Simple Linear Model (Complete).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Model\n",
    "\n",
    "## Introduction\n",
    "Similar to how most programming languages have a \"Hello World\" exercise, machine learning has MNIST.\n",
    "\n",
    "We are going to train a model to look at the images and predict what digits they are. Let's start with a very simple model called Softmax Regression.\n",
    "\n",
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MNIST Data\n",
    "\n",
    "The MNIST data is hosted [here](http://yann.lecun.com/exdb/mnist/). To download and read in the data automatically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting MNIST_data/train-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/train-labels-idx1-ubyte.gz\n",
      "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"MNIST_data/\", one_hot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MNIST data is split into three parts:\n",
    "1. 55,000 data points of training data (`mnist.train`)\n",
    "2. 10,000 data points of test data (`mnist.test`)\n",
    "3. 5,000 data points of validation data (`mnist.validation`)\n",
    "\n",
    "Every MNIST data has 2 parts:\n",
    "1. an image of a handwritten digit (call it \"x\")\n",
    "2. corresponding label (call it \"y\")\n",
    "\n",
    "Each image is 28px by 28px, we can interpert it as a big array of numbers. Let's flatten it into a vector of $28\\times 28=784$ numbers. \n",
    "\n",
    "From this perspective, the MNIST images are just a bunch of points in a 784-dimensional vector space. \n",
    "\n",
    "The result is that `mnist.train.images` is a tensor with the shape of `[55000, 784]`. The first dimension is an index to the list of images and the second dimension is the index for each pixel in each image. Each entry in the tensor is a pixel intensity between 0 and 1, for a particular pixel in a particular image.\n",
    "\n",
    "## One-Hot Encoding\n",
    "\n",
    "Since we want the digit of a handwritten sample, we're going to want our labels as \"one-hot vectors\". A one-hot vector is a vector which is 0 in most dimensions and 1 in a single dimension. For example, 3 would be represented as `[0,0,0,1,0,0,0,0,0,0]`. So, `mnist.train.labels` is a `[55000, 10]` array of floats.\n",
    "\n",
    "For example, the One-Hot encoded labels for the first 5 images in the test-set are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.test.labels[0:5, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need the classes as single numbers for various comparisons and performance measures. So we convert the One-Hot encoded vectors to a single number by taking the index of the highest element. \n",
    "\n",
    "Note that `class` is a Python keyword so we will use `cls` instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 2, 1, 0, 4])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.test.cls = np.array([label.argmax() for label in mnist.test.labels])\n",
    "mnist.test.cls[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_images(images, cls_true, cls_pred=None):\n",
    "    assert len(images) == len(cls_true) == 9\n",
    "    \n",
    "    # Create figure with 3x3 sub-plots.\n",
    "    fig, axes = plt.subplots(3, 3)\n",
    "    fig.subplots_adjust(hspace=0.3, wspace=0.3)\n",
    "\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        # Plot image.\n",
    "        ax.imshow(images[i].reshape((28, 28)), cmap='binary')\n",
    "\n",
    "        # Show true and predicted classes.\n",
    "        if cls_pred is None:\n",
    "            xlabel = \"True: {0}\".format(cls_true[i])\n",
    "        else:\n",
    "            xlabel = \"True: {0}, Pred: {1}\".format(cls_true[i], cls_pred[i])\n",
    "\n",
    "        # Show the classes as the label on the x-axis.\n",
    "        ax.set_xlabel(xlabel)\n",
    "        \n",
    "        # Remove ticks from the plot.\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": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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blBmKiKDKUEQEiPE22a99HNVKV36VreXLl6feKzvM7/bbb4/k2j90LVu2BILuEeGJGvwQ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\nzM0W5d8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9b01e3048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# Get the first images from the test-set.\n",
    "images = mnist.test.images[0:9]\n",
    "\n",
    "# Get the true classes for those images.\n",
    "mnist.test.cls = np.argmax(mnist.test.labels, axis=1)\n",
    "cls_true = mnist.test.cls[0:9]\n",
    "\n",
    "# Plot the images and labels using our helper-function above.\n",
    "plot_images(images=images, cls_true=cls_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TensorFlow Graph\n",
    "\n",
    "A TensorFlow graph consists of the following parts which will be detailed below:\n",
