practical1.ipynb

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    "colab": {
      "name": "Practical 1: Non-linearity, manual backprop and the value of autodiff",
      "version": "0.3.2",
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      "provenance": [],
      "last_runtime": {
        "build_target": "//learning/deepmind/research/go/data:go_data_notebook",
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  "cells": [
    {
      "metadata": {
        "id": "JVvNUpj6ZKmM",
        "colab_type": "text"
      },
      "source": [
        "# Practical 1: From linear to non-linear models\n",
        "\n",
        "In this practical we will develop our intuition of machine learning models, and implement a linear and non-linear model from scratch that can classify a variant of the classic \"swiss roll\" dataset."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "j9-CLiXs36tt",
        "colab_type": "text"
      },
      "source": [
        "# Building Intuitions: Our First Classifier on Simple Toy Data\n",
        "\n",
        "Run the code in the cell below, and look at the resulting plot. It should produce a simple 2D data set consisting of 2 classes of points, a weight vector in black, and a decision boundary in red. The goal is to obtain a decision boundary that best separates the different classes of points."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "Kx2JGMPS3_4O",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
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              "item_id": 1
            }
          ],
          "height": 509
        },
        "outputId": "296871e3-9957-45f2-b0cc-3faf07e17fcb",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706244211,
          "user_tz": -60,
          "elapsed": 461,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "import numpy as np               # Numpy is an efficient linear algebra library.\n",
        "import matplotlib.pyplot as plt  # Matplotlib is used to generate plots of data.\n",
        "\n",
        "centre = 1.0\n",
        "points_in_class = 20\n",
        "# Setting a random seed allows us to recreate the same data each time we run the cell.\n",
        "np.random.seed(0)\n",
        "\n",
        "# Generate data.\n",
        "x_pos = np.random.normal(loc=centre, scale=1.0, size=[points_in_class, 2])   # Generate random points in the \"positive\" class\n",
        "x_neg = np.random.normal(loc=-centre, scale=1.0, size=[points_in_class, 2])  # Generate random points in the \"negative\" class\n",
        "x = np.concatenate((x_pos, x_neg), axis=0) \n",
        "  \n",
        "# The class (or \"y\") value is +1 or -1 for the two classes\n",
        "y_pos = np.ones(points_in_class)  \n",
        "y_neg = - np.ones(points_in_class)\n",
        "y = np.concatenate((y_pos, y_neg), axis=0)\n",
        "\n",
        "# N is the total data set size\n",
        "N = 2 * points_in_class\n",
        "\n",
        "# Plot the data using Matplotlib\n",
        "fig = plt.figure()  \n",
        "plt.scatter(x[:, 0], x[:, 1], c=y, s=40)\n",
        "plt.axis('equal')\n",
        "\n",
        "# Pick a weight vector. In the exercise below, you are going to change the\n",
        "# values in this weight vector to see how the decision boundary changes.\n",
        "w = [-0.5, 1.6]  # CHANGE ME!! \n",
        "\n",
        "# Add the weight vector to the plot.\n",
        "plt.plot([0, w[0]], [0, w[1]], 'k-')\n",
        "\n",
        "# Plot part of the decision boundary in red. It is orthogonal to the weight vector.\n",
        "t = 2\n",
        "plt.plot([-t * w[1], t * w[1]], [t * w[0], -t * w[0]], 'r-')\n",
        "\n",
        "# Add some labels to the plot and display it\n",
        "plt.xlabel('x0')\n",
        "plt.ylabel('x1')\n",
        "plt.show()"
      ],
      "cell_type": "code",
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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6i1VYWFhu7dixYwoICDKUyP1t2LBWY8eOKbfWoEEDhYYGcVsVuA0KGQC3Nnz4j++2TDWc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\nUcgAAAAMo5ABAAAY9v8D2U21tfLHxl0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0xd7bf0d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "OidhcGh6xtwN",
        "colab_type": "text"
      },
      "source": [
        "# What do parameters do?\n",
        "\n",
        "* Change w = [0.5, 1.6] to different values, and re-run the above code.\n",
        "\n",
        "* How does the decision boundary change?\n",
        "\n",
        "* Where in x-space is the inner product w' * x positive? Negative? Zero? Can you relate that to the class labels y?\n",
        "\n",
        "* By changing w, can you manually find a weight vector that does a good job of discriminating between the two classes?\n",
        "  * How did you manually find it? What made you move from one choice to the next?\n",
        "\n",
        "* Now that you've found it manually, chat with your friend next to you.\n",
        "  * How will you find it automatically?\n",
        "  * Can you devise a function, where minimizing it does the same thing as the way you manually searched?\n",
        "  * Pause here and think.\n",
        "    * Which values of w give \"bad solutions\", according to you?\n",
        "    * Which ones give good solutions?\n",
        "\n",
        "* Try to draw the function that you devised on a piece of paper. It should be small when w gives a \"good solution\", and it should be big when w gives a \"bad solution\". Be creative and think of your own function. Show your drawing it to your neighbour.\n",
        "\n",
        "DO NOT PROCEED ANY FURTHER UNTIL YOU'VE THOROUGHLY ATTEMPTED ALL THE ABOVE QUESTIONS. (Ask your tutors for help if you're stuck!)"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "c58IjWnlyMh2",
        "colab_type": "text"
      },
      "source": [
        "# A loss function of w\n",
        "\n",
        "* Below we will formulate it as a loss function.\n",
        "\n",
        "* Run the code below, and look at the plot of the loss function. Note that it is not in x-space any more, but that our axis labels are w[0] and w[1]!\n",
        "\n",
        "* Do the weights w that you found manually correspond to the minimum of the loss function?\n"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "oFSdDg89xBW4",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 524
        },
        "outputId": "2ff465a0-fc85-46e6-9f76-86f49ddba603",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706244863,
          "user_tz": -60,
          "elapsed": 562,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "def compute_loss(w0, w1, x, y, alpha):\n",
        "  # We start with a regularizer.\n",
        "  # What is its effects on the loss function? Does it change the loss function's\n",
        "  # minimum?\n",
        "  loss = alpha * (w0 * w0 + w1 * w1)\n",
        "  \n",
        "  # Add the data point's contribution to the loss. We do this for every data\n",
        "  # point. (We don't have to do it in a for-loop, but below, you can really see\n",
        "  # what is happening...)\n",
        "  for n in xrange(N):\n",
        "    # Get the inner product x' * w for data point x.\n",
        "    inner = w0 * x[n, 0] + w1 * x[n, 1]\n",
        "    \n",
        "    # Now look at the plot with a weight vector in our \"data space\".\n",
        "    loss += np.log(1 + np.exp(- y[n] * inner))\n",
        "  \n",
        "  return loss\n",
        "  \n",
        "lim = 5\n",
        "ind = np.linspace(-lim, lim, 50)\n",
        "w0, w1 = np.meshgrid(ind, ind)\n",
        "\n",
        "# You will change the value of alpha (below), to see how the loss function\n",
        "# changes. It has to be alpha >= 0. No negative values (otherwise the loss\n",
        "# function's minimum is at negative infinity)!\n",
        "alpha = 0.1\n",
        "loss = compute_loss(w0, w1, x, y, alpha)\n",
        "\n",
        "fig = plt.figure()\n",
        "plt.pcolor(w0, w1, np.exp(-loss))\n",
        "# We plot exp(-1oss) here, to let the colours show clearly in the plot. This is\n",
        "# incidentally also proportional to the joint distribution\n",
        "# p(y, w | x) = p(y | x, w) p(w), which you'll encounter on Wednesday in the\n",
        "# Indaba, and can safely ignore for now.\n",
        "plt.title('A plot of exp(-loss), as a function of weight vector [w0, w1]; '\n",
        "          + 'alpha = ' + str(alpha))\n",
        "plt.xlabel('w0')\n",
        "plt.ylabel('w1')\n",
        "plt.axis('equal')\n",
        "plt.show()"
      ],
      "cell_type": "code",
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KEsI8rbckc0vSgNbTXE9/0lNTTziOo/Q1alTH7Zj1e8IAAACqogrztUVRUVGK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\nwtfr7CQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0xfc08250>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "ViYDcDH1cbx3",
        "colab_type": "text"
      },
      "source": [
        "# Trying different loss functions\n",
        "\n",
        "* As a first exercise, look at the function that computes the loss. There is a for-loop, essentially a sum.\n",
        "  * Can you write down the loss function on a piece of paper? As a mathematical expression...\n",
        "  \n",
        "* On a piece of paper, can you draw\n",
        "        log(1 + exp(- y[n] * inner))\n",
        "  as a function of the inner product, the value of y, etc.\n",
        "  * When is it almost zero, and the contribution to the loss is neglible?\n",
        "  * Where does it become almost linear?\n",
        "    \n",
        "    After you've done your drawings, explain to yourself why the function is equivalent to\n",
        "        inner = y[n] * (w0 * x[n, 0] + w1 * x[n, 1])   \n",
        "        loss += np.log(1 + np.exp(- inner))\n",
        "    What is the effect of the class label y on the weight vector. What happens if we multiply a weight vector with -1?\n",
        "\n",
        "* Now change the setting of alpha. Make it bigger, and smaller. What happens to the minimum?"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "hwxeymnrToNF",
        "colab_type": "text"
      },
      "source": [
        "# Working with More Complex Data\n",
        "\n",
