Digit Classification with Softmax.ipynb

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   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
    "    </a>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Digit Classification with Softmax</h1>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Objectives</h2>\n",
    "\n",
    "<ul>\n",
    "    <li>Download the Training and Validation MNIST Digit Images</li>\n",
    "    <li>Create a Softmax Classifier using PyTorch</li>\n",
    "    <li>Create a Criterion, Optimizer, and Data Loaders</li>\n",
    "    <li>Create a Data Loader and set the Batch Size</li>\n",
    "    <li>Train a Model</li>\n",
    "    <li>Analyze Results and Model</li>\n",
    "</ul> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of Contents</h2>\n",
    "<p>In this lab, you will use a single-layer Softmax Classifier to classify handwritten digits from the MNIST database.</p>\n",
    "\n",
    "<ul>\n",
    "    <li><a href=\"#Makeup_Data\">Make some Data</a></li>\n",
    "    <li><a href=\"#Classifier\">Build a Softmax Classifier</a></li>\n",
    "    <li><a href=\"#Model\">Define Softmax, Criterion Function, Optimizer, and Train the Model</a></li>\n",
    "    <li><a href=\"#Result\">Analyze Results</a></li>\n",
    "</ul>\n",
    "<p>Estimated Time Needed: <strong>25 min</strong></p>\n",
    "\n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Preparation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll need the following libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: torch in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (1.13.1+cpu)\n",
      "Requirement already satisfied: torchvision in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (0.14.1+cpu)\n",
      "Requirement already satisfied: torchaudio in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (0.13.1+cpu)\n",
      "Requirement already satisfied: typing-extensions in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from torch) (4.5.0)\n",
      "Requirement already satisfied: numpy in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from torchvision) (1.21.6)\n",
      "Requirement already satisfied: requests in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from torchvision) (2.29.0)\n",
      "Requirement already satisfied: pillow!=8.3.*,>=5.3.0 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from torchvision) (8.1.0)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from requests->torchvision) (3.1.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from requests->torchvision) (3.4)\n",
      "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from requests->torchvision) (1.26.15)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from requests->torchvision) (2023.5.7)\n"
     ]
    }
   ],
   "source": [
    "!pip3 install torch torchvision torchaudio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Import the libraries we need for this lab\n",
    "\n",
    "# Using the following line code to install the torchvision library\n",
    "# !conda install -y torchvision\n",
    "\n",
    "# PyTorch Library\n",
    "import torch \n",
    "# PyTorch Neural Network\n",
    "import torch.nn as nn\n",
    "# Allows us to transform data\n",
    "import torchvision.transforms as transforms\n",
    "# Allows us to get the digit dataset\n",
    "import torchvision.datasets as dsets\n",
    "# Creating graphs\n",
    "import matplotlib.pylab as plt\n",
    "# Allows us to use arrays to manipulate and store data\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the following function to plot out the parameters of the Softmax function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# The function to plot parameters\n",
    "\n",
    "def PlotParameters(model): \n",
    "    W = model.state_dict()['linear.weight'].data\n",
    "    w_min = W.min().item()\n",
    "    w_max = W.max().item()\n",
    "    fig, axes = plt.subplots(2, 5)\n",
    "    fig.subplots_adjust(hspace=0.01, wspace=0.1)\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        if i < 10:\n",
    "            \n",
    "            # Set the label for the sub-plot.\n",
    "            ax.set_xlabel(\"class: {0}\".format(i))\n",
    "\n",
    "            # Plot the image.\n",
    "            ax.imshow(W[i, :].view(28, 28), vmin=w_min, vmax=w_max, cmap='seismic')\n",
    "\n",
    "            ax.set_xticks([])\n",
    "            ax.set_yticks([])\n",
    "\n",
    "        # Ensure the plot is shown correctly with multiple plots\n",
    "        # in a single Notebook cell.\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the following function to visualize the data: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Plot the data\n",
    "def show_data(data_sample):\n",