    "\n",
    "* Placeholder variables used to change the input to the graph.\n",
    "* Model variables that are going to be optimized so as to make the model perform better.\n",
    "* The model which is essentially just a mathematical function that calculates some output given the input in the placeholder variables and the model variables.\n",
    "* A cost measure that can be used to guide the optimization of the variables.\n",
    "* An optimization method which updates the variables of the model.\n",
    "\n",
    "In addition, the TensorFlow graph may also contain various debugging statements e.g. for logging data to be displayed using TensorBoard, which is not covered in this tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "img_size = 28\n",
    "img_size_flat = img_size * img_size\n",
    "img_shape = (img_size, img_size)\n",
    "num_classes = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Placeholder variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = tf.placeholder(tf.float32, [None, img_size_flat])\n",
    "y_true = tf.placeholder(tf.float32, [None, num_classes])\n",
    "y_true_cls = tf.placeholder(tf.int64, [None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quick recap, `x` is a `placeholder`, a value that we will input when we ask TensorFlow to run a computation. We will represent the MNIST images as 2-D tensor of floating-point numbers, with a shape of `[None, 784]`, `None`, means that a dimension can be of any length.\n",
    "\n",
    "### Variables to be optimized\n",
    "\n",
    "We also need the weights and biases. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "weights = tf.Variable(tf.zeros([img_size_flat, num_classes]))\n",
    "biases = tf.Variable(tf.zeros([num_classes]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`weights` has a shape of `[784,10]` as we want to multiply the 784-dimensional image vectors by `weights` to produce 10-dimensional vectors of evidence for the difference classes. `biases` has a shape of `[10]` as we can add it to the output.\n",
    "\n",
    "### Model\n",
    "\n",
    "The simple mathematical model multiples the images in the placeholder variable `x` with `weight` and `biases`. The result is a matrix of shape `[num_images, 10]` and `W` has shape `[784, 10]`.\n",
    "\n",
    "`logits` is typical TensorFlow terminology."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "logits = tf.matmul(x, weights) + biases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now `logits` is a matrix of shape `[num_images, num_class]`. Where the ith row and jth column is an estimate of how likely the ith input image is to be in the jth class.\n",
    "\n",
    "Since the values maybe be very small or very large, we want to normalize them so that each row of the `logits` matrix sums to 1 and each element is between 0 and 1. This is calculated using the softamx function and we store the result in `y_pred`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = tf.nn.softmax(logits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predicted class can be calculated from the `y_pred` matrix by taking the index of the largest element of each row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_cls = tf.argmax(y_pred, axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost-function to be optimized\n",
    "\n",
    "We will try to minimize the error, which represents how far off our model is from the our desired outcome. \n",
    "\n",
    "The cross-entropy is a performance measure used in classification. It is a continuous function that is always positive and if the predicted output of the model is exactly matches the desired output then the cross-entropy equals zero.\n",
    "\n",
    "The goal of optimization os therefore to minimize the cross-entropy by changing the `W` and `b`.\n",
    "\n",
    "TensorFlow has a built-in function for calculating the cross-entropy. Note that it uses the values of the `logits` because it also calculates the softmax internally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits=logits,\n",
    "                                                        labels=y_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cross-entropy gives us a meaure of how well the model performs on each image individually. But `Optimizer` takes in a single scalar value, so we simply take the average of the cross-entropy for all the image-classifications. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cost = tf.reduce_mean(cross_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization Method\n",
    "\n",
    "Use Gradient Descent where step-size is 0.5 to minimize the cost measure. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.5).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance Meaures\n",