        "Real-world data is unfortunately not as simple as our toy bimodal Gaussian example above. Real data (e.g. pixels from vision, or speech phonemes, or words of a language) can have very complex, high-dimensional distributions. Before we get our hands dirty with that, we'll move one step up and work with another toy dataset, but this time non-linear."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "T0eBZ4aq2IH2",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 51
        },
        "outputId": "989f3277-dc68-47b2-9128-165e2842a6c1",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706245144,
          "user_tz": -60,
          "elapsed": 232,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "import numpy as np  # Numpy is an efficient linear algebra library.\n",
        "import matplotlib.pyplot as plt  # Matplotlib is used to generate plots of data.\n",
        "\n",
        "%matplotlib inline\n",
        "plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots\n",
        "plt.rcParams['image.interpolation'] = 'nearest'\n",
        "plt.rcParams['image.cmap'] = 'gray'\n",
        "\n",
        "# for auto-reloading extenrnal modules\n",
        "# (if you're curious, see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython)\n",
        "%load_ext autoreload\n",
        "%autoreload 2"
      ],
      "cell_type": "code",
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The autoreload extension is already loaded. To reload it, use:\n",
            "  %reload_ext autoreload\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "nlzlDave2e8K",
        "colab_type": "text"
      },
      "source": [
        "Let's generate a dataset with three spirals arranged in a swiss-roll type structure, and where each spiral forms a \"class\" that we want to be able to classify (i.e. the classes are very non-linearly distributed).\n",
        "\n",
        "## Hyperparameters\n",
        "\n",
        "First we define some hyperparameters that will be used by the next few cells. Try changing these values to see how the models work with different data. "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "O3WJV8EI-4xp",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "num_classes = 3  # The number of classes (distinct groups) of data (these are our \"y\" values)\n",
        "dimensions = 2  # The number of dimensions of our input or \"X\" values\n",
        "points_per_class = 100  # number of X points to generate for each of the y values"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "gGuvwWo72eFH",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 499
        },
        "outputId": "dc3d406b-2589-49cc-b383-ae57314fa0f9",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706245854,
          "user_tz": -60,
          "elapsed": 415,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# Setting a random seed allows us to get the exact same data each time we run \n",
        "# the cell.\n",
        "np.random.seed(0)  \n",
        "\n",
        "def generate_spiral_data(num_classes, dimensions, points_per_class):\n",
        "  \"\"\"Generate `num_classes` spirals with `points_per_class` points per spiral.\"\"\"\n",
        "  \n",
        "  X = np.zeros((points_per_class*num_classes, dimensions), dtype='float32')  # Create an empty matrix to hold our X values\n",
        "  y = np.zeros(points_per_class*num_classes, dtype='uint8')  # Create an empty vector to hold our y values\n",
        "\n",
        "  for y_value in xrange(num_classes):   # Generate data for each class\n",
        "    ix = range(points_per_class*y_value, points_per_class*(y_value+1))  # The indices in X and y where we will save this class of data\n",
        "\n",
        "    radius = np.linspace(0.0, 1, points_per_class)  # Generate evenly spaced numbers in the interval 0 to 1\n",
        "    theta = np.linspace(y_value*4, (y_value+1)*4, points_per_class) + np.random.randn(points_per_class) * 0.2  \n",
        "\n",
        "    X[ix] = np.column_stack([radius*np.sin(theta), radius*np.cos(theta)])   # Convert polar coordinates to standard Euclidian coordinates\n",
        "    y[ix] = y_value\n",
        "  \n",
        "  return X, y\n",
        "  \n",
        "  \n",
        "def plot_data(X, y):\n",
        "  \"\"\"Use Matplotlib to plot X, y data on a figure.\"\"\"\n",
        "  fig = plt.figure()\n",
        "  plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)\n",
        "  plt.xlim([-1,1])\n",
        "  plt.ylim([-1,1])\n",
        "  return fig\n",
        "\n",
        "X, y = generate_spiral_data(num_classes, dimensions, points_per_class)\n",
        "fig = plot_data(X, y)\n",
        "\n",
        "# fig.savefig('spiral_raw.png')  # Uncomment this line if you want to save your image to a file"
      ],
      "cell_type": "code",
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Jz78EhinD+vWR4PF4uHHjJnJzC5GcnDX6i37PrVt56OioBADIZN6YO3cJlcMgI0bJGCGE\nfIeDgxOWL3+J6zCG1NbWisePyxEYGAoHByeuwzEbjcYGGo0WItHAXrl6vR4KhXhU19PpdOjuvo91\n62b3t82ZEwKl8gEaGurh4eE15pjPnNmHxEQZAgL6ypI8edKOkyc/x/Llm8d8bWJdaNY2Gbaenm50\ndXVyHQYhVqmv7MZnqKs7hpiYTlRVHcHJk7umzAT3JUuysG1bPh4/bgIA1Ne34aOPrmPRotHNF7t/\n/y7mzfM3aV+0KAxFRVfHFCsAtLe3ws1NgYCAgbmEnp6OCA3loa7u2dthEfJdNDJGnqnhSQM+/PMX\naKjRgWUBNy8+tvxwDQKDArkOjRCzKCq6iYaGIkgkLBQKBgEB8Zg+PerZJ46j8+ePICsroL/af2qq\nE1paOnH+/AksXjz5txkTiUTIynobd+/ewJUrj+Ho6IHs7HdG/cpPLrdHW1ulyXZVCoUKItHY5//d\nu1eA9PQQk/Z586Zh9+58eHv7DXIWIYOjZIw8FcuyeP93n0HfMw1ySd9DUdUO/P9/+ALvf/B/qCQG\nmfSKim5CLq9EcnJ0f9v583fw6JEAwcETqSp+G+ztjXfJcHGxh073mKN4zI9hGMTGJgBIGPO1goJC\ncPToaURHBxi1HzlSiIULfzDkeUqlEpcvnwSPp4JWy8Py5dkATOvLeXn5o6ysEDExxtevrm6Gm5v3\nmOMn1oWSMfJUd+8WobvFETKp8bdTvcIHuTkXkJK6hKPICBmdtrZWnDq1HxKJFhoNDwpFO15/PdHo\nmKSkGdi16+aESsZ4vMFfR9Jc8aElJGRj27ZDCAqSQiIRorS0CyEhSyAWDz4Prbu7E7m527FpUzwk\nEhH0ej2OHNkGf/9l8PU1fhMQHDwNhw6dQWSkL/jfrDLo2wC9HFlZGRb/28jUQskYeaqmxmYIBbYm\n7SKBDM3NbRxERMjodXS0IT//C2zaFN//+uvzz88OeqxIpB/P0J5JqZRAp9Mb7Q7wbdV6Mjg3Nw+s\nXPlDtLS0QKvVID396ZP28/KO47XX5vWP+PP5fGRlxWHXrosmyRgApKa+gp0790MmU4JhgJ4eMZYu\n3UyrKcmIUTJGnmrBwnk4vPcvAEKN2hXaKqSkTtwVZ4QM5tq1r7Fx42yjD0updPAtjtTqifV4TErK\nxscff4SMjBD4+7vh0aMnOHv2MVaufIPr0MzCYDAgN/cg+PwOMAygUkmRlJRtloK4Li4uwzpOKtUO\nOvVCItEMerxMJsOKFS+PKTZCAFpNSZ7BxsYGKSvC0asemJfSq67DvCU+cHUd3gOOkIlCItGZfNhG\nRATg+PHrRm1HjtxBRMSi8QztmaRSKbKz30FpqTP27HmMqiovZGf/eMz7ZU4Ux49/hpUr3fD88zFY\nty4G69cH4cSJj8c1Bs3gORe0WvqoJJY1sb76kQkp67kViI6twJlTl8GyLBYnJyM8fOLMpSGTE8uy\nuHUrD11d1TAYGPj4RGLGjOhnnzgGGo3ph2pYmB/OnCnFrl0PIBYboFLxEBm5bEKuhjPnBPeJpKmp\nEUFBfMjlA6schUIBUlMDUFiYj+jouHGJw8srCrdvV2DmzID+ttraFojFPkOfNI7y8k5Cra6FSGSA\nSiVEQEACQkMjuA6LmAHDTuAiNc3N3VyHMGW1traioqISYWHTIJfbcR3OmLm6yul+mWSOH9+BpUvd\n4OvbN8J6924VHj2SYuFCy5VpqKmpQnv7RSxdGt7fVlpaj9JSWyQkJFus34msr6zHPYhELFQqASIi\nFsPHx7Q+13B1d3fh+vWzYFkd/P0jMW1a+DPPuXnzMubMUcHFxXST9j17qpGSkj3s/ltamlFb+xgh\nIdNhaysfUewAkJ9/Ee3tDyGTsVAqAQeHIMyalTri65jbpUsnMHs2Az+/gVIdJ08WwssrFV5evhxG\nRr7l6jry++1bNDJmZQwGA/7791tRdl8BnsEBEF5A7Bw3vPEjqhhNxk9l5SNERYn7EzEAiIkJQFXV\nbSiVSrPtA/l9vr4BsLEBdu0617+a0s4uGAkJ1rkq+M6dq3B2rkVy8kBNtQMHTkEoXAV3d88RX6+4\n+A5aWq5h7dpYCIUC3L1bjJMnC5CRsemp5wUFTcfdu8ewdKlxMlZSUgcvr+HtJanX63HixGcICOAh\nIsIDd+7cQUeHHVJTnx/R3xAXtwjAIuj1evD5/AnzRU+jqYGfn/EIYXp6FHbtugQvrw0cRUXMhZIx\nK/PZp3tRU+IAW7HHNy1OKLrRhWPep7ByVTqnsZGp7+rVXPT2VqO8vATvvvucye8TEvxRWFiImTMt\n9xouLCwKzs4BFrv+ZNLSch+pqbFGbVlZs7Br1zmkpY3sA55lWdTUXMOmTQPbD8XEBIDPr8bDh0UI\nCxu6iK6zswuuX+ejtbULzs59I/UqlQbnz9chO3v1sPrPydmP9eunwcamb8K/l5cLamtbcOVKDhIT\nl47obwHQX65iNFiWRXd3F2Qy2zFd57tEItOXWAzDQCQymOX6hFuUjFmZkuJGCPgBRm1igR3u5Fdi\n5SpuYiLWISfnABITpfDzi8T58zq0tnbC2dl4JKS6uhVubjQfcbyIxablOxiGgVisG/G1mpoaERJi\nOuUhMtIPu3cXPzUZA4CMjE3IzT0Ovf4xGIaFTidHZubrw+5fKOzuT8S+5ePjgry8+8O+hjncuHEO\n3d2lcHcXo61NDbXaCSkpa8dc7kKtFpq0abU66HSj27uTTCyUjFkZvW7wKYJDtRNiDn2vHlvh5zcT\nALBwYRT27MnFpk0Dc3H0ej3u3etCZubUnf9SWfkIZWWFCAiYPqy5VJamUpkuaGBZFirVyEdzpFIp\nnjxRm7QbDAYMZ+E+wzBISlo54n6/NVRR3PHcJOTevQJ4e7chNnbgdWJzcyfOnTuKJUvG9m3X0zMW\nFy4UY/Hivi8rer0eO3feQHLyljFdl0wMlIxZGW9/OWoeGMAwA08ovV6DgGAnDqMiU11tbTXCwpz7\nf+bz+UhOnom9e89Br+dBKJSip0eC5OSnzy2arPR6PY4d24aZM+XYsCEI9+8/xMGDF7BixRZOS1O4\nukaioKASs2YNFDQ9eLAAM2eOPHGws7NHdbUGBoPBqHzIyZOFiIvLMku8T9PbKzbpW6FQQa8f/aTq\nkXry5D6WLDEe2XV1tQfLVo752hERcaiokGPXrhsQCg3QasVYsuQVyGRU9HcqoNWUVqa7uwvv/dtf\noWjzhERkD4W6GS4+XXj3//4EQqHpMPhkMVEm2ZLB9fT04OHDvcjIiDFqb23txMWLBsyfnzJuVcu5\nuFdycg5i5UoX2NoOLEzQaLTYu7cK6ekvjmss31dUdBNPntyDRAIoFDxERiaNejVlV1cHLl7ci4AA\nCZycpHjwoB0uLrGIibF8KY7u7k6cObMdq1bNgKenE8rK6pGbW4tVq96AQDD6cYeR3C/nz+/AunWm\nI55ffVWARYumRnFeMjRaTUmGTS63w+/e/z+4cO4SqqrqER4RizkJ8VyHRaY4W1tbNDeL0d7eA0fH\nvu21WJbFl19eAMM4obMzDg4Og4/OPnpUgoqKAjAM4OYWiujo2YMeN5HxeJ2wtTV+/SoSCSEW93IU\n0YCoqHhERZnnGWBn54CVK99Ea2srenq6kZzsP25Jtlxuj6ysn+DWrTycP/8YHh5ByM4e34mwWq0U\nWq0OQqHxR6tKNTUK8xLLoWTMCjEMg6TkiVVdnEx96ekb8eGHv0VIiBBisRAajRbr1yfD3l6GHTsO\nY/nyV03OuXz5FLy9O7FhQ992XKWl9fj66y+QlrZ+vMMnI+Ds7AxnZ+dnH2hmDMMgPn7huPf7rQUL\nVuKTT7Ziw4ZY2NnJoNXqsH9/PsLDRz8XjlgHSsYIIeOCYRgEB/vg+edNV0vKZFqTNqVSCaAa8fGz\n+tumTfNCS0sJ6uqqJ2SF/KE5oaOjBw4Otv0tKpUGGo3tU84hk41UKsWqVW/hzJmz0OmeQK8XYt68\nl0ZVfJZYF0rGCCHjRq8ffIrqYDNXi4vvIDEx0KR93rxp2LPn1qRKxhYvXokDBz7DjBlixMUFoqio\nGrdvd2LFite4Ds1qtba2oKDgIgQCEebOXWq2QsNCoRCLFmWY5VrEelAyRggZNw4OgaiqakRAgHt/\nm1qtgVJpuiLM2dkddXU1cHNzNGpvb++BjY3ptjkTGY/HQ2bmq6ivr8GhQ0UICorH6tVBXIc1pV27\n1ldgmMdjoVKJsWjR6v6Vh3l5JyGTNWD9+gio1VocPbod7u7zEB4e+4yrEmIZlIwRI83NzaiqfIwZ\n4aPb142Qp4mPX4icnAMoLr6DuDg/lJc34eFDJdLTXzY5NiAgCIcPn0JsbKDRJPAjR+4hPf2t8Qzb\nbLy8fK1mH0GtVotLl04A6IReD7i5hSEmZs649H3+/GHMmSOEv38kgL7SIh9//DFWr/4x2tpaYWvb\ngNTUviK0UqkYzz8fj127rmDGjJhxW3BAyHdRaQsCoO9h9Yff/Q2VDzXgGewBYRvi5nphy5uTY88z\nKm0xufT0dKO09D68vf2fugdiZ2c78vK+gpOTHnw+D21tQFRU2pheUdK9Ynksy+LAgb/gpZdi+6vi\nFxfXoqREjAULLPsKT6PR4Pr17cjOnmXU3tbWjQsXdFAqu7B+va9RPTIAKCurw5MnwZgxI9Koncv7\nRa1W49y5ryCRKMCygFYrx5Il2f1liFiWRWHhLTQ3V0EkssW8eSmTukTRZEelLciYfbp1N56UucBW\n/O3WGk64c7UDJ33OIGNF6lPPJdanvr4GhYWXvtkvT44FC9JHVLzU1laOWbPmPvM4e3tHrFjxA2i1\nWuj1ekgkkmeeY0nV1ZV4+PDiN5uMM7C3D0Z8fBKnMU1EBQVXkJkZarQ9UXi4D+7fvwWtVmvRhKG5\nuQkBAaavsZ2c5FCrK8HjiaDXG0ySMZVKC7H42feXXq9HY2MDHB2dLLah/bdOnvwEr7wyq79Uhkql\nweefb8Pq1W9Ar9fj8OGtSE31RUpKILq7Fdi//0PEx6+Fu7uXReMi5kfJ2AR0+dJ1HD98Fa1NStjY\nCjB7XhA2bMq26PB56YNmCATGc1jEQgcU3HpEyRgxUlx8ByrVbWzaFAmGYdDbq8TOnX9DZuYPLVZN\nXigUcv6Nv7m5CY8fn8bGjQNb3ZSW1uPq1TOYN4/+jXxXe3sdvL1N58SFhbmgrq4WAQGmCzPMxcXF\nFbdudWKW8cAYurp6IRTKMWvWfBw9ugvZ2cb16goKmrB8echTr33lymloNFUICrJDYWEP2tokSEvb\nYJLYmUNJyT0sWOBpVLNMIhEhJsYOjx9XoKrqIV58MRx2dn3z4ORyG7z6aiJ27DiFjAxaGDLZmOUO\nunjxItLT05GWloatW7ea/P7gwYOYN28esrKykJWVhf3795uj2ynp4YMS7P70OjSdAZCLZ4CvDcW1\nnB7s3X3Iov0ahljlZqA9K8n31NbeQFpaVP+XA5lMis2bZ+Ly5a85jsyyCgpykJVl/Ak/bZoXenvH\nvtXNVCMU2qK3V2nSXlPTARcXV4v2LRaLoVA4oqGhvb+NZVns3XsbiYkpsLWVw95+Fr744gaqq5vw\n4EENtm+/jujo5U+9bmHhLQQH92LdulmIiwvBypWxWL3aFzk5X1nk73j8uAwzZpjOL4yK8kNVVSn0\