    "    plt.imshow(data_sample[0].numpy().reshape(28, 28), cmap='gray')\n",
    "    plt.title('y = ' + str(data_sample[1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Makeup_Data\">Make Some Data</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the <em>training</em> dataset by setting the parameters <code>train</code> to <code>True</code> and convert it to a tensor by placing a transform object in the argument <code>transform</code>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
      "Failed to download (trying next):\n",
      "HTTP Error 403: Forbidden\n",
      "\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz to ./data/MNIST/raw/train-images-idx3-ubyte.gz\n"
     ]
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     "metadata": {},
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/train-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
      "Failed to download (trying next):\n",
      "HTTP Error 403: Forbidden\n",
      "\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz to ./data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
      "Failed to download (trying next):\n",
      "HTTP Error 403: Forbidden\n",
      "\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
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     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
      "Failed to download (trying next):\n",
      "HTTP Error 403: Forbidden\n",
      "\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz\n",
      "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
      "\n",
      "Print the training dataset:\n",
      "  Dataset MNIST\n",
      "    Number of datapoints: 60000\n",
      "    Root location: ./data\n",
      "    Split: Train\n",
      "    StandardTransform\n",
      "Transform: ToTensor()\n"
     ]
    }
   ],
   "source": [
    "# Create and print the training dataset\n",
    "\n",
    "train_dataset = dsets.MNIST(root='./data', train=True, download=True, transform=transforms.ToTensor())\n",
    "print(\"Print the training dataset:\\n \", train_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the <em>testing</em> dataset and convert it to a tensor by placing a transform object in the argument <code>transform</code>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Print the validation dataset:\n",
      "  Dataset MNIST\n",
      "    Number of datapoints: 60000\n",
      "    Root location: ./data\n",
      "    Split: Train\n",
      "    StandardTransform\n",
      "Transform: ToTensor()\n"
     ]
    }
   ],
   "source": [
    "# Create and print the validation dataset\n",
    "\n",
    "validation_dataset = dsets.MNIST(root='./data', download=True, transform=transforms.ToTensor())\n",
    "print(\"Print the validation dataset:\\n \", validation_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access the data by indexing the train_dataset and test_dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First Image and Label\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaEAAAGxCAYAAADLfglZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAc3UlEQVR4nO3df2zU9R3H8dfJjxNYe66B9lopXWdQN8swAhYbFVDpbCYT0ARwP8pcjAplkvojQ+KsW6QEBzGm6hxxHWyiZJk/cBKkC7TgGKwwGAQMwVlslTaNHdyVgq21n/1BuHhSS7/Hlfdd+3wkn4T7fr9vvu9+/doXn/vxOZ9zzgkAAAOXWDcAABi4CCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIISCJ+Hy+bsfy5cutWwNiMti6AQDe3H333Xr44Yejto0ZM8aoG+DCEEJAksnIyNDkyZOt2wDigqfjgB5s375dPp9Pr7766jn71q5dK5/Pp9raWoPOgP7BxyraQM+uu+46DR8+XO+9917U9uuvv16S9K9//avH+s7Ozl6dZ9CgQfL5fD0e4/P59M1vflOnT59WV1eX8vLyVFJSop/97Ge9OgeQaJgJAefxi1/8Qv/4xz+0b9++yLba2lrV1taqpKSkx9qjR49qyJAhvRo1NTXn7eWee+5RRUWFNm/erHXr1ikjI0P33nuvnnjiiQv9MQETzISA82hvb9eYMWP0wx/+UKtXr5Yk/fSnP9WmTZvU0NAgv9//tbUdHR3av39/r85z1VVXKSUlxXN/M2bM0KZNm3Ts2DGNGjXKcz1giRACeuFXv/qVVq5cqU8++USff/65srOzVVpaqmXLlp23Np5Px3Vn/fr1mjt3rjZu3KiioiLP9YAlno4DeuHBBx/U559/rj/84Q9avXq1Ojs79cADD5y3Lt5Px3Xn7L8jL7mE/52RfJgJAb30ox/9SLt27VJHR4cmTJigN95447w1F+PpuB/84AeqqqrSsWPHNHLkSM/1gCU+JwT00kMPPaT8/HxJUmVlZa9qhg4dqokTJ8bl/M8884wOHTqkW2+9VaNHj1Zzc7Nefvllbd68WWVlZQQQkhIzIcCD3NxcDRs2TIcOHbro53777be1YsUKHT58WMePH9ewYcN07bXXasGCBZo7d+5F7weIB0II6KX9+/dr/Pjxev7557VgwQLrdoB+gRACzuO///2vPvroIz3++OOqr6/XBx98oOHDh1u3BfQLvJ0GOI/f/OY3mj59uk6ePKm//OUvBBAQR8yEAABmmAkBAMwQQgAAM4QQAMBMwn1YtaurS8eOHVNKSkpM62gBAGw559Ta2qqsrKzzLieVcCF07NgxZWdnW7cBALhADQ0NGj16dI/HJNzTcbGsnQUASDy9+X3eZyH0wgsvKDc3V5deeqkmTJig7du396qOp+AAoH/oze/zPgmh9evXa/HixVq6dKn27t2rm266SUVFRaqvr++L0wEAklSffFg1Pz9f1113nV588cXItu985zuaOXOmysvLe6wNh8MKBALxbgkAcJGFQiGlpqb2eEzcZ0IdHR3as2ePCgsLo7YXFhZqx44d5xzf3t6ucDgcNQAAA0PcQ+jTTz/VF198oYyMjKjtGRkZampqOuf48vJyBQKByOCdcQAwcPTZGxO++oKUc67bF6mWLFmiUCgUGQ0NDX3VEgAgwcT9c0IjR47UoEGDzpn1NDc3nzM7kiS/3y+/3x/vNgAASSDuM6GhQ4dqwoQJqqqqitpeVVWlgoKCeJ8OAJDE+mTFhNLSUv3kJz/RxIkTdcMNN+j3v/+96uvr9cADD/TF6QAASapPQmjOnDlqaWnRr3/9azU2NiovL08bN25UTk5OX5wOAJCkEu5L7ficEAD0DyafEwIAoLcIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmBls3QCQSAYNGuS5JhAI9EEn8VFSUhJT3fDhwz3XXHXVVZ5rFi5c6Lnmt7/9reeaefPmea6RpM8++8xzzfLlyz3XPPXUU55r+gtmQgAAM4QQAMBM3EOorKxMPp8vagSDwXifBgDQD/TJa0LXXHON/v73v0cex/I8OwCg/+uTEBo8eDCzHwDAefXJa0JHjhxRVlaWcnNzNXfuXH344Ydfe2x7e7vC4XDUAAAMDHEPofz8fK1du1bvvvuuVq9eraamJhUUFKilpaXb48vLyxUIBCIjOzs73i0BABJU3EOoqKhId911l8aNG6fbbrtN77zzjiRpzZo13R6/ZMkShUKhyGhoaIh3SwCABNXnH1YdMWKExo0bpyNHjnS73+/3y+/393UbAIAE1OefE2pvb9f777+vzMzMvj4VACDJxD2EHnnkEdXU1Kiurk67du3S3XffrXA4rOLi4nifCgCQ5OL+dNzHH3+sefPm6dNPP9WoUaM0efJk7dy5Uzk5OfE+FQAgycU9hF577bV4/5VIUGPGjPFcM3ToUM81BQUFnmtuvPFGzzWSdNlll3muueuuu2I6V3/z8ccfe6557rnnPNfMmjXLc01ra6vnGkn6z3/+47mmpqYmpnMNVKwdBwAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADCEEADBDCAEAzBBCAAAzhBAAwIzPOeesm/iycDisQCBg3caAcu2118ZUt2XLFs81/LdNDl1dXZ5r7r33Xs81J0+e9FwTi8bGxpjqjh8/7rnm8OHDMZ2rPwqFQkpNTe3xGGZCAAAzhBAAwAwhBAAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADCEEADBDCAEAzBBCAAAzg60bgL36+vqY6lpaWjzXsIr2Gbt27fJcc+LECc8106ZN81wjSR0dHZ5r/vSnP8V0LgxszIQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYYQFT6H//+19MdY8++qjnmjvuuMNzzd69ez3XPPfcc55rYrVv3z7PNdOnT/dc09bW5rnmmmuu8VwjSQ899FBMdYBXzIQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCY8TnnnHUTXxYOhxUIBKzbQB9JTU31XNPa2uq55qWXXvJcI0k///nPPdf8+Mc/9lzz6quveq4Bkk0oFDrv//PMhAAAZgghAIAZzyG0bds2zZgxQ1lZWfL5fHrzzTej9jvnVFZWpqysLA0bNkxTp07VwYMH49UvAKAf8RxCbW1tGj9+vCoqKrrdv2LFCq1atUoVFRWqra1VMBjU9OnTY3peHwDQv3n+ZtWioiIVFRV1u885p2effVZLly7V7NmzJUlr1qxRRkaG1q1bp/vvv//CugUA9CtxfU2orq5OTU1NKiwsjGzz+/2aMmWKduzY0W1Ne3u7wuFw1AAADAxxDaGmpiZJUkZGRtT2jIyMyL6vKi8vVyAQiIzs7Ox4tgQASGB98u44n88X9dg5d862s5YsWaJQKBQZDQ0NfdESACABeX5NqCfBYFDSmRlRZmZmZHtzc/M5s6Oz/H6//H5/PNsAACSJuM6EcnNzFQwGVVVVFdnW0dGhmpoaFRQUxPNUAIB+wPNM6OTJk/rggw8ij+vq6rRv3z6lpaVpzJgxWrx4sZYtW6axY8dq7NixWrZsmYYPH6577rknro0DAJKf5xDavXu3pk2bFnlcWloqSSouLtYf//hHPfbYYzp9+rQWLFig48ePKz8/X5s3b1ZKSkr8ugYA9AssYIp+6Zlnnomp7uw/qryoqanxXHPbbbd5runq6vJcA1hiAVMAQEIjhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJhhFW30SyNGjIip7u233/ZcM2XKFM81RUVFnms2b97suQawxCraAICERggBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADCEEADBDCAEAzBBCAAAzhBAAwAwLmAJfcsUVV3iu+fe//+255sSJE55rtm7d6rlm9+7dnmsk6fnnn/dck2C/SpAAWMAUAJDQCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmGEBU+ACzZo1y3NNZWWl55qUlBTPNbF6/PHHPdesXbvWc01jY6PnGiQPFjAFACQ0QggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZljAFDCQl5fnuWbVqlWea2699VbPNbF66aWXPNc8/fTTnms++eQTzzWwwQKmAICERggBAMx4DqFt27ZpxowZysrKks/n05tvvhm1f/78+fL5fFFj8uTJ8eoXANCPeA6htrY2jR8/XhUVFV97zO23367GxsbI2Lhx4wU1CQDonwZ7LSgqKlJRUVGPx/j9fgWDwZibAgAMDH3ymlB1dbXS09N15ZVX6r777lNzc/PXHtve3q5wOBw1AAADQ9xDqKioSK+88oq2bNmilStXqra2Vrfccova29u7Pb68vFyBQCAysrOz490SACBBeX467nzmzJkT+XNeXp4mTpyonJwcvfPOO5o9e/Y5xy9ZskSlpaWRx+FwmCACgAEi7iH0VZmZmcrJydGRI0e63e/3++X3+/u6DQBAAurzzwm1tLSooaFBmZmZfX0qAECS8TwTOnnypD744IPI47q6Ou3bt09paWlKS0tTWVmZ7rrrLmVmZuro0aN6/PHHNXLkSM2aNSuujQMAkp/nENq9e7emTZsWeXz29Zzi4mK9+OKLOnDggNauXasTJ04oMzNT06ZN0/r165WSkhK/rgEA/QILmAJJ4rLLLvNcM2PGjJjOVVlZ6bnG5/N5rtmyZYvnmunTp3uugQ0WMAUAJDRCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlW0QZwjvb2ds81gwd7/6Lmzs5OzzXf//73PddUV1d7rsGFYxVtAEBCI4QAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYMb7ioMALtj3vvc9zzV3332355pJkyZ5rpFiW4w0FocOHfJcs23btj7oBFaYCQEAzBBCAAAzhBAAwAwhBAAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADCEEADDDAqbAl1x11VWea0pKSjzXzJ4923NNMBj0XHMxffHFF55rGhsbPdd0dXV5rkHiYiYEADBDCAEAzBBCAAAzhBAAwAwhBAAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADAuYIuHFsnDnvHnzYjpXLIuRfutb34rpXIls9+7dnmuefvppzzUbNmzwXIP+hZkQAMAMIQQAMOMphMrLyzVp0iSlpKQoPT1dM2fO1OHDh6OOcc6prKxMWVlZGjZsmKZOnaqDBw/GtWkAQP/gKYRqamq0cOFC7dy5U1VVVers7FRhYaHa2toix6xYsUKrVq1SRUWFamtrFQwGNX36dLW2tsa9eQBAcvP0xoRNmzZFPa6srFR6err27Nmjm2++Wc45Pfvss1q6dGnkmyPXrFmjjIwMrVu3Tvfff3/8OgcAJL0Lek0oFApJktLS0iRJdXV1ampqUmFhYeQYv9+vKVOmaMeOHd3+He3t7QqHw1EDADAwxBxCzjmVlpbqxhtvVF5eniSpqalJkpSRkRF1bEZGRmTfV5WXlysQCERGdnZ2rC0BAJJMzCFUUlKi/fv369VXXz1nn8/ni3rsnDtn21lLlixRKBSKjIaGhlhbAgAkmZg+rLpo0SJt2LBB27Zt0+jRoyPbz36osKmpSZmZmZHtzc3N58yOzvL7/fL7/bG0AQBIcp5mQs45lZSU6PXXX9eWLVuUm5sbtT83N1fBYFBVVVWRbR0dHaqpqVFBQUF8OgYA9BueZkILFy7UunXr9NZbbyklJSXyOk8gENCwYcPk8/m0ePFiLVu2TGPHjtXYsWO1bNkyDR8+XPfcc0+f/AAAgOTlKYRefPFFSdLUqVOjtldWVmr+/PmSpMcee0ynT5/WggULdPz4ceXn52vz5s1KSUmJS8MAgP7D55xz1k18WTgcViAQsG4DvfB1r/P15Lvf/a7nmoqKCs81V199teeaRLdr1y7PNc8880xM53rrrbc813R1dcV0LvRfoVBIqampPR7D2nEAADOEEADADCEEADBDCAEAzBBCAAAzhBAAwAwhBAAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADMxfbMqEldaWprnmpdeeimmc1177bWea7797W/HdK5EtmPHDs81K1eu9Fzz7rvveq45ffq05xrgYmImBAAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADCEEADBDCAEAzBBCAAAzhBAAwAwLmF4k+fn5nmseffRRzzXXX3+955rLL7/cc02iO3XqVEx1zz33nOeaZcuWea5pa2vzXAP0R8yEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmGEB04tk1qxZF6XmYjp06JDnmr/97W+eazo7Oz3XrFy50nONJJ04cSKmOgCxYSYEADBDCAEAzBBCAAAzhBAAwAwhBAAwQwgBAMwQQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADAjM8556yb+LJwOKxAIGDdBgDgAoVCIaWmpvZ4DDMhAIAZQggAYMZTCJWXl2vSpElKSUlRenq6Zs6cqcOHD0cdM3/+fPl8vqgxefLkuDYNAOgfPIVQTU2NFi5cqJ07d6qqqkqdnZ0qLCxUW1tb1HG33367GhsbI2Pjxo1xbRoA0D94+mbVTZs2RT2urKxUenq69uzZo5tvvjmy3e/3KxgMxqdDAEC/dUGvCYVCIUlSWlpa1Pbq6mqlp6fryiuv1H333afm5uav/Tva29sVDoejBgBgYIj5LdrOOd155506fvy4tm/fHtm+fv16feMb31BOTo7q6ur0xBNPqLOzU3v27JHf7z/n7ykrK9NTTz0V+08AAEhIvXmLtlyMFixY4HJyclxDQ0OPxx07dswNGTLE/fWvf+12/2effeZCoVBkNDQ0OEkMBoPBSPIRCoXOmyWeXhM6a9GiRdqwYYO2bdum0aNH93hsZmamcnJydOTIkW73+/3+bmdIAID+z1MIOee0aNEivfHGG6qurlZubu55a1paWtTQ0KDMzMyYmwQA9E+e3piwcOFC/fnPf9a6deuUkpKipqYmNTU16fTp05KkkydP6pFHHtE///lPHT16VNXV1ZoxY4ZGjhypWbNm9ckPAABIYl5eB9LXPO9XWVnpnHPu1KlTrrCw0I0aNcoNGTLEjRkzxhUXF7v6+vpenyMUCpk/j8lgMBiMCx+9eU2IBUwBAH2CBUwBAAmNEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGCGEAIAmCGEAABmCCEAgBlCCABghhACAJghhAAAZgghAIAZQggAYIYQAgCYIYQAAGYIIQCAGUIIAGAm4ULIOWfdAgAgDnrz+zzhQqi1tdW6BQBAHPTm97nPJdjUo6urS8eOHVNKSop8Pl/UvnA4rOzsbDU0NCg1NdWoQ3tchzO4DmdwHc7gOpyRCNfBOafW1lZlZWXpkkt6nusMvkg99doll1yi0aNH93hMamrqgL7JzuI6nMF1OIPrcAbX4Qzr6xAIBHp1XMI9HQcAGDgIIQCAmaQKIb/fryeffFJ+v9+6FVNchzO4DmdwHc7gOpyRbNch4d6YAAAYOJJqJgQA6F8IIQCAGUIIAGCGEAIAmCGEAABmkiqEXnjhBeXm5urSSy/VhAkTtH37duuWLqqysjL5fL6oEQwGrdvqc9u2bdOMGTOUlZUln8+nN998M2q/c05lZWXKysrSsGHDNHXqVB08eNCm2T50vuswf/78c+6PyZMn2zTbR8rLyzVp0iSlpKQoPT1dM2fO1OHDh6OOGQj3Q2+uQ7LcD0kTQuvXr9fixYu1dOlS7d27VzfddJOKiopUX19v3dpFdc0116ixsTEyDhw4YN1Sn2tra9P48eNVUVHR7f4VK1Zo1apVqqioUG1trYLBoKZPn97vFsM933WQpNtvvz3q/ti4ceNF7LDv1dTUaOHChdq5c6eqqqrU2dmpwsJCtbW1RY4ZCPdDb66DlCT3g0sS119/vXvggQeitl199dXul7/8pVFHF9+TTz7pxo8fb92GKUnujTfeiDzu6upywWDQLV++PLLts88+c4FAwP3ud78z6PDi+Op1cM654uJid+edd5r0Y6W5udlJcjU1Nc65gXs/fPU6OJc890NSzIQ6Ojq0Z88eFRYWRm0vLCzUjh07jLqyceTIEWVlZSk3N1dz587Vhx9+aN2Sqbq6OjU1NUXdG36/X1OmTBlw94YkVVdXKz09XVdeeaXuu+8+NTc3W7fUp0KhkCQpLS1N0sC9H756Hc5KhvshKULo008/1RdffKGMjIyo7RkZGWpqajLq6uLLz8/X2rVr9e6772r16tVqampSQUGBWlparFszc/a//0C/NySpqKhIr7zyirZs2aKVK1eqtrZWt9xyi9rb261b6xPOOZWWlurGG29UXl6epIF5P3R3HaTkuR8S7qscevLV7xdyzp2zrT8rKiqK/HncuHG64YYbdMUVV2jNmjUqLS017MzeQL83JGnOnDmRP+fl5WnixInKycnRO++8o9mzZxt21jdKSkq0f/9+vffee+fsG0j3w9ddh2S5H5JiJjRy5EgNGjTonH/JNDc3n/MvnoFkxIgRGjdunI4cOWLdipmz7w7k3jhXZmamcnJy+uX9sWjRIm3YsEFbt26N+v6xgXY/fN116E6i3g9JEUJDhw7VhAkTVFVVFbW9qqpKBQUFRl3Za29v1/vvv6/MzEzrVszk5uYqGAxG3RsdHR2qqakZ0PeGJLW0tKihoaFf3R/OOZWUlOj111/Xli1blJubG7V/oNwP57sO3UnY+8HwTRGevPbaa27IkCHu5ZdfdocOHXKLFy92I0aMcEePHrVu7aJ5+OGHXXV1tfvwww/dzp073R133OFSUlL6/TVobW11e/fudXv37nWS3KpVq9zevXvdRx995Jxzbvny5S4QCLjXX3/dHThwwM2bN89lZma6cDhs3Hl89XQdWltb3cMPP+x27Njh6urq3NatW90NN9zgLr/88n51HR588EEXCARcdXW1a2xsjIxTp05FjhkI98P5rkMy3Q9JE0LOOff888+7nJwcN3ToUHfddddFvR1xIJgzZ47LzMx0Q4YMcVlZWW727Nnu4MGD1m31ua1btzpJ54zi4mLn3Jm35T755JMuGAw6v9/vbr75ZnfgwAHbpvtAT9fh1KlTrrCw0I0aNcoNGTLEjRkzxhUXF7v6+nrrtuOqu59fkqusrIwcMxDuh/Ndh2S6H/g+IQCAmaR4TQgA0D8RQgAAM4QQAMAMIQQAMEMIAQDMEEIAADOEEADADCEEADBDCAEAzBBCAAAzhBAAwMz/AXRGFJU6iWhZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Print the first image and label\n",
    "\n",
    "print(\"First Image and Label\") \n",
    "show_data(train_dataset[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each element in the rectangular tensor corresponds to a number which represents a pixel intensity, as demonstrated by the following image:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DL0110EN/notebook_images%20/chapter3/3.32_image_values.png\" width=\"550\" alt=\"MNIST elements\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this image, the values are inverted i.e black represents white.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print out the label of the fourth element:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The label:  1\n"
     ]
    }
   ],
   "source": [
    "# Print the label\n",
    "print(\"The label: \", train_dataset[3][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result shows the number in the image is 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot  the fourth sample:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The image: \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the image\n",
    "\n",
    "print(\"The image: \")\n",
    "show_data(train_dataset[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You see that it is a 1. Now, plot the third sample:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the image\n",
    "\n",
    "show_data(train_dataset[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"#Classifier\">Build a Softmax Classifer</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build a Softmax classifier class: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Define softmax classifier class\n",