    "\n",
    "We need a few more performance measures to display the progress to the user.\n",
    "\n",
    "This is a vector of booleans whether the predicted class equals the true class of each image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "correct_prediction = tf.equal(y_pred_cls, y_true_cls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the accuracy by first type-casting the vector of booleans to floats, so that False becomes 0 and True becomes 1 and then calculating the average of these numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TensorFlow Run\n",
    "\n",
    "Once the TensorFlow graph has been created, we have to create a TensorFlow session which is used to execute the graph. \n",
    "\n",
    "The variables `weights` and `biases` must be initialized before we start optimizing them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "session = tf.Session()\n",
    "session.run(tf.global_variables_initializer())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper function to perform optimization iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using small batches of random data is called stochastic training -- in this case, stochastic gradient descent. We would like to use train on the entire data set but that that's expensive.\n",
    "\n",
    "`optimize` is a helper function that perform user-specified number of iterations so as to gradually improve performance.\n",
    "\n",
    "In each iteration, a new batch of data is selected from the training-set and then TensorFlow executes the optimizer using those training samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def optimize(num_iterations):\n",
    "    for i in range(num_iterations):\n",
    "        x_batch, y_true_batch = mnist.train.next_batch(batch_size)\n",
    "        feed_dict_train = {x: x_batch,\n",
    "                           y_true: y_true_batch}\n",
    "        session.run(optimizer, feed_dict=feed_dict_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper-functions to show performance\n",
    "\n",
    "Some helper functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "feed_dict_test = {x: mnist.test.images,\n",
    "                  y_true: mnist.test.labels,\n",
    "                  y_true_cls: mnist.test.cls}\n",
    "\n",
    "def print_accuracy():\n",
    "    # Use TensorFlow to compute the accuracy.\n",
    "    acc = session.run(accuracy, feed_dict=feed_dict_test)\n",
    "    \n",
    "    # Print the accuracy.\n",
    "    print(\"Accuracy on test-set: {0:.1%}\".format(acc))\n",
    "    \n",
    "def print_confusion_matrix():\n",
    "    # Get the true classifications for the test-set.\n",
    "    cls_true = mnist.test.cls\n",
    "    \n",
    "    # Get the predicted classifications for the test-set.\n",
    "    cls_pred = session.run(y_pred_cls, feed_dict=feed_dict_test)\n",
    "\n",
    "    # Get the confusion matrix using sklearn.\n",
    "    cm = confusion_matrix(y_true=cls_true,\n",
    "                          y_pred=cls_pred)\n",
    "\n",
    "    # Print the confusion matrix as text.\n",
    "    print(cm)\n",
    "\n",
    "    # Plot the confusion matrix as an image.\n",
    "    plt.imshow(cm, interpolation='nearest', cmap=plt.cm.Blues)\n",
    "\n",
    "    # Make various adjustments to the plot.\n",
    "    plt.tight_layout()\n",
    "    plt.colorbar()\n",
    "    tick_marks = np.arange(num_classes)\n",
    "    plt.xticks(tick_marks, range(num_classes))\n",
    "    plt.yticks(tick_marks, range(num_classes))\n",
    "    plt.xlabel('Predicted')\n",
    "    plt.ylabel('True')\n",
    "    \n",
    "def plot_example_errors():\n",
    "    # Use TensorFlow to get a list of boolean values\n",
    "    # whether each test-image has been correctly classified,\n",
    "    # and a list for the predicted class of each image.\n",
    "    correct, cls_pred = session.run([correct_prediction, y_pred_cls],\n",
    "                                    feed_dict=feed_dict_test)\n",
    "\n",
    "    # Negate the boolean array.\n",
    "    incorrect = (correct == False)\n",
    "    \n",
    "    # Get the images from the test-set that have been\n",
    "    # incorrectly classified.\n",
    "    images = mnist.test.images[incorrect]\n",
    "    \n",
    "    # Get the predicted classes for those images.\n",
    "    cls_pred = cls_pred[incorrect]\n",
    "\n",
    "    # Get the true classes for those images.\n",
    "    cls_true = mnist.test.cls[incorrect]\n",
    "    \n",
    "    # Plot the first 9 images.\n",
    "    plot_images(images=images[0:9],\n",
    "                cls_true=cls_true[0:9],\n",
    "                cls_pred=cls_pred[0:9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper function to plot model weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_weights():\n",
