 1]\n",
        "col_r2 = a[:, 1:2]\n",
        "print(col_r1, col_r1.shape)  # Prints \"[ 2  6 10] (3,)\"\n",
        "print(col_r2, col_r2.shape)  # Prints \"[[ 2]\n",
        "                             #          [ 6]\n",
        "                             #          [10]] (3, 1)\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2vhUALs-LyOe",
        "colab_type": "text"
      },
      "source": [
        "**Integer array indexing:** When you index into numpy arrays using slicing, the resulting array view will always be a subarray of the original array. In contrast, integer array indexing allows you to construct arbitrary arrays using the data from another array. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QKO_27_RLu5_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a = np.array([[1,2], [3, 4], [5, 6]])\n",
        "\n",
        "# An example of integer array indexing.\n",
        "# The returned array will have shape (3,) and\n",
        "print(a[[0, 1, 2], [0, 1, 0]])  # Prints \"[1 4 5]\"\n",
        "\n",
        "# The above example of integer array indexing is equivalent to this:\n",
        "print(np.array([a[0, 0], a[1, 1], a[2, 0]]))  # Prints \"[1 4 5]\"\n",
        "\n",
        "# When using integer array indexing, you can reuse the same\n",
        "# element from the source array:\n",
        "print(a[[0, 0], [1, 1]])  # Prints \"[2 2]\"\n",
        "\n",
        "# Equivalent to the previous integer array indexing example\n",
        "print(np.array([a[0, 1], a[0, 1]]))  # Prints \"[2 2]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mikKxD5pL3nW",
        "colab_type": "text"
      },
      "source": [
        "One useful trick with integer array indexing is selecting or mutating one element from each row of a matrix:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9amg_dAuL1bw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Create a new array from which we will select elements\n",
        "a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
        "\n",
        "print(a)  # prints \"array([[ 1,  2,  3],\n",
        "          #                [ 4,  5,  6],\n",
        "          #                [ 7,  8,  9],\n",
        "          #                [10, 11, 12]])\"\n",
        "\n",
        "# Create an array of indices\n",
        "b = np.array([0, 2, 0, 1])\n",
        "\n",
        "# Select one element from each row of a using the indices in b\n",
        "print(a[np.arange(4), b])  # Prints \"[ 1  6  7 11]\"\n",
        "\n",
        "# Mutate one element from each row of a using the indices in b\n",
        "a[np.arange(4), b] += 10\n",
        "\n",
        "print(a)  # prints \"array([[11,  2,  3],\n",
        "          #                [ 4,  5, 16],\n",
        "          #                [17,  8,  9],\n",
        "          #                [10, 21, 12]])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RG8cQrgXL94O",
        "colab_type": "text"
      },
      "source": [
        "**Boolean array indexing:** Boolean array indexing lets you pick out arbitrary elements of an array. Frequently this type of indexing is used to select the elements of an array that satisfy some condition. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3hkCqWyZL53A",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a = np.array([[1,2], [3, 4], [5, 6]])\n",
        "\n",
        "bool_idx = (a > 2)   # Find the elements of a that are bigger than 2;\n",
        "                     # this returns a numpy array of Booleans of the same\n",
        "                     # shape as a, where each slot of bool_idx tells\n",
        "                     # whether that element of a is > 2.\n",
        "\n",
        "print(bool_idx)      # Prints \"[[False False]\n",
        "                     #          [ True  True]\n",
        "                     #          [ True  True]]\"\n",
        "\n",
        "# We use boolean array indexing to construct a rank 1 array\n",
        "# consisting of the elements of a corresponding to the True values\n",
        "# of bool_idx\n",
        "print(a[bool_idx])  # Prints \"[3 4 5 6]\"\n",
        "\n",
        "# We can do all of the above in a single concise statement:\n",
        "print(a[a > 2])     # Prints \"[3 4 5 6]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "68KTBZCuMHWO",
        "colab_type": "text"
      },
      "source": [
        "###Datatypes\n",
        "Every numpy array is a grid of elements of the same type. Numpy provides a large set of numeric datatypes that you can use to construct arrays. Numpy tries to guess a datatype when you create an array, but functions that construct arrays usually also include an optional argument to explicitly specify the datatype. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8MbwWL2_MCL3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.array([1, 2])   # Let numpy choose the datatype\n",
        "print(x.dtype)         # Prints \"int64\"\n",
        "\n",
        "x = np.array([1.0, 2.0])   # Let numpy choose the datatype\n",
        "print(x.dtype)             # Prints \"float64\"\n",
        "\n",
        "x = np.array([1, 2], dtype=np.int64)   # Force a particular datatype\n",
        "print(x.dtype)                         # Prints \"int64\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PNS3LfqgMOAG",
        "colab_type": "text"
      },
      "source": [
        "###Array math\n",
        "Basic mathematical functions operate elementwise on arrays, and are available both as operator overloads and as functions in the numpy module:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PHrc1XjJMLgY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.array([[1,2],[3,4]], dtype=np.float64)\n",
        "y = np.array([[5,6],[7,8]], dtype=np.float64)\n",
        "\n",
        "# Elementwise sum; both produce the array\n",
        "# [[ 6.0  8.0]\n",
        "#  [10.0 12.0]]\n",
        "print(x + y)\n",
        "print(np.add(x, y))\n",
        "\n",
        "# Elementwise difference; both produce the array\n",
        "# [[-4.0 -4.0]\n",
        "#  [-4.0 -4.0]]\n",
        "print(x - y)\n",
        "print(np.subtract(x, y))\n",
        "\n",
        "# Elementwise product; both produce the array\n",
        "# [[ 5.0 12.0]\n",
        "#  [21.0 32.0]]\n",
        "print(x * y)\n",
        "print(np.multiply(x, y))\n",
        "\n",
        "# Elementwise division; both produce the array\n",
        "# [[ 0.2         0.33333333]\n",
        "#  [ 0.42857143  0.5       ]]\n",
        "print(x / y)\n",
        "print(np.divide(x, y))\n",
        "\n",
        "# Elementwise square root; produces the array\n",
        "# [[ 1.          1.41421356]\n",
        "#  [ 1.73205081  2.        ]]\n",
        "print(np.sqrt(x))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QcxjxMR6MX7-",
        "colab_type": "text"
      },
      "source": [
        "Note that unlike MATLAB, * is elementwise multiplication, not matrix multiplication. We instead use the dot function to compute inner products of vectors, to multiply a vector by a matrix, and to multiply matrices. dot is available both as a function in the numpy module and as an instance method of array objects:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vWUN4Q57MTEv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.array([[1,2],[3,4]])\n",
        "y = np.array([[5,6],[7,8]])\n",
        "\n",
        "v = np.array([9,10])\n",
        "w = np.array([11, 12])\n",
        "\n",
        "# Inner product of vectors; both produce 219\n",
        "print(v.dot(w))\n",
        "print(np.dot(v, w))\n",
        "\n",
        "# Matrix / vector product; both produce the rank 1 array [29 67]\n",
        "print(x.dot(v))\n",
        "print(np.dot(x, v))\n",
        "\n",
        "# Matrix / matrix product; both produce the rank 2 array\n",
        "# [[19 22]\n",
        "#  [43 50]]\n",
        "print(x.dot(y))\n",
        "print(np.dot(x, y))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7PUegPOuMd4P",
        "colab_type": "text"
      },
      "source": [
        "Numpy provides many useful functions for performing computations on arrays; one of the most useful is sum:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J2qLBKHQMawY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.array([[1,2],[3,4]])\n",
        "\n",
        "print(np.sum(x))  # Compute sum of all elements; prints \"10\"\n",
        "print(np.sum(x, axis=0))  # Compute sum of each column; prints \"[4 6]\"\n",
        "print(np.sum(x, axis=1))  # Compute sum of each row; prints \"[3 7]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_65bDwT-MjEO",
        "colab_type": "text"
      },
      "source": [
        "Apart from computing mathematical functions using arrays, we frequently need to reshape or otherwise manipulate data in arrays. The simplest example of this type of operation is transposing a matrix; to transpose a matrix, simply use the T attribute of an array object:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jeNHEZUGMgAx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = np.array([[1,2], [3,4]])\n",
        "print(x)    # Prints \"[[1 2]\n",
        "            #          [3 4]]\"\n",
        "print(x.T)  # Prints \"[[1 3]\n",
        "            #          [2 4]]\"\n",
        "\n",
        "# Note that taking the transpose of a rank 1 array does nothing:\n",
        "v = np.array([1,2,3])\n",
        "print(v)    # Prints \"[1 2 3]\"\n",
        "print(v.T)  # Prints \"[1 2 3]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pm-o7tYSMo-e",
        "colab_type": "text"
      },
      "source": [
        "###Broadcasting\n",
        "Broadcasting is a powerful mechanism that allows numpy to work with arrays of different shapes when performing arithmetic operations. Frequently we have a smaller array and a larger array, and we want to use the smaller array multiple times to perform some operation on the larger array.\n",
        "\n",
        "For example, suppose that we want to add a constant vector to each row of a matrix. We could do it like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OZi7KsdhMlvH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# We will add the vector v to each row of the matrix x,\n",
        "# storing the result in the matrix y\n",
        "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
        "v = np.array([1, 0, 1])\n",
        "y = np.empty_like(x)   # Create an empty matrix with the same shape as x\n",
        "\n",
        "# Add the vector v to each row of the matrix x with an explicit loop\n",
        "for i in range(4):\n",