    "# Inherits nn.Module which is the base class for all neural networks\n",
    "class SoftMax(nn.Module):\n",
    "    \n",
    "    # Constructor\n",
    "    def __init__(self, input_size, output_size):\n",
    "        super(SoftMax, self).__init__()\n",
    "        # Creates a layer of given input size and output size\n",
    "        self.linear = nn.Linear(input_size, output_size)\n",
    "        \n",
    "    # Prediction\n",
    "    def forward(self, x):\n",
    "        # Runs the x value through the single layers defined above\n",
    "        z = self.linear(x)\n",
    "        return z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Softmax function requires vector inputs. Note that the vector shape is 28x28.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28, 28])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the shape of the training dataset\n",
    "\n",
    "train_dataset[0][0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Flatten the tensor as shown in this image: \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DL0110EN/notebook_images%20/chapter3/3.3.2image_to_vector.gif\" width=\"550\" alt=\"Flattern Image\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The size of the tensor is now 784.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DL0110EN/notebook_images%20/chapter3/3.3.2Imagetovector2.png\" width=\"550\" alt=\"Flattern Image\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the input size and output size: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Set input size and output size\n",
    "\n",
    "input_dim = 28 * 28\n",
    "output_dim = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Model\">Define the Softmax Classifier, Criterion Function, Optimizer, and Train the Model</h2> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Print the model:\n",
      "  SoftMax(\n",
      "  (linear): Linear(in_features=784, out_features=10, bias=True)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Create the model\n",
    "# Input dim is 28*28 which is the image converted to a tensor\n",
    "# Output dim is 10 because there are 10 possible digits the image can be\n",
    "model = SoftMax(input_dim, output_dim)\n",
    "print(\"Print the model:\\n \", model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "View the size of the model parameters: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W:  torch.Size([10, 784])\n",
      "b:  torch.Size([10])\n"
     ]
    }
   ],
   "source": [
    "# Print the parameters\n",
    "\n",
    "print('W: ',list(model.parameters())[0].size())\n",
    "print('b: ',list(model.parameters())[1].size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can convert the model parameters for each class to a rectangular grid:  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a>     <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DL0110EN/notebook_images%20/chapter3/3.3.2paramaters_to_image.gif\" width=\"550,\" align=\"center\"></a> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the model parameters for each class as a square image: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the model parameters for each class\n",
    "# Since the model has not been trained yet the parameters look random\n",
    "\n",
    "PlotParameters(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can make a prediction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 28, 28])\n",
      "torch.Size([1, 784])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[ 0.1357,  0.2446,  0.1891, -0.0175,  0.1361,  0.1867, -0.0965,  0.0016,\n",
       "          0.2423,  0.0106]], grad_fn=<AddmmBackward0>)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First we get the X value of the first image\n",
    "X = train_dataset[0][0]\n",
    "# We can see the shape is 1 by 28 by 28, we need it to be flattened to 1 by 28 * 28 (784)\n",
    "print(X.shape)\n",
    "X = X.view(-1, 28*28)\n",
    "print(X.shape)\n",
    "# Now we can make a prediction, each class has a value, and the higher it is the more confident the model is that it is that digit\n",
    "model(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the learning rate, optimizer, criterion, data loader:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Define the learning rate, optimizer, criterion, and data loader\n",
    "\n",
    "learning_rate = 0.1\n",
    "# The optimizer will updates the model parameters using the learning rate\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)\n",
    "# The criterion will measure the loss between the prediction and actual label values\n",
    "# This is where the SoftMax occurs, it is built into the Criterion Cross Entropy Loss\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "# Created a training data loader so we can set the batch size\n",