n+tb+ROy7ZDKNReIhljXmkTGDwYD33nsP27dvh5ubG9auXYulS5ciODjY6LgVK1bgX//1X8fa3ZR3\n4uhFSAXG82HEQnvkX6/A+o2W69fb3xZ1pcZ7Vmp1agRNs+yDk0weLMvi2rVz4PFM58/IZFKwbDUH\nUY0fkUg/6Oi0RGLgIJqJbd68FOzb9ze8+mpif1tPjxJNTULEx1u+tlpKylrk5Z2CVlsIHs8AlUqC\npKSX+rdFio6eA70+Dvfu3YFUaoPly9c8881DY+MDLF1qXCPP3l4GgaB9iDPGJjQ0GgUF+Zg1y3iE\n8ebNCkyfnox793IHPc9goAUIk9GYk7HCwkL4+/vD29sbQF/SlZOTY5KMTeB1AuNKq9UiN+cCwLJI\nTkkyefWiVg3+YFcp9BaNa8ubL+C9f/sr1B0+EIvsoFA3w8O/B+s3/MSi/ZLJgWVZHDy4FatXB+LK\nFdOHPcthqZZsAAAgAElEQVSy0Gqn9oeAViuEXq8Hn883alep+EOcYb1EIhHi49di586vIZVqYDAw\n0GrtkZGxeVz6ZxgGCxc+faEAn89HTEzcU48xPn7wzzAezzKfbYGBwTh8+BxCQhSws7MB0FfWpbxc\nj5UrvdDUFIb792sQETEweqZUqqFUjj7Z7ehoR3V1JQIDQyCX2435byDDN+ZkrLGxEZ6eA6uh3N3d\nUVRUZHLc6dOncevWLQQEBOCf//mf4eHhMdauJ53rV2/h821nwWh8ATA4duCPePGVZCTOH1ju7e4p\nR/NjHXg84/81Lh6WnShqb++A3//pn3Eu9yJqHjcgIioOs+NnPftEYhVu376G9HRfeHg4gc/no729\nG46OAyuHzpy5j6iopf0/19fXgc/nw9196vw7nzs3Dbt27cTmzXP7R1Hy8yvg7BzBcWQTk7u7F9LT\nTbe4mqwMBlsolWpIpWKjdqXScvtOZma+hpMnjwJ4BLVajYqKOoSHB+PUqZ2IilqM0tJmlJQUIDLS\nFY8fd6C2lkV6+ksj7sdgMODkyZ3w8WERFuaOe/fuoKXFBsuWvUClPsbJmEtbnDp1CpcvX8Z7770H\nADh8+DCKioqMXkl2dnbCxsYGQqEQX3zxBU6ePInPPvtsbJFPMlqtFq9u+BX42mlG7Tp+Kbbtebd/\n4rNCocA7b/4G6o4A8PkisCwLHVOJn72bhVlx0VyETgiOHNmBVav6voGzLIujR69ArzdArzdArbZF\nZGQSYmJmo7z8IfLzTyA42BY6nQGVlUosWJAFX98Abv8AM2lpacL580cgEmmh0/EQFDQLsbHm2WSb\nTGxarRY7d76PFStC4e7uCKVSjYMH72Dx4o3w9rZs7bja2scoKPgKmZmx/cnR118XITQ0HT4+Aaio\neAQPD084ODiM6vrHjn2BRYtsjeagNTV14O5dPlJTx3ezdWs15pExDw8P1NfX9//c2NgINzc3o2Ps\n7QeWGT///PP4wx/+MKxrT6VaQKdP50DX6w3+975EsWo/7N51GCtWpve3/ft//gT79x1FQ10rZLYC\nrH5uPby8vKbUfw9zo9pRltXba4BWq4NQKADDMFi1aj4A4MSJO5g9+0XIZDI0NHTg6tVD2Lw5of+8\nuXOBbdv2YMWKtyfMN+yx3StSLF78glEL3XdT23fvlxUrfogbNy6it7cCPJ4ECxdugUgkGfE9UFX1\nCA8fnoNMpoVeDyiVcqSkvDDkiuFz545h8+aZRm1paVHYtes0li17Gc7OPtBqR38v9vY2wM4uxqjN\nzc0Bra1FdH+PAKd1xqKiolBdXY26ujq4urri+PHjeP/9942OaW5uhqtr30TwnJwchIQ8ffnwlMQC\ng38WMWANxoOTEokEm15aNy5hETIcCQmpOHx4N9auHSgHoNFo0djIQ3x837fpa9fOY+VK01d2SUmB\nuHfvDqKiZpr8jpDJhMfjYe7cpDFdo7e3F+Xlp4y+tKhUGuze/TkyMwd/rSuRDD5nWCo1z1zioea9\nMQzN9R4vY07G+Hw+3n33Xbz22mtgWRZr165FcHAw/ud//gdRUVFYsmQJdu7cidzcXAgEAtjb2+M3\nv/mNOWKfVJYkL8LR/X8EEGbUrhdUYVn6T7kJipBhksvt4O29CLt2XYG9vQFqtQHd3VIsW7ap/xil\nsgd2dqZzxBwdZSgs7BhRf99WFm9paURcXCIcHJzG/DcQMhFcv34W2dnGX0wkEhE8PPTo6emBra3p\nBHyNZvAqVGq1eUablUqpyeIUjUYLrda0dAaxDNoOaRxduXIDe7blgqf1BxgGen4VXnx5CeYvTHj2\nyeSp6DXl+NFoNBAIBCaFLjs62lBRcQhpacZzGw8cyEd8/MvDrp7f1NSAa9e+REpKMLy8nJCbW4zO\nTmcsWbLaLPHTvUJGwtz3S07Ol1i/3rTobX5+Ofj8BfD29jH53YMHdyEUFmPevND+ttu3q9DW5ofo\n6LHv99nb24tTpz5BZuZ0eHs7o7KyEadPV2LlyjcsVsh5KhrLa0pKxsaZRqPBmdN99WFSlyXTjW4m\n9AE7MeTlnYSzcwsWLuwbAT579h40mgDMmbNk2Nc4dmwrXnllptEcs9u3K9HbG47p08e+cpHuFTIS\n5r5f8vOvICKiC76+Lkbte/fmIynp9SGr+d+7dwtPntyFRGKAWs2Di0sEYmOfvaXYcLEsi/z8q2hv\nfwI3N19ER8dPmHmekwUlY1ZMoVDgq33H0NzYDTsHCda+sBwODo6jvh7Lsjh29BRK7tdBIORh0ZKZ\nmBU38ef60AeseZWXP0BlZT74fIBh7LFgQfqwtyOqr6/B/fvXAAAxMYvg5uY+7H5VKhUKC3dixQrT\ne2737jKkpr447GsNhe4VMhLmvl/6avb9DevWhcHJqe/D+/r1R2htdad9Tic52ijcSnV0dODff/FX\nMKpQ8PnOqGUN+Ndb/4uf/cuLCAjwH9U1f/vrD1Bf7gCxqO9b28dF17B0ZR2eW7fSnKGTCSw//yIc\nHOqxYUPf6FZvrxI7dvwN2dlvD2sPPi8vX3h5jW6pP8uy9G2cTGkMw2DNmjdx4cJZaDQl0OmAoKA4\nxMeHPftkMmVRMsYRpVKJvXsOo76mExIpH0vTEhATEzWia+zecRB8TRgYft8HJI/hQYIw7Nt9Cv/0\nizdHHFP+rQLUlIlhIx7I7m1Enjh/uhiZq5fRK1UrwLIsOjoeID19oDK5TCbF2rXhuHLlPBITky3a\nv1QqRVOT6S4Ut29Xws9vZP8+CJmoeDweFixYxnUYZAKhZIwDGo0G//bzP0HXEwo+r+8Vztbii8je\n2I6lqYuGfZ3GBgUYxvSVZGN976jiulPwEDZiN5N2dY89ysvLER4ePqrrksmjvb0N3t42Ju2urvZQ\nKsvHJYbZszPxySf7sWxZKDw9Hb+ZwO+EpKTIEV2nu7sTly4dhkymgcEA6PWOSE7OslDUhBAyepSM\nceDQwRPQdAVCKBj4zy8VeuPUsZtITlk47Nc0UqkAg6VdUpvR/W91crGDVtsNodB46yWeoBceHsOf\n90MmL1tbOYqLFSbtWq0OBsPw5ox9X09PD27cuACJRIaEhIUmezt+n7u7JzIzf4y7d28iL68Rs2ev\nHnFpC4PBgDNntuH11xP7X612dvbi4MGdeOWVH4/q7yCEEEt59gQQYnb1Ne0QCkyX+Xe26aFWq4d9\nnUVLZ0KlazRqU2nbEJ8YOsQZT7di5TKwkkqjNr1BB/9pIjg5OY/qmmRyEYlE6O6WoavLOCE7cKAA\nc+emjvh616/n4t69PcjKcsKCBQacPfs3VFSUPPM8hmEQGzsHKSmZo6oxduPGRaxZE2E0x83eXgYv\nLwM6OkZW84wQQiyNRsY4ILMVwsAawGOMc2GJDSAWi4c4y1Ri4hx0tXcj5/QddLZpIZPzsTA5FKvX\nZIwqLpFIhJ/98ybs+PQI6qp7IBAwCAl3xg9//Pqorkcmp7S0DTh2bD+Ewnbw+SyUSjGmTVsGudxu\nRNdpaWmGUFiFtLS+lZHOzkJs2pSAHTtyEBg4zaIT9bu7W+DuHmDSPm2aK6qrq+DpGWyxvgkhZKSo\ntAUH2tpa8e4/fgQpb2D1jEbbg5kLBHj1B+tHdU2dTgeBwHpzaypXMPGcOfMV1q/3NVmBWVRUBYUi\nFkFBltsW7fbta5g+vQ3+/sZzII8fv4OkpDegUJguEiBkMPRsIcM1ltIW9JqSA05OznjnH7Pg4FkH\nNcrASCswJ1mCV7a88OyTh2DNiRiZXMajfEVsbAJOnnwEtVrT31ZX14quLgfIZLTFCyFkYqGRMTIl\n0LfXiaetrRUVFQeRkRFr1L5jx01kZPzI4v1rNBpcuHAEAkEPDAYGNjY+mDdvKd0rZETofjEfrVaL\nCxeOgs/vhsHAQC73x5w5i7kOy2yo6CshZMJxcnLGo0chOHgwH8uWhaOrS4nTp0sRHp4+Lv2LRCKk\npq4dl74IIU/HsiyOHNmKl1+OhVTqBwCoqmrCuXOHsGTJGo6j4x4lY4QQi4mPT4JSmYBTpy7BxsYW\n6elvDauKPyFkarlz5zoyMgIhlQ4sUgsIcMPdu7ehVCohlUqfcvbUR8kYIcSipFIpFi2iauOEWLPW\n1lr4+weYtEdEuKG6ugrTp88Y/6AmEErGCJmEnjypRWHhJQiFLPh8B8yfv8yiizhYlsW9e3fQ1dWO\nWbPmWf23WELIyEiljmht7YKzs3GJnEePWhEc7MlRVBMHvS8gZJIpLr6DJ0/OYOPGELzwwjSkpdni\n0KG/QqfTWaS/+voaHD/+FwQF1SM5mY+Cgp24fj3XIn0RQqamuXOTcOBAEb67ZrC7W4knT/iwt3fg\nMLKJgVZTkinBmlY8nTnzETZsmGnU1t2twOnTvVi0aHQFf5/mxIm/4eWXZxu15eTcg7t7GtzdJ983\nWmu6V8jY0f1iPu3trbh69ShkMg30egZ6vQOWLn1uyswjpdWUhFgJg8EAmUxv0i6X20CnqzV7f01N\nTQgJMa3LlZwcgT178pCaus7sfRJCph6dTof7929DJHJETMzCUW1zNpVRMjYFsCyL4uJiKHqVmBU3\n85kbMZPJi2EYaDSm7SzLorKyEGfPquHlFYPw8Flm6Y9lDUPeTyxLVewJIc9WUVGCsrKzyMyMgK2t\nB86ePYTeXg8sXLic69AmDErGJjiNRgM+nz/kB2LFo0r87X/2o7tVDgZCfC7PxboXF2HBornjHCkZ\nD33JmCM6Onrg4GDb356bexubNy+Gt7crrlwpwcOHAoSFRY+5P3d3D9y+3Y2537ud8vJKEB6+cMzX\nJ4RMfaWl57B5c0L/z2lp0bhw4QHq62vg5eXLYWQTByVjE1RpSTl2fXYCT2qU4AuAwFA7vP13L5ls\n5fK/H+yHQREK2beL23TO2L39AmJnRcLW1tb0wmTSS0lZh2PH9kEkagegBI/HIjTUB97ergCAxMRQ\n7N592yzJGACEhS3Fjh2nsGJFOBwcZDhz5h4UCg+Ehfmb5fqEkKmrrq4WM2bYm7QvWhSGPXuuUTL2\njakxa26KUavV+PP7X6K32Q92kumQCaajocIdf/zdx0bHlZaUoqPJdD6PmAnGsSOnxytcMs54PB7S\n0tYjKemHYFk51q5djJiYYKNjRCLzvUIMCAjBsmU/Ql4esG9fA4KDs7Bw4QqzXZ8QMnXx+XxotabP\no761g5bdo3YyoWRsAjp65BR4miCjNh7DQ12lAc3Nzf1tKrUKzCCDmzyGB41Ga/E4CbcYhoFWKxz0\ndyrV0+cNPnhQiHPnTqCjo21YffH5fCQmJiMlZTVNvCWEDJuHhydKSkxXo545cw+xsYs4iGhiomRs\nAurq6IVQIDZpZ3U2RslYZGQkpPYdJsf1aCqQvjzZojGSiWH69AU4ebLQqO3YsbuYMWPw+VwdHW04\ndOgDeHhUYvVqB1RVHcGZM/uhUqnGI1xCiBWKjV2Obduu49GjJ2hr68KBA/nQ64Pg6urGdWgTBs0Z\nm4DiE6Jx8+IlyCTGNZwkdp2YNm1a/888Hg/rX0rGjo/OQsQGgeEJoNBWYFlmGNzcXMc7bMKBgIAQ\n8Hh8fP55HsRiA1QqHiIjU+DjM/h8rsuXD+AHP0gAw/S9HkhNjcT9+1U4evR3kMs9ERq6EMHB1r0t\nCSHEvLy9/eDl9RaKi++iuLgLc+a8ArHYdMDBmlEyNgFFRUdiWvQVlN9rh1TkCABQaGqw/LlYky1v\nEubORnRMBE4cPwOVUo20jFfh4uLMRdiEI35+gfDzC3zmcSzLQi7X9idi34qICEBZWS3WrJmFvXvP\nwd3dlxZ/EELMimEYRETEch3GhEXJ2AT19z97HRcu5OFufjkEQgapaemYNj100GOlUimeW7tqnCMk\nkxHzjPmyWVkzceDAWSxdumZ8AiKEEELJ2ETFMAySkhYiKYlqORHzYBgGXV1CsCxrNDr26FEdvL1d\nAAAikRAsO0hVWUIIIRZDE/gJsSJz567Bxx9fRXV1MwwGAy5evIt796oQHx8GACgrq4e7ewjHURJC\niHWhZIwQK+Ls7ILVq99BSYkz/uu/LqG1VY1VqxIBALW1LTh/vglRUebZSokQQsjwMGxf5bUJqbnZ\ntDYJIYNxdZXT/TIKNTVVePDgGvh8A+zt/RAXN99kgv9UQ/cKGQm6X8hwubrKR30uzRkjxIr5+gbA\n1zeA6zAIIcSq0WtKQgghhBAOUTJGCCGEEMIhSsYIIYQQQjhEc8YIIYQQMqnV19egqOgiRCIWGo0A\niYkZkMvtuQ5r2CgZI2QKU6vVyM39ElKpAgwD9PaKMH/+atjbO3IdGiGEmMWjRw/Q3n4VGzdGgWEY\n6HR6fP75DixYsGnSPOvoNSUhU9ipU9vx4oshWLduFtaunYWXXopAbu5OTOCKNoQQMiLl5VeRkRHd\nX5ZHIODjpZcScPXqKY4jGz5KxgiZourqqhEVZQehcGAAnGEYLF8+DQUFVzmMjBBCzEcq1Zm08Xg8\nSKVaDqIZHUrGCJmiamsfIzTU3aTdx8cFbW0NHERECCHmp9EMXqharZ48BaxpzhghU9SMGVG4efMg\n0tKijNpv365EUFA0R1ERQoipgoI8tLYWQyploVLxYGcXgjlzlgzrXBsbf1RWNiIwcODLZ15eKYKD\n4y0VrtlRMkbIFGVn54DWVls8ftwEf383AEBraxcKCrqwatV0jqMjhFiLnp4uXLjwFeRyDQAW3d1i\nLFyYBTs7BwBAYeEtuLs3Ii1tYF/c4uJa5OfnIS5uwTOvn5i4DJcvn8b167chFhugUgng4RGD6dPD\nLPUnmR0lY4RMYXFxyfjssz/B2ZkBj8egqUmDFSte5zosQogVOXt2J7ZsiQeP1zczimVZfPTRTqxZ\n82MwDIPGxntYujTS6JzwcB8UFhYBeHYyBgDz5y8zd9jjipIxQqawvLy9ePfdVUabf3/22XH4+LwF\nPp/PYWSEEGtQUnIf8+d79SdiQN9CotTUIBQVFSA6Og5C4eCru0Ui61n1TRP4CZmiHj0qRUKCu1Ei\nBgCZmZG4du08N0ERQqzKkyfVCA42XUgUEOCGxsYaAIBSOfgXw95e6/nCSMkYIVNUW1szPDwcTNod\nHW3R29vBQUSEEGsTFRWPvLxSk/a8vBJERycAAOLilmH37uswGAwA+l5j7t9/C5GRSeMZKqcoGSNk\nEnta8daoqDh8/fUdk/ZLl4qgUmksGRYhhAAAnJ1d0Nhog6qqxv62mpoWVFXx4O7uCQBwc/NAfPyL\n2L27Al9++RC7dj1CRMRz8PHx5yrscUdzxgiZhK5dy0FPTzlsbPqWgUskAUhMNJ7AKpFIUFfXgatX\n72PevAgAwL17lejo6IatLf3TJ4SMj9TU53HrVh6uXn0IgIVc7of09A1Gxzg4OCEtbT03AU4A9EQm\nZJIpKLiM4OBuhIfH9beVlNTj1q1LmD17odGxgYG+8PBwwqFDeWAYBsHBXli1aj6++KJ4vMMmhFix\n2bMXYLgrI60RJWOETDJtbWVISzNeBj59uhdu3y4CYJyMKRRS+Pq6ITDQs7+tqakDIpHphFpCCCHc\noGSMkAlCq9Xi6tWz0Os7odMJMXduKuRyO5PjhloGLhCYti9ZshaffvopEhM9MWOGNy5fLkVFBYvl\nyzebPX5CCCGjQ8mYmVRWVCL37BWIxEKszkqDnZ091yGRSUCj0UAgEECtVuPEia3YuHEm5HJXaLU6\nfPXV55g2LQO+voFG5ygUfLAsa1KyQqUSmlxfKpUiK+ttlJYWY9++R4iMXIoVK7ws+jcRQggZGYZ9\n2nIsjjU3d3MdwrB89uleXD3XCJnYFyxrgMpQjk1bkpC4IIHr0KyGq6t80twvAPDwYSGqq6/BwQFQ\nqQwoLq7Dz36WDqlUbHTc558XIS3tVaO25uZG3Lq1Dxs2zIFAwIdOp8fevTcRE/Nc/+okMrTJdq8Q\nbtH9QobL1VU+6nNpZGyMqqqqcO18I2wlfgAAhuHDhjcdX+65gHnz55iMXhDS2tqC9vZr2LhxYB+2\n5cujcOzYVaxbl2R0rFSqNTnf1dUdCxe+gn37ToHP10KvF2Lu3E39+7wRQgiZXCgZG6PcM1dgI/I1\naVe026GkpARhYRNjo9KGhgZ8ffI8xBIRMlelQSaTcR2S1crPz8GLL8YatUmlYkilYmi1OgiFA/8s\ndbrBSwHa2sqRmrrOonESQggZH5SMjZHURgwDqwefMf5PyTJqyOW2HEVlbO/uQzj3dQVkwkAYDDpc\nOvNnvPRGChLmzuY6NKvE57NG+7R9SyIRQaFQwd6+775pbu4Cw7iNd3iEEELGGSVjY5S5Og2Xcj6A\nDQZGwFiWhZuPHt7ePhxG1qe+vh7nTlXCVhwEAODzhZAiDF/syMWchDh6jcoBGxs3NDa2w93d0ai9\noqITTU0P4OYmQXu7GlqtC1JSnuMoSkIIIeOFkrExsrW1xctvpGDv57noabUBeDq4+Rjwzk83ch0a\nAOD0qQuQiQJM2hUddnjw4AHCw8PHPygrl5CQhAMHPsS6dWFwcbEHy7I4e/Y+goOTEBUVj97eHkil\nNuDzrWeTXEIIsWaUjJlBwtzZmJMQh8rKR5DJbOHu7sF1SP3EYhFYVg/me69RwWghlUq5CcrK8Xg8\nZGf/CHl556BWl0GrBaKjU+Dp2TeSams7+hU5hBBCJh9KxsyEYRgEBYVwHYaJzNXLcCnnr7DBdKN2\nJw81AgMDhziLWBqPx8P8+UvHfB2NRoNr13KhVisQG7sArq40x4yMXdHNfFzfcRC6pk6IA92R/vbL\n8PQ1XahECDEPSsamOFtbOTa9loR9uy5A1eUIltHA0U2JH/3dC1yHRsaovLwYlZXnsGpVNGxsnHDu\n3Ancv++MpKRMrkObkrRaLb7609/Qeu0+GIYH1wXRyH7n9XF7ndzc3AyJRDzorgzmlH/hEm68/T58\nm78pQXm+Bnuu3MPGL96HuxcVDCbEEqjoq5UwGAwoKiqCra0tgoODuQ7H7KyxMOOpUx9i8+Z4o7bL\nlx9CqZyOJ0/uw8ZGC52OAcO4Iilp1bAWaxgMBtTX18HBwRG2thNjNbC5jfZe+fMbP4PPoVIImb6V\nsGpWj5YNMXjzT782d4hG7t24hdzfbgXvbh30Uj6EidOw8b/+BfYOjs8+eRT+uvnv4Hf6sVEby7Jo\nf3MeXnrv5xbpcyKzxmcLGR0q+kqeicfjISYmhuswiJnU1tYgPNz0wzgxcTp+9au9+OUv1/e3tbR0\n4uuv92HZsqePht68eR7d3SUIDXXAw4fdaGjgIy1tE4RC022WrM2Du3chPf0Qwu/MvRQzfOhP3EXN\n31fBNyDAIv329vbi1E//C2HlGgBCoAdgD5Vhp/ZX+PG2/7ZIn5rHzSZtDMNAXWvaTggxD0rGCJmE\nhEIRurp0Ju0syyIy0nhLJBcXe9jYPIJGo4FIJBr0emVlD+Ds/ATLl8f1t6lUGuzbtxcZGZvMG/wk\n9ODmbXgoTR+XHh3Ag/zbFkvGzuz+EsFlKoAZqEvHMAzYS6VobGyEu7u72fsUejkCJQqTdpGHZUbi\nCCHA4OW9ybjp7OxAQ8MTTOC3xYRDBoMB584dRW7uduTmbseFCyfAsizc3d1RWtpjcvzRozeweHGs\nSbunpy06OjqG7KeysgAJCaFGbRKJCFIpvZ4BgBlz4tBgY5r8NjgyCJ89a5AzzEPd2dP/WvS7JD06\ndHUO/f9zLGI2ZqLBzvh5VOEnxOLX1g9xBiFkrGhkjCNdXZ340x8+Q12lBqxeCHsXLdZuSKKq+MTI\n8ePbkZ0dBAeHvtGulpZOHDu2EytWvIS4uExs23YICQmecHSUIS+vEnV1DBYsMJ0bVl3dhUWLnIfs\nh88f/MsAn9832