        "    y[i, :] = x[i, :] + v\n",
        "\n",
        "# Now y is the following\n",
        "# [[ 2  2  4]\n",
        "#  [ 5  5  7]\n",
        "#  [ 8  8 10]\n",
        "#  [11 11 13]]\n",
        "print(y)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e9eC0A6yMv9A",
        "colab_type": "text"
      },
      "source": [
        "This works; however when the matrix x is very large, computing an explicit loop in Python could be slow. Note that adding the vector v to each row of the matrix x is equivalent to forming a matrix vv by stacking multiple copies of v vertically, then performing elementwise summation of x and vv. We could implement this approach like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kt6KvuLmMtCH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# We will add the vector v to each row of the matrix x,\n",
        "# storing the result in the matrix y\n",
        "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
        "v = np.array([1, 0, 1])\n",
        "vv = np.tile(v, (4, 1))   # Stack 4 copies of v on top of each other\n",
        "print(vv)                 # Prints \"[[1 0 1]\n",
        "                          #          [1 0 1]\n",
        "                          #          [1 0 1]\n",
        "                          #          [1 0 1]]\"\n",
        "y = x + vv  # Add x and vv elementwise\n",
        "print(y)  # Prints \"[[ 2  2  4\n",
        "          #          [ 5  5  7]\n",
        "          #          [ 8  8 10]\n",
        "          #          [11 11 13]]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jWaRzfEZM2vQ",
        "colab_type": "text"
      },
      "source": [
        "Numpy broadcasting allows us to perform this computation without actually creating multiple copies of v. Consider this version, using broadcasting:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "byf5lgZgMyyv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# We will add the vector v to each row of the matrix x,\n",
        "# storing the result in the matrix y\n",
        "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
        "v = np.array([1, 0, 1])\n",
        "y = x + v  # Add v to each row of x using broadcasting\n",
        "print(y)  # Prints \"[[ 2  2  4]\n",
        "          #          [ 5  5  7]\n",
        "          #          [ 8  8 10]\n",
        "          #          [11 11 13]]\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9RS92ZF8M6k-",
        "colab_type": "text"
      },
      "source": [
        "The line y = x + v works even though x has shape (4, 3) and v has shape (3,) due to broadcasting; this line works as if v actually had shape (4, 3), where each row was a copy of v, and the sum was performed elementwise.\n",
        "\n",
        "Broadcasting two arrays together follows these rules:\n",
        "\n",
        "1.   If the arrays do not have the same rank, prepend the shape of the lower rank array with 1s until both shapes have the same length.\n",
        "2.   The two arrays are said to be compatible in a dimension if they have the same size in the dimension, or if one of the arrays has size 1 in that dimension.\n",
        "3. The arrays can be broadcast together if they are compatible in all dimensions.\n",
        "4. After broadcasting, each array behaves as if it had shape equal to the elementwise maximum of shapes of the two input arrays.\n",
        "5. In any dimension where one array had size 1 and the other array had size greater than 1, the first array behaves as if it were copied along that dimension\n",
        "\n",
        "If this explanation does not make sense, try reading the explanation from the documentation or this explanation.\n",
        "\n",
        "Functions that support broadcasting are known as universal functions. You can find the list of all universal functions in the documentation.\n",
        "\n",
        "Here are some applications of broadcasting:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rgMsiMWfM5Fp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Compute outer product of vectors\n",
        "v = np.array([1,2,3])  # v has shape (3,)\n",
        "w = np.array([4,5])    # w has shape (2,)\n",
        "# To compute an outer product, we first reshape v to be a column\n",
        "# vector of shape (3, 1); we can then broadcast it against w to yield\n",
        "# an output of shape (3, 2), which is the outer product of v and w:\n",
        "# [[ 4  5]\n",
        "#  [ 8 10]\n",
        "#  [12 15]]\n",
        "print(np.reshape(v, (3, 1)) * w)\n",
        "\n",
        "# Add a vector to each row of a matrix\n",
        "x = np.array([[1,2,3], [4,5,6]])\n",
        "# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),\n",
        "# giving the following matrix:\n",
        "# [[2 4 6]\n",
        "#  [5 7 9]]\n",
        "print(x + v)\n",
        "\n",
        "# Add a vector to each column of a matrix\n",
        "# x has shape (2, 3) and w has shape (2,).\n",
        "# If we transpose x then it has shape (3, 2) and can be broadcast\n",
        "# against w to yield a result of shape (3, 2); transposing this result\n",
        "# yields the final result of shape (2, 3) which is the matrix x with\n",
        "# the vector w added to each column. Gives the following matrix:\n",
        "# [[ 5  6  7]\n",
        "#  [ 9 10 11]]\n",
        "print((x.T + w).T)\n",
        "# Another solution is to reshape w to be a column vector of shape (2, 1);\n",
        "# we can then broadcast it directly against x to produce the same\n",
        "# output.\n",
        "print(x + np.reshape(w, (2, 1)))\n",
        "\n",
        "# Multiply a matrix by a constant:\n",
        "# x has shape (2, 3). Numpy treats scalars as arrays of shape ();\n",
        "# these can be broadcast together to shape (2, 3), producing the\n",
        "# following array:\n",
        "# [[ 2  4  6]\n",
        "#  [ 8 10 12]]\n",
        "print(x * 2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-K8zrv-gQTDY",
        "colab_type": "text"
      },
      "source": [
        "##Pillow and Matplotlib\n",
        "Pillow is the standard Python Imaging Library and provides a large number of functions that operate on images.\n",
        "\n",
        "The best way to get familiar with Pillow is to [browse the documentation](https://pillow.readthedocs.io/en/stable/handbook/tutorial.htmll). We will not be using Pillow  a whole lot in this course, but it is still useful to know about it.\n",
        "\n",
        "Pillow provides some basic functions to work with images. For example, it has functions to read images from disk into numpy arrays, to write numpy arrays to disk as images, and to resize images. Here is a simple example that showcases these functions:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0J_8oPTpXr5Z",
        "colab_type": "code",
        "outputId": "e995796a-040d-4745-80f8-c9186d0b59c6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# First download a test image\n",
        "import urllib.request\n",
        "\n",
        "url = \"https://github.com/aivclab/dlcourse/raw/master/data/cat.jpg\"\n",
        "urllib.request.urlretrieve(url,'/content/gdrive/My Drive/cat.jpg')\n",
        "\n",
        "# Check that the file is in your Drive\n",
        "!ls \"/content/gdrive/My Drive/cat.jpg\""
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "'/content/gdrive/My Drive/cat.jpg'\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sHHuJRJUnshZ",
        "colab_type": "text"
      },
      "source": [
        "Note: You may want to use a different folder than /content/gdrive/My Drive/, which the root folder of your Drive. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YODFNoTTQ1AB",
        "colab_type": "code",
        "outputId": "f00e3ab6-9a19-4f91-ddb3-73d75e4c7247",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "from PIL import Image\n",
        "\n",
        "# Read an JPEG image into a numpy array\n",
        "im = Image.open('/content/gdrive/My Drive/cat.jpg')\n",
        "\n",
        "# Convert to numpy array\n",
        "im_np = np.array(im)\n",
        "print(im_np.dtype, im_np.shape)  # Prints \"uint8 (328, 582, 3)\"\n",
        "\n",
        "# Convert numpy array to image\n",
        "im_new = Image.fromarray(im_np)\n",
        "\n",
        "# Resize the tinted image to be 300 by 300 pixels.\n",
        "im_resized = im_new.resize((300, 300))\n",
        "\n",
        "# Write the tinted image back to disk\n",
        "im_resized.save('/content/gdrive/My Drive/cat_new.jpg')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "uint8 (328, 582, 3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CGBR4Z-ZboDP",
        "colab_type": "text"
      },
      "source": [
        "[Matplotlib](http://matplotlib.org/) is a plotting library. You can use the imshow function to show images.\n",
        "\n",
        "Let's display the cat image before and after our manipulation:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UASIiqsjbylJ",
        "colab_type": "code",
        "outputId": "a12e4183-a2d3-4424-a70c-6f567a6189d8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 205
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "im = np.array(Image.open('/content/gdrive/My Drive/cat.jpg'))\n",
        "im_tinted = np.array(Image.open('/content/gdrive/My Drive/cat_new.jpg'))\n",
        "\n",
        "# Show the original image\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.imshow(im)\n",
        "\n",
        "# Show the tinted image\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.imshow(im_tinted)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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O4He7gvAW8R5mAPcvGWbiPzTBpswRHShJAm/WxJCr+ObUT2MS/9f/+t/x1P6T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\nGwC22GKLLR5RbAPAFltsscUjiv8fXOveawcgL1kAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7KfqcUOZcTsw",
        "colab_type": "text"
      },
      "source": [
        "###Plotting\n",
        "The most important function in matplotlib is plot, which allows you to plot 2D data. Here is a simple example:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ieDFtq6ycMl5",
        "colab_type": "code",
        "outputId": "40529dee-084b-42c6-f5af-28eda5b5e2e0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "# Compute the x and y coordinates for points on a sine curve\n",
        "x = np.arange(0, 3 * np.pi, 0.1)\n",
        "y = np.sin(x)\n",
        "\n",
        "# Plot the points using matplotlib\n",
        "plt.plot(x, y)\n",
        "plt.show()  # You must call plt.show() to make graphics appear."