    "train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=100)\n",
    "# Created a validation data loader so we can set the batch size\n",
    "validation_loader = torch.utils.data.DataLoader(dataset=validation_dataset, batch_size=5000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How Cross Entropy Loss uses SoftMax\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have X which is the X values of the first image and `actual` which is the the digit class the image belongs to. The output `model_output` is the value the model assigns to each class for that image.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:  tensor([[ 0.1357,  0.2446,  0.1891, -0.0175,  0.1361,  0.1867, -0.0965,  0.0016,\n",
      "          0.2423,  0.0106]], grad_fn=<AddmmBackward0>)\n",
      "Actual: tensor([5])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_output = model(X)\n",
    "actual = torch.tensor([train_dataset[0][1]])\n",
    "\n",
    "show_data(train_dataset[0])\n",
    "print(\"Output: \", model_output)\n",
    "print(\"Actual:\", actual)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The criterion will take these values and return a loss\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.2255, grad_fn=<NllLossBackward0>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "criterion(model_output, actual)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cross Entropy Loss takes probabilities and we can see that `model_output` are not probabilities, this is where softmax comes in\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0.1026, 0.1144, 0.1083, 0.0881, 0.1027, 0.1080, 0.0814, 0.0898, 0.1142,\n",
      "         0.0906]], grad_fn=<SoftmaxBackward0>)\n"
     ]
    }
   ],
   "source": [
    "softmax = nn.Softmax(dim=1)\n",
    "probability = softmax(model_output)\n",
    "print(probability)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have probabilities, we can just calculate the negative log of the probability of the class that this image belongs to. The image belongs to the target class so we calculate the negative log of the probability at the target index.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.2255], grad_fn=<MulBackward0>)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-1*torch.log(probability[0][actual])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see the result above matches the result of the criterion, this is how Cross Entropy Loss uses Softmax.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the model and determine validation accuracy **(should take a few minutes)**: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Number of times we train our model useing the training data\n",
    "n_epochs = 10\n",
    "# Lists to keep track of loss and accuracy\n",
    "loss_list = []\n",
    "accuracy_list = []\n",
    "# Size of the validation data\n",
    "N_test = len(validation_dataset)\n",
    "\n",
    "# Function to train the model based on number of epochs\n",
    "def train_model(n_epochs):\n",
    "    # Loops n_epochs times\n",
    "    for epoch in range(n_epochs):\n",
    "        # For each batch in the train loader\n",
    "        for x, y in train_loader:\n",
    "            # Resets the calculated gradient value, this must be done each time as it accumulates if we do not reset\n",
    "            optimizer.zero_grad()\n",
    "            # Makes a prediction based on the image tensor\n",
    "            z = model(x.view(-1, 28 * 28))\n",
    "            # Calculates loss between the model output and actual class\n",
    "            loss = criterion(z, y)\n",
    "            # Calculates the gradient value with respect to each weight and bias\n",
    "            loss.backward()\n",
    "            # Updates the weight and bias according to calculated gradient value\n",
    "            optimizer.step()\n",
    "        \n",
    "        # Each epoch we check how the model performs with data it has not seen which is the validation data, we are not training here\n",
    "        correct = 0\n",
    "        # For each batch in the validation loader\n",
    "        for x_test, y_test in validation_loader:\n",
    "            # Makes prediction based on image tensor\n",
    "            z = model(x_test.view(-1, 28 * 28))\n",
    "            # Finds the class with the higest output\n",
    "            _, yhat = torch.max(z.data, 1)\n",
    "            # Checks if the prediction matches the actual class and increments correct if it does\n",
    "            correct += (yhat == y_test).sum().item()\n",
    "        # Calculates the accuracy by dividing correct by size of validation dataset\n",
    "        accuracy = correct / N_test\n",
    "        # Keeps track loss\n",
    "        loss_list.append(loss.data)\n",
    "        # Keeps track of the accuracy\n",
    "        accuracy_list.append(accuracy)\n",
    "\n",
    "# Function call\n",
    "train_model(n_epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Result\">Analyze Results</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the loss and accuracy on the validation data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the loss and accuracy\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "color = 'tab:red'\n",
    "ax1.plot(loss_list,color=color)\n",
    "ax1.set_xlabel('epoch',color=color)\n",
    "ax1.set_ylabel('total loss',color=color)\n",
    "ax1.tick_params(axis='y', color=color)\n",
    "    \n",
    "ax2 = ax1.twinx()  \n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('accuracy', color=color)  \n",
    "ax2.plot( accuracy_list, color=color)\n",
    "ax2.tick_params(axis='y', color=color)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "View the results of the parameters for each class after the training. You can see that they look like the corresponding numbers. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the parameters\n",
    "\n",
    "PlotParameters(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We Plot the first five misclassified samples and the probability of that class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([7])\n",
      "probability of class  0.6780633330345154\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([7])\n",
      "probability of class  0.7085821628570557\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([5])\n",
      "probability of class  0.7326186895370483\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([8])\n",
      "probability of class  0.3735627233982086\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([6])\n",
      "probability of class  0.5076082348823547\n"
     ]
    }
   ],
   "source": [
    "# Plot the misclassified samples\n",
    "Softmax_fn=nn.Softmax(dim=-1)\n",
    "count = 0\n",
    "for x, y in validation_dataset:\n",
    "    z = model(x.reshape(-1, 28 * 28))\n",
    "    _, yhat = torch.max(z, 1)\n",
    "    if yhat != y:\n",
    "        show_data((x, y))\n",
    "        plt.show()\n",
    "        print(\"yhat:\", yhat)\n",
    "        print(\"probability of class \", torch.max(Softmax_fn(z)).item())\n",
    "        count += 1\n",
    "    if count >= 5:\n",
    "        break       "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the first five correctly classified samples and the probability of that class. We see the probability is much larger.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([5])\n",
      "probability of class  0.8640551567077637\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([0])\n",
      "probability of class  0.999725878238678\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([4])\n",
      "probability of class  0.8645159006118774\n"
     ]
    },
    {
     "data": {
      "image/png": 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99tue1/CJ2EhHXAkBAMwQIQCAGSIEADBDhAAAZogQAMAMEQIAmCFCAAAzRAgAYIYIAQDMECEAgBkiBAAwQ4QAAGb4AFP0ebt27fK85mtf+1oSJunawYMHPa8pKytL/CBACuJKCABghggBAMwQIQCAGSIEADBDhAAAZogQAMAMEQIAmCFCAAAzRAgAYIYIAQDMECEAgBkiBAAwwweYos/7+te/7nlNR0dHEibp2po1azyvuXz5chImAVIPV0IAADNECABghggBAMwQIQCAGSIEADBDhAAAZogQAMAMEQIAmCFCAAAzRAgAYIYIAQDMECEAgBk+wBS3VFVVlec1Awb07e+VDhw4YD0CkLL69v+7AQBpjQgBAMx4ilBlZaUmT56szMxM5eTkaO7cuTpx4kTcPs45VVRUKBwOa8iQISosLNTx48cTOjQAID14ilBtba0WLlyogwcPqrq6WlevXlVRUZFaW1tj+6xcuVKrVq3S6tWrVVdXp2AwqFmzZqmlpSXhwwMAUpunFybs3Lkz7uuqqirl5OTo8OHDuvfee+Wc0yuvvKLly5erpKREkrR+/Xrl5uZq48aNeuKJJxI3OQAg5d3Uc0KRSESSlJ2dLUmqr69XY2OjioqKYvv4/X7NnDnzS19B1NbWpmg0GrcBAPqHXkfIOafy8nLNmDFDBQUFkqTGxkZJUm5ubty+ubm5sfu+qLKyUoFAILaNGjWqtyMBAFJMryO0aNEiHT16VG+88Uan+3w+X9zXzrlOt123bNkyRSKR2NbQ0NDbkQAAKaZXb1ZdvHixtm3bpr1792rkyJGx24PBoKRrV0ShUCh2e1NTU6ero+v8fr/8fn9vxgAApDhPV0LOOS1atEhbtmzR7t27lZ+fH3d/fn6+gsGgqqurY7e1t7ertrZW06dPT8zEAIC04elKaOHChdq4caPefvttZWZmxp7nCQQCGjJkiHw+n5YsWaIVK1ZozJgxGjNmjFasWKGhQ4fq8ccfT8pfAACQujxFaO3atZKkwsLCuNurqqpUVlYmSXrmmWf0ySefaMGCBbp06ZKmTJmiXbt2KTMzMyEDAwDSh88556yH+LxoNKpAIGA9BnpgwoQJntf89a9/9bwmHA57XtPe3u55jSS9+uqrntc899xzntdcuXLF8xog1UQiEWVlZXW7D58dBwAwQ4QAAGaIEADADBECAJghQgAAM0QIAGCGCAEAzBAhAIAZIgQAMEOEAABmiBAAwAwRAgCYIUIAADO9+s2qgCR99atf9bzm+m/fTbb//e9/vVq3dOnSBE8CoDtcCQEAzBAhAIAZIgQAMEOEAABmiBAAwAwRAgCYIUIAADNECABghggBAMwQIQCAGSIEADBDhAAAZogQAMAMEQIAmCFCAAAzRAgAYIYIAQDMECEAgBkiBAAwQ4QAAGaIEADADBECAJghQgAAM0QIAGCGCAEAzNxmPQBS1wcffOB5zYEDBzyvmTFjhuc1AFIDV0IAADNECABghggBAMwQIQCAGSIEADBDhAAAZogQAMAMEQIAmCFCAAAzRAgAYIYIAQDMECEAgBmfc85ZD/F50WhUgUDAegwAwE2KRCLKysrqdh+uhAAAZogQAMCMpwhVVlZq8uTJyszMVE5OjubOnasTJ07E7VNWViafzxe3TZ06NaFDAwDSg6cI1dbWauHChTp48KCqq6t19epVFRUVqbW1NW6/2bNn68KFC7Ftx44dCR0aAJAePP1m1Z07d8Z9XVVVpZycHB0+fFj33ntv7Ha/369gMJiYCQEAaeumnhOKRCKSpOzs7Ljba2pqlJOTo7Fjx2r+/Plqamr60j+jra1N0Wg0bgMA9A+9fom2c04PPfSQLl26pH379sVu37Rpk77yla8oLy9P9fX1+sUvfqGrV6/q8OHD8vv9nf6ciooKvfDCC73/GwAA+qSevERbrpcWLFjg8vLyXENDQ7f7nT9/3mVkZLjNmzd3ef+VK1dcJBKJbQ0NDU4SGxsbG1uKb5FI5IYt8fSc0HWLFy/Wtm3btHfvXo0cObLbfUOhkPLy8nTy5Mku7/f7/V1eIQEA0p+nCDnntHjxYr311luqqalRfn7+Ddc0NzeroaFBoVCo10MCANKTpxcmLFy4UH/84x+1ceNGZWZmqrGxUY2Njfrkk08kSZcvX9bSpUv1z3/+U2fOnFFNTY3mzJmj4cOH6+GHH07KXwAAkMK8PA+kL/m5X1VVlXPOuY8//tgVFRW5ESNGuIyMDDd69GhXWlrqzp071+PHiEQi5j/HZGNjY2O7+a0nzwnxAaYAgKTgA0wBAH0aEQIAmCFCAAAzRAgAYIYIAQDMECEAgBkiBAAwQ4QAAGaIEADADBECAJghQgAAM0QIAGCGCAEAzBAhAIAZIgQAMEOEAABmiBAAwAwRAgCYIUIAADNECABghggBAMwQIQCAGSIEADBDhAAAZogQAMBMn4uQc856BABAAvTk3/M+F6GWlhbrEQAACdCTf899ro9denR0dOj8+fPKzMyUz+eLuy8ajWrUqFFqaGhQVlaW0YT2OA7XcByu4Thcw3G4pi8cB+ecWlpaFA6HNWBA99c6t92imXpswIABGjlyZLf7ZGVl9euT7DqOwzUch2s4DtdwHK6xPg6BQKBH+/W5H8cBAPoPIgQAMJNSEfL7/Xr++efl9/utRzHFcbiG43ANx+EajsM1qXYc+twLEwAA/UdKXQkBANILEQIAmCFCAAAzRAgAYIYIAQDMpFSE1qxZo/z8fA0ePFgTJ07Uvn37rEe6pSoqKuTz+eK2YDBoPVbS7d27V3PmzFE4HJbP59PWrVvj7nfOqaKiQuFwWEOGDFFhYaGOHz9uM2wS3eg4lJWVdTo/pk6dajNsklRWVmry5MnKzMxUTk6O5s6dqxMnTsTt0x/Oh54ch1Q5H1ImQps2bdKSJUu0fPlyHTlyRPfcc4+Ki4t17tw569FuqTvvvFMXLlyIbceOHbMeKelaW1s1fvx4rV69usv7V65cqVWrVmn16tWqq6tTMBjUrFmz0u7DcG90HCRp9uzZcefHjh07buGEyVdbW6uFCxfq4MGDqq6u1tWrV1VUVKTW1tbYPv3hfOjJcZBS5HxwKeLuu+92Tz75ZNxt3/rWt9zPf/5zo4luveeff96NHz/eegxTktxbb70V+7qjo8MFg0H34osvxm67cuWKCwQC7rXXXjOY8Nb44nFwzrnS0lL30EMPmcxjpampyUlytbW1zrn+ez588Tg4lzrnQ0pcCbW3t+vw4cMqKiqKu72oqEgHDhwwmsrGyZMnFQ6HlZ+fr0cffVSnT5+2HslUfX29Ghsb484Nv9+vmTNn9rtzQ5JqamqUk5OjsWPHav78+WpqarIeKakikYgkKTs7W1L/PR++eByuS4XzISUidPHiRX322WfKzc2Nuz03N1eNjY1GU916U6ZM0YYNG/TOO+9o3bp1amxs1PTp09Xc3Gw9mpnr//v393NDkoqLi/X6669r9+7devnll1VXV6f7779fbW1t1qMlhXNO5eXlmjFjhgoKCiT1z/Ohq+Mgpc750Od+lUN3vvj7hZxznW5LZ8XFxbH/HjdunKZNm6ZvfvObWr9+vcrLyw0ns9ffzw1JmjdvXuy/CwoKNGnSJOXl5Wn79u0qKSkxnCw5Fi1apKNHj2r//v2d7utP58OXHYdUOR9S4kpo+PDhGjhwYKfvZJqamjp9x9OfDBs2TOPGjdPJkyetRzFz/dWBnBudhUIh5eXlpeX5sXjxYm3btk179uyJ+/1j/e18+LLj0JW+ej6kRIQGDRqkiRMnqrq6Ou726upqTZ8+3Wgqe21tbXr//fcVCoWsRzGTn5+vYDAYd260t7ertra2X58bktTc3KyGhoa0Oj+cc1q0aJG2bNmi3bt3Kz8/P+7+/nI+3Og4dKXPng+GL4rw5M0333QZGRnud7/7nXvvvffckiVL3LBhw9yZM2esR7tlnn76aVdTU+NOnz7tDh486B588EGXmZmZ9segpaXFHTlyxB05csRJcqtWrXJHjhxxZ8+edc459+KLL7pAIOC2bNnijh075h577DEXCoVcNBo1njyxujsOLS0t7umnn3YHDhxw9fX1bs+ePW7atGnuG9/4Rlodh6eeesoFAgFXU1PjLly4ENs+/vjj2D794Xy40XFIpfMhZSLknHOvvvqqy8vLc4MGDXJ33XVX3MsR+4N58+a5UCjkMjIyXDgcdiUlJe748ePWYyXdnj17nKROW2lpqXPu2styn3/+eRcMBp3f73f33nuvO3bsmO3QSdDdcfj4449dUVGRGzFihMvIyHCjR492paWl7ty5c9ZjJ1RXf39JrqqqKrZPfzgfbnQcUul84PcJAQDMpMRzQgCA9ESEAABmiBAAwAwRAgCYIUIAADNECABghggBAMwQIQCAGSIEADBDhAAAZogQAMDM/wGN1DkEmCqpWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([1])\n",
      "probability of class  0.9641903042793274\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat: tensor([9])\n",
      "probability of class  0.9263759255409241\n"
     ]
    }
   ],
   "source": [
    "# Plot the classified samples\n",
    "Softmax_fn=nn.Softmax(dim=-1)\n",
    "count = 0\n",
    "for x, y in validation_dataset:\n",
    "    z = model(x.reshape(-1, 28 * 28))\n",
    "    _, yhat = torch.max(z, 1)\n",
    "    if yhat == y:\n",
    "        show_data((x, y))\n",
    "        plt.show()\n",
    "        print(\"yhat:\", yhat)\n",
    "        print(\"probability of class \", torch.max(Softmax_fn(z)).item())\n",
    "        count += 1\n",
    "    if count >= 5:\n",
    "        break  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://dataplatform.cloud.ibm.com/registration/stepone?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-CV0101EN-Coursera&context=cpdaas&apps=data_science_experience%2Cwatson_machine_learning\"><img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/Template/module%201/images/Watson_Studio.png\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>About the Authors:</h2> \n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\">Joseph Santarcangelo</a> has a PhD in Electrical Engineering, his research focused on using machine learning, signal processing, and computer vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other contributors: <a href=\"https://www.linkedin.com/in/michelleccarey/\">Michelle Carey</a>, <a href=\"https://www.linkedin.com/in/jiahui-mavis-zhou-a4537814a\">Mavis Zhou</a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                                          |\n",
    "| ----------------- | ------- | ---------- | ----------------------------------------------------------- |\n",
    "| 2020-09-23        | 2.0     | Shubham    | Migrated Lab to Markdown and added to course repo in GitLab |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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