mbtxYFnREchNz0cmq8eQMT0TdhXQg/Bylnw8fe3WL8zM5Jx/sOv4dVjvEigN9Id\nwSGhQ5w1Ngsy08ET8FG4+zh0zX2rKdN+tBEBoRNvtTghUwUlYxz50+8/Q+cTH8glfd96WSXw2dYc\nhM0Igb09bfhMgMePKxAVJYODw8BEehcXewQHP0Fj4xN4eHhj5cq3UVb2EDU1HZg/fwt4PB727fsA\nP/hBQv8elw8e1EEsDnzqqj+RyBWtrV1wdjZeqadQiKw+EfvWm3/+TxyYthWNV+8DPAZuC2Lwg7e2\nWLTPaRHhOL06GnV7b8FbJ4WBZVHpyUP8TzcOuqWWuSRmpCIxI9Vi1yeEGKPVlBxob2/Dz3+yHXJJ\nkFG7waBH7AItXnqVXgeM1FRc8XT69EFs2OBjkgyp1RocOdKJpKSMQc9TKpXIyzsGgUABnY6Bq+s0\nxMbOfWpfBoMBhw79LzIyAuDn5wq1WoMDB24jJCQdAQFTa/UtF/eKWq1GQ8MTuLm5j6jY8uld+1D+\nq8/Ba1egCUr0CAwIfm0F3vz1v1owWvJdU/HZQiyDVlNOMr29vTDoTVeo8Xh8KFWmE2eJdfL3D0VJ\nSTnCwoz3OL1/vxYBAUO/zpZKpUhNXTeivng8HrKyfojbt6/h8uUK8HhiJCa+Chsbm1HFTgYc/PNH\nePzFWUirOqD0ksNtzXy8+Iu/f+aIo1qtRvEHXyGkgwcwtvCBLaAHqr+8jtrXH1v09SghZHzRBH4O\neHv7wM5ZbdLeq27AvPmmk6+JdZo+PRIXL9ZBqx2YOK5Wa5Cf34aAgKAhz2NZFgUFV3HmzAE8elQy\n7P4YhsGsWfOQkvI8kpNXUyJmBrkHjqDn90cQUq6Gt06KkGod+B/k4OhHO5557u2r1+D6yHRExred\nh2vHTlsiXEIIR2hkzMIuXriMG1eKYWCBqJgApC9PAcMweO6Fhfj8k4uQ8IPBY3hQqBsRMUuE6Ogo\nrkMmE0hGxhbs2bMfNjYqAIBCYYPly18b8viurg6cPbsDK1ZMg4+PH/Lzb+PDDz9GeHgo1Goxpk1b\nMOVeO05k5ccuwkttPFdPZhCg+sx14I2Xn3qum5cn7koBe5Vxu5LRw9HdxdyhEkI4RMmYBW3/ZC9u\nXloujOAAACAASURBVOyBVOQKADhR8gQPH3yMn/7sdSQuSEBYeAiOHDwDtUqLufPnISY2muOIyUQj\nkUhGVOfr8uXDeP31uf2Tu+PiQhAU5I6bNx9i2bIIHDhwFjKZnPawHCcGpekIOAAYFIO3f1fQtGlQ\nLQgCe6bG6JXm42gHZK/hZssrg8GAc4eOoeVRNXxjZ2BeSjIt8CDEDCgZs5Curk7cuFQDG9HAcnCx\nyA6lhbV49KgCwcFBcHJyxitbaLI+eTqWZXH+/BGwbCsYBtBobJCUlAWxWGxyrI2N2mSVnaOjHEql\nBgCwZs1M7NqVg/T0F8cldmsnjw6CPucx+N+pFcayLGRRgcM6/6U//wp7fv4bqK+XAVo9hDMDsPbf\n3oFAMP6P7o72Nnz06s/ge60JtqwAFYJTuJ5yCG9/9MchiwkTQoaHkjELuXXzNvisp0m7TOyDa5dv\nITh46Dk/33f3biHuFT5EZPQMxMTQa0xrc+LEDqxe7Q9HR28AgEajxbZtHyE7+8cmxw61NvrbRdM8\nHg8ikd5isZIBLU1NqLleiCamHrNZV9gxYvSyOjxOcMHr//TWsK7h6OSEt7b+HkqlEnq93iz7hT56\n8ADnPtwFzeMmCNzsMXvzGsxaNP+Z5x343V8QdqUVzDdbQjnoBJCdfIyDH3yMF/6/4f09hHDp7t0b\naG4uAwA4OQVh1qx5HEc0gJIxCwkM8ofWcA9iyIzaVZpO+PgNLxHTarX4j3//M5pqZLARu+PKmStw\n9TuDf/nlO7RfoJVobW2Bry8LR8eBD2GRSIjU1AAUFRUgKsq4+rtSaQONRguRaOD+qK1t7q8fptXq\noNOZjqgR8/vy3T8g4kobwuGNMnSggu2GSshi1T/8ExydnAAANVVVeFhwBxFzZsPLx2fIa42kHMZQ\nWJbFge07UfLbXYju+PZ6TbiZ93voPtBiztKkp57fc7cCbt97JSlkeGjKLx1zbIRYWk7OAcyaJUBK\nynTg/7F3n4FRVfnDx793+mTSeyckIfSEXqQJCEhHBBVdFbHXv67rtkd32aK7rmtbu2sBRUQs9N57\nMaGEloQS0nufTDL1Pi/iJg4TJJCEJOR8XpGTW85MLvf+7im/A5w/n8+WLcuZMOGONq5ZHTGbspV0\n7dqV4EgrDkdDK4Qsy+i8chk9ZmSTjrH4s+VU5EXgpq1bf06vDaIiN5wvPl/eKnUW2p/09DTi410f\n0tHRweTnp7uUjx9/B198kczBg2mUllaybt1BkpLSGDUqHofDwZIlh7nppsbzkwktx+FwUJ14FkmS\nUEgS3SUf+kn+DLMFkLJhN3a7nQ+ffZE1E56m8rFPWTn+Cf77wkIcDker1KekqIjXZz9E0u/f+1kg\nViesFJIWrbjiMRTaxl8AFTrxYii0b6WlJfj6VhAXF1pfFhMTTGiomaKiwjasWQMRjLWi3/6/Rwnv\nXoJFSqNWTiUgKo8//PmRJg94vXiuBKXS+UanVGpIP1fSGtUV2qGuXeNITs52KT9/Po+goCiXco1G\nw8yZj6LTjWT/fjXQj+pqH7799hRffXWOUaPubZGuLuGXORwObDbXtSwBkCS+e/sjApYeJ7JSiVZS\nElmuwPuLJFZ/vOiKx7bZbOTl5WI2X3kSwP98//e36b6vGL3ceGeINefK95TgcQMw4dzFXa51ED2l\naS+XgtBWjh8/xJgx3V3KR4/uzrFj+9ugRq5EN2UrcnNz49e/feTaD3CZoE3MXuo8/Pz8OXBAoqzM\nWN9VabFY2bo1g9mzLz+jLiwskrCwyJ9+Eg/L62n/+s0cemsJRfn5yHKo0//XQr2NftPHcfCNL4iU\nnFNe6FGSvesYPHb5Y6/7dAlpX6xHe7EUc4gHQTNuYt4frpxAtvrIOSRJwn6ZQYXq8Cunypj91CN8\nWVxO3upDuOdWUxXlRfhdYxl/+8wr7isIbSk4OJyLF9Pp3j3MqTwrq5jAwLDL7HV9iWCsHeveO4ik\nnTWoVA3dClZbDQm9gtuwVsL1NnXqfWzZshpZvlA/m3Lq1IfbulqdWklREevfX4Q5owBVgDdjFtyB\nzWZj/X8+pXr9EeItXoTIgewnn26yF77oyAxWEPrAVAaMGM7B1xc3fuBfWJ1u34bNFP19Od1MCkAH\n6Vaq39nGKh8vZj1++dxzAKjqAr9oPEmWS4iXGhaNz/GTGDR/9hU/s0Kh4P6//p6qFyrJycoiMqqr\nSAwstHt5edmkpx/i8OFzxMXNqX9xkWWZLVvOM2NG+xi2IYKxduyee+eQn/cx508XoFUEYXEUEtNL\nyz33NqO1TehwJEli7NjWa32QZZldu9bhcBQjSRKy7M3NN09v1YWoO7KigkK+mPcscSer62/sX67b\ngwdaqgpL6I8/SOAuqRlBCJlyFTs8S3hh/TLCwyMA8B7SE+veXNQ/S3lhke34Det92fOeWbmdYJPz\n38TgUJH07UYKjpzBkl6IMtCT+LunMnLarU7b+Yzoje3UQXwlHQ5ZJlEuRFaAbmgck194lH4jmz6r\nzMPDkx69Ll9PQWgvHA4HSUkreOCB4ZSXd2P58p1oNCqMRgsOhz+jR9/dbnqaRDDWjikUCl74/WPk\n5ORw8sQZ+saPITQ09Mo7CjckWZY5cGAHNTW5OBwQHNzLZTbltVi37gtmzeqCj09di2tlpYnlyz9j\n5syHmn3sG9HG9z93CsQAHIVVdJP0HMV1GEGk5IENLXp9QyvSnF8/zofnMjBsTSOoRkW+mw3zrb14\n9KnLf+d2U61LWaFcgya1nLBTlp9KKkg5/AHIMHJ6Q0B214u/5tPil5C2ncG7QolPRAjh907k9mcf\nvbYvQRA6gMOHdzN9ei8AvL3dufPOsciyzPHjFzGb++Pj43eFI1w/IhjrAMLCwggLax/92kLbWbt2\nEVOmhBEc3AOAU6cy2L07l9Gjp13zMfPzc4mNVTqlzvD0dKN/fw8uXrzwi2tgdlY1F/LxuSTgUlL3\nsx868mUTwdIl3XfxEfj5Ndz4NRoNz3zyBqeOHCXtyHFGDhlEj/g+v3her4QYbJsuoPpZa1omVQyy\nOa+mEFwlkbx0nVMwptPpePLD18jOzCTr3HlmDBmEu7vHVX1uu93O9h9WUZyWgX9cFONmz0CpVF55\nR0FoI1VVpfj5RTiVSZJERIQvBw7kER0de5k9rz/RDyEIHcC5cykMHOhBcLBvfVnv3hEolbnU1NRc\n83FTUo4zeLBrwDVgQDRnzyZf83FvFMXFxaSmnHGaGakO9HLZzkHdWK9IyYMsjOTIRgBssoOUaDVj\nf+fa4mWz2TixfS+5Gw6ybeE7fP2vd7BarZety8wnH+Lc2BCM1NXFLNsxeTWeVsKaX9poeXhkJMPH\njb3qQKyqqpI35jxC6VOf4fGfXZQ89Smvz32EqqrKqzqOIFxPvXsPZv/+VJfyffvS6dt3YBvU6PKU\nCxcuXNjWlbgck8ly5Y0EATAYtDf09XLkyC5uuSXKpdzDQ0VKSjXBwdfWfS1JSgoLzxAa6utUfuZM\nNhpNN/z9b7w1LJtyrZhMJv779P8j+aVPyPtwHXs3bKJaJxHdpyduIf4cWLEOf0tDIFSACRM2fCUd\nYZIBI1aOGCrRPDCaBR//k4ho1+WPPnjqD3j/9yB+WSa8s6pR7D/Hzoxkhkyb0Gid1Go1Q2dPoaCr\nG2VdPHC7fSiGUH/cknJcukZrBkcyaNaka/h2GvfNK28R/kMq2p9mgGpQ4Jdp4pitkISbG8/eX1pc\nzFcvvsqeVz/l8DdruJCdQa/hg1tkLKLVauXrV95k58sfceCz7zmZfJzoIQnoWiA57qVu9HvLjczD\nw4vExNPo9bX4+dW9gBw5coHSUl9iY1t+3KPBcO0JtUU3pSB0AG5uPpSUVNZn0v+fjIxSgoMTrvm4\nXbpEs3LlFvr0saDT1a0vaLFY2bcvj1mzbmtWnTuyr178J2E/pKCUlICeoDMm0hYupkt8T7rH92F5\n9wASEy+gRMKOjCcaVCjY7VlGRNeuaCO7ce+Dc4kfPqTR459PSUW16TSan6W3UEtK1JtPc+7MGWJ7\n9mx0P6VSyYS5s2Fu3c8Fubl8teck3VJM9QFZZoiSEQ+3bFbxquQL+F4S8CkkCWPyhUa3t9vtfLLg\nBXoeLK2vlzlxK58Xl/HQawubXZ9Pn/8zQctO4P3T9yefOsZ/L77Ab77/pN0MyBbah0mT7iI5+UcS\nE88iy9ClSwKjRvVq62q5EMGYIHQAQ4eOYdWq91iw4Kb6MpvNzunTRmbObN6kjqlTF/D99z+gVlcB\nYDa7MXnyg806Zkdmt9vJX3+QkEvGfUWUSRxYtprYv/YkOCyUkCSjy74VIWqe3rzoiuc4/eMRQqoU\ncEncEFyl5NSPRy4bjF0qKDSUu7/+N5veX4z5Yt1ak+MemEOP+JZdw1ahb/yNX6FvfIHwnavXEXm4\nqH4dSwCtpMS04QhlfyzFx8e30f2u5EJKKiv+8Q5sPoVaauguliSJsAP57N24hVGTJ17TsYUbV3z8\nYGBwW1fjF4lgTBA6AKVSyZAhc/nii/UYDFYcDqiu1jNx4n3NPrZarWbixDtboJYdk8Ph4Ns33iN/\naxKyyUyezoJHqQkuHYQPOGrrxnTFTB5FxtpkAhy6+t+ZZCvFOcXkZmf/4jqTAH1vGspGr6WEVzoP\ngM/zcjBxWOOtaZcTHBbG/S//8ar2uVpRt95E2a50PG0N9a1U2wkcO4Dv/vMhlopqokcMZOjYMUiS\nRMmFLNwbyfbvWWgmJyPzmoKxsrJSVj70J9RpRfihcwlkPR1qCs5dvOrjCkJ7IIKxduT06TNsWLMX\nk9GGb4COu+6Z4TQDS+jcgoJCOnWLVWv54k//xPDfA8RQF2hUyIU0Noy+RDITPa4uUBo1/VbW/P41\n/MqNBKGnhFpqsXNzlT87F3/L3f/vuV88Z1RMNExNoHbpMXQ/tR7Vyjbkqf3oGtetRT9fS5h83118\nU1jMue92o8+qoCbCC2l4LLZP1hJ7wYJOUpD20XaO3r6Fx976O9GDEzil2YCfxfkRUx7lSXRc3DXV\nYdMnXxGbVosZN85TgRfOrXX5eivDR7Tv1g9BuBwRjLUThw4m8uXH+9ApuwBQnifz19Mf8+dXHsXX\n99qa9IXOKTc3iwsXUgkKCufChWOo1TasVhVDh07E21tcSz/37TsfkbVoE/3xqS9TIBGBO4flAhLw\nRyspyZGrSYtUct+kusH1FouFSKUnUUiUYCYWr/qgyl7dtNmtD7/+F1Z2+4ysvSeQkPEfEc/DV8qk\n34bu/M1T1D71EAUF+QQFBfPJ/c8Tk26Dn1Jt+FrVKL89zp6Jmxg99Vb2T+6O+8q0+kH/JVobEb+a\nfE1Z+2VZJvvYGXpIEnpU2GSZErkWP6muZbIGO5bp8fQe0L/lPrAgXEciGGsn1q/aXx+IQd0YCJWt\nO8uXruGxp+5vw5oJHYXdbmfdukX07q1n0qRIDh7ci0JRwty5dYkOly9fRt++swgKEomDoW6dx7xX\nvyXAonbq8rIhEyjp8ZG1pFCGTXbgh47Bd8yoHxxuMBhQ9g5HvSefYBqCi3KllS4jmzZlXqlUcvuT\nD8OTLfqxWpVOp6NLlyhqamqwnswEnLtZvewqLu5JYvTUW3ni/VdZM/BL8g6dQqFV023qaEZPu/ql\nZ+x2O+8/+XvKth/DLPuhlZT0k/w5K5eTIVdh9NUw6rcLeGz+PS30KQXh+hPBWDtRWmzm0iGykqSg\ntNg167YgNGb79h+46644DIa66f3jxvWjosLIxo2HmTJlGPPmDWHJkm1MmnRvG9e0fTi/aieRFjdO\nUEI4DUlvI3EnSS6kPwH0lfywynbODQ/g/iecW63GPP8A2zJfI/aiFYUkUaa2UTU7oVMMIFer1cgG\nDRTbncplWUb50/R+lUrFbY8+AM1M8r/xq+UErUghXPbnEAUMl4NQSgq6Sd7keUPcPx5izG3XnvhY\nENoDEYy1EwYPFbYq13I3D/EnEppGparEYHDOZ+Xl5Y7V2vDA1OkaRkM5HA4SE/djNFYwZMjoq04E\n2tE5So2oJAUaWUmeXE2IZADAGy0ne2gw3noz1uJKPOMieHr+3eh0Oqf9E4YPJXLTx2xZtAxrRTXd\nRg5i6PibO0VqBZVKhefovti+OOK0IsDFIIlZ985p0XMVHDpJIEqQYLAcyHFKkGQoc5e4b9Hr9Bs+\ntEXPJwhtQTzp24mRY3qx8YcsdBr/+rJaRzozb5vVhrUSbjQ2W92DMzMznRMn1nHrrXH4+vqyZcs3\n2GwR3HRTyyUKbW/2rF7Psc9XYcspRhnkTeVP+UF7S76ky5UkyUWATB4mhmSGE9arG2Nm/XKLi4+P\nL3c890TrV74duvflP/CF/WWqdySjKTdj6RnMkKfnEREV1aLnkX6WPkMrKRlAAADnuhhEICa0moKC\nfJKT96HR6Bk2bDxa7bUndG0KEYy1E9NmTkKh2sq+naeorrLiF6jnvjkT6dpI5m5BaIzZbMBisaLR\nNGSGN/1scenTp7Px8ambqXfy5Cbmzx9W/7upU/uxa9cZcnOzCA2tW8vt2LEDFBWdRqt1UFOjJCpq\nMN27t2z+quslceceUn7zMV0rfirIKOGM1shJfw29i9R0lTyJkB0cooBbCEdXo+L0t1uuGIx1Zlqt\nloff/CvV1dVUVVUSFBTcpFbBwoJ8tn7yNfaKavziY5l41xxUKudHUUlJCbt/WIPB25O+M2/h2Moj\nBFc1HNsq2/G7uV+LfyZBANi5cxUBARXMm9eTmhozq1d/SmTkGLp1a/ms/f8jybIst9rRm6moqJF+\nO0FoRECAR6e/XiwWC2vXfsKoUSH06hXBkSPnWbv2R3r1isJm0+LuHsPQoeMoKCigomIzI0Y4JxaV\nZZmvv05nwoQ7OHbsIAEBOfTr1zCpZMeOM7i5DSE6uvv1/mjN9t/Hfk/IihSX8tMj/Ci8mI13djUy\nMr3wrZ/9d3GgL0+t/+x6V7VdkmWZysoK3NwMqNWNr4fZFCcPJ7L1yX8Qk2FDkiRMso2sCV14ZtFb\n9cdd9+kSzr39HV3zZczYyejtid+4fpRtOYr72RJqAtwwTOrH/H+86BLEtQZxb+lcMjPTsVgOMHy4\ncwqWJUsSmTjx0V984QgIuPahHqJlTBBuEBqNhtmznyAl5QRLl54nKiqexx93Teb6SzcTk8nE1q0r\nSU09xO9+59wqNHZsT7766nCHDMbspY0/TPU1Mt3HDyd48VGX70UX98uJWzuyzPSL7PhsGfaSKtzj\nwpn2yP2XTTmxZ/V6jnz0LVJaITY/NwImD+Gel56/pjUmd7+9mNhMO/z0XbtJKqK2ZLJxyTdMf+BX\n5GRmkv7v5cSUKuCnNBY9Tps475nGU1sXk52dhb+/P56erou1C0JLSE39kXnzXHP99erlQ05ONuHh\nEa1yXhGMCcINpkePvvTo0dCdWFNTg9FoxN/fH0mSCAwMJDGxmhGXrO+8bVsyen05d9zRE4tlGhs2\nHCImJoyEhJj6bbRax/X6GC1K3y0MeWe2S8BV662hfEcSGRQxWA5EKSlwyDLnuuuZ8/T8tqlsKztx\n8Ed2PPlPumbVtU7Z5BO8u+0QTy57D4PB4LTtmePJnPrdx8SUAqhxVFhIfm8VC/f+SI+bhzF2/p2E\nhIU1+dym01kuZVpJSfGxNAD2freWLiWSS3Z97ZFscnNziI6OcdlfEFqWElmWXe4VNTUWvL1bb9zY\n1b/aCILQIVitVtauXURy8leUl29i+/aPOXp0PwB9+05i0aKD5OaWYDZbWLUqiTNnMrnnnjEolUr0\nei2zZ48mNTULh6MhAKusvLpg7MSJI2zZ8j3JyUkt+tmu1pRnHiKlrzuOn0ZlOGSZtG5ajIWl9M9S\nkoA/xynhqFzEXmUBg158kMiY6Datc2vZ+/5XRGfb6x82KklB3KFS1n602GXbQ0tXE15a92+HLLOP\nPLrhxZBkCx5v72L5jKc5tudAk8+t9DY0Xu5Z1yqnVClobNyMQ1HX8isIrW3AgDFs2nTCpfzs2WoC\nAwNb7bzKhQsXLmy1ozeTyWRp6yq0SxfTL/LuW1+xbMkOtm48SPrFs/Qf0Oeaug1uFAaDVlwvl9i0\naSl33dWNXr3CiIjwp0+fULKz0zCZPIiMjKZbt8EcO1ZEcnI5FRUyjzwyzOVtUK/XkJ1dRGCgDytW\n7MVqNVFUZCQiIga73c7Fi+koFAqXtA9ms5nVqz+kf3+JMWMigHzWrdtMdHTCdRnncymDu4E+s8Zz\nRluFOcabmtExGAbGYv8+ET90qCUFIZKBEMlAF9mdojAdfcfcdOUDd0B7Xv0Uv3LnoFohSZQHqOk/\n/Ran8qMrN2E4XQTAacroiQ8GqW5slyRJ+FbKJBekM2Tu1Cad+2JBNvYD51H/rB0gI0jilleexdvP\nl6CYKHatWIPvz9ZgL5JrSAl2UF1QQomxgq494q5r+hBxb+lc3NzcyM+v4ciRo3h6qsnIKGLdujQG\nD551xfQ/BsO1t5x13qd3B1VbW8vr/1hKeW4YboruKG2xpCbpeOdNMdBYaCDLMm5uRnQ659aEMWN6\nkpp6EKh7mA4cOJyxY6fg5mbAZrO7HKe6upZ9+07yww97GDasJ/ffPwY/vyLWrv2a3bv/i8FwhPT0\nFaxe/Qlms7l+v507V/DAAwOJja3L9h8dHcyCBYPYuXNFK37qX+bl5c3YX82hpraG3O93cfIfX2KV\nXT+zQ5ZR6lt3GntbUvk1/kBR+nm6lPn2j8P803dkwV4fiP2c+XQWVmtjq3m6uvOFp7E9M460OB2p\n/nbSbwpi8BvPENUtFgA/f3/6L3yItG5aqmQLRxTFFKutjMsx4PfFEQqe+Jj3n/kD7XjemXADGDBg\nBKNGPUxqahA1NQlMn/4EQUEhrXpOMWasg1m1YgNKW6zTKiQqlZazpyoxGo24u7tffmeh03A4HGg0\njb9rNdYwNXToeNauXcLs2YOcynfvPskTT8xwaokYMSKO48fX8MADMwDo0wcsFitLly5j6tS6pbvU\napNTio26MhVarak5H6tZZFlmyZMvEbevmCIqGUIARynCIcsofvb5TvuYefC+O9qsnq2t66ybqTi+\nHC9rw4WQEaxg8n23u2w75f67eWfXj4RuvogDudGxNJKXW5NbOxUKBXf/v+dw/MGB1WptNHfTmFnT\nGD5lIod37Sb9Lx/S86yt/neesgr7ihMcmrWLYeNvbuInFoSrp1KpSEho2tJmLUG0jHUw5aXVqJSu\nYydsFh2lpSVtUCOhPVIqlVRVKV3Ki4sr0Ghcxz24u7vj5TWAZcsOk51dRFpaDp9+ug8/P2/Xh68k\nER7u51RWF3jlc+jQrl9stXBcMuSstLSE1NQzWCyt3w20Zuk3BOzPRZIk1CgwYycBfw5TQKpcRrZs\n5JBcgN+9YwloxbEhbW36w/fh8dIczvf3JjVSQea4CIa/8zzRPVxnyarVav5v0dv4v/cgfneN5pSH\nczBtlu0ETBx01d2GCoXiF5NoajQaYvr0wjvL6PI7H6uaC/vbdgyiILS0FmkZ2717N6+88gqyLHP7\n7bfzyCOPOP3eYrHwu9/9jlOnTuHj48Obb75JaKhYrPhadO/dhROHzqHT+jiVu3maCAu7cafiC1cv\nJuYmvvtuN7Nm9UelUpKTU8KaNee57bbHGt0+Pn4IdvtATp48ilarZ/r0GWzY8LHLdvv3n6Z37yiX\ncl9fHf371/LDDx/h4xNCWZkRH5+GltryciPgC9TdEzZsWEzXrmq6dPHh0KE9KBSRjBhxa4t89ksZ\njUY2v/ohE2UvkCAWLxIpZIgUxDCCMcpWTNjw6hvNgj/8plXq0J7MeHQ+PDq/SdsqlUpumXMbt8y5\njaTb93DgnaVYzmSDt56AiYO4+8Vft0odPTw8MfvoIc85uLfJDnS+rl2qgtCRNTsYczgc/O1vf2PR\nokUEBgYyZ84cxo8fT0xMwxTk7777Di8vLzZv3sz69et57bXXePPNN5t76k5pzJiR7NhymLIcHRp1\n3XouNdY8Jk6NR6l0bQkROq/Y2F4EBoaxfPlWFAorXl7hzJ79+C+2YiiVShISGroq+/adyOefr2Xa\ntF74+rqzbdtpkpPLuO8+15cpi8VGWJgfM2ZIHDmiZdWqDCIiHMTHh3PyZC4ZGTJTptwHwLZty7nv\nvj71XZmxsWEkJ2dw6tQxKipKMZlykWUICelNnz79m/1dbF68jKAy+DZehZtHAJayfJTpSr5WlBBv\nUuKv1lHRL5Qpf33G5f+RLMvs2b2Pc2mZRHQJYfwtYzrtZJmBY0YxcMwozGYzarW6Vb8Hd3d3DOP6\nYltyzGn9y/OxOh69/65WO68gtIVmZ+A/duwY7777Lp988gkAH39c9yb989axBx98kGeeeYaEhATs\ndjsjRozg4MGDVzy2yHrcOLvdzorv13I+rQC1RsGYcQMZOKj5D6yOTGTJbj0Oh4PDh/diNJYxcOBI\nvL19Wbnyv4wdG0y3bqE/LReynyFDetC1a90g16+/Psstt8yjpKSY9PQ0unaNw8+vYd3VnTs/Yu5c\n1/EYCxcuoW/fSGbPHoUkSZw8mUVamoZRo5xn66WknCAz8xwxMb2IiblyEtrfzJtPOZF4uw+gqrqI\notKzRAT3R6XSUVpxluheCl5c+LxLoGo2m/nLS29TmR+ATuuD2VKJzieHP//9qU63sHpbsFgsfLXw\nX5TuOI5cbcatbxRjX3iQnv0SrlsdxL1FaKo2zcBfUFBASEjDLIOgoCBOnHDO0VFYWEhwcDBQ9+bt\n6elJeXk53t7ezT19p6RUKplzx8y2robQSSgUCoYNG43NZmP//q1YreW4u/tx8qQ7K1d+R58+Ecyc\nOaJ+5qYsyzgcdS0Zfn7+TkGY2Wxm375N5ORksmpVLePG9cfDoyHze//+XRk5sg9ffbWVX/1qAn36\nRHD+/FFqamrQ6/WYzWbWr/+UUaNCGDUqgmPHTrBixU5mzHgIpbIuWWNpaSkeHh71eakKCvLIhLtq\niAAAIABJREFUt8sEew0AoKT8AtERdWkrjKZijKYKjifa+f3z/+Du+6cRGRmOt7cPkiTx5aLvqC2J\nRqetu1VqNZ44jO589t/lPPPcg63/5XdyGo2GB155EVmWsdvtbZIWRRCuh2Zf2U1pWLt0m8Zm5AiC\n0H7V1taydu1H3H13Al5esVitNr77LgmVKphx4/qj1TZMKtmw4Tj9+k13OYbRWMmWLZ9zzz0DMBhu\nw2q18cMPexg5sg9hYQGUlFTg7q7Hz8+LwYO7k5x8nvj4GAYNCufMmdMkJAxk+/bvmT+/f333Zr9+\nUXTrFsTq1avw9vajoiKF8HA3zpwxUVVlYMSIGaxc+Q7+/l3ACjabGY26LvGo0VRERVUeXUIHY3fY\nOJeSyCsvLsfd4IVfsIJZc0aSmV6GQuE8FlOSFGRfrGzFb1u4lCRJIhATbmjNvrqDg4PJzc2t/7mg\noMAlS21wcDD5+fkEBQVht9sxGo14eV15bbHmNPkJnY+4Xq7ehQtnOXp0BxqNA4tFyeDBtxAZ2dVl\nu9Wr1/Dgg0PqgyC1WsW8eUP55pvTrFp1EYPBhLu7muJiO9HRN9G7d6zLMfbu/YGHHhpeP85IrVZx\n551j+f773cTHmzl48DT33FOXdLR790hWr95HfHwMWVll9Oo1goAADzw9LS4pMwwGPTZbPoGBNiZP\nbuj6rKw08e9/v8iCBRP5+9l9WCvqAin5p7xZJeXpdAkdAkBmXiKRIYNQKlRUGvNJP5vJm/9cgUJp\nISLQdWKMm0FD+oU0Tp1MZdSYYcTG3pjZ+m80FouFxX99g4I9J0GCoFF9mf+nX19x8XNxbxFaW7OD\nsb59+5KZmUlOTg4BAQGsW7eON954w2mbsWPHsmLFChISEti4cSPDhg1r0rFFP73QVGJcx9W7cCGF\nioqD3H57n/qyNWtWUlQ03iUgq60tQ6NxTXqoUtUyevQjWCwWamtr6NWr7iWrsb+FzVbV6IDv0tIq\nTCYz9947sb6sosL4U5Bl59SpKmJiPCkqqsJicU3SClBZWcrAgUOcyjw93ejXL4qoqGDumNedz97L\nQasMw2I1IcsyCkXdA9jhsKFWalEqVJhqy6msLqgP0vKKTmGqKcNN70NJ+UWqTcVYbbWQW85rCzXo\nNf6s+34Zsb3U/Pq3j4oW/3bunUd+Q/jKNMJ+mhBg3ZXNy6fTmfWHp9n8wRdYMgpRBnoxYv7t9Ozf\nDxD3FqHpmhO0N3sqjFKp5KWXXmLBggVMmzaNqVOnEhMTw3/+8x927NgBwNy5cykrK2PixIksXryY\n559/vrmnFQShmc6ePcDEiX2cyqZP78eZM3tctrXZGg8y/leu0Wjw9KwLxC5cOMeWLd+xY8daamtr\nr3gMs1miZ89Ip7LFi7dSXGxlyZIUJky4r77cavWgpsbstG1ZmZHy8ro8ZSkpmaxZs5+zZ7MB6mdG\nTry1D/c95obkdoiAIEjLXElNbd2ii3a7FaWyLudVUelZwgLj648dEtCb4vILnD6/HoWkJDJ0EEql\nhq4hU3DTBiBJEgZNBBln3Fnx/dpGP5/QPqSdPI1uSwrqn83MVEtKajccY8mc/yPg80TCtmcSvOwE\nO+f/jWP7rjzJTBBaSot0wo8ePZrRo0c7lT3zzDP1/9ZoNLz99tstcapOx+FwsHP7bvJyCxl983Ai\nIiPaukrCDUKvb3zRb63WtfUpLCyeo0fP0r9/VH1ZcXEF4O+03caNX9Ozp4K7746hpsbMypWf0rXr\nOGJiehIQ0J1Tp7Lo3bvhGs7JKSEoqD/Llp1HrzeiUEB1tZqxYx8nODjMpR7jxs3m3/9+BX9/B/7+\nHpSV1aBWR9ClSzyffbaeoUN7Mn36TSQnn2fJki2o1Q1pKqZM7UtMrBcXLhRgNo+l2qjk+yXH8dDF\nYrHWJRdVKFQurVthQQlk5f+Ij1fET9soUUjO77EatTtnTubAnEa/UqEdOJN4hKBqJVzyTlBRY2Rw\nhhv87O8ekW/n4Cff0m9E03pxBKG5xIjIdiw3N49/v7IIa1UYGrUHe7f+QPwQbx5/6v62rppwA6it\nbbxh3GJxLe/VK4EffywjLS2JoCAtJSVmamu9mTChYdmgU6eOMXiwnh496sZY6fVa5s0byldf7SEm\npicJCUM5eHArJ04k4eenprzcgiwHM3bsrCbXeevWH5g8uTuDBtXlMbx4sYDdu8twOCzcc88t9RMJ\n4uNjiI0NY/nynU77b9t2kgEDphMTU5cKJiAgiHWr9lJWI5NblIjsAIfDjkLREMRVGQvw82rCmDDR\nQ9muJYy6iY1e3xBe6ZxHzqZSINld/3iWzMLrVTVBEMFYe/bZh9+jMPfkfxPVDNounPyxmD279zNq\n9E1tWzmhwwsNTeDQobMMHdqQoHnPnlSiohpfj23w4JuR5TFUVlbQvbu7y+y2vLwUbr7ZdeB+WJiG\n8vIyvL19GDbsFmR5PNXV1bi5uTU5aWh2dgZHj64nIMBOcbGCr7++yKRJg4mKCiI/v4Jjx/LQauOc\n9nFz02G317UuWyw2Vq8+Ru/eMxg2bFT9GKD+A+LpP6CuW7KoqJhvl61iz/a9hPqNQvpf65eqGqtD\nBoIAkGU7druVwtKzWG01QN3EgB6Du1BUVERAQECTPpNwfUXFRKOY1p+apUfR/7S4bw12rF194Jzr\n9upgH9dCQWglIhhrpxwOB1kZRjwuWYZSr/En6XCqCMaEZuvTZwAnTzpYujQZnU6mpkZBRMQA4uL6\nXHYfSZLw8mo8P6DDITWatqa21o5a3XAhl5aWUlxcSHR0bJOCMbvdTnLyGhYsaOgykmWZJUu2cO+9\nExk6tBubNh1vdF+NJoBly7JQqbQMG/YAer3+sucJCPDniacf5O57y1m2ZBVFBSb0BhX3Tp7MhjV7\nKLhgRalUEx7UjxNpa4jrOh43nRcl5elUGPM4sL2aw7uXEBwJz70wHx8f8TBvinOpqVitFnr07tOi\nEyDKy8vYu24TgRHhDB41AkmSeOj1hayKW0TOvrrrJXBkAg+PGsbm+/5EVHbDguT5XpDwK9f0LELH\ncOLEEQoKUpFliIrqR7duPZu0n9FYxaFD25FlBwMHjsbHx+/KO7WQZmfgb02deQaLw+HgiQX/wl3d\nw+V3kT1LeebXC9qgVu2XmPHU9nJzsygp2c64cb3ry2RZZtGiY0yb9jC1tbVs2fIl0dFawsO9OH68\nALW6K8OHT/jF4+7fv51RoyR8fZ1nKp08mY5Go8LLy51PPkniuedG4uamq/99RUU1GzeWMW6cczfo\ntVwrFouFj95fwrmUEsorSlHY/fDzisVsMVJcdp6woIaM8LIs4xGUwcKXn72qc3Q2F1JSWf37f2NI\nzEbhkKnsF8wtf3qSvsMGN/vYqz74nIsfraZLrp1KtYPCwUH86t2/EBze+Pq9p5OOsvejrzFfLEQV\n7E3/e6YzbNJ4QNxbOpotW5YzYICmfrhEUtIFMjIMLqt4XOrYsQOYTMlMmZKAQiGxZctJrNYohg0b\n3+Rzt2kGfqF1KBQKusR4UJzhaOguAUzmPEaOGd6GNROExoWGRpCX15XlyxMZMCCEoiIjZ85UMWZM\n3TqC27Z9w7339kWtrrvtxMaGkZh4nrS0U8TF9b7scaury/HxcZ24EhzsS0pKJnv3ZjF//q9ZunQx\nffu6k5DQhSNH0klJMTN16vwW+WwajYann617Afrqy+Uc2VWXFqOwJI2w4H5O20qSRF6Gg7KyUnx8\nfFvk/DcaWZZZ+cKrxB0uBepmsgYllbPpt6/TfesX9asnXIszyckU/PsHYoxKkBT42hT4Hijh+xdf\n58lFja+J3Gtgf3p93LmXlLsR5OfnEh5upkePhjGeAwdGk5NzlOrqagwGQ6P7Wa1WysqOcccdDS8C\nt96awLp1x6iqqsTDo/UXpu+cq912EE88cw96v3SMtbmYLdWY7GcZNTGIAQP7XXlnQWgDAweOZvTo\nh8nNjcHdfSzTpz+Gp6c3sizj7l5TH4j9z6BBMVy8eOwXj9m371D27k11Kd+69QhnztQydOgdaDQa\nZs58GI3mJtaurcRgGM306QtaZSHrqK4R1FrKAJCRXWZWAjgcKkwmU4uf+0Zx/MdE/JLyncpkWSY8\npZLtK9Y069hJP2wk1Kh0Kbcknhd/kxtccvIhRo1y7U0aNSqWEyeSLrvf0aOHGDu2m0v5pEl9OXx4\nZ0tW8bJEy1g75uXlzd9ffZ7U1DSys3IYOmwm7u7uTdq3oqKc/37wDTkZVUgKiZjuvjz82D3NeuMU\nhKZQKpX07Ok67kzp+nwE4ErxUnBwGCdOaDl5MpM+ferykR08mIZOF8/48ZOctg0P70J4eJdrqndT\n3TRiGKu+24Xd6IOXewhllVn4eDq33Hn5WwgNdU3NIdQxVVWhtgESOGSZoxQDoEai9s0v8PXzZcgt\nY9u2kkKH4+npQ3FxJQEBziv85OSU4u9/+bGwOp2e6uoKLp17U1trQa3WtkZVXYiWsQ6ge/c4xt8y\ntsmBmCzLvPznD8k7F4DSFovCEsO5Y+689spHrVxTQWicJElUVbm+++Xnl2IwuGb2v9SECXMpKYnh\n66/PsmTJWSRpCCNGTLrifq1BkiT+8OdHCYouAHU+WQUHOZ+5m8y8JPKKTnMheysqtY3tW3e1Sf06\ngsGjR5Hfo+6BeZxieuLDQCmAeMmfIekSP/76P1w828gUxyYYeNskct1dc+VpBsXg5ubWyB7CjWLI\nkNGsXXvaqUyWZQ4ezCc2tvtl9+vbdwA7d6a7lK9de4Jhw67PS4Fy4cKFC6/Lma6ByWRp6yp0SHt2\n7+f4AQsqVcPMMYVCSXFROf2GhOPp2fr939ebwaAV10s7p9f7sWXLNmJi/NFo1Jw+ncW2bfmMHz+7\nSbPoAgKCiY7uS2xs32aNxWqJa0Wv1+Pn78GRQxcJ9RuJr3cUlcZ83Nx8CA3oj8Psz8kjeZzLOMLQ\nYQPYuXMP3yzZyK7tiRzYv5fN63/k+693sWvHISqrSujVO+7KJ72BKJVK5CBPjiclYa400kVyHvjs\nXQ2pqkoSxo286mMHBAeTraklPTUNQ5WNJEUxZwMdBA3uSVRC76sOyMS9peOQJAkPjzA2btxDTk4+\nqal5HDhQyKhRd6DTXX4mtSRJaDS+bN26G63WQUWFkfXrU4iIGElQUGiTz28wXHsrmphNeQP6cvFy\nju917Y6sNVdxx4NdGT3m6m9w7Z2Y8dQxWCwWDhzYisVSTURED3r06Hvd69BS18orCz+gNKeuVc9q\nraGo7Byhgc6fp9qcRZ9Bek4nyeg1AVRVF2I0FRES0DBhodZaytipAdw+t/OlUqisrODtgbfTv9K1\n1b/4znjm/+ev13zswsJ8Xp/zKINS7OglFQ5Z5ly0hikfvUSPhPgrH+An4t7SMZnN5p+CrKYPzZFl\nmbNnU7DZbPTsefWpVtp0bUqh/RkwqA8mc65LuV1RQL/+1//hJwj/o9FoGDNmChMmzG2TQKwlFRY0\nDAYvrcjAz9s1S79WGcihvRnoNQH12/08EAPQqX05vO9s61a2nfL09MJvSC+XcrNsx6+f64Dqq7H3\nu3UMS3Ggl+q6xxWSRFy6lZ1vLW7WcYWOQavVXvUYaUmSiIvrSa9efVs0511TiGDsBtS7dy8i42Ss\n1ur6slpLGQOHh9Yv5iwIQvMYDA1j4Nz0vpRXZpOVd4Ss/KMUlKQiyzIlFenolA0D+RWKxudMVRtt\njZZ3BqP/7z7ORSpx/NRJY5JtXJwQwa333tWs45afOI9acp01YjqT2azjCkJrELMpb1C//ePj/PD9\nWtJO56JQKBgwJJaJk8a1dbUE4YYxdFR3Nq/IRaf2xeGwYzQV0TV8OAqFkpraCs5l7ia8izt2S8Nt\nVnbYccgOl3QYfoG6Sw/fafQZMojAte+x9dOvsZUZCUiI4//uut1lua2rpfRsfGyY0ksM4hfaHxGM\n3aAUCgVz5s5o62oIwg1rxsxbsVrWcnBPGsVZF4mJbHjZ0eu8iAwZyOCRSgrzK8hOMaNSafH16sKJ\n1FX4eEUiyw58vbqg1lUzb3bnTuMQGBTM3X98rkWPOfSemexcm0h4cUNZtWQn9NZhl99JENqI6Kbs\noKqrq7FYxAwfQWhLt8+dxqtvPUtgoOuMK63GnaK8ap77zcP0HmqlVj5BUfkZ4rvPIjJkIF1CB1Nr\nLWDq7b0ZOEgkcm5pPeL70ufVx7kwNICzfnbSuuuQn7uFOc8+1tZVEwQXomWsg0lOPsWyLzdTnGdF\npYIu3dx55te/vACyIAitR5Ik1NrGB/tqtEqUSiUPP/Yr3nnrM7Q4z9AK8O5L4qE0Jk+deL2q26mM\nnDaJEVMnUltbi1arbZUVGQShJYgrswMxGo189J81WMq74qmPw00dR8GFIN741ydtXTVB6LQkSaJH\nn0BsdueWapM1g8nTRtf/XFpU2+gMrbJic6vXsTOTJAm9Xi8CMaFdE1dnB7Lyhw1o5FinMoVCSeY5\nMxUV5W1UK0EQHnvyXqJ6VWCyn6XClA66c9z+q/7Edoup38bgocZqM1NTW8HP0zsaPNRtUWVBENoR\n0U3ZgVRX16JUuCaVc9h1lJeX4+Xl3Qa1EgRBpVLx7G8exmw2YzQa8fX1dWoFq6mpoaiokIKSbLRq\nDwpLU3F3C8RgcGPSuI6db00QhOYTwVgHMnBQL44fOIKb1nk1Uw+fWiIiItuoVoIg/I9Wq0WrdV0S\n5e3XP8Na3oPwoIa8V7lFR5g8OZIJkzr3TEpBEEQ3ZYcyaPBAonvZqDGXAnVLN5isF5k6a4gYDyEI\n7VRNTQ0ZZ6tRKJwTkIb496OyvKaNaiUIQnsiWsY6mOd/9xh7du/jWNJZNFoVk6fNpkuXpreKlZSU\n8MO3G6isMBMY5M7td0y/6oVzBUFoutraGux211utJCkw13bezPuCIDQQwVgHI0kSo8eMvKbFvi+c\nT+eNf36DVo5DktzJTrWSdPgtFr7yBN7eYryZILSGosISKqsvUF5eRqBvN3RaTwBqzCX0G9T7CnsL\n18vFs+fY/cV3OIw1BA7syaR5c1EqXZdTEoTWIIKxTmT50o3o6AE/jStWKtXIlh4sXbKKJ566v20r\nJwg3oMWffcPBnUWE+9+CLDvILTyFRq3H3d2bqJ4WbrppqNP22VnZrF29HYvZTny/GMaMHXXdFyzu\njA5t3kbi8+/SpbBulqvxqyTe2XaAZz59s41rJnQWYqBRJ1KU7zo+RZIUFOZWN7K1IAjNkZWZxcFd\n+Ri04UDd/7WwoL7YKOHuh3vzwh+ecAq0du3cxysvLefsUQ8yz/jw3aLz/OuV99qq+p2GLMscendZ\nfSAG4CapCN5wnh0r17ZhzYTORLSMdSI6NyXmRlZQ0ru5NsUfPpTI3l3Hsdsd9OoTyZRpE8UbuiBc\nhR3b9uGmdh3P6amPQad3nnEpyzJrvj+Am7ohj6BO60NmqoODBw4zbPiQVq9vZ1VdbcSRmgs453tz\nl1XkJp6ER9umXkLnIlrGOpEhN8VRay11Kqux5XHzLQOdyr5ZupLF7yeRe9aPggsBbPyugNf+8f71\nrKogdHgGDzfsDqtTWUFxCgXFqbz3+jp+8/S/WfXDhrrygnwqS1yTv+q1fhw9knpd6ttZ6XR6HD6u\nk5gcsozG1zWvoyC0BhGMdSIzb5vM6El+yJpzVNacQWm4wMw7ezB02KD6bWpqatiz7Sx6TVB9mVbj\nycVUJSdPnGqLagtChzR12kTsygv1PxeVnker9SQ6YgS+hr5QG8uW1Tls2bQTd3cPlGqryzEcDjsG\nN831rHano1Kp8L91EGbZ7lR+vquaW+bPa6NaCZ2N6KbsZO6YN5M75oHD4Wg0N9npU6exm/3gknXH\n3TTBJP54gj59xewvQWgKnU7Hw09NY8nnGykvVFNZnUVMxM3O26j92b/7FBMm3UyXbnoK020oFA23\nZTPnmHX7Y9e55p3PPS/9hq+VSjK2JOGoNOHWO5IJz87Hz9+/rasmdBIiGOukLpckNiw8DIe0B/B1\nKrdYqwkMFDcmQbga8Ql9+NdbfcjLy+XNf36Nw+S6TW1NXa6xZ3/zIO+8+TkX0iqxWxX4B6u45+7J\neHp6Xedadz5KpZJfvfQbeKlu/J4YHytcbyIYE5wEBwcTEa2gNNv5DV3hlsGkyXe1Yc0EoeMKCQkl\nJNyT7NS6B73DYSMr/yiSpEBTZuOt1z/h4cfm8cIfHsdisWCxWHB3d2/randKIhAT7HY7OTnZ+Pr6\n4u5+fcYNSrIsy1ferG0UFVW1dRU6pdraWj58dwnn00qxWx2EdfFgwSOzCQkNaeuqXVZAgIe4XoQm\nuZprpaiomK1bdhEQ4Mu48WOatexYQUEhL//5U1TWblzMOUyX0EEolXXjwRyyA633OV557YVGg4HU\nlDQ2bdiHzeKgW49QpkybKBKSXiOTyURZWSnBwSFX/A7tdjtJ27dy/vBpvKPDmDB3NiqVaMO4kR04\nsAWzOZ24OG9ycyvJy1MyefK9Tfq7BwRce+AmgjGhURcvXuRIUjL9+vUhOia6ratzRSIYE5qqqdfK\nl4u/Zd/2LAzqKCzWapSGbJ59YR5RXaOu+dxGYxUfv/8FJxJr8PWMobjsHDXmSgC0Gj1P/fYWhg5z\nTmOxdfNOfliaXJ8mw2Ktxje8gD//7TnRinMVHA4HX/z5VcrX/4i2yIQ5xo+eD8xg0n13Nrq9yWTi\nvfufJXJPLgZZhUm2cXFoAI988TrePr6N7iN0bGfOJOPhkUb//lH1ZTU1Zr799iKTJ99zxf2bE4yJ\n2ZSCE7vdzqsvv8erf1rD3vVWXvvLel7+6zvYbGINPaHzOHXqNPu3FeKuiUaSFGg1HqisPfnkwxXN\nOq67uwfx/Xvi4RZCRu5h9DofIkMGEhkyEJXSjRXfbXDaXpZlNqxOdMpXplEbKM7yY8f23c2qS2fz\n7evvYfh4P7HZDiLMOmJPV5P91684smd/o9uveOtDuu8qwCDXtYi4SSp6Hipl5WsfXM9qC9dRdnay\nUyAGoNdr0euNrX5uEYwJTpZ++R255/wwaCNQKJQYtOEUpQfyxefL27pqgnDd7N6RiEEb5lJemGOn\nsrKiWcfu1z+BMuMZPN2DcXdrmBTj5x1FaaGS2tra+rKioiKqylzzj+k0XqSczmhWPTqbgq1J6HHu\nlgyqUnD8+02Nbl95/AKKS1oeJUnCmHyh0e2Fjk+haLyj8HLlLXruVj+DcM2MRiOpqamYTI1MwWol\naSmFqFU6pzKVSsv51KLrVgdBaGuX6/2TpMvPRG4qf38/3L1r8fXq4vI7lSOUE8kn63/28PBApXFd\nNsPhsGFwF/nHrobdVHtV5Uo3XaPlCjdto+VCx6dW+1NR4doKZjK1/v81EYy1Q7Is8/67i/nt0x/y\n+sIdvPDUe3z60dLrdPLLlIuxKUInMuHWkVSbM53KZFkmOELVIrOrpswYj8Xq+pJlp4qQ0OD6n/V6\nPd16eWGzOwdkZukcs+dMaXY9OhND3yiXMrNsx29A90a3j502ijKNcyLYKqWdiInDWqN6QjswYsRE\nvv76NFlZxUDdeLEvvzxAnz7jW/3cIhhrh5YvW0lKohI3VSye7sHold04dtDGyhXrW/3csd0DsNnM\nTmU2u4Xobn6tfm5BaC9iYqK5ZXo0NfazWKw1mGoLUXqc5fGnWya9y+QpE5D0zt2MDtlBcKSD8PBw\np/Knn1tAbEI1ZlKpMp/BPTCLJ5+biYeHZ4vUpbOY8tvHOdPHDctPmfYrFVYyp3Rl2oP3Nrr9uNtn\nYnhhOund9eSoazkXpUJ+evxltxc6PqVSyezZj3P6tBdff32BNWtKufnmhwkPd23FbmliNmU79OJv\n36G2LMKl3CMwhz+//GSrnrtuAP/7ZJ1T4KYJxWTJIyzayu9ffLJdT+kWsymFprqaa8VkMrFn936C\nggPp1y++ReuRkZHJ4k9Wk5NhRKGErt28eOKZe38xv5hISNo8tbW1bF6ynOq8IsIG9GLUlFuv+H16\neWk5cSKNwMAgdLrGuy4FAZo3m7L9Pl07MZvV3mi51epo9XPX1tbiZtCj0BRSasqlazcffvvHZy4b\niImHg3Ajc3NzY9Ktt7TKsbt0ieRPf3sKu92OJElNGosm/q81j06nY8ZD913VPhqNhsjI1m8ZETo3\nEYy1Q6GRnmScciBJDTdnh8NORNfWXxbl5YXvU1sWg17yR2+Asmwb//z7B/zpr/9Xv43dbufjD5Zw\nOjkfS62DoFA35swbT3xCn1avnyC0Z8eOnmDVdzspLqzFzV3J8JE9mHX7L4/tEslb257ZbEalUom/\nhdBmxJixduiBh+YgGVIwW+qSQdZaKlB7neW++XNb9byJPyZRXuCD4mdBoFKhIjddSfqF9PqyD95d\nTEqSFq3cHQ9tT0wlXfjw7fUUF5e0av0EoT1LT0/nv+9spaowAi3dsBuj2bomnxXfr2vrqt3QTh05\nyvLX32PDV8uxWFxnnv6S5AOHefeOJ3h3wBzeGnEnn//xZaxWayvVVBAuT7SMtUMeHp78683fs3nT\ndrIzC4mOiWLs+PtavYvibFo6blrXxcC1qgBSUtLoGt0Vm83GmeQi9CrnGUh6RSyrftjIg49cOUux\nINyIVq/Yjl7Z1alMp/bl4J5Ubrt9ahvV6sYlyzKf/O4vKJYnElSjolq28fbnq5j7wV+I6hZ7xf1L\niovZ9syrdMu0A0ootmH95CBfOv7Jgn++1PofQGiXLlxI5dy5A+h0NqxWBd7e3Rg4cFSrn1cEY+2U\nQqHg1smtM1blcgYP7c/uTRswaJ1nc1kcuQwcNA6A2toarGYler3zvpKkoNp4dW+lgnAjMRkbX6XC\naGx8DKjQoKamhs1fLcdUUErUkASG3TL2ii+fu9asx21JIl72useYTlLR80Q1619+nycWvXHFc25d\ntIyYDJtT2h61pKRi2zEsFgsajcjj1tnk5GRSUrKXe+5JqC87dSqLxMRdDBo0plXPLbrt8/ETAAAg\nAElEQVQphXqxsTF07anAaq2uLzNbK+kz0JvAwAAADAZ3vBvJcmGxGomNc81YLgidhX+QAYdcN8nG\n4bCTmZdEZl4SJcVFfPTBl1fdhdZZXEw7x7tTFmD/43d4/GcXZ+e/wTuPvYDd/stBbMbupPpA7OdM\nxy/gcFx5spOt3OiSYR9AWV6LyVTdyB7Cje7Eid1MmZLgVNa7dwTl5Wdb/dwiGBOcvPD7xxk52YBP\naD4+YflMvC2AJ56eX/97SZKYettwTNaL9WUWaw2eQXlMmtz6ifEEob266+4ZONQpOGQHF3MOEhrY\nl8iQgYQH3ETKjzpe+dt7bV3Fdmnjvz6k5+kaNFLd4Hlfm4rgFSls+vrbX9xP0jbesSNpVU0a0hEx\nPIFKRSPjw3qG4uXlfeWKCzccna7xIF6rbf1MBqKbUnAiSRJz75z1i9uMuXkE4REhrF+zC4vZQdeY\nQGbMek7MRBI6NQ8PT/766pO895/PKK8MQaVs6OZSKtUUZug4deo0vXv3asNatj/VJ9JdytwkFfmH\nTsKvLr/f4LlT2f3tQcIqGtoU7LIDr5F9mhSMjZpyK+/M3AYrU/CUVciyzMUQBUOfukukEOmkamqU\njaZrqq1t/WebCMaEaxITE83Tz0a3dTUEoV2pqjJSUlxGZbUdhUKLt0dD171eE8zJ5DMiGLuEwk0H\nuHYLKvW/nGC1Z78EMv90D6c/XolXSikmbzWK8b144G+/a9J5JUniqff/xc5Ja8k+mIzSXcdt980l\nvIvIKdZZDRkyiWXLlnPXXYPrA7J9+9IIDe3X6ucWGfiFG4LIwC80VWtdKxs3bGfVsmO4qbsiSRKl\nFZlUm4qJCBkAgMmczXMv3kq3uCvP9OtMvvzLaxje213fTQmQ5+Vg+NKF9Bk04Ir7W61W0lLOEBgc\nQkBAQIvXT9xbOpeiogISEzfj5ubAbIaoqIHExTUth6bIwC8IgtCGrFYr61cmYtDE1Zf5ekVit5up\nrilFozYQHiuLQKwR8/7fcyyurqFq81F0xSZq4/zp/dBtTQrEANRqNb37tuxSVULnFRAQxOTJ13/9\nUdEyJtwQxNur0FQtfa2YzWY+fP+/7NqcRWTIQKexYrIsU1C5gwm33oTVauPsmSJsVgdhXTx44OG5\n+Pj4tFg9Ojqj0UhpaQlhYeHtavypuLcITdWcljERjAk3BHHDFJqqJa+V/fsOs/Tz7SjtdV2TuYUn\ncNP54O9TN57Saqtl7HR3zp/NJjPFG7WqbhyULMugT+G1t3/ntCalyWRi794DBAb4k9AvXgwkbwfE\nvUVoKtFNKQiCcJ1ZrVaWLd6BTupRfyeNDBlIZl4SdrsFpVKDQ5XO8BEL2LgyFXdtcP2+kiRhrgxj\n25YdTJhUlxJm5Q/r2bL2FEpHGDb7edz9NvHsb+8lNDSkLT6eIAjXkcgzJgiCcA1279qLbA53KQ8N\n7MuF3L2o/z979xkYVbE2cPx/tiSbCglpkISShBAQpHeULr13LICCYLkolut77V70etVrr6hYAUGk\nKV0QQQHpKD2UhATSe8+2834IBpYNkL5JeH6f2MmcOc+Gk7PPzsyZ8TzHnEdGkxAfDxZPu3rOTp5c\niE0GIOpcFJtWn8ZF2xwnvSuuBj+sueF88v6yKn8fQgjHk54xUeNZLBZiY2Pw8vKSxRhFjaHRakCx\nXQzSaMolOe0s/Ya04JFHHgIgNzcXrfPPgO2TfvnGVFre0gaAzRt/x9Wpsd05Ei9YyMrKxNOzXtW8\niTrm+IFD7PhgEfmnL6L1did0dB+G3XudxcqEqCEkGRPVKjMzgxXfrycrs5CARvUYM24Yzs7O16y/\ncd1WNq49QF6GKxp9IU2aO/PYP2dd9xghqsPtt/di9bL/gaUFALEJh9Bq9Ph6h3FifxrP/+st/u+5\nObi5udGpRzAHfk/HoC+asG+2GGkQmEG37l0ASlxo8m+l2dpHwMXz5/l5ziuExvy9R2gB6YeW8ZPF\nyohZ9zg0NiFuRIYpRbWJOhfNM098wtE/nLlwyovdP5v41xNvkptb8j5wJ0+e4sfvj6Mzh+PpHoS7\ncyjJ0QF88O5X1Ru4ECXQarXcM3MQJu0pLib+ST33QBr5tcZJ74q7IYicpCYs+HAxADNmTmb4pGC8\ngxLw9I+j4+3w/L8fKW6rT78u5BZesDuHb0MN9evLE5el8csXSwk5b7u9UX2jlnMrf3FQREKUnvSM\niWqzdPEGDEQUfwXQ65yx5kewZNFqZs2+067+lo27cXUKtinTaHScPZl+3Z4EIapLx07taNe+Df+c\n9ypKvp/NzzQaLVFn0otfDx4ygMFDBpTYTkTLCHr2P8rvv5zDTd8UozkXresFZtw/qUrjr0vMKVkl\n3hPMyVkOiEaIspFkTFSbxLg8uwtOo2hIuFDyzdJotJRYbjapWK3WGrUWkbh5abVa/P39SYq2/5la\nhhHGu6aNZ9DQFLb8vB0f30D697/TZtkLcX3uzYMxq0fQKba/M+dQeRpV1Hzyly6qjcGl5OTJ2VDy\nZdiqTRMKjfaJWkCQqyRiokZp064pmTkXiU04RHzyMaxWM6qqEtysbOsO+fr6MGXqOAYO7CeJWBkN\nnXU3kZ29sFyRAcf4KXSZPdGBUQlROvLXLqpNhy7NKDRl2pQVmOPpM6BjifUHDe5PYPMs8o0pAFgs\nRgrU40ydNrjKYxWiLNLTsyk0ZRDk35YG9UOIuriHbMseZs6RYcbq4ubmxoPLPiDviYEkjAgn+Z4O\n9F8yny79ejs6NCFuSFbgF9Xq26+Ws393FPm54OmlYcDg9gwe1v+6x+zds4/DB0/hWc+FkaOH4Orq\naldHVskWpVXZ18rZs+d446WfcHduYlOu8zjLf996vNLOI8pn/47fidr/Fz6hjek9YmiZexzl3iJK\nS7ZDErWKqqoUFBRgMBgqbRK+3DBFaVXmtaKqKv98/EXOR1pBVXF18S7eCikrL5p/vzmJgACZs+QI\nZrOZD+c8Sf2Np2lg0pGtmLnQzY9ZX/6P+l7epW5H7i2itCqSjMkwpah2iqLg4uIiT0OKWu/tNz4l\nL7kZjRt2pHGjTjjpXbiY+Neln6potfKMlKOsWfAlQT+eoYGp6P/AQ9URsSuVFa+85+DIhLAnyZgQ\nQpTDyZOnOHPUgovh8q4Qnu4NUVExmQvwC1Lx9fW9TguiKqXtP4mzYvugj6Io5P55zkERCXFtkoyJ\nm1ZOTg579uwlMTHJ0aGIWmjfH3/i6tzIrrxBvaZkmvcwfeZIMjMzHBCZAFCc9CX/4FrlQjiQ9KGL\nm9JXC5exd2csGBtg1eyiSbieJ566H71ebtR1maqqbPvlN06diqH/gNsqtLp9QCNf9hpjcXay3QQ8\ntzCeRk0DeGP+SlSrFp8Ahcn3DOLWW2+paPiiDJoPvY2Y9cfwMl7uHStQzfj3be/AqIQomfSMiZvO\nz5u3sX9HLq7aMFxdvHB3bkrSOV8+X7DE0aGJKhQbE8sTc19jwf8Os3ODkX/NW8jSxavK3V7/Ab3R\ne1zkymegrFYLecZYCtOa4+EcjqdLKMbMED597yfy8vIq422IUuo9ahgujw3lTGMtKWo+53xVMqZ3\nZvy8BxwdmhB2pGdM3HQO7InE4ORvU6bVOnH2ZCwmk4kfV28gJjoFg4uWsRMG4+/vf42WRG3y2Ucr\nUAoicHYqeu2mCWP7pljadTxFRESLMren0Wh46rn7WLhgOReis9FqNfgFackpDEW5ahV4vTWUH1dv\nZPLUsZXxVkQpjZ/3AHmzp3E2MpLgpk1kn09RY0kyJm46FkvJq7mYzFae/b83KUhtgl7vjaqqvHTw\nG2Y9dAftO7at5ijrltOnz7L8u00kJ+Tj6qqjc4/mjB47tNrOn52dRcJFM54G23I352C2bdlTrmQM\nwN/fj6eff6j49enTp3nj+Z/t6mm1enJzpGfMEVxdXWnTrp2jwxDiuiQZEzed0HA/dp/PR69zKS5T\nVZVCcypKWnv0emeg6MkrV21zVv+wXZKxCkhJSeXd137AoLRACxRmwpYfEyksXM2kKaPL3N7BA4fY\n/stBzGYrLVoGMnzk4BqzdVBISAiuXrlgsi3PK4yne68+NmUFBQVER0fTqFFDPD3rVV+QAqB4eFmW\n2BE1gSRj4qYzcfJoTke+T/w5A67O/hSasnDyuEgjr0ZkxTvb1U+Mkx6Nili5fD3ONLcpM+i92Pv7\nGSZNKVtbq1asY8uP53FxKnqKMeZUKkf++oBnnp973eM8PDwJCNKRl2JbnlsYS78Bg8oWxHVotVqG\nj+7CiiUHcNU1Q1EU8gqTadXBmVatWhbXW/T1D/zxWxTGXA+0Trk0b+3BI4/dJ3uuVoPU5GSWP/8m\nOfsjAQWPLuFMnP8kXt6lXwhWiMomyZioVf48fIStm/dgKrTSJNSHcRNGlPkJSI1Gw3MvPsKhg3/y\n1+GTBAYH06//XXz43tdkxdvXN7jKB2RF5GQZURT7lamzs4s20y5tz4TJZGLbpmO4OIUXlznrPYg7\nW8C+fQfo3LnkPU7/dv+D43nnjUUUZPqj13lQaImmz5AwWkSEX/e4shpwR29atgpj3U+/YDardOra\nni5dOhX/fNvWHez+JRMXp+YY3IvKzh8v4MvPlzJz9p2VGouwpaoqXz3wDOE7EouvO/X8cb5MeZrH\nln3i4OjEzUySMVFrbFi3lbXfn8TFKRCAuHOFHDn8DndNH8GyP4+h0WgZMWowBoPhBi0Vad+hLe07\nXB5+HDqiN2/9+SMuuqbFZSZTLm27BFbq+6gIVVXJz8+vVTsY+Pq7ExtpRquxvd14NXAq03s4d+4c\nBdkeOLnblrs4+XLk0KkbJmNBwUG88e5THD/2F5GR5+k/YFaVDQ8GBgVy/wN3l/izPbtO4uLkZ1Om\n1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hHNCYuQXrGbUX5+Pq+88Bk6U0sUxQdTNqxdfp6srDVMnDLqhsf/8P2P5Kc2Ra8v6hXS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\nnh3aUAgFURS8JBgUhgbQFEQVKBogGBwlY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            "text/plain": [
              "<matplotlib.figure.Figure at 0xff0dc50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "4NPYAO6t2yyL",
        "colab_type": "text"
      },
      "source": [
        "# Implementing a Classifier from Scratch\n",
        "Before experimenting with libraries like TensorFlow, we start by implementing a simple linear classifier and then a more complex nonlinear classifier from scratch in Numpy. This allows us to be able to go through all the low-level details of how to make predictions and how to train our models, as these details are very important. \n",
        "\n",
        "Later on, we will then reimplement these two classifiers using TensorFlow, and hopefully we will see that this makes things much easier (especially as the models get more complex!).\n",
        "\n",
        "## Implementing a linear classifier\n",
        "How do we define and train a model that learns to separate the num_classes different classes, based on their coordinates in X space? We start by using a **linear classifier**.\n",
        "\n",
        "A linear classifer is a function that takes an object's characteristics (or features) as inputs and outputs a prediction of the class (or group) that the object belongs to. It may make a single prediction for each input or it may output some score (for example a probability) for each of the possible classes. A classifier is **linear** when the scores are derived through some linear combination of the input features. \n",
        "\n",
        "The linear classifier we will implement computes the scores for a given input X using the formula $y' = Wx + b$ where $W$ is a weight matrix of shape $d\\ X\\ k$ where $d$ is the dimensionality of the input and $k$ is the number of possible classes and $b$ is a bias vector of length $k$. \n",
        "\n",
        "By normalising the output score vector, using the so-called **softmax** function, we can derive a probability distribution: \n",
        "\n",
        "$P(y=j\\ |\\ x) = \\frac{e^{x^TW_j}}{\\sum_{i=1}^k e^{x^T W_i}}$\n",
        "\n",
        "Here j refers to the jth possible class and $W_j$ to the jth column of matrix W. Earlier in the practical, you had to experiment with a loss function that looked like this (in code):\n",
        "\n",
        "```\n",
        "inner = y[n] * (w0 * x[n, 0] + w1 * x[n, 1])   \n",
        "loss += np.log(1 + np.exp(- inner))\n",
        "```\n",
        "    \n",
        "Can you relate this to a softmax function, for two classes?\n",
        "\n",
        "In this probabilistic form, we can also describe the classifier as a linear **discriminitive** classifier. This means that it directly models the probability distribution of the unobserved class conditioned on the input. In contrast, **generative** models, which we will encounter later in the Indaba, model the generative process of the data. \n",