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xzyaGjQWVhAX587mxWkZytbNjJ23SqwaPcKSqgcLqRhZn6tWCqw0NCWTOqBg2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\n1YcmBqWUUn1oYlBKKdXH/wMx3clddjjO9wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EiqYKr2Ucf2L",
        "colab_type": "text"
      },
      "source": [
        "With just a little bit of extra work we can easily plot multiple lines at once, and add a title, legend, and axis labels:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p-1XPJ3kcdOp",
        "colab_type": "code",
        "outputId": "46d49e24-f56d-4b31-c87d-f0be5204a797",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "# Compute the x and y coordinates for points on sine and cosine curves\n",
        "x = np.arange(0, 3 * np.pi, 0.1)\n",
        "y_sin = np.sin(x)\n",
        "y_cos = np.cos(x)\n",
        "\n",
        "# Plot the points using matplotlib\n",
        "plt.plot(x, y_sin)\n",
        "plt.plot(x, y_cos)\n",
        "plt.xlabel('x axis label')\n",
        "plt.ylabel('y axis label')\n",
        "plt.title('Sine and Cosine')\n",
        "plt.legend(['Sine', 'Cosine'])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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e++4TkVLH6z7PKr90Wju6WLP3JIszEokKu0gw/kIiEiDtBiPYavHmWzPGjiIt\nPpznLJgS6fWUrIGOZiM70OK8mF+On8AtMy9hNt/DzPuMCgG+EHecPYaDNY2WWTlvmkEREX/gcWAJ\nkA7cKSLpfRz6gqrmOl5/dJwbDTwMzAXmAA+LyCgPSR8SW0pqaDjfwe2D9QdfyPS7oakayt5yrTAP\nIyLcPnsMBeVnOVRj/Q51XsWepyFmkuVXxnd2dfNSfgXXToknMSrk4idcyNh5Rtxx7zMu1+Zpluck\nExbkzwsWGYCZOUOZAxxW1SOq2g48D+QN8txFwFZVrVfVM8BWYLGbdLqEl/LLSRkZyrxL8Qf3Jm0R\nhMX4hNtr5fQUAvyEl3dVmC3Fdzh9GE58ZJRzt/jK+HcP1XKqsW3ogy8Ro2L30ffgrLUTQMKDA7gx\nO4n1BSdpafd+74SZBiUF6G12KxzbLmSViOwTkdUi0vMbNthzEZEHRCRfRPJra2tdofuSqTjTwgeH\nT3PrpfqDexMQBFm3wcHN0FLvWoEeJjY8mGunxPHqnko6u+yy9i5h7zNGnC3nTrOVOM3qXRXEhgdx\n/dT4oV8k5w7jveAF14gykVtmGnHH1y1Qsdvbg/LrgXGqmo0xC7nk1A1VfUJVZ6nqrLi4OJcLHAwv\n7zKyNAa1OGsgpt8NXe1GFVmLs2rGaE41tvHB4dNmS7E+3V1Q8BxMWgARiWarcYqzLe28uf8UK3JS\nCPR34s/TyLEw/mrD0FokoN0fs1JHMSY69JO/I96MmQalEug9px3t2PYJqlqnqj0V0v4IzBzsud6C\nqvLKngrmTYjpu1LqpZCYBYnZPuH2un5aPFGhgby82yv/26xF2VvQWGW4uyzOhn1VtHd1c/PFyhIN\nhpy74MxRY22OhfHzE26aPpoPy057fc95Mw3KTiBNRMaLSBBwB7Cu9wEi0qs1GyuA/Y7PrwM3iMgo\nRzD+Bsc2r2P3ibMcr2vhpukuanA0/R6jimx1kWuuZxLBAf7k5Sazpbiac612wUinKHgeQkfBZK8O\nIw6KV3ZXMCUhgoxkF9QgS19hrMnxgeD8qhkpqMKaPd6dbm+aQVHVTuAbGIZgP/CiqhaLyI9FZIXj\nsG+KSLGIFADfBO53nFsP/ATDKO0EfuzY5nW8sruCkEA/lmQlXfzgwZB1K/gFwr7nXXM9E1k1YzRt\nnd1stHDLU9Npa4QDGyHjZiPOZmGOnm5m94mz3Dwjpf8q3JdC0AhjTUrxGmhvcf56JpIaM4JZqaN4\neXeFV69JMTWGoqqbVHWyqk5U1Ucd236kquscn7+vqhmqmqOq16nqgV7n/llVJzleXlmXpK2ziw37\nqliUkUh4cIBrLhoWbaxJKVyUEPypAAAgAElEQVRt+M4tTPboKCbFh7PazvYaOvvXG4UgfaBM/au7\nK/ATIwvQZeTeBe2Nlm9UB3DzjNEcPtVEoRc3qvP2oLyleftALQ3nO1zn7uoh+zbDZ37sfdde18OI\nCKtmjGbX8TMcPW3tVc2mUfA8jBoPY+aYrcQpuruVV/ZUcsWkWBIih7D2pD/GzoOosbDP+tley7KT\nCArw4xUvjjvaBsWNvLqngtjwYK4cqDHQUJi8GIIjjfISFmfl9GREsPukDIWGSmOtRfbtll97svNY\nPRVnzrNqhpOZkBfi52f0hSl7G5rMWTbgKqJCA1mYnsDavZW0d3pnur1tUNzE2ZZ23jpwirzcZAKc\nSX/si8AQI+BYss7yvuGkqFDmjo9m7d6TXu0b9kqKVgNqzFgtziu7KxkR5M8NGQmuv3j27aBdUPyK\n66/tYVbNSOFMSwfvHvJO42gbFDexYV8VHV3qendXD9m3G77hQ5vdc30PsjI3haOnm+0+KZdKwQtG\nD5CYiWYrcYrWji42FVWxODOJsCAXxRp7Ez/VSLn3AbfXVWlxjAoLZJ2XFle1DYqbWLOnkskJ4a5J\nf+yL1CshMsUn3F5LspII8vdj7V7vfEi8kupCOFXsE8H4dw7W0tjaSV5usvtuknUbVO6CujL33cMD\nBPr7sSw7ia0l1TR5YQsI26C4gfL6FvKPnyEv10Xpj33R4xs+/AY0W3u1eVRoINdNjWP9vpN0WayH\ntmnsewH8Aox0YYuzrqCS2PAgLp84xDp3gyHrFkCMnvMWJy83hdaObraWeF8pFtuguIH1+4yR9ooc\nN464wBiddncaPTAszsrcFGob29hWZm3j6BG6u6HoFaPUygg3/hH2AI2tHbyx/xQ3Zrsh1tibyGQY\nf5VhiC0eq5s5dhQpI0O9ckZvGxQ3sG7vSWaMHcmYaCdLrVyMhAyIz/AJt9d1U+OJCA7w+pXAXkH5\ndjhXCZmrzFbiNK8X19De2c0Kd7q7esi6DeqPQOVu99/Ljfj5CStyk3m/9DR1TW0XP8GD2AbFxRyq\naeRAdaP7Zyc9ZK2Cih2WL9MdEujP4sxEXi+uprXD2gs23U7haggIhSlLzVbiNGv3VjImOpTpY0a6\n/2bpK8A/GAqtPwDLy02mq1vZVOhdVSZsg+Ji1u09iZ/AsmwPGZSeUWqR9VMiV05Poamtkzf215gt\nxXvp6jA6M05ZbPk2v7WNbXx4+DR5OW6MNfYmJAom32C4iC1eZWJqYiRTEiJY42VuL9uguBBVZV3B\nSa6YFEtcRLBnbjpqHKTMcqxJsDaXTYghLiKYDQXeNeryKo68Cy11kHmL2UqcZlNhFd2Ke7O7LiRz\nFTTVwPEPPXdPN7EiN5ldx89QXu89a9Fsg+JC9paf5UR9C8s95e7qIXOVkUZae8iz93Ux/n7Csqwk\n3jp4ika7AnHfFL0MwVGQttBsJU6zdm8lUxMjSEuI8NxN0xZB4Ajj39Hi9LjVvWlNim1QXMi6gpME\nBfixONPDTY4ybgLEJx6S5TlJtHd2s7XEdnt9ho5Wo8jhtOUQ4KEZsJsor29h94mzngnG9yYoDKYu\nhZK1hvvQwoyJDmP62JFs8KJq3bZBcRFd3cqGfVVcNyWOyJBAz948MgnGXWkYFIunRE4fY6REetND\n4jWUboG2c0YihsXZ6AgmL/dUrLE3mavg/Bk48o7n7+1ibsxOZn/VOcpqm8yWAtgGxWXsOFpPbWOb\n591dPWTeDHWlhuvLwvj5Ccuyk3jvUC1nW9rNluNdFK2GEXEw7mqzlTjNhn0nyRnjgdT6vph4vRGg\n94EZ/bKsJETwmrijqQZFRBaLyEEROSwiD/Wx/0ERKRGRfSLypoik9trXJSJ7Ha91F57raTbsO0lo\noD/XT403R8C0PGPltA8E55dnJ9PZrbxe7H0rgU2jrQkObTEaRvm7od6VBzl2upmiynMsz3ZR07lL\nJSDYcBvu32C4ES1MYlQIs1Oj2bDPO+IophkUEfEHHgeWAOnAnSKSfsFhe4BZqpoNrAZ+1mvfeVXN\ndbxWYCKdXd28VlTN9dPi3VPcbjCMiIEJ1xnpwxZ3e2WmRJIaE8Z6Lxl1eQWHXjMaaWVav9RKzx+/\npa7qYjoUMlcZxVUPbzVPg4u4MSeJ0lNNHKxuNFtK/wZFRH4jIv/T38sF954DHFbVI6raDjwP5PU+\nQFXfVtWenLjtgIubJbiG7UfqqWtuN2/E1UPmzdBQbhTBszAiwvLsZLaVnea0l60ENo3iVyE8EcZc\nZrYSp9mwr4pZqaNIHhlqnohxV0NYrE+4vZZkJuEneMUsZaAZSj6wa4CXs6QA5b2+Vzi29ccXgd61\n2kNEJF9EtovIyv5OEpEHHMfl19a6p4fAxsKTjAjy59opJrm7epiy1Og37wO1vW7MSaJbYbOXrQQ2\nhdZzULoVMlYaRUEtzOFTRiWJG80efPkHQHoeHHwN2q3dLTQuIph5E2PYsK/K9J5C/f52qupTvV/A\nSxd89xgicg8wC/ivXptTVXUWcBfwKxHpsymEqj6hqrNUdVZcXJzLtXV0dbO5qJoF6QmEBPq7/PqX\nROhImDQfitcYBQQtzJSECNLiw1lvZ3sZ7q6uNp+oLLy+oAoRk91dPWTcZLgRS7eYrcRpbsxO5ujp\nZopPnjNVx0WHOyIyT0RKgAOO7zki8r8uuHclMKbX99GObRfefwHwQ2CFqn7i/1DVSsf7EeAdYLoL\nNF0y28rqONvSwY1mpD/2RcZNcK4CKvPNVuIUIka2185j9Zw6Z+3AqdMUvWL0vhk922wlTqGqbNh3\nkrnjo4l3Zd/4oZJ6OYyI94kZ/eKMRAL85JNK52YxmPnzr4BFQB2AqhYArshb3Amkich4EQkC7gA+\nla0lItOB/8MwJqd6bR8lIsGOz7HAFUCJCzRdMhsKThIRHMDVk13cN36oTFkC/kE+8ZAsy0pCFTYX\nDeNsr/NnoexNI7vL4u6ugzWNlNU2e67O3cXw8zcKRh7aYnm316gRQVwxKZZNhea6vQb1G6qq5Rds\ncrqymqp2At8AXgf2Ay+qarGI/FhEerK2/gsIB166ID14GpAvIgXA28Bjqupxg9Le2c3rxdUszEgg\nOMBkd1cPIVEwaaFPuL3SEiKYnBD+ySK4YcnBTdDV7qiGYG027qvCT2CJpytJDESP2+vQ62YrcZpl\nWUmU15+nsNK8VtqDMSjlInI5oCISKCL/jGEAnEZVN6nqZFWdqKqPOrb9SFXXOT4vUNWEC9ODVXWb\nqmapao7j/U+u0HOpfHj4NOdaO80PMF5Ixk3QeNIoa29xlmYNc7dX8asQNQZGzzJbiVOoKhsLq7hs\nQgyx4V5UNmbsPAhP8IkZ/Q0ZCQT4iakDsMEYlK8CX8fIwDoJ5Dq+D3s2FlYRERLAlZNcH+x3iimL\njb4PPvCQDGu31/kzUPa2kY3kifLubuRgTSNHapu9IxjfGz9/49+3dIuxeNTCjAwL4nKT3V4XNSiq\nelpV73bMFOJU9R5VrfOEOG+mvbObLcXVLExPICjAy3zbwRFGNdqStbbby8oc2ATdHT6R3bXJ4e7y\neOHUwZC+EjpbodT6bq8bTXZ7DSbLa4KIrBeRWhE5JSJrRWSCJ8R5Mx+WGe6uZd424uoh4yZorDLa\nxVqcZVnJw9PtVbIGosZCygyzlThFj7tr7ngvc3f1MPYyY9GoD8zozXZ7DWZo/SzwIpAEJAMvAc+5\nU5QV2LSviojgAK5M85LsrguZvMhwe5WsNVuJ0yzLThx+bq/zZx3urhWWd3cdqmmirLaZpd4Wa+zh\nE7fXVmgzv3yJM5jt9hqMQQlT1b+paqfj9TTgBUnk5tHR1c2WkhoWpntRdteFBEfApAVQss7ybq9J\n8RFMSYhg43Ba5Hhws+HuSu+3CIRl2FjocHdleKG7q4eMHreX9Rc5LstKpLz+PEWVnl/kOFAtr2gR\niQY2i8hDIjJORFJF5HvAJs9J9D4+PHyahvMd3hdgvJCMlUa2l8UXOYIj2+v4MHJ7layByNE+kd21\nqbCKOeOjPdcWeyiMmevI9lpjthKnuSHdWOS4odDzixwHmqHswqjndRvwFYz1Hu8AXwNud7syL2Zz\nYTURwQFc5S2LGftj8iLHIkfrPyQ9bq/XhkNJ+9YGKHvLJ7K7DtU0cfhUk/fGGnvw84dpKwy3lw8s\ncjTL7TVQLa/xqjrB8X7ha9gG5Tu6unm9xKjd5bXurh5ComDifCOOYvGS9pPijdpem4ZDttfB14zF\njOl5Fz/Wy9lUaNTuWuSN2V0Xkp7nqO1l/ZL2PW4vT9f2GlS+q4hkishtIvK5npe7hXkrHzlqd3nV\nat+BSM9z1Paydkl7gCVZSZ90xvRpStZARLLla3cBbC6qYs64aOIjLBB2Tb3cKGlfYv0Z/cL0RPz9\nxOMDsMGkDT8M/Mbxug6jyZWpDa3MZHNRFeHBAVw92csWM/bHlCVGSXsfeEiWZiXSrfh2J8fWc3D4\nTWMgYPHaXYdPNXKopsn7Y409+PkbnRwPbYH2losf78VEjwhi3oQYj7u9BvMbewswH6hW1c8DOUCU\nW1V5KZ1d3bxeXMP8afHml6ofLKEjYeJ1UGx9t9eUhAgmxI1gc5EPu70OvW6UqvcBd9fmQsPwe+Vi\nxv7IWAkdzUZBTouzJCuRY3UtHPBgJ8fBGJTzqtoNdIpIJHCKT5edHzbsOFpPfXM7SzItMuLqIT0P\nGk7Ayd1mK3EKEWFpZhIfldVR56udHEvWODozzjVbidNsKqpmVuooEryhVP1gSb0SQqN9IpFlUUYi\nfuLZJnWDMSj5IjIS+ANG5tdu4CO3qvJSNhVVERrozzVWcXf1MGUp+AUYa1IszhKH22tLSY3ZUlxP\nWxMcfsNYzGhxd9fR083srzrHEqu4u3rwD4BpNxpNzTqsnaIeGx7M3PExbPLgguDB1PL6B1U9q6q/\nBxYC9zlcX8OKrm7ltaIarp8aT2iQRdxdPYRFw/hrfCLbKz0pktSYMN/M9irdYiyu8wV3l8MtaSl3\nVw/pK6G9ySfcXkuzEjl8qonSGs+4vQZa2DjjwhcQDQQ4Pg8r8o/Vc7qpjSVZFnxAwPgjdeYoVBea\nrcQpRISlWUlsK6vjTHO72XJcS8laGBFnlFS3OJsKq8gdM5KUkaFmS7l0xl8NISN9Yka/KCMREdhU\n6JlZykAzlP8e4PVz90vzLjYXVRMc4Md1U+LNljI0pt4I4u8Ttb2WZibR1a1s3e9Dbq/2FmOGMm25\nkW1kYU7UtVBUeY6lVh18+Qcaz8vBzdBp7VhdfGQIs1OjPZbIMtDCxusGeF3vipuLyGIROSgih0Xk\noT72B4vIC479H4vIuF77vu/YflBEFrlCT390dyubi6q4dkocI4ID3Hkr9zEiBsZdaQR9Le72ykyJ\nZPSoUI8GG91O2ZvQ0eJT7i7LJa/0Jj0P2hrgyLtmK3GaJVmJHKhupKzW/f1eTIv8iYg/8DiwBEgH\n7hSR9AsO+yJwRlUnAb8Efuo4Nx2jB30GsBj4X8f13MKe8jPUnGuzTj59f6TnQd1hOOWShpum0eP2\n+sBRU80nKFlrZBelXmm2EqfZVFRNZkokY6LDzJYydCZcA8GRPjGjX5aVxP+7OcsjtdTMTCWZAxxW\n1SOq2g48D1w4PMsDnnJ8Xg3MFxFxbH9eVdtU9Shw2HE9t7CpsJogfz+un2pRd1cP05YD4hMPyZLM\nRDq6lDd9we3V0WqUW5l2o5FlZGEqzrRQUH7W+oOvgGBjUfCBDdBl7UFLfGQId84ZS2RIoNvvZaZB\nSQHKe32vcGzr8xhV7QQagJhBnguAiDwgIvkikl9bWzskoec7uliQHk+