    "    # Get the values for the weights from the TensorFlow variable.\n",
    "    w = session.run(weights)\n",
    "    \n",
    "    # Get the lowest and highest values for the weights.\n",
    "    # This is used to correct the colour intensity across\n",
    "    # the images so they can be compared with each other.\n",
    "    w_min = np.min(w)\n",
    "    w_max = np.max(w)\n",
    "\n",
    "    # Create figure with 3x4 sub-plots,\n",
    "    # where the last 2 sub-plots are unused.\n",
    "    fig, axes = plt.subplots(3, 4)\n",
    "    fig.subplots_adjust(hspace=0.3, wspace=0.3)\n",
    "\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        # Only use the weights for the first 10 sub-plots.\n",
    "        if i<10:\n",
    "            # Get the weights for the i'th digit and reshape it.\n",
    "            # Note that w.shape == (img_size_flat, 10)\n",
    "            image = w[:, i].reshape(img_shape)\n",
    "\n",
    "            # Set the label for the sub-plot.\n",
    "            ax.set_xlabel(\"Weights: {0}\".format(i))\n",
    "\n",
    "            # Plot the image.\n",
    "            ax.imshow(image, vmin=w_min, vmax=w_max, cmap='seismic')\n",
    "\n",
    "        # Remove ticks from each sub-plot.\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance before any optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 9.8%\n"
     ]
    }
   ],
   "source": [
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance after 1 iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 31.7%\n"
     ]
    }
   ],
   "source": [
    "optimize(num_iterations = 1)\n",
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6qvPuu+8C8Mgjj6S9P2jQoOTyzTffDKSGk4vCT9SmgUGKz9KlS5PLt99+O5C6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\n08a60ahL3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9cd069400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance after 10 iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 47.6%\n"
     ]
    }
   ],
   "source": [
    "optimize(num_iterations = 9)\n",
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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luNOmTQNg2bJl1bZ17twZCJuXSX5FX+heffXVAKxcuRIIH7f5hupPP/00AJ06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\nEYlBlaaISAz/DyMkerY8CLluAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9a7e1db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KCjfOjpyMJ2BSGADgsFiqZg2RmsyZH5iUCkiz+zCFKjvomP+TKrooduYADA7UUnnLjjaa\nPswOwAgy9uuzZXZDfWPJ99AE3N+NN34RANCpCvgJ/X3BD9Nhy/irv/JlnEt0HFpvpoANwzByono+\n4Hi+MjplwhgedfScd54PfFq8+BgAwNat9M0yxPrXwY40WjpRwH7Y8sU6L9QJL/8sXVVr2Xoqi3e+\n05dMdhJXu+H51zK78bOG7kBG3TQOaBD7Cq3ldXAKQ/JK2hzt7SW7Z6MlVNYkzq3SGP8Qn3PWb7WG\nzh0IqiQd6tqtUmxHsGo8zL0lKhNXZhCOV79oEYDU5okK0uTryWzJCMLYOIkfFTCfYQ7j51hoYPhg\njVqC1xGpTD5rjFYNTJBkM6BrfFUYlYrUDb91axjy6I+zbJlvgf/hyScDAJo0f+iO4H4kz2ycdjJu\nAlYBU8CGYRg5UflXOx0yVLz0s7LGCXtzo5qFAmDJEh/psH07fcJvD9ZSp6YOQT7nHO/P1Q5R4PL/\nl65K/zNVA7tTWXJ5rSuymMhuOwd9PcrLCDvB67pf8B/YrRxN00utVGIB9Te2RAKbu6AvODxmckoD\nE8D3y8gCTeK9XpUvVe6MYBO1bvJbA0phYyRMJ0XFRfXcyP8Vyr7nnkvW5RDxFvqJKQO5DaVjmMKy\n1ggH48RTKGlESR39r9p8a5r7oWG7YT8GE25RoPIVc//9+wXr+s/JBNPa2mV/UDhoIzkX+qfjtAnx\nOy38bYyYAjYMw8iJ6k1JFCc5p+OG3fJAUhuyg5euK9Za3d1e3XZ1HTfscBSvTFHXvPoB/yH0Mb/v\nfb5kjcaeY44pZY0W+n5qWbmV8f3GnbZ1PRvTbeK4bG6rNmDMb6i6+FuX7i/0xwGp2zHjVIod/RCn\nUlU1xt4MPiV3B5uwl4J+YUY9UCtR5b4rPM4HPqArlT5/feobDgcdMw0Vn+ojVQk38aawuZM1/rwW\n4f8aFW88Q4A+e2E/Bl8lvFT+i7NFxkd7YGBSsg19yfOatI2icpkKuKSPiufAVkT8LmMYRhWeaVPA\nhmEYOWEvYMMwjJyofCcc/QhsanDsa9aQSg04P/OjXtoff+25ANIxG2xl0QcOpN6Ds/wEGGjfpc3t\n/rbS44XHZMnOgKzwswJTN+AbwM09ariw/cZr5rBr9nTy2rn84YfTbdReLaVToSVlGOXEZmFd/7bS\n4xXRBRFnbtML5qAKuhvCnFi8ymlasmHLO5C4Huh2ANIhr3xW9UFvUTfdUDAUuUvLZDYXwmnAwwEe\ntUr4f8bPdPPQNcnwtI98BADQ2f9ssknnQv2n12eqqcl3dfL9wNt29dXpYZjgDF+4AQDwkk7nQjdS\na5jUmufEOEs+6HGu5SqEUpoCNgzDyInKS0BKIgazUwmzSgrnhKO01eDoZt22Y7qfITVriiwue/NN\nX+7Q2Qoa1+tgjbDzLw4n4W/xnFxFVGtAGoeT9kKUlkDaW8nBKPyN9ynukASSmv6YOV53rZrl62mK\nhnC+roY+HYQbhxfFarJINua5qx3qdOjwkTqbdqhaGCYWDz1uon0/9jFf6uwiALBzth9w1NDPwTGa\n/FYHC7QipZXKkPvjM81WDu06aRJqllA58ry5jOdNJczO4O98J93m85/3pTa9Zug1z1Cb/B5fKWFS\no6v9VOrd+m7hUPGkRcJeOiB9J7H3n88ySz74WTOVjBFTwIZhGDlRvVmRtTZPapEsXxVrHNZ66tRp\n1drx/fN9DbezKdUE8QQArJSGTvJ1W936YIaoOEaKyibOr1gUYnVJHxW/M5B81650G4bW8JqppKh4\naYPQJ8Z0ieqvX7jQB8Uz/Kx5MJhBrpwtixiOVh85vWkrbb01aQvqeIZQAWn4FxM8XXEFAGBjm2/F\ncQbl+iCU7yyNhmz/bZTvk8fnkPkQ9lvwmeb3WbN8GcYG1jKRTZPrYStOQ75eoY8YQNtf/iUAoE6f\n0W36nMcvr0a28gAMrlsHIA0H7GJL8O/+zpehAi7XIo5nKrEwNMMwjIlD5X3A8dS8rPHofw17Filn\nqYDpE478RA1Br/7AQEPJppo3JlVn4UAMKguuXM4/WTQiH2VyffEMuuEyrkP76PKhFt+6qAvHLy/2\n/jPeh/a52iP9ZsbM1ll+56ISZ61nJiMuZ2si9JerQ/xHt3kt86Or/WI+ejR3VtfEwoW+1dZK27NF\nGPpMqbDjIcixzzc8p1qG1xaPuuJy9QVPe/LJZJMdqngbWOryyWxl08jMyAWgXtdtofLVAUdDTX4o\nRl3vK8m6wwZkxf9f8Rx+FcQUsGEYRk5ULxCWKimaSXRLxzHJ58TL88EzAQzvIOWmb/