        "\n",
        "Finally, we need to define a loss function, such that minimising the loss function by gradient descent, results in parameters $W$ and $b$ which make good predictions about the class of each input $X$. For this purpose we use the **cross entropy** loss (also called the negative log likelihood loss). The cross entropy loss compares two probability distributions, the true distribution $y$ and the predicted distribution from our classifier, $y'$ using the formula:\n",
        "\n",
        "$H(y, y') = \\sum_{j=1}^k y(j)log[y'(j)] $\n",
        "\n",
        "Let's implement these in Numpy! \n",
        "\n",
        "(Remember that Numpy is a linear algebra library that works most efficiently with vector and matrix operations, try to define all your formulas in vector and matrix form, rather than using loops!)"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "V6Y5ebQLj--W",
        "colab_type": "text"
      },
      "source": [
        "### Defining helper functions\n",
        "Begin by defining some re-usable helper functions. You may want to look ahead to the LinearModel class before implementing these to see how they get used. "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "vzxWhYPVj-et",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "def softmax(logits):\n",
        "  \"\"\"Convert un-normalised model scores(logits) into a probability distribution.\n",
        "\n",
        "  Args:\n",
        "    logits: The un-normalised scores assigned by the model.\n",
        "  \"\"\"\n",
        "  exp_logits = np.exp(logits)\n",
        "  probs = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n",
        "  return probs\n",
        "\n",
        "def cross_entropy(predictions, targets):\n",
        "  \"\"\"Calculate the cross entropy loss given some predictions and target (true) values.\n",
        "\n",
        "  Args:\n",
        "    predictions: The model predictions (of shape [num_examples, num_classes])\n",
        "    targets: The correct labels for the data (of shape [num_examples])\n",
        "  \"\"\"\n",
        "  num_examples = predictions.shape[0]\n",
        "  correct_logprobs = -np.log(predictions[range(num_examples), targets])\n",
        "  crossentropy = np.sum(correct_logprobs) / num_examples\n",
        "  return crossentropy\n",
        "\n",
        "def l2_loss(parameters):\n",
        "  \"\"\"Calculate the L2 regularisation of a list of parameters.\"\"\"\n",
        "  reg = 0.0\n",
        "  for param in parameters:\n",
        "    reg += 0.5 * reg_lambda * np.sum(param * param)\n",
        "  return reg"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "7VMrjzqdnUzW",
        "colab_type": "text"
      },
      "source": [
        "### Define the hyperparameters\n",
        "\n",
        "Model hyperparameters include all choices about a model that are made prior to training. In a sense, these are the \"meta parameters\": parameters chosen by the practitioner and are not set by the optimization algorithm. This includes choices of learning rate, number of examples in a batch, etc."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "PAFbADHinYZl",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "learning_rate = 1e-0  # How far along the gradient do we want to travel when \n",
        "                      # doing gradient descent?\n",
        "reg_lambda = 1e-3  # Regularization strength.\n",
        "\n",
        "# Define the initial random value of W here so we can re-use it later.\n",
        "W_init = 0.01 * np.random.randn(dimensions, num_classes)"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "LksU46NvBjlt",
        "colab_type": "text"
      },
      "source": [
        "### Defining the linear model\n",
        "Now we define the linear model itself. We put this in a class so that we can think of it as a \"black box\" that takes in our inputs and returns some predictions and a loss value that tells us how good our predictions are. We can also update the model using its update method. Doing it this way gives a clean separation between the model and training of the model and will be a useful pattern to use going forward."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "QzlF2JiS2d5E",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "class LinearModel(object):\n",
        "  def __init__(self):\n",
        "    # Initialize the model parameters.\n",
        "    self.W = np.copy(W_init)\n",
        "    self.b = np.zeros((1, num_classes))\n",
        "  \n",
        "  def predictions(self, X):\n",
        "    \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
        "    # Evaluate class scores/\"logits\": [points_per_class*num_classes x num_classes].\n",
        "    logits = self.get_logits(X)\n",
        "\n",
        "    # Compute the class probabilities.\n",
        "    probs = softmax(logits)\n",
        "    \n",
        "    return probs\n",
        "  \n",
        "  def loss(self, probs, y):\n",
        "    \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
        "    num_examples = probs.shape[0]\n",
        "    data_loss = cross_entropy(probs, y)\n",
        "    regulariser = l2_loss([self.W])\n",
        "    return data_loss + regulariser\n",
        "  \n",
        "  def update(self, probs, X, y):  \n",
        "    \"\"\"Update the model parameters using back-propagation and gradient descent.\"\"\"\n",
        "    # Calculate the gradient of the loss with respect to logits\n",
        "    dlogits = self.derivative_loss_logits(probs, y)  \n",
        "    \n",
        "    # Gradient of the loss wrt W\n",
        "    dW = self.derivative_loss_W(X, dlogits)\n",
        "    \n",
        "    # Gradient of the loss wrt b\n",
        "    db = self.derivative_loss_b(dlogits)\n",
        "    \n",
        "    # Don't forget the gradient on the regularization term.\n",
        "    dW += self.derivative_regularisation()\n",
        "    \n",
        "    # Perform a parameter update.\n",
        "    self.W += -learning_rate * dW\n",
        "    self.b += -learning_rate * db\n",
        "    \n",
        "  \n",
        "  ##### Now we define some helper functions   \n",
        "  # (This is probably where students will have to add lines of code)\n",
        "  def get_logits(self, X):\n",
        "    \"\"\"Calculate the un-normalised model scores.\n",
        "\n",
        "    Args:\n",
        "      X: The input values.\n",
        "    \"\"\"\n",
        "    return np.dot(X, self.W) + self.b \n",
        "\n",
        "  def derivative_loss_logits(self, logits, y):\n",
        "    \"\"\"Calculate the derivative of the loss with respect to logits.\"\"\"\n",
        "    num_examples = y.shape[0]\n",
        "    dlogits = logits\n",
        "    dlogits[range(num_examples),y] -= 1\n",
        "    dlogits /= num_examples\n",
        "    return dlogits\n",
        "  \n",
        "  def derivative_loss_W(self, X, dlogits):\n",
        "    \"\"\"Calculate the derivative of the loss wrt W.\"\"\"\n",
        "    return np.dot(X.T, dlogits)\n",
        "  \n",
        "  def derivative_loss_b(self, dlogits):\n",
        "    \"\"\"Calculate the derivative of the loss wrt b.\"\"\"\n",
        "    return np.sum(dlogits, axis=0, keepdims=True)\n",
        "  \n",
        "  def derivative_regularisation(self):\n",
        "    return reg_lambda * self.W   "
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "tc3wrrwVCQNU",
        "colab_type": "text"
      },
      "source": [
        "### Training the linear model\n",
        "Now that we've defined our \"black box\" linear model. We can train it on our dummy spiral dataset"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "ARwVZj5zEPTv",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "# Define a function that trains a model for a given number of epochs\n",
        "def train_model(model, epochs, report_every):\n",
        "  for i in xrange(epochs):\n",
        "  \n",
        "    # Get the model predictions for our spiral dataset X\n",
        "    probs = model.predictions(X)\n",
        "\n",
        "    # Compute the loss\n",
        "    loss = model.loss(probs, y)\n",
        "\n",
        "    # Print the loss value every `report_every` steps.\n",
        "    if i % report_every == 0:\n",
        "      print \"iteration %d: loss %f\" % (i, loss)\n",
        "\n",
        "    # Use back-propagation to update the model parameters:\n",
        "    model.update(probs, X, y)  "
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "OuR6eFwoCXcf",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 377
        },
        "outputId": "fd8902fa-461f-4d8e-9e1a-2e10d39999ea",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706247144,
          "user_tz": -60,
          "elapsed": 267,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# Create an instance of our LinearModel\n",
        "linear_model = LinearModel()\n",
        "\n",
        "# Now we train the linear model for 200 epochs\n",
        "train_model(linear_model, 200, 10)"
      ],
      "cell_type": "code",
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration 0: loss 1.096919\n",
            "iteration 10: loss 0.917310\n",
            "iteration 20: loss 0.851535\n",
            "iteration 30: loss 0.822352\n",
            "iteration 40: loss 0.807594\n",
            "iteration 50: loss 0.799452\n",
            "iteration 60: loss 0.794683\n",
            "iteration 70: loss 0.791765\n",
            "iteration 80: loss 0.789921\n",
            "iteration 90: loss 0.788726\n",
            "iteration 100: loss 0.787937\n",
            "iteration 110: loss 0.787408\n",
            "iteration 120: loss 0.787049\n",
            "iteration 130: loss 0.786803\n",
            "iteration 140: loss 0.786633\n",
            "iteration 150: loss 0.786514\n",
            "iteration 160: loss 0.786431\n",
            "iteration 170: loss 0.786373\n",
            "iteration 180: loss 0.786331\n",
            "iteration 190: loss 0.786302\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "1gPfOe1E3W5j",
        "colab_type": "text"
      },
      "source": [
        "### Evaluating the model\n",