EB/5D3Ep4PKRe4RMGJXfM\nSJKjQjwWbHQrR96G9kafcHe95khRtbS7q4f0PGg9C0ffM1uJZRhM6ZUrRGSE4/M9IvILEUl1vzTX\noKpPqOosVZ0VFze09SP/eVMWj9/lI4lt6Sugdj/UHjRbiVOICIszk3ivtJamtk6z5ThHyVqjkOe4\nq81W4jSbi6qZlhTJ+NgRZktxnonXQ1A47Ld+tpenGMwM5XdAi4jkAN8ByoC/uuDelXx6xf1ox7Y+\njxGRAIySL3WDPNeliMXLiH/CtOXGuw/MUpZmJdLe2c1bB06ZLWXodLYbveOn3ggBQWarcYrqhlZ2\nHT/DUiuuPemLwFCjBcT+DdBl8UGLhxiMQelUo7pYHvBbVX0ciHDBvXcCaSIyXkSCMILsFw4F1gH3\nOT7fArzl0LIOuMORBTYeSAN2uECT7xOZbJT18IEc+xljRxEfEWztbK8j7xjZRD7h7nJkd1k9ftKb\n9DxoOQ0ntpmtxBIMxqA0isj3gXuAjSLiBzgdTHDERL4BvA7sB15U1WIR+bGI9FQz/hMQIyKHgQeB\nhxznFmP0uS8BXgO+rqpdzmoaNqSvhJpCqCszW4lT+PkJizMTefvgKVraLTqCLFlrZBNNuNZsJU6z\nuaiayQnhTIoPN1uK65i0EALDfKK2lycYjEG5HWgDvqiq1Rjupf9yxc1VdZOqTlbViar6qGPbj1R1\nneNzq6reqqqTVHWOqh7pde6jjvOmqOpmV+gZNviQ22tJZhKtHd28c3BoCRem0tVhZBFNWWJkFVmY\n2sY2dhyr941gfG+CwiBtIexfD932mPViDKaWV7Wq/kJV33d8P6Gqroih2JjFyDGQMssneqTMGR9N\nbHiQNWt7HX3PyCLyAXfX68XVqGL9dOG+SM+D5lNwYrvZSryegWp5feB4bxSRc71ejSLi2b6SNq4n\nPQ+qCqD+qNlKnMLfT1iUkchbB07R2mGxEWTJWiOLaKJLCk+YyuaiKibEjWBygg+5u3pIWwQBIT4x\no3c3A5VeudLxHqGqkb1eEaoa6TmJNm4h3RGm8oGUyKVZSbS0d1nL7dXVabi7Ji8ysoksTF1TG9uP\n1LMkM9F3siF7ExwOkxYYz0p3t9lqvJrBrENZ0Me2+/o61sZCjBoHSbk+MeqaOz6a6BFB1urkePxD\naKkzEiQszuvFNXR1q2+6u3pIXwmNVVBhJ5MOxGCC8j8Skd+JyAgRSRCR9cBydwuz8QDpeVC5C86e\nMFuJUwT4+7EoI4E391vI7VWy1sgemvSZ8Zrl2FxUxbiYMNKTfNhxMXkR+Af7xADMnQzGoFyDsZhx\nL/AB8Kyq3uJWVTaeoScY7ANrUpZkJtHU1sn7pafNlnJxuruMrKG0hUYWkYWpb25nW1kdS7OSfNPd\n1UNIJEyabxgU2+3VL4MxKKMwCi+WYaQPp4pP/+YMI2ImQmKWT2R7zZsYw8iwQGtkex3fZmQN+YC7\na0txte+7u3pIz4Nzlcas3qZPBmNQtgOvqepiYDaQDHzoVlU2niM9Dyp2QkOF2UqcItDfjxvSE3ij\npIa2Ti93e5WsgQBHWQ+Ls6momrHRYWQk+7C7q4fJi8Ev0CcGYO5iMAZlgar+GUBVz6vqN3GsWLfx\nAdJvMt59we2VlURjWycfeLPbq7vL+LdOWwhB1i6geLalnW2HT/u+u6uH0JFGinfJWss3qXMXg1nY\neEJERonIHBG5WkSsXxLV5u/EToKELCh+1WwlTnPFxFgiQwLY6M1urxMfGe6uDF9wd9XQ2a0sGw7u\nrh4yVkJDOVTuNluJVzKYtOEvAe9h1Nz6d8f7I+6VZeNRMvKMdEiLu72CAvy4ISORrd7s9ipeYyyS\nS/MFd1cVo0eFkpkyDNxdPUxZari9il8xW4lXMhiX1z9hxE6Oq+p1wHTgrFtV2XgWH3J7LctOorHV\nS91e3V3G4ri0hcZiOQvT0NLBh4dPs2y4uLt6sN1eAzIYg9Kqqq0AIhKsqgeAKe6VZeNRYidBQqZP\nBBu92u11Yjs01fhGdldJNR1dwyS760IybnK4vexsrwsZjEGpEJGRwBpgq4isBY67V5aNx0lfCeUf\nQ4Nb+5S5naAAPxZlJLK12AvdXiUOd9fkxWYrcZoN+6oYEx1K9ugos6V4nilLHG4v68cdXc1ggvI3\nqepZVX0E+DeMHiXWH2LZfJqeILEP1PZalm1ke71/yIvcXt3dhktx0gLLu7vONLc73F3Jw8vd1UPo\nyL8vcrTdXp9iMDOUT1DVd1V1naq2u0uQjUnEphluLx8YdV0xKZao0EDvcnud+Aiaqg13icXZUlJN\nZ7dyY/YwdHf1YLu9+uSSDIqrEJFoEdkqIqWO91F9HJMrIh+JSLGI7BOR23vte1JEjorIXscr17M/\ngY/yidvL2tlegY7aXm+U1HhPba/iVxyLGX3D3ZUaM0wWM/bHlCXgH+QTAzBXYopBwVgY+aaqpgFv\n0vdCyRbgc6qaASwGfuWI5fTwXVXNdbz2ul/yMCDzZuPdB9qdLstONtxe3pDt1dVpuEcmL7K8u6uu\nqY1tZXXDL7vrQkKiYOJ841mxa3t9wmDWofxjXzMIJ8kDnnJ8foo+YjKqekhVSx2fTwKngDgX67Dp\nTcxESMz2iRz7yx21vTbuO2m2FDj+ATTX/t1gW5ieUvXLhrO7q4eMm+BcBVTmm63EaxjMDCUB2Cki\nL4rIYhcVhkxQ1R4Hd7XjHv0iInOAIIwClT086nCF/VJE+m3ILSIPiEi+iOTX1lqoAZNZZK4y/MJn\njpmtxCkC/f1YlG4scjTd7VX0CgSOgLQbzNXhAjYWnmRC7AjfLlU/WKYsMUraF71sthKvYTBZXv8K\npGFkd90PlIrIf4rIxIHOE5E3RKSoj9enGmirqgL9pkqISBLwN+Dzqtozt/w+MBVjwWU08C8D6H9C\nVWep6qy4OHuCc1F6gsZF1p+lLM9Jprm9i7cPnDJPRFeHkTk3ZYnlOzOebmrjo7I6lmUPc3dXDyGR\nMPkGI47S7SWxOpMZVAzF8Ue/2vHqxChpv1pEfjbAOQtUNbOP11qgxmEoegxGn0+8iEQCG4Efqur2\nXteuUoM24C8Y5fVtXMGoVEiZ5RNur8smRBMbHsR6M91eR96F82d8wt21uaiabmV4Lmbsj8xVxmLV\n49vMVuIVDCaG8k8isgv4GUbZ+ixV/RowE1g1xPuuA3raCN8HfKYNmogEAa8Cf1XV1Rfs6zFGghF/\nKRqiDpu+yFwF1YVwutRsJU4R4O/Hsqwk3tx/iqa2TnNEFL8CwZE+0Zlx/d6TTIoPZ2pihNlSvIe0\nRYY703Z7AYOboUQDN6vqIlV9SVU7ABzupxuHeN/HgIUiUgoscHxHRGaJyB8dx9wGXA3c30d68DMi\nUggUArHAfwxRh01fZKwExGfcXm2d3bxRUuP5m3e2wf4NMHUZBPQb5rMEVQ3n2XGsnhU5w3QxY38E\nhRnuzJK1hntzmDOYGMrDqtpnqRVV3T+Um6pqnarOV9U0h2us3rE9X1W/5Pj8tKoG9koN/iQ9WFWv\nV9UshwvtHlVtGooOm36ITIax83zC7TVj7CiSo0JYX2CC26vsLWhrgAzru7s2FBg5NCtykk1W4oVk\nroLz9YZ7c5hj1joUG28n82aoPQA1xWYrcQo/P+HGnGTeK63lbIuHCzwUvgSh0TDxOs/e1w2sKzhJ\n9ugoxsVauymYW5g0H4KjfGIA5iy2QbHpm/SVIP5QuPrix3o5y7OT6ehSXi+u9txN25rgwCbDfegf\n6Ln7uoGjp5sprGywZyf9ERAM026E/esNN+cwxjYoNn0THgcTrjUMisUL4GWmRDIuJoz1BR6s7XVw\nM3Seh6xbPXdPN7Fu70lE4MZs26D0S+bN0HYOSrearcRUbINi0z9Zt0LDCSjfYbYSpxARlucks63s\nNLWNHhpBFr4EkSkw5jLP3M9NqCrrCiqZPS6axKgQs+V4L+OvhbBYKHzRbCWmYhsUm/6ZdqPRv6Pw\nJbOVOM2KnGS6FTZ4Yk1KSz2UvWkEa/2s/Yjtr2qkrLbZdnddDP8AY5Zy8DVobTBbjWlY+7fdxr0E\nRxgpkcWvWD4lMi0hgozkSNbs8UADsZI10N3pG+6ugpME+Im9mHEwZN0GXW1GLGWYYhsUm4HJug1a\n6uDIO2YrcZqVuSkUVDRwpNbNWeaFqyF2MiRmufc+bqa7W1m3t5Ir02KJHhFkthzvZ/QsGDXeJ2b0\nQ8U2KDYDM2kBhIz0iYdkeU4yIrBmrxvdXg0VcPxDY3Zi8QWAHx+t52RDKzdNTzFbijUQMf7fj74H\njR7MKPQibINiMzABQZCeZ6z4bm82W41TJEaFcPnEGNburUTdlbnWk2adOdSqRN7Dmj2VjAjy54b0\nRLOlWIfs20C7h20pFtug2Fyc7Nugo9lIhbU4ebkpHK9rYU/5WddfXBX2vQCjZxu9ZSxMa0cXmwqr\nWJyZRGiQv9lyrENsGiTlwr7hme1lGxSbizP2ciMFdt8LZitxmsWZiQQF+LHWHcH56kI4VQLZt1/8\nWC/nzf2naGzrtN1dQyH7Nqjaa/niqkPBNig2F8fPz/gjefhNaDShyKILiQwJZOG0BDbsq6Kjy8Wt\nWwueB79An3B3vbqnkoTIYOZNjDFbivXIXAXi5xMDsEvFNig2gyPnTtAunwjO5+UmU9fczvulLuzg\n2dVpLGqbvAjCol13XROob27nnYOnyMtNwd/P2okFphCRaFSZKHh+2PWbtw2KzeCImwwpM6HgObOV\nOM21U+IZFRbIy7td6PYqe8voG59zp+uuaRIb952ks1tZmWu7u4ZMzl3QUA7HPzBbiUexDYrN4Mm5\nE2qKjFiBhQkK8CMvN4WtxTU0tLhowea+5yF0lE/0jX91TyVTEyNIT7b7xg+ZqcuMxmp7rT8AuxRM\nMSgiEi0iW0Wk1PE+qp/juno111rXa/t4EflYRA6LyAuO7o427iZzlREj8IGH5JaZo2nv6madK0qx\ntDbAgY3Gv0+AtX8Vy2qb2H3irB2Md5agMKPSdMlao/L0MMGsGcpDwJuqmga86fjeF+d7Ndda0Wv7\nT4Ffquok4AzwRffKtQGM2MDkRUasoMuklrouIiM5kqmJEazOL3f+YiVrobPVJ9xdL+VX4O8n3DTD\nNihOk3u3kW6/f93Fj7vK/OYAAB4HSURBVPURzDIoecBTjs9PYfSFHxSOPvLXAz2NOi7pfBsnyb3L\niBWUvWm2EqcQEW6ZOZqCigYO1TQ6d7G9z0HMJCPGZGE6u7p5ZXcF102JIz7CrizsNGPmQvQE2Pus\n2Uo8hlkGJUFVe5pTVAMJ/RwXIiL5IrJdRHqMRgxwVlV7hsgVgD2c8hSTFhpdCH3gIVk5PYUAP+Hl\nXRVDv8jpw3BimzEatXiplfdKaznV2Mats8aYLcU3EDFmrcfeh7MnzFbjEdxmUETkDREp6uOV1/s4\nNWpg9FcHI1VVZwF3Ab8SkUtefiwiDziMUn5trQvTRIcrAUHGmpSDm6C5zmw1ThEbHsy1U+J5ZU8l\nnUNdk7Lnb0Zny9y7XCvOBF7KryBmRBDXT403W4rvkHOH8V7wvLk6PITbDIqqLlDVzD5ea4EaEUkC\ncLyf6ucalY73I8A7wHSgDhgpIgGOw0YD/eZ/quoTqjpLVWfFxcW57Ocb1sy4F7rafWLh1i0zR1Pb\n2Mb7pacv/eSuTiONevIiY+2BhalvbueN/TXcND2FQH87+dNljBwL46+Gvc8MizUpZv3mrAPuc3y+\nD1h74QEiMkpEgh2fY4ErgBLHjOZt4JaBzrdxIwkZkDILdj9l+fbA10+NJ3pEEC/sHEJwvnQLNNXA\n9HtdL8zDrNlTSUeX2u4udzD9c3DmGBx912wlbscsg/IYsFBESoEFju+IyCwR+aPjmGlAvogUYBiQ\nx1S1xLHvX4AHReQwRkzlTx5VbwMzPge1B6Bip9lKnCIowI9VM1J4Y38NpxpbL+3k3X+F8ATLrz1R\nVV7MLydndBRTEiPMluN7TFturFHa/dTFj7U4phgUVa1T1fmqmuZwjdU7tuer6pccn7epapaq5jje\n/9Tr/COqOkdVJ6nqrarqoUbhNp+QeTMEjvCJh+SOOWPp7FZWX0pwvrHamKHk3Gm0f7UwhZUNHKhu\n5BZ7duIeAkOM35P9G6B5CK5VC2E7S22GRnCEYVSKXoHWc2arcYqJceHMHR/N8zvK6e4epAtv77NG\nbTMfcHc9s/0EoYH+5OXafePdxoz7oLvDJ7IjB8I2KDZDZ+b90NFi9Jy3OHfNHcuJ+hY+LBvECLK7\nG/Y8DalXQOwk94tzIw3nO1hXcJK83GQiQwLNluO7xE+FMZf5RNxxIGyDYjN0UmZCfDrssr7ba1FG\nIqPCAnluxyDWCxx9F+rLjFGnxVmzp5LzHV3cPTfVbCm+z8z7oO6w0SLaR7ENis3QETH+qJ7cDSf3\nmK3GKUIC/Vk1YzRbimuobbxISG7nHyEsxqjVZGFUlWc+Pk726CiyRkeZLcf3SV8JwVGw60mzlbgN\n26DYOEfOHRAYBjv+ePFjvZw75xrB+Zd2DZBC3FBhLOqc8TkICPacODeQf/wMh2qauHvuWLOlDA+C\nwoxujiXrfDY4bxsUG+cIHWmsnC9aDS31Zqtxip7g/HM7TtDVX3A+/y+GD3zWFzwrzg08s/04EcEB\nLM+xg/EeY/YXoavNJ7Ij+8I2KDbOM+fLRrXdPX8zW4nTfG7eOMrrz/PWgT6KN3S2G38IJi82VkBb\nmPrmdjYVVnPzjBTCgqyd9mwp4qcZK+d3/tnyFbv7wjYoNs6TkAGpVxqxhe4us9U4xaKMBJKiQvjL\nh0c/u3P/OqPS8uwveV6Yi3lhZzntXd3cZQfjPc/cr8K5Cji40WwlLsc2KDauYc6XjYqqpVvMVuIU\nAf5+3DsvlW1ldRysvqCs/c4/wqjxMPF6c8S5iI6ubp7adowrJsXYK+PNoGeG+/H/ma3E5dgGxcY1\nTF0GEcmw4wmzlTjNnbPHEhzgx5Pbjv19Y3UhnPjI8IH7Wfux2VRYRfW5Vr5wxXizpQxP/Pxh9peN\n9OHqIrPVuBRrPxk23oN/IMz6PJS9BbWHzFbjFKNGBHHT9BRe3VPB2ZZ2Y+O230JQuOVXxqsqf/7g\nKBNiR3DdFLtM/f9v787DoyqvB45/T0IggYBhDRqWBEHZwmKQRRYjKAilKiqbS1VARBbRKkpbfy1t\n3bBUqdRiBVSwKJZFsAjVoiggi0kghCUioCzBgGnQhACBLOf3xx1ohIQkZJI7Q87nefKY3Llz58yV\n5Mz73vee45qO90CVEPjy0hqlWEIx3hNzPwRWg42vuh1Jmd3fPZLsnHwWxB2EjEPOKrZrfuGsavNj\nCft/YGtKBg90jyQgwL8bgvm16nWcJcRJC/1+dWRBllCM94Q2cBpNJb4Lx464HU2ZtGxYi27N6jJv\n/T7yN84EzXcupvq5Oeu+5bKQIO6IaeR2KKbLGMg9CXGXTrF0SyjGu66b4DTfugSG8iN7RJGZcZS8\nuDedu5xr+/eKqINHT/DRjsMM79zElgr7gvDW0KIfbJoJp0+4HY1XWEIx3lX3Sqf/Q9xsOHWs+P19\nWO+WDZgQtoGg3Czyu01wO5wye/OLfQSIcN91/p0YLyk9HoMT6U6x0UuAJRTjfd0nQnYGbPbvGx0D\nNJd75UM25rfik8wIt8Mpk/SsU7z75QFuaX8Fl18W4nY45oym3ZwqxOtnQF6O29GUmSvjXhGpA7wH\nRAL7gCGq+sM5+9wAvFxgU0tgmKouFZG3gOuBDM9j96tq4sXEkpOTQ0pKCtnZpezWd4kKDg6mUaNG\nBAWVoZR5o07OjY4bXnXuTwn007Lo25dQ/eRh3g8ZwVer93BjqwaI+OeF7NnrviU7N4+xN/h3uf1L\nUo/H4N2hTm+h9kPdjqZM3JpInQx8oqoviMhkz89PFdxBVVcDHeBsAtoDFLxrbpKqLiprICkpKdSs\nWZPIyEi//WPhLapKeno6KSkpREWV8R6F7o/AO0Ng2yLoMNw7AVakvFxY8yI0aE10xyG8t2wnG/am\nc13zem5HVmo/njjNvPX7+Fn05TRvEOp2OOZcLfo6bSDWvQzRg/36Pie3Ir8VOFMdbS5QXB3wO4GV\nqur1K1fZ2dnUrVu30icTABGhbt263hmtNb8JwqNhzZ/8s2bR9kVO74rYydzZqQn1a1bjb5/tdTuq\ni/LGF/s4fjqP8b1tdOKTAgKg+6OQlgy7P3I7mjJxK6GEq2qq5/vDQHgx+w8D3j1n27MikiQiL4tI\nkXXERWS0iMSLSHxaWlpR+5Q07kue185FQADc8GunEVXSAu8cs6Lk5cLnUyG8LbT8OcFBgYzqEcW6\nPf9ly4Efin++D8nMzuHNL76lX5twWjas5XY4pihtb4ewprD6OacjqJ8qt4QiIqtEZHshX7cW3E9V\nFSiyJ6aIXA5EAwVT969wrqlcC9ThnOmyc47/uqp2UtVO9evXL8tbMqV1dX+44hr4bKpTqddfbPsn\nHP0GYiefnX64u2tT6taoyrSPd7kcXOnMW7+PY9m5TOjdwu1QzIUEBjkfwA4nQfIyt6O5aOWWUFT1\nRlVtW8jXMuCIJ1GcSRiF1Ao/awjwvqqeXQKhqqnqOAW8CXQur/dREZ599lnatGlDu3bt6NChA5s2\nbWLUqFHs3LnT7dDKRgR6/wYyDsCWeW5HUzJ5ufD5i9AwGloOPLs5tFoVxvduzhd70lm7u/CRrq/J\nOJHDrLXf0rtlA9pGWEdGnxc9GOq3gk+f9c9pYtyb8voAONOQ+z7gQil5OOdMdxVIRoJz/cVvK6xt\n2LCB5cuXs3nzZpKSkli1ahWNGzdm9uzZtG7d2u3wyu7KPs6yyDXTIOek29EUL2kB/PAtxP7KSYgF\n3NWlCRFhIbz4713kF9WAy4e8+tkeMrNzeKLv1W6HYkoiIBB6Pw3pu2HruTP8/sGtVV4vAP8UkZHA\nfpxRCCLSCRijqqM8P0cCjYHPz3n+fBGpDwiQCHilJsbv/7WDnd9leuNQZ7W+oha/+3mbIh9PTU2l\nXr16VKvmXAaqV89ZRRQbG8u0adPo1KkToaGhTJw4keXLlxMSEsKyZcsIDw8nLS2NMWPGcODAAQCm\nT59O9+7dvRp/mYk4vyRzB0L8G9BtnNsRFe30CWcO+/IOcPWA8x6uViWQX950FY8v3MqK7akMbOe7\nnQ4PHj3BW1/s4/aOjWh9hV078Rstf+aZJn7BqfXlZ22mXRmhqGq6qvZR1RaeqbGjnu3xZ5KJ5+d9\nqhqhqvnnPL+3qkZ7ptDuUdWsin4P3tK3b18OHjzIVVddxdixY/n883NzJxw/fpyuXbuydetWevXq\nxaxZswCYOHEijz32GHFxcSxevJhRo3y08VNUT2gW66z48uVCeOtfgcxDcPPz541OzritYwRXh9fk\nzx9/TU6e7148/fPHuxCBJ/pd5XYopjREoM9vnQZc8W+4HU2pWUGfAi40kigvoaGhJCQksHbtWlav\nXs3QoUN54YUXfrJP1apVGTjQmc+PiYnhP//5DwCrVq36yXWWzMxMsrKyCA31wXsN+j0Hr/WE1c/C\nz/7sdjTny0iBddOdml1Nrytyt8AAYVK/qxk1L54FcQe5t6vvlTHZlpLB0sTvGBt7pd0V74+axULU\n9c4oJXoI1KjrdkQlZgnFBwQGBhIbG0tsbCzR0dHMnTv3J48HBQWdXc4bGBhIbq5zwS4/P5+NGzcS\nHBxc4TGXWngbp3Vu3CynzH3DaLcj+qlVU5yKwjf9odhd+7RqQNdmdZj20S4GtG1I3VDfmZZQVZ5b\nkUydGlUZE3ul2+GYiyEC/afCzO7wyRS4ZYbbEZWY/96SeYnYtWsXu3fvPvtzYmIiTZuW7FNv3759\nmTHjf//YEhMvqvpMxbnhVxBSG1Y8CepDF7UPfgnbFsJ140tUUVhE+OOtbTl+KpfnV35VAQGW3PKk\nVDZ8k87EPi2oFeynJW8MNGgFXR+GzfPgYJzb0ZSYJRSXZWVlcd9999G6dWvatWvHzp07mTJlSome\n+8orrxAfH0+7du1o3bo1r732WvkGW1YhtZ354QPrYftit6Nx5OfByqcgtCH0+GWJn9YivCajezVj\nUUIKm75JL8cAS+6H46eZ8sEO2jW6jHt8cCrOlFLsZKh5Oax43Pl36gdEfemTYjnr1KmTxsfH/2Rb\ncnIyrVq1ciki31Su5yQ/D2bdAFnfw9iN7ndAXDcdVv0O7pgD0XeW6qknT+dx08ufExIUyIeP9KRq\nFXc/nz2xcCvvbznEv8b3sJVdl4rti2HRCBgwzSm06hIRSVDVTsXtZyMUU7ECAmHgdDieBismuRvL\n9185iwRaDoS2d5T66SFVA/n9LW3Y/X0Ws9d9Uw4Blty63f9lUUIKD/VqZsnkUtLmducC/Sd/hB8P\nuh1NsSyhmIoXcQ30etIpcbJ9iTsx5OXC0jFQraaT4C6yhlmfVuH0b9uQ6f/ZzfZDGcU/oRycPJ3H\nr9/fRlS9GjzSx0qsXFJE4Od/Ac2DJaN9furLEopxR8/HISIGlj8Gmd9V/Ot/MR2+2+IsYQ4tW423\n5wZFU6dGVSa8u4WsUxVfMmPKBzs4cPQEzw2KJjgosMJf35SzOlHOv9MD62HtS25Hc0GWUIw7AqvA\noNed/vPLxlXsqq+Dcc4a/za3Q5tBZT5c7RpVmT6sA/vTj/PbZRVbBei9uAO8F3+QCb2b0+1K/7lf\nwZRSu6HQ9k747HlnVaKPsoRi3FOvOfR9BvZ+6vyiVISMQ7DgLrgswqs3WHZtVpdH+rRgyeZDLE5I\n8dpxL2T7oQz+b9kOejSvx6M32h3xlzQRGPgS1IqAxaPgpG+2UbCEYtzVaQR0vMfpP5JYzgXxTp+A\nBcOdIpXDF0D1Ol49/ITeLegSVYenl24v974pGSdyGDt/M3VrVOUvwzoQGGA9fS55wZfBHbOdKeIF\nd0OO77Utt4TiAw4fPsywYcO48soriYmJYcCAAXz99delOsaAAQP48ccfyynCciTiXBSP6gUfTIB9\n68rndVSdqbXUJLhzjnPjmJcFBggz7upI/ZrVeOCtOL4+cszrrwFw4nQuo9+OJzXjJK/efY1P3alv\nylmTLjDoNdj/BSx50Ocu0ltCcZmqMmjQIGJjY9m7dy8JCQk8//zzHDlypFTHWbFiBWFhLt/TcbEC\ng2DI21CnmfPJ6/tk7x4/Px9WPgk7lsCNU+Cqft49fgENagbzj5FdqBoYwL1zNnHwqHe7Vp88ncfI\nt+KJ23eUPw/pwDVNanv1+MYPRN8JfZ+F5A/g35N9quqE1fIqaOVkOLzNu8dsGA39Xyjy4dWrVxMU\nFMSYMf+rwN++fXtUlUmTJrFy5UpEhKeffpqhQ4eSmprK0KFDyczMJDc3l5kzZ9KzZ08iIyOJj48n\nKyuL/v3706NHD9avX09ERATLli0jJCSEvXv3Mm7cONLS0qhevTqzZs2iZcuW3n2/FyskDO7+J8zp\nC2/cDMPegUgvlOLPy4GlDzulVbqNh+4Ty37MYjSpW515Izsz5LUN3DtnE/Mf7EpEWNmLNGbn5DFq\nXhybvk3npSEduKW975bPN+XsuvFwLBU2/BUCqjjXIgPcX+FnIxSXbd++nZiYmPO2L1myhMTERLZu\n3cqqVauYNGkSqampvPPOO/Tr1+/sYx06dDjvubt372bcuHHs2LGDsLAwFi92ypyMHj2aGTNmkJCQ\nwLRp0xg7dmy5v79SqR0JIz+GGvXh7dtg26KyHe/0CecC/LaF0Od3zi/dRd5vUlotG9bizQc6k551\nmp/PWMf6Pf8t0/EOZ2Tzizlfsn5vOtMGt+e2jhFeitT4rZv+CJ0fgo1/g3eGQrY790EVZCOUgi4w\nkqho69atY/jw4QQGBhIeHs71119PXFwc1157LSNGjCAnJ4fbbrut0IQSFRV1dntMTAz79u0jKyuL\n9evXM3jw4LP7nTp1qsLeT4mdSSoL7oLFI53pr15PQFApP+Ef2AT/mghpXznXaDo9UC7hXkhM09os\nG9+dh95O4J45m5jcvyUP9mx2tnJ0SX204zBPLU7idG4+04d24NYOlkwMEBAAA16EBi2dqhOzb4Jh\n86Geeze3ujJCEZHBIrJDRPI9XRqL2u9mEdklIntEZHKB7VEissmz/T0RqVoxkXtfmzZtSEhIKPH+\nvXr1Ys2aNURERHD//fczb975vdrPdH+E/5W7z8/PJywsjMTExLNfyclevlbhLdXrwL1Lof1wWDsN\n/toZdiwt2VxxdgYs/yW80Q9OHYO7F7mSTM5oVj+U98d15+a2DXluxVcMfm0Da3enUZIaegfST/DU\noiQeejuBxrWrs3xCD0sm5nydRji/L8e/h791hQ8fh2OluwbrLW5NeW0HbgfWFLWDiAQCrwL9gdbA\ncBE502R9KvCyqjYHfgBGlm+45ad3796cOnWK119//ey2pKQkwsLCeO+998jLyyMtLY01a9bQuXNn\n9u/fT3h4OA8++CCjRo1i8+bNJXqdWrVqERUVxcKFCwFnMcDWrVvL5T15RVCws5rlvuUQXAsW3gez\neju96b/b4lxoPyPnJCT/y1mf/1IbSHgTuo6FcZugxY3uvQeP0GpVePWua3huUDSHfjzJvXO+5PaZ\n61kYf5Dk1MyznR/z85Ujmdl8knyEEW/Fcf201SzanMJD1zdj8cPX0ay+DzZOM74hqqdTbPWaX0DC\nW/BKB6dNRPJypxBrBXFlyktVk4Hihv6dgT2q+o1n3wXArSKSDPQG7vLsNxeYAswsr3jLk4jw/vvv\n8+ijjzJ16lSCg4OJjIxk+vTpZGVl0b59e0SEF198kYYNGzJ37lz+9Kc/ERQURGhoaKEjlKLMnz+f\nhx9+mGeeeYacnByGDRtG+/bty/HdeUFUT3hoDWye6/yifPpH56tqKEgA5J6CPM/UXUgdaDsIOo2E\nK86fCnSTiHBXlybcERPBooQU/rZ6L5MWJQFQtUoA9UOr8f2xbHLynJFLvdBqTLihOcO7NLGui6Zk\najaEgS87i09WP+d8sPry785jtaNg+Lvlsly+IFfL14vIZ8ATqhpfyGN3Ajef6TEvIvcCXXCSx0bP\n6AQRaQysVNW2RbzGaGA0QJMmTWL279//k8etfP35fPqcZH0Pe1fDoQQnoVSpClVCoElXiOzhLEH2\nA3n5yrf/zWLHd5ns/C6TtGOnaHhZMJeHhdCkTnW6Navrejl84+dysiF1Kxzc6JRruW2mM9q/CCUt\nX19uIxQRWQU0LOSh36jqsvJ63XOp6uvA6+D0Q6mo1zXlJLQBtB/qfPmxwACheYOaNG9Q066LmPIR\nFOzcCNmkS4W9ZLklFFUt6+T1IaBxgZ8bebalA2EiUkVVcwtsN8YY4yJfHlPHAS08K7qqAsOAD9SZ\no1sNnGmvdx9QphFPZepaWRw7F8aYi+XWsuFBIpICdAM+FJGPPNuvEJEVAJ7Rx3jgIyAZ+Keq7vAc\n4inglyKyB6gLzLnYWIKDg0lPT7c/pDjJJD09neDgYLdDMcb4oUrfUz4nJ4eUlBSys32vcqcbgoOD\nadSoEUFB/nFx2xhT/ly/KO8vgoKCiIqKcjsMY4zxe758DcUYY4wfsYRijDHGKyyhGGOM8YpKdVFe\nRNKA/cXuWLh6QNlqkPs/Owd2Dir7+4fKeQ6aqmr94naqVAmlLEQkviSrHC5ldg7sHFT29w92Di7E\npryMMcZ4hSUUY4wxXmEJpeReL36XS56dAzsHlf39g52DItk1FGOMMV5hIxRjjDFeYQnFGGOMV1hC\nKQERuVlEdonIHhGZ7HY8FUlEGovIahHZKSI7RGSi2zG5RUQCRWSLiCx3OxY3iEiYiCwSka9EJFlE\nurkdU0UTkcc8vwfbReRdEbHS3AVYQimGiAQCrwL9gdbAcBFp7W5UFSoXeFxVWwNdgXGV7P0XNBGn\nlUJl9Rfg36raEmhPJTsXIhIBPAJ08rQcD8Tp02Q8LKEUrzOwR1W/UdXTwALgVpdjqjCqmqqqmz3f\nH8P5I1LpetaKSCPgZ8Bst2Nxg4hcBvTC03tIVU+r6o/uRuWKKkCIiFQBqgPfuRyPT7GEUrwI4GCB\nn1OohH9QAUQkEugIbHI3EldMB54E8t0OxCVRQBrwpmfab7aI1HA7qIqkqoeAacABIBXIUNWP3Y3K\nt1hCMSUiIqHAYuBRVc10O56KJCIDge9VNcHtWFxUBbgGmKmqHYHjQGW7nlgbZ3YiCrgCqCEi97gb\nlW+xhFK8Q0DjAj838myrNEQkCCeZzFfVJW7H44LuwC0isg9nyrO3iPzD3ZAqXAqQoqpnRqeLcBJM\nZXIj8K2qpqlqDrAEuM7lmHyKJZTixQEtRCRKRKriXIT7wOWYKoyICM68ebKqvuR2PG5Q1V+paiNV\njcT5//+pqlaqT6aqehg4KCJXezb1AXa6GJIbDgBdRaS65/eiD5VsYUJxKn0L4OKoaq6IjAc+wlnV\n8Yaq7nA5rIrUHbgX2CYiiZ5tv1bVFS7GZNwxAZjv+WD1DfCAy/FUKFXdJCKLgM04qx+3YGVYfsJK\nrxhjjPEKm/IyxhjjFZZQjDHGeIUlFGOMMV5hCcUYY4xXWEIxxhjjFZZQjKlAIrK+FPt+JiKditln\nn4jUK8Ux7xeRv5Z0f2NKwxKKMRVIVe3OanPJsoRiTCFE5FoRSRKRYBGp4emB0baQ/ZaKSILn8dGe\nbU1FZLeI1BORABFZKyJ9PY9lef57uYisEZFET2+NnsXEM1NE4j2v8/tzHn5SRLaJyJci0tyzf30R\nWSwicZ6v7l45McZcgN0pb0whVDVORD4AngFCgH+o6vZCdh2hqkdFJASIE5HFqrpfRKYCM4EvgZ2F\nVKW9C/hIVZ/19NypXkxIv/G8TiDwiYi0U9Ukz2MZqhotIr/AqYo8EKd3ycuquk5EmuBUemhV+jNh\nTMlZQjGmaH/AqeWWjdNYqTCPiMggz/eNgRZAuqrOFpHBwBigQyHPiwPe8BTeXKqqiYXsU9AQzwio\nCnA5TrO3Mwnl3QL/fdnz/Y1Aa6fkFAC1PBWjjSk3NuVlTNHqAqFATeC8Vq8iEovzh7ubqrbHqe0U\n7HmsOk5lajzH+AlVXYPTsOoQ8JZndFEoEYkCngD6qGo74MNz4tFCvg8AuqpqB89XhKpmFfuOjSkD\nSyjGFO3vwP8B84GphTx+GfCDqp4QkZY4LZLPmOp53m+BWec+UUSaAkdUdRZOF8gLlYKvhdN/JENE\nwnHaURc0tMB/N3i+/xinmOOZ1ytslGSMV9mUlzGF8IwYclT1Hc91i/Ui0ltVPy2w27+BMSKSDOwC\nNnqeez1wLdBdVfNE5A4ReUBV3yzw3FhgkojkAFlAkSMUVd0qIluAr3C6h35xzi61RSQJOAUM92x7\nBHjVs70KsAZn+s2YcmPVho0xxniFTXkZY4zxCksoxhhjvMISijHGGK+whGKMMcYrLKEYY4zxCkso\nxhhjvMISijHGGK/4fzMXhJO6g5/uAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6xiKycpclhO",
        "colab_type": "text"
      },
      "source": [
        "###Subplots\n",
        "You can plot different things in the same figure using the subplot function. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gi8yb9hecjJK",
        "colab_type": "code",
        "outputId": "dfbe9a51-743d-44e8-a184-6f141109b2b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "# Compute the x and y coordinates for points on sine and cosine curves\n",
        "x = np.arange(0, 3 * np.pi, 0.1)\n",
        "y_sin = np.sin(x)\n",
        "y_cos = np.cos(x)\n",
        "\n",
        "# Set up a subplot grid that has height 2 and width 1,\n",
        "# and set the first such subplot as active.\n",
        "plt.subplot(2, 1, 1)\n",
        "\n",
        "# Make the first plot\n",
        "plt.plot(x, y_sin)\n",
        "plt.title('Sine')\n",
        "\n",
        "# Set the second subplot as active, and make the second plot.\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.plot(x, y_cos)\n",
        "plt.title('Cosine')\n",
        "\n",
        "# Show the figure.\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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C7wKvAC2BMOB9YKiRuYQwgk0Vu1JqoFJqj1IqUyn1uNF5LEkp1UYptVYptUsp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\n+1BEwaAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}