xm+O6peBm6\n1zCog0HDWipW4xMNSimqiLhnHEiSneDwwwEAm97yird9qo9wqBv0g2XpQweAOoY5sEXCG5Glsork\n491ThmUaGg4TITFRzEUX+ZKPHm9J2MCgYEsbdk2lP4TPK8+BGWfiKAgSp3+tdeJcp0ynyWePieYB\nNNIfrL/V8/s73uFLKuEgPGdHh09xS1O21vv3Qx0jqjPS4iY3bRwjeUwBG4Zh5ET1h4KxFtFaq3Vy\nmvimNU6pp+WO+uaSxWFlP0zprh+h1iqnfCeaauP1ZCWQVuXLZcnIQTY/GOsa2iTuBY57h7N8wBOZ\n2CcYtLIaur1//IQ2/7CecH5LybpDk33iQ7Y0SrbviVpo3H/4wGctmwjEvmCWXJ4MZUN67XGzggxv\nUqBR3xONA+wHit4TWc97Ds+yKWDDMIycsBewYRhGToxfNposmR/PwaTNj0b1PTQmiTuCjrWxDB+e\naK6HmKzri5tV/B532mS5bia6vfaULHvEHb38rvato533pHO4SPPnVZqRnuG4M7Sl1N1T0uEfDyeu\nUUwBG4Zh5MT452MMa7iiDQUuClkdDDFm+71nNPat1P73VUZ6T8SDiwqMKWDDMIycEOfc6FcW2Qzg\nt9U7nZrj7c65qeN5QLNxddkH7QuYjceDvbLxHr2ADcMwjMphLgjDMIycsBewYRhGTuz1C1hEviEi\nVwbf7xKRG4PvXxeRv97NPh4YxXG6RaQtY/lCEVmwp+cdbH+iiKwSkbUi8i0Rkb3dV7WYADb+3yKy\nTkRqNuSiyDYWkUYR+ZmIrBGRJ0XkK3uzn2pTZBvr9neKyONq4xtEZL+93VfMWBTwcgALAEBE6gC0\nATg2+H0BgBGN5pzba6MAWMjj7yX/AuBTAI7Qv/eOYV/Voug2XoRgGq4apeg2vs45NwfAOwGcJiLv\nG8O+qkXRbfwHzrl3AJgLYCqAD49hX6U45/bqD0AngHX6+TgA/wbgbgBTAOwPPwN0g/7+GQCPAHgC\nwDXBPvq1rAPwzwDWALgHwM8BXKS/dQO4BsBjAFYBmAM/W3cPgA0AVgI4Q42yGsDjAO7bzbkfAmBN\n8P0SAN/dW1tU66/INo6uoz9vW050G+sxvgngU3nbdKLaGMAkeFHxkUrZZq8HYjjnNorIoIjMgK9d\nHgRwKIBTAbwGYJVzbqeInAuvMN8FQAD8VETOdM7dF+zuQ2qoYwBMA/A0gJuC33udcyeIyKcBXOWc\nu0xEbtCbch0AiMgqAO9xzm0QkRZd1gngRufc+6PTPxRAMDUH1uuymqLgNi4EE8XGuu4H4F/CNcVE\nsLGI3KXn9QsAt1fALADG3gn3ALxBadQHg+/LdZ1z9e838DXTHHgjh5wO4Dbn3JBzrgfAvdHvP9Hy\nUXjjZ7EcwM0i8ikA+wH+xhf1xRBgNq4+hbaxiNQD+CGAbznnXhjxSvOj0DZ2zr0HvuW8P4DfHelC\n94SxDkWmb+c4eEm/DsDfANgG4Hu6jgD4R+fcd8dwnDe13IUy5+ycu1xETgFwHoBHReRE59yrZfa3\nAUAwcRqm67JapKg2LhJFt/G/AnjOOXf9GM6t2hTdxnDODYjIfwH4fXj3x5iphAI+H8AW59wu59wW\n+JmgT0XqVL8LwKUi0gQAInKoiEyL9rMcwIUiUici7fBO892xHUAyl7qIzHLOPeyc+yKAzQAOK7eh\nc+5lANtEZL5GP/wxgP8axTHzoJA2LhiFtbGIXAvgbQCuHGm9GqCQNhaRJhE5RD/Xw7+014zimKNi\nrC/gVfA9mg9Fy15zzvUCgHPubgA/APCg+l5uR2AM5cfwftinANwC3/x4bTfHXgTggyKyUkTOAPA1\n8WFlq+Fv6OMi0ikiPy+z/acB3AhgLYDn4X07tUhhbSwi/yQi6wE0ish6Ebl61Fc9vhTSxiIyHcDf\nwvtDH9N9XLYnFz6OFNLGAA6E90U/Ad+J9wqAG0Z70bujZoYii0iTc65fRA4G8GsAp6mPx6gQZuPq\nYzauPhPJxuOfjrI8i7VHsgHAl4tq0BrHbFx9zMbVZ8LYuGYUsGEYxr6G5YIwDMPICXsBG4Zh5IS9\ngA3DMHJijzrh2lpaXFdHR7XOpebo7ulBb1/fuGZJMxtXl33NvgDw6DPP9LpxnBHDbDx69ugF3NXR\ngRU33bT7FfMknG693LTfo+SkSy8d48nsOYWwcQUZbxvXtH052eTmzemyww8f827ltNPGdXqgmrZx\nldhbG5sLwjAMIyfGPw64PuOQXEbFyu8jrctpq1lS+YbbxOvsK4zGxiOtS1vSbvF9CdnXbAtkP2Nb\nt/pyyhRfvviiL1/VFAPbt6fb/FbFUpvmDj/tNF8+84wve4Kw1kmTfMl7wHvDbcMW30RiT94TWcR2\n4TY19ryaAjYMw8gJewEbhmHkRPVdEHEzIWwa8DcuYydEU5Mv24ZN75Q2z7jtdJ9Vcqi+AQBQN7Aj\nXXf9+tL9lmt+1FizZI+JbRx+j21M28ZNtKxtyjX1Qnv19ZWuW44i23gk+/K66CogGzS76UOae2bF\nivQ32uz44315o58erU8731rCfV17rS8ZVcBnurvbl4fqPAIV6KzLldE8wyz35hmO3Wnh85jjs2sK\n2DAMIyfGTwGztgprLdZkLS0AgJ3wKra31y9e97QvX3893aSrqxlAKiL6un05Z44vOweCDozVq325\n//6+pEoYqXOuiEotVgihEqCNI1tv2ly+7j1IV21s2ek/xEqYNyjcb6wsRupILaKNgeyO3vg6+WC+\n9dbwdQkf1ueeAwC8osqXd2SQ2wKoX7mydJv9dEJevY8J/cHE07wnRSTLxlzGa9ZyY4+3GB+9gQwT\n8F//AN20ebI+07xPwHB1zN/G4Tk1BWwYhpETlVfA5Xy+WX5drbW3DXjlS8Gqbl28qZOL0I0GAHfc\n4cu5c31J11giAJ57Ol25q8uXrDl5LjxQ7FMqGnFIXuxDB4b715V2iWr9QFG90NOsu/f3paPDlw33\n/MyvsHx5si7Wri09Fx6Him3+/OHnRIXHkK1aZTT+89jXyPIwnWRh1y5fvuMd6Tb0D+uDPi1+PsP9\nxyGBXPeQQ3xJiVf0ZzhWvuF7hNesy7b0ed14551+8ZIlvgwFaxydyvfF3Ln+WW5vTyfaOPpoXza3\n7CjdOP6/qoIiNgVsGIaRE9VTwKx6qAjoNwx7HHVZb4evjejuonDl99uDSaC57IorSg+TDD2/48l0\n5Sf1M9UYa1LWaLHyCH+rZWIbE15PqIbKKSP2yj/yiC8PS6fFmkk/I5sga3QKLBqf3wH0r1sHwM8R\nA6QznTapfzO537Nnp8emHKl1aGfaNWPww5BqmLo1T/kFHHBBG7I5x4caAJ7WVtrHP+5LPp/xYAsg\njfqJo3/iMkv+1SLl+l/i7xzYAqTPm0aNdPf6Fhpbxvz5jTfSTdjI4OPPRi9vAxtmISef3AgAqItb\nHbGPOOt89xJTwIZhGDlROQVcrmamorz/fl9u2pRuc8opfpWmBSWbxC63rMNQRFFYNfe+4D+EvZvc\nEdUDYydnzSr9PesAtawiSLkIk6xIE8oE2ofOdMaV/lcwKTTtpGpuUGt+7T9GaJmXtORvjI/Yoceb\nRh/o2WenG7G5QnVYa8R9A6p8d9Z7hdQbBNpwlWbanM83n584fhcALrkEAPBUTysAYO1Sv7hHfe/h\ncz9rll92yun6oMfRJny2w5ZbLT+7fP543vFzyYsPI21ou/PPBwCccNFFAIDrr58JAGgc2DJ8myhK\nZKjNt7LrBv2TynEDAFDXp9sPRMO843MO3y3h5zFgCtgwDCMnKq+A497MeKRQWHPQx6i8972lm1Ig\nhblJWDnRbZa41voHowUYXsueeGLpcakaQsVYy+qhXOuC50zbhrV/bAP6cakqslQzVZuOsqpXxVbP\nfTHyAcDcWNHEcbBcHvrPskZSOuEDAAAgAElEQVQ41gKxfaM+gn69NDYQwlWO6Q0ULpA+h7RHmB9X\nN1qmfRv0Zb78si+nBlllTz/dl4cd5rVSU5NX4c3Yln3OtUh472k8DV3YtmgRAGBIf+Y41leCzbdw\nmbaimz77WQAALcrWV9h7w2WtWrJRoa8NNHAUIgCcc44v6Rjmi4j/V3GsO1CxlrIpYMMwjJywF7Bh\nGEZOjK3dkjVcMA7ZCB3j4XrBuvMGfu2/P9TtS22iDgz8bvgVQNrpduZJ2li5915fsmnDnKrhOdBf\nwYhrNgtrudmWRbmkJHRFsA37dDAYhddKu9AVEbsxwibZUUf5ks3oU0/1ZTzMGEhdGatW+ZLxPzwO\nXRCha6iW3TxA2eYlvSqMMAOAgw/WD/euKt0Hnz12doYPsXZI0pOzPvJejDTOI/1thOQytUbYQcj/\nU7UHXQO6NHE9hO4EpjGiA4CuB7or+DRuQQqdcNwvt6U3cw5dcQBm8AN9nvQJsaef5581fHmMmAI2\nDMPIicp3wsXhMSxZzYe1CMcQLl5cuq8//dOSVZlxDwji+VlL/fd/l+4/hHKBG1Exxkllxjh3XG7E\nQyXZuRh2bv5Mhw/zGrkuZVzWQAltKWyc41sg99/jF1PchuMo5szx3RwzTo3Ch4491pfsfM1qLdUq\ncStObbZrlw8JCzvJ2jc85j88/LAv2dnGsD4+p9pxBKRJZOJxM/zOBhuQCmeWiRn7ovtZywo4bDJE\nA53qPvYxAMBMbTHN5ACeIAPXCdr04KUnIX98tmiwsKOTLa5vfxtAqqL59tkWngRnLYmT8cQJlqrw\nnjAFbBiGkRNjU8BhrRsP4eV3jgGkT1CHrgLAgPqDWK+0fPCD/oMOi11xl/8aCrokSJ1+TqrorNEb\n9GuyZox9vly3ltVDSNZQVWB48HrQGuj7xS8AAC0qr4a0NucACl75bCZ3AZIxnfRR0n3M3WaJ2Rmn\nd/kPtDVbPjynItg4PsdI8VDIzax/KV14882l62qo1BZVvq0c4n3GGckmtCvdoVS+dL2fdFK6e35u\nHKRmi3z3ReCgg9LPjKvj83Hggb7k/2rcSgXQqgMwNjk/mKJXxTEnj37ttWGbJDY9YeFCAMAxF14I\nAKDnt2SMF5/ZKOnPeLSMTQEbhmHkROV8wHFvbDQEeUgVcDiAjz2SM7lAa8Ff9s4DkCquIO4fWqEB\nBxzgS/a+sxYLe9vjRM6xAh7N7Kq1SDk1SZsHI1dYwy5V5cuA941aJrEPbKkAwPPPAwDOvNj3SXdo\nsiQqtrCRQdPuHPRHaihCr/zuKJMwJsme+bXvpwup8LV8RZUv7YyLLwYAPNV2ZrLJg37sQRL3T3f5\nccf5snH9s+n+l2jLkXbl812k9JPh/xf7GmLVqX7coabSCRcA4JZbfMn8UVS+9MXHrlsAOOssX54w\nqRtA+q7h/0PJfzxtSjXOcxuHWdVNARuGYeRE9aQf5ZJ2ncdJWwBAE/iBaTFmq2JlhcOKKaxAk5wu\nNywFkCrqlqwhr/S7sZaNIwFYZdbq0NhyxNmm2UTIqKlZwzL9NO21UMvpcaxvuF+1ExUwV21Y/8Lw\nc+rNmEom/F5ERRwNr2/o0aeYTkcgfbY0Z2qjLm6i31NlbthB/9lLdD98Htk/8qOlvgzHOsf5Vtks\npHyO4++LQhT6QeVLU4QmYDdP2EgD0r6JrEAQKmBGWPH9w3bD9HDiU75UjjjCl4yq4I6r+AybAjYM\nw8iJ6iVk19pjp6Y0ZJ9teEAqX/ojZ2us5Llf9d/PZQq+UKE+5B1Bg9/3fjgqumS8XeAIml0uGXyc\nbKWoxCPjOJIn6CFv0pq+VWMpj+EPmmAHl1/uy7DrXXmhx+u5+igssjNUuZQqXBb79ooaYw0MVz5x\nIiNgWLKdJrbEOERO99G69CfpNnHce9xqCDs9qHB5b5l1nFKRPtWi9WMQVcJxgE+Q8z9Rvlzn5Zc1\nxWkSzevLgw56e7ING799n/MjZekDTjzxF1yQHoCtCb5n4n4sluGzXCEfvClgwzCMnLAXsGEYRk5U\nzwWhEr1BA9Gn6wCMcAggRTyXPaHlPA7bpDOcsyoA6Nehit36nW5xdjKVXBDHzMaDNNjEKNIggZFg\nsz+rWfSlL/lVwo4jYFhza2hyY/JTnCq4s2lbybpYEbQPuR/akk3wcGhzUeGzHA+rDxNMcQ44fb6Z\nEKaVMVJ0J4RJrcPPQDoIIWtd/kZ7xm40fi9SWBowrIOTjxZDzLIyC6SetaHoF9+BF066smDNTQAA\nnTgZXVp28n8lXJnusjhcNXZFVMHNYwrYMAwjJ6qngDnkUMdvtmg4WksQSzKDHRhMwEHVEA6mAEpi\nUjT1SaJ8OatYJ8NKdNgigFQ9cPs4wDprRowiEHcKRBPlPTGYdLVh3p9rBwPVFW3LfahNqDyAVEy1\nNmnQ4FqVI1kJleLBLllR8UUlDsRftsyXwbUN6qzSfB6TthSV8Z2qwZiUB0g7fXRus+T+cZ2ws4ef\n+ezy2LQ7c2QWjail/IZOgszGbpjwiebnv/Fzz/n/9ddf9yNj+Kr5znfSbfoP/iSAtHWdTIL8Vd/D\nP/TRP07Wpdmb1LTs72zlM13FpF2mgA3DMHKi8gqYNTP9t2FuPaA0iQjVWJAcGUBay3Pd669PfuoM\nkvkAQBKgxvGcV12V/kgFHGeRiX06oQIuQtgUVQ/LRx8t+bn9qHTY630rvX+sv/8Ev0Ddiyee6NNI\ncnRtGJeeKN9y88mFLRQqPUoWrhvbOPSf1brPPfav8pmjIgqeQT7NLapQe9RmA2qHBi3Dvo8WSjb6\nddkq1Od0kDYFUM97zGOylchhsxwfXST7Asn5cnZiZhbI6s6gIt2qKplKmGqZDYnWC9Ln/pdaMtS1\n5TOfAQDsuMgr3xXL0v1zHgM+1sMaFVV8hk0BG4Zh5ETVoyBe6vMKbP/9/eJJwZgKVnINOghgx4Cv\nDxoHtC/5hz8s2RcAzH7f+0qPQ+XFXs1gap2Nvb7+a5vu0/00DO5AJkVQvSFhej8gzZOoiY/aw9r5\nWJ9U/ckn/VdeKkUz3ZGJ6g1Xou+LWVCo2ChJgOF+9DjCpGjDvIHyw3t5/UELoDkaAk9FvFRLjkAu\naQeylUC//G23AQCe1X00B6t2MJ0l1XecoZ0U5RmOBkHxtKlqR9MtQ7XMxFxH3vktAECPPv9A2uJg\nrMPOa/8JAHDrLaWnAaTvJv5bJa1BS8ZjGIYxcan8lERRPGKclz2sqFmJ9/XVaem/X3CB9082s6oL\nh8lSfbGKpAJW5btpc1qnUGhwkyO7onOMp56pdWIbMxUns5LQgEHyb7oMY1c8Lz3xd4W1PO1B33ns\nzw2HcMf+0jjhUZEUcNwnEMd9cmYAJm0BUEdHpN4LTirJSF5GQ0+mkgVSu2oExVNqM4q+DualBIB3\nv9uX3J5OUp5jPOltrRPZOG5sZYVCx5k42cidN1nTdl53HYA04Q4AdGrZ9M1vAgBuUuUbz7cZfubo\n8dYWjTPujbL8WDIewzCMiYO9gA3DMHKi8p1wUa5atpTYOl66NF2VzQ4meGJEDefGOkW97JsOTObM\nQPtB2pHGJKFsW+vO2qekzeNdc3wnXOIViZvHRQjXyYLNOLpo4oEZQdhenfZudMZDg+MBFM8EYz/Z\n1qOLo9zQTCA1LtuObF7T9RDlFi4UcUwU7RC6xKJMaVQ0fLI4t8XkIHRtmn7mgFo2l1s+8AH/IczU\nxXtBe/JcxiFXbVXR862P+jsZahYmhONvNEHyKN9yhy/VX5EOpgfm6r174fy/AADc+Tm/nO6LMJKS\nLspktus4C1oVMQVsGIaRE9VTwFozx1OEhRU1azmKJNZK7G/Y1uSV738H6VPPP9/Xc82MQaHi4iCB\noNOnkzscjC4zVsBFUw+ECo2xZDorQ8nAFvZ+6txkiZFZ7fPaw6HDbF3o3HCJbGBTJZzegTc4zpWb\n2L6gtgWGJ7qhzUKFGiVwWahNvAWqctlFFoaWNUQP+mTuj6GUYccle6PiwUlFnQkj+p+jaXnJDAUL\nH7F4bFdnjyYkYOya9p7NDTuHdcgx55NjRxvLZG7J4BzqerULtZwCtoEYhmEYE4fKKeDYP6g19/Tp\n3sNFYRS6ImN1zGnJOlu8n/fZ9V7thiEjzU3qOetWbREnJQmdR1QNPCjXjUOmikIcNkfZEM9GEYQC\nvnCvnxGg7ctfBgA0M4SKtuCQVvqTw98oE3hc7jcMfaJvk+o4TotYJN9vlo8bSOw61OLDI9f3tyY/\n9Z/kh7bWz/fl5Gv9cgb3t2m/RkMwG+KOQd83wceTh+XtS+aeyyIO+yuqAtaLpwKcPXsGgOHZTYH0\nX/uQQ3TByihXJZXvySeny977XgBAl9qYjQ6+S5p7g3kNeay4RTwOYaqmgA3DMHKi8j7gyL/a3OJr\nj4ULvT839O3MmuXLYSnodFtWPPNaAkXwHe355I/0f3InYV5FVp2s/oqqGmLiGpnJXSgbmDYRwExV\nszt0m15N/UkLMFlJazhQgPvjSBbeNMqTMEr+9dd9SXlS9FSfQNnnpK6L19KQLKPJH3zQlxwTw4YA\ny8mT020o2E45xZdslGQOlY99vUXvtyBR5A6HdDfrMzZjIHjGkparGpPPZVyGClgV9nve46dqaJ+0\npeR4JRI79vWPo41NARuGYeRE9aZSjRJzN/T+GgAwL3ACz53rfWl1g+ofS2ocf1rz5qq/96HA58PE\nMJTLPA7HEYbpKjl0NIrMmDDEU8kyGX047lgjGBp13Uaq2SiJTInvNk6uzlSfVLmhqo2jHeLpdopM\nrOa1131G0IzrmO/jGxggwY75+NbQ1Q6kPf00XeOgpo7py4hPnyittnLEyZs4UCCYhCGB6yxa5FdR\n27DdcMwdd6Tr6mCC9qOPLt0HnfMcdBCeQw59QqaADcMwcqL6kjCeNidQSHXxyLR4kkyq3HDYChOu\nx4m/uU6YqpFqOO7VnmhqoszURABSH3mcYCaOBAlbB3FLYST/Y+xTiyMmJgKxCg2epwa1K33tM+cm\nTt/SMrRZ8rxH9yBL7U60Z7UcbHWxqRCqUY3kwauvAkjTdnICVMY9NQaJ7Lt+9Sv/gbkl+UxnJYfi\nELgcbG0K2DAMIyfsBWwYhpET49crleXojnOZshkSJ3DJCuaPk8uQsIMoyNu6T5DVhIptGLsispLl\nlOv4iefUA4aPJmATciK5IEiWfWP3Qdz7lmWz3Q0EKtr8bpWA18xwSHagh6gNj9Q8yq9oRx2dCl3B\nbDiJ661cCCrDJ4HSDrlxxhSwYRhGTox/XFalQj3KBagbI3fijMX+UapRAKUja/YVqmXfcvvcl4jT\nbgJpflpy2WUAgGmqiKfFQ/KB4Umm2DJjJ32NhKSaAjYMw8gJcc6NfmWRzQB+W73TqTne7pybuvvV\nKofZuLrsg/YFzMbjwV7ZeI9ewIZhGEblMBeEYRhGTtgL2DAMIyfsBWwYhpETe/0CFpFviMiVwfe7\nROTG4PvXReSvd7OPB0ZxnG4RGTaAW0QWisiCPT3vjP38VERWj3U/1aDoNhaRpSLyjIis1L9pe7uv\najEBbNwgIv8qIs+KyBoRuXBv91UtimxjETkoeH5XikiviFy/+y1Hx1gU8HIACwBAROrgB6QcG/y+\nAMCIRnPOjeUFupDH31tE5EMAannOnMLbGMAfOeeO179XxrivalB0G/8tgFecc0cCOAbAr8awr2pR\nWBs757YHz+/x8NEdPxnDuQw7wF79AegEsE4/Hwfg3wDcDWAKgP0B9AFo0N8/A+ARAE8AuCbYR7+W\ndQD+GcAaAPcA+DmAi/S3bgDXAHgMwCoAcwB0AegBsAHASgBnAPgwgNUAHgdw3yjOvwnAMviHdvXe\n2qGafxPAxksBnJS3HSe4jdcBODBvO05kGwfncKTaWyplm70eDuKc2ygigyIyA752eRDAoQBOBfAa\ngFXOuZ0ici6AIwC8C4AA+KmInOmcuy/Y3YfUUMcAmAbgaQA3Bb/3OudOEJFPA7jKOXeZiNygN+U6\nABCRVQDe45zbICItuqwTwI3OufdnXMKXAXwdaT7nmmMC2BgAviciuwD8GMC1Tp/kWqHINubvAL4s\nIgsBPA/gCufcpspYpzIU2cYRFwP4USWf4bF2wj0Ab1Aa9cHg+3Jd51z9+w18zTQH3sghpwO4zTk3\n5JzrAXBv9Dsl/6Pwxs9iOYCbReRTAPYD/I3PMqiIHA9glnPuP0d3mblSSBsrf+ScOw5edZwB4GMj\nXml+FNXG9QCmA3jAOXeCnvd1u7vYnCiqjUMuBvDD3ayzR4x1QDR9O8fBS/p1AP4GwDYA39N1BMA/\nOue+O4bjMDXSLpQ5Z+fc5SJyCoDzADwqIic6514ts79TAZwkIt26v2kistQ5t3AM51gtimpjOOc2\naLldRH4Ar2z+fQznWC2KauNX4VtwfOncBuCTYzi/alJUG/sTE3kHgHrn3KNjOLdhVEIBnw9gi3Nu\nl3NuC4AW+Bccnep3AbhURJoAQEQOzegNXw7gQhGpE5F2eKf57tgOIJn+QkRmOeceds59EcBmAIeV\n29A59y/OuU7nXBd8jfpsjb58gYLaWETq2SMtIpP0Gmoy2gQFtbE2hRcFxzkLwFOjOGYeFNLGAZeg\nwuoXGPsLeBV8j+ZD0bLXnHO9AOCcuxvADwA8qL6X2xEYQ/kxgPXwD88t8M2P13Zz7EUAPqihIWcA\n+JqIrBIfUvYAgMdFpFNEfj6mK8yfotp4fwB3icgT8J0fGwD839Fe9DhTVBsDwGcBXK12/hi8qqxF\nimxjAPgDVOEFXDO5IESkyTnXLyIHA/g1gNPUx2NUCLNx9TEbV5+JZOPaSIrpWaw9kg0AvlxUg9Y4\nZuPqYzauPhPGxjWjgA3DMPY1LBeEYRhGTtgL2DAMIyf2yAfc1tLiuvahOcC6e3rQ29cn43lMs3Fl\naWtrc12cGdcAADz66KO9roIzZJiNhzNaG+/RC7irowMrbrpp9ytOEE669NJxP6bZuLJ0dXVhxYoV\nVT1G0RCRik4XZDYezmhtXEtREJUhnLG3UjMwG4ZhVAHzARuGYeTE+Cvg+oxDchkVK7+PtC7hNqHy\n3dcZjY1HWpe2HBzMLg3DqAimgA3DMHLCXsCGYRg5UX0XRNzEDV0F/K2pqfR7W1v2tiG9vSVfd7ZM\nG7ZJ3dpn/Qc2u2MXx0RpWsd2Cr/H7hzafySXTWwfQvuFy+Nl8bkU3baGUUVMARuGYeTE+ClgKi6q\n3fCzllv6GwAAK5f5xRRPbcE8pz093O20kl1k7b6r60gAQAN2+gVUzf39pWVIkRUbjRCq0FjxtvhZ\nbHagEUB2IyDepG5Q7dfXN3xlfqYSpk2LbEfDGCdMARuGYeRE5RVwOZ8jh9cGvsed9V6FdXf777/5\njS8P0/z0C/rv9h9WdKf7T/ZD9azyePp0AMAWtCarbt3qy6lTG3TbzpJTret+wX8I/cnl/J+1SLnW\nRejf1WVDTc0AgM2b/eJnnvHlgw/68vXX000oZg8+2JeHHebtN2uWb3WEo07bO4b8B6rjeCdZfmPD\nMACYAjYMw8iN6vmAqcJUmVKt0fcIAD3rfUm34Tnn+LJ1tc5CTYdvmJxm7Vpfzp7tSyovlWWtk3cm\nqw7Ve+VGEdY4uK10v7H/MjjPQhBHkWS0MjZt9nXsQbpq++O+VdGu13zmIWq/7dvT/R53nC8j2ybf\nd81O1+0vE8GS5S8mpoYNA4ApYMMwjNyong+YqozyVnvfQ1chxdLMjh3+w5o1vqRConoOFPDQ+b8H\nAHhIp/abNcuXP7vdl8cfn+7/BDwGAGjk/lbrpLwvv+zLo48uPefwpGqZMsqXrYu+YIKWTvpob77Z\nlzQc/d7qeB+iIz6g7uST/YfLLvPl3Lml24boueyY7H3wjW2RLz2MODEFbBgATAEbhmHkRuUUcNwj\nT5WkipLqTIUwAKBxYIv/oILohZYTAAAzJz9Vuo9gI4pYph+9/npf0k1J0aw78MUtt+hx9ED0H2fs\nH+vXZ+2oNohtrLYdmlyqfDvbUj84fnibL+N8rZF6rnv11fLHbSuNNClpxug5bYOPshj2QI2UWMkw\n9nFMARuGYeSEvYANwzByovIuCMJOF20uN07XzqCwAyfqoJtZ/5L//uKLvtQRGU/1pQMoli71JaPR\n2Cp+73t9uXBhcA5X3AEAGPz+9/0pMryKTWr22IUuiFpuKpdJdEPPSuJ6uPXWdJ0lS3wZu4bos6EN\nPvGJdBt2yPH+0F5xaCHSTje6kRqhHap0U9hADMMoiylgwzCMnKic3IsTwVD5sFMrTgUJpMqKiouq\nScfF7pg9DwDQmzHf39ln+/KUU3zZLq/4D1d/J11p8WJ/yEmT/HeGs7ETbv/9fZmViaaWiUK7GnjO\nN9zgy+uuS9dlnB472ah458zxJZsOoQ3YYcd7xeYGjxOMReZmSRKkHr2HvO9FGtptGOOMKWDDMIyc\nqJwCjny+iSRiRhyq23CgAwdeUCVxgIT6fulPnD07Hb580km+bOzRRDornvblhg2+VH8vgFSpzZ/v\ny3e/25ccgMFzpkKudeJWBL9ToVK5hkOrtXUxqMOv67XpMHTZn5Ss2jh5KN2GPvFf/MKXy5aVHocD\nMwA0J0l39L7Hvt8wP6hhGCWYAjYMw8iJyingOLENvx9wgC+pquh7BBLFtuP4BQCAxu0/88upolVx\ndYbDZNetKz3uIYf4kv7dH/84/S2Mbsg6N6qzovkn4yzqbDmobXYGiXX69XMrI0CuuAJAmo+IJmlr\nS+viZuaopC2puOnX5cAWALjggtJ10h2WfjcMYximgA3DMHKiekGvVETqf90x6FNDdq9NV+kd9Mr3\nwW/775/9hCZ/YeIYKlhmEQeAXbt8qb33G6e/CwDwla8MPwXGBNNvPKNNIyUmWg/9pk2+POggAElI\nLgAgielg5Ie2LthgSKYbCpXqypW+pE+ZK59+ui+ZqT3Y37BWxUSb+NQwqoApYMMwjJyovAKOlBAn\n2mQSnXAg3D33+JJu4sQxSQVGP2Konq6+GgDwF9f66XG+o2G/zvlk62ec0ZysyuCHRNy1qTqjss6a\nlLOIMJ5ZR6iFWpOfG3mt6t+tixMRhfHZy5f7Mk6Iz++XX56uG9sy9v1OFBsbRhUwBWwYhpET9gI2\nDMPIiarPiMGWLiOlwrSz2meU9A8lIWb33utLBvVfckmyzWPrvevh29/mNL6LtfR+jP7+30vWHdb/\nMzkaLFB02OE1daov9fqaf+d30nXUlkPq76mjsek64D44KCZcxs62t97yJd0LyQ1DYtyhNn9f6hAM\n6ABqO7mRYeSMKWDDMIycqLw8iVIWbvVTjiUjhUNBxJHCv//7uuDzPvB/p3b2NHCa5C98Idlm5VJf\nHnLIgQCAl1/mUFdfl4T9dRw5y+PsHPTrNHAlKuGiDpelrZlg57nnfBkaQZVuHZsgNAoHWcQzHodw\niDY73446atgq7GQlrRz7YuFnhrFbTAEbhmHkRNUU8KatXhk9/7xfTIEVjkT+w/maUOfPrgIAbPvP\n/wSQ1goNOmz2H26dmWzDUcnMonj77ecBALZv92FodFcCoxBh8RxrQDGGzsbzrNE3e+qpvtRkRgBS\ng8WDTw70LYhkYEvYNKHBOKSZPuYjjgAAbOxJ6236+Nvbo3OMjZ61f8PYxzEFbBiGkRNVi4J4803/\nlQqJsfwlUwYt0TSHOjiASSfrT/ZDkh9u9xENS65PN+GwYnbE06XZ3e0HYCSDOoJ16CJt6Hul5ByH\nzY5cFKLk99v61f/d5WeVbg2bGVT08Y2Ifw99wEzoHoepaMlBNQDwtrf5MsnoaerWMEaNKWDDMIyc\nqPyknBpRMFg632YSaNDZEcSJMvZUJ4SsZ2/7lVcCAG7+F/81HM0auz8p9niciy9O16Vabu1TXzOV\nYzz8tig+4Ph89TtFJ929q/sbg00adR0/eWavqldeZkeHbznMnz8t2aaR9mGEhBpyqEt98UFCJbY4\nEhPGQ5AtGsIwymIK2DAMIyfsBWwYhpETVcuGxignRkgFE+mmcCHbrxddBAC49Ho/GzKToq0NmrwX\nXuhLtnTpgmCq2rPOStdtP8jPKYf12vyNc9TG/oyiETXrGYIXTiDC8ReMNqNngC4h9smVzAnH+0Ef\njsLcwV1d6eAL3l/O3zfM9WAYRllMARuGYeRE1RTwAaqwqFApjF7oTt/5MymfKNNUEasQ5vRlJX1k\n7LeLp5jrbNlRugKQDj6I54bjDnlStdzxlkXUsTVZbc0OMaYHBlLly01ocipfmuCl9el9mUF7sYyG\nbh/ZFdgzCXOLZkMumk0NIwdMARuGYeRE5WdFVpXUrE7G5um+3DbQULIagFSqMUflMj8w4/2cyuKR\nR3xJGQfgmPN1DDKlm26TDJsN1a4mBErWjRVvPEtyrRPPPK22blRbT5/uQ87eeCPd5LXXfEm/ME1C\nBUz3d8n4DO7gdU35yfDAxZr6kyNbwg3jZD5Fs61h5IApYMMwjJyovA+YKpOqSWnOmoH44Yd9eeut\nvlyyxJeMjli1ypdTpqTbUMrRj8sZk5mAJlw3VmFx+smiqrMy6rJV5e1hhzXGWwyLRmFDgdEqDXf8\nR7ry44/7kveMsyPT9qHaZaRE6KjPODfDMIZjCtgwDCMnqhcASyUcD5998cV0HfoSGbkQz4b8znf6\nMkwuE/ofgXTqY6rasPed50CfZpipZyIQK3ulk/YD0Hm4rjMlUv+8H7T57benO1i0yJdsVXBdRpWE\nkSZM1MNjFjWm2jBywBSwYRhGTlRPrsRJWFgefni6DtUYh7Hp903bvQ+TnfBhYENri47Yorql+svy\nOVKNMaF4fG4ThVgJh+k1wxYHkKpaRo1wrqhQRTMNJUMm6OelzQOFjf32yz4XwzB2iylgwzCMnLAX\nsGEYRk6MX49JPIggXEbUBdGedNxp2RskBF4/hqGuE715HCcZAoCjjy5dxpLuBZ3nrSRbUlae5Hi/\n8TENw9hjTAEbhmHkxCmY0KQAAAP/SURBVPjHDI2kXMOpL3ZH1sAOwxPaZLT2YYfoaPdrGMaYMQVs\nGIaRE+KcG/3KIpsB/LZ6p1NzvN05N3X3q1UOs3Fl2QftORoqanOzcSajsvEevYANwzCMymEuCMMw\njJywF7BhGEZO7PULWES+ISJXBt/vEpEbg+9fF5G/3s0+HhjFcbpFpC1j+UIRWbCn5x1sf4mIrBKR\nJ0Tkzqxj5M0EsPFH1L5PishX93Y/hjFRGYsCXg5gAQCISB2ANgDHBr8vADDiP79zbq//uQEs5PH3\nFBGpB/BNAL/jnJsH4AkAV4zhXKpFkW18MICvATjLOXcsgA4ROWs3mxnGPsVYXsAPADhVPx8LYDWA\n7SIyRUT2B3A0gMcAQEQ+IyKPqBq6hjsQkX4t60Tkn0VkjYjcIyI/F5GLgmP9uYg8pop1joh0Abgc\nwF+JyEoROUNEPiwiq0XkcRG5bzfnLvp3oIgIgGYAG8dgi2pRZBvPBPCcc04z5mMJgAvHZA3DmGDs\n9UAM59xGERkUkRnwKulBAIfCvzBeA7DKObdTRM4FcASAd8G/9H4qImc658J/4A8B6AJwDIBpAJ4G\ncFPwe69z7gQR+TSAq5xzl4nIDQD6nXPXAYCIrALwHufcBhFp0WWdAG50zr0/Ove3ROTPAKwC8DqA\n5wD8j721RbUoso0BrAVwlL7I1wO4AEBDRQxjGBOEsXbCPQD/YuDL4cHg+3Jd51z9+w28WpsD/7II\nOR3Abc65IedcD4B7o99/ouWj8C+RLJYDuFlEPgVgP8C/wDJeDBCRSQD+DMA7AXTCuyA+v/vLzYVC\n2tg5txXexj8CcD+AbgC74vUMY19mrEOR6aM8Dr55vA7A3wDYBuB7uo4A+Efn3HfHcJw3tdyFMufs\nnLtcRE4BcB6AR0XkROfcq2X2d7xu8zwAiMh/APjcGM6vmhTVxnDOLQKwCABE5E9gL2DDKKESCvh8\nAFucc7ucc1sAtMA3kdk5dBeAS0WkCQBE5FARmRbtZzmAC9VP2Q7f+bM7tgM4iF9EZJZz7mHn3BcB\nbAZw2AjbbgBwjIhwpMo58E3yWqSoNgbPQUSmAPg0gBtHWt8w9jXG+gJeBd8z/1C07DXnXC8AOOfu\nBvADAA+qD/F2BP/Uyo/h/YRPAbgFvhn92m6OvQjAB9lBBOBr2oG0Gv7F9LiIdIrIz+MNnXMbAVwD\n4D4ReQJeEf/DHlz3eFJIGyvfFJGn4F/+X3HOPTu6SzaMfYOaGYosIk3OuX4NX/o1gNPUV2lUCLOx\nYdQWtTSF7WLtWW8A8GV7MVQFs7Fh1BA1o4ANwzD2NSwXhGEYRk7YC9gwDCMn7AVsGIaRE/YCNgzD\nyAl7ARuGYeSEvYANwzBy4v8Dxu/BAkYCrogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9a549fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance after 1000 iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 92.0%\n"
     ]
    }
   ],
   "source": [
    "optimize(num_iterations = 990)\n",
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3c6HTIrmhPK75Sj2PS6rQFBEpNA2jFBGJQIWmiEgEKjRFRCLIaDXKZs2aubKy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\nspQh3zEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9a547e9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KCjfOjpyMJ2BSGADgsFiqZg2RmsyZH5iUCkiz+zCFKjvomP+TKrooduYADA7UUnnLjjaa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\nyAl7ARuGYeSEvYANwzBy4v8Dxu/BAkYCrogAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9a549fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can plot the confusion matrix to see more details about mis-classifications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 967    0    0    1    0    1    7    1    3    0]\n",
      " [   0 1107    2    2    0    1    4    2   17    0]\n",
      " [  13   10  885   21   15    2   13   14   51    8]\n",
      " [   3    1    9  925    1   21    3    9   29    9]\n",
      " [   2    1    1    1  916    0   11    2   13   35]\n",
      " [  13    3    0   36   10  742   15    8   57    8]\n",
      " [  14    3    3    2   13   12  902    1    8    0]\n",
      " [   3    9   19   10    7    1    0  937    4   38]\n",
      " [   6    5    3   17    9   10    9   10  900    5]\n",
      " [  11    5    1    8   34    3    0   17   11  919]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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cliYSQtKxKeY8inmOb0iT8rxCMQT6cIrf5RVAzomBzCrlBGzbs/uoYdL/QjF3\nxQHAkxFxTzp/JHAo8MM0ZHgK8CPgHRQTxDwKkCbpGW86yWOAM6CYvQ14Mc3uNdqxabs/He9JkZD3\nAq6LiFdTjMbNCWL9zQnYtueXI7XQESnJvjL6FMVcw6eNue5N37eTBPy/iPiHMTG8LI41mtuAbWfd\nAxwl6SD49Qxm/4Zi5rXZkn43XXfaNr7/NuCT6XsH0goVL1PUbkfcDHxiVNvyjDQz113AKZJ2T7Om\n/YeK35tZVk7AtlMiYhPwceAKSQ+Qmh8i4jWKJod/Sg/hNm6jiHOAD0h6kKL99tCIeJaiSWOVpL9L\nqztcDvwoXbcU2Cst6XQVxbqA/0wxValZY3g2NDOzmrgGbGZWEydgM7OaOAGbmdXECdjMrCZOwGZm\nNXECNjOriROwmVlN/j+GMCocgzrXIQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd9cf81eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_confusion_matrix()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "92% is not too bad but we can definitely do better. Stay tuned!\n",
    "\n",
    "### References\n",
    "- https://www.tensorflow.org/get_started/mnist/beginners\n",
    "- https://www.oreilly.com/learning/not-another-mnist-tutorial-with-tensorflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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