        "The training of the model should have converged to a value around 0.786 if you used the default data parameters earlier. (Convergence means that the loss decreases to a point and then stops decreasing). But how do we interpret this? Is our model actually good at making predictions? Let's work out the **accuracy** of the model to see:"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "PH-cpnO-Er6F",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "# Define a function that calcuates and prints the accuracy of a model's predictions\n",
        "def evaluate_model(model):\n",
        "  # Get the probabilites/scores that the model assigns to each class for each X datapoint.\n",
        "  scores = model.get_logits(X)  # The shape of scores is [num_data_points, num_classes]\n",
        "\n",
        "  # The index of the maximum score along the 2nd dimension is the class that the model thinks is most likely (y^) for each datapoint.\n",
        "  predicted_class = np.argmax(scores, axis=1)\n",
        "\n",
        "  # What proportion of the class predictions made by the model (y^) agree with the true class values (y) ?\n",
        "  print 'Accuracy: %.2f' % (np.mean(predicted_class == y))  "
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "KC_V-9pn3Zpi",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 54
        },
        "outputId": "f8370335-7a2f-4b66-8cde-8a69440fe0bb",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706247541,
          "user_tz": -60,
          "elapsed": 168,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# Now evaluate the trained linear model\n",
        "evaluate_model(linear_model)"
      ],
      "cell_type": "code",
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy: 0.49\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "z_b6b1GyGmod",
        "colab_type": "text"
      },
      "source": [
        "This is not a very good result (we are misclassifying around 50% of the data points, and these are data points that we've seen before!), lets visualise the decision boundary to determine what's going on."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "i00J82lT3iKt",
        "colab_type": "text"
      },
      "source": [
        "### Visualizing the linear model's decision boundary\n",
        "\n",
        "Let's visualize the decision boundary of this linear classifier on the swiss roll dataset.\n"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "2qtWT9HYlwZ2",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "# Define a function that plots the decision boundary of a model\n",
        "def plot_decision_boundary(X, model):\n",
        "  \"\"\"Overlays the classifier's decision boundary on the dataset [X, y].\n",
        "  \n",
        "  Args:\n",
        "    X: 2-d matrix input data,\n",
        "    model: The model to evaluate\n",
        "  \"\"\"\n",
        "  \n",
        "  step_size = 0.02  # Discretization step-size\n",
        "  \n",
        "  # Get the boundaries of the dataset.\n",
        "  x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
        "  y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
        "  # Generate a grid of points, step_size apart, over the above region.\n",
        "  xx, yy = np.meshgrid(np.arange(x_min, x_max, step_size),\n",
        "                       np.arange(y_min, y_max, step_size))\n",
        "  \n",
        "  # Flatten the data and get the logits of the classifier (the \"scores\") for \n",
        "  #   each point in the generated mesh-grid.\n",
        "  meshgrid_matrix = np.c_[xx.ravel(), yy.ravel()]\n",
        "  Z = model.get_logits(meshgrid_matrix)\n",
        "  \n",
        "  # Get the class predictions for each point.\n",
        "  Z = np.argmax(Z, axis=1)\n",
        "  Z = Z.reshape(xx.shape)\n",
        "  \n",
        "  # Overlay both of these on one figure.\n",
        "  fig = plt.figure()\n",
        "  plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)\n",
        "  plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)\n",
        "  plt.xlim(xx.min(), xx.max())\n",
        "  plt.ylim(yy.min(), yy.max())\n",
        "  #fig.savefig('spiral_linear.png')"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "-oAjAAmp3mK-",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 514
        },
        "outputId": "f6a06361-109c-41c5-dfb7-2ac4817c71b6",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706248226,
          "user_tz": -60,
          "elapsed": 459,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# Plot the decision boundary of our trained linear model on the dataset X\n",
        "plot_decision_boundary(X, linear_model)"
      ],
      "cell_type": "code",
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PP8wencz0vAw2vbGdD98t5KN3drHykcm+JPppk7I5eOBcwP0H9p9l2iT/pVdF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\ngg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0xff003d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "AjDp48EyGymu",
        "colab_type": "text"
      },
      "source": [
        "What can you deduce from this decision boundary? Does it help explain why the linear model makes bad predictions? "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "69-CauTN3z5a",
        "colab_type": "text"
      },
      "source": [
        "## Using a nonlinear model\n",
        "\n",
        "The linear model resulted in decision boundaries that were straight lines in 2D space. Using these straight lines, it is impossible to accurately separate our spiral-shaped data. Let's see how converting our model to be a non-linear function of its parameters could resolve this. "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "w4yeK8xcDqUv",
        "colab_type": "text"
      },
      "source": [
        "### Define helper functions\n",
        "We will re-use the helper functions we defined earlier, but we also need a new helper **activation function** to introduce non-linearity into our model."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "gEkGKe7ZD35_",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "def relu(value):\n",
        "  \"\"\" ReLU is the \"Rectified Linear Unit activation function\", defined as:\n",
        "        relu(x) = x if x > 0, and 0 if x <= 0\n",
        "  \"\"\"\n",
        "  return np.maximum(0, value)  "
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "szd3eAeboLnc",
        "colab_type": "text"
      },
      "source": [
        "### Define the hyperparameters"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "PQf5k56goOV5",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "learning_rate = 1e-0  # How far along the gradient do we want to travel when doing \n",
        "                      # gradient descent?\n",
        "reg_lambda = 1e-3  # Regularization strength\n",
        "num_hidden = 100  # Size of hidden layer.\n",
        "\n",
        "non_linear_W_init = 0.01 * np.random.randn(dimensions, num_hidden)\n",
        "non_linear_W2_init = 0.01 * np.random.randn(num_hidden, num_classes)\n"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "vOZd0ZxxD7Um",
        "colab_type": "text"
      },
      "source": [
        "### Define the non-linear model\n",
        "We define this as a class with the same interface as the LinearModel. This way we can reuse exactly the same training and evaluation functions we defined earlier!"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "1HsSVOuQ37R0",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "class NonLinearModel(object):\n",
        "  def __init__(self):\n",
        "    # Initialize the model parameters.\n",
        "    self.W = non_linear_W_init\n",
        "    self.b = np.zeros((1, num_hidden))\n",
        "    self.W2 = non_linear_W2_init\n",
        "    self.b2 = np.zeros((1, num_classes))\n",
        "\n",
        "  def predictions(self, X):\n",
        "    \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
        "    # Evaluate class scores/\"logits\": [points_per_class*num_classes x num_classes].\n",
        "    logits = self.get_logits(X)\n",
        "\n",
        "    # Compute the class probabilities.\n",
        "    probs = softmax(logits)\n",
        "    \n",
        "    return probs\n",
        "  \n",
        "  def loss(self, probs, y):\n",
        "    \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
        "    data_loss = cross_entropy(probs, y)\n",
        "    regulariser = l2_loss([self.W, self.W2])\n",
        "    return data_loss + regulariser\n",
        "  \n",
        "  def update(self, probs, X, y):  \n",
        "    \"\"\"Update the model parameters using back-propagation and gradient descent.\"\"\"\n",
        "    hidden_output = self.hidden_layer(X)\n",
        "    \n",
        "    # Calculate the gradient of the loss with respect to logits\n",
        "    dlogits = self.derivative_loss_logits(probs, y)  \n",
        "    \n",
        "    # Backpropate the gradient to the parameters.\n",
        "    \n",
        "    # We first backprop into parameters W2 and b2.\n",
        "    dW2 = self.derivative_loss_W2(hidden_output, dlogits)\n",
        "    db2 = self.derivative_loss_b2(dlogits)\n",
        "\n",
        "    # Next, backprop into the hidden layer.\n",
        "    dhidden = self.derivative_hidden(hidden_output, dlogits)\n",
        "\n",
        "    # Finally, backprop into W,b.\n",
        "    dW = self.derivative_loss_W(X, dhidden)\n",
        "    db = self.derivative_loss_b(dhidden)\n",
        "\n",
        "    # Add regularization gradient contribution.\n",
        "    dW2 += self.derivative_regularisation_W2()\n",
        "    dW += self.derivative_regularisation_W()\n",
        "\n",
        "    # Perform a parameter update (one step of gradient descent).\n",
        "    self.W += -learning_rate * dW\n",
        "    self.b += -learning_rate * db\n",
        "    self.W2 += -learning_rate * dW2\n",
        "    self.b2 += -learning_rate * db2\n",
        "    \n",
        "\n",
        "  ## DEFINE THE MODEL HELPER FUNCTIONS  \n",
        "  \n",
        "  def hidden_layer(self, X):\n",
        "    \"\"\"Calculate the output of the hidden layer.\"\"\"\n",
        "    return relu(np.dot(X, self.W) + self.b)\n",
        "    \n",
        "  def get_logits(self, X):\n",
        "    \"\"\"Calculate the logits from the input data X.\"\"\"\n",
        "    hidden_output = self.hidden_layer(X)\n",
        "    logits = np.dot(hidden_output, self.W2) + self.b2\n",
        "    return logits\n",
        "  \n",
        "  def derivative_loss_logits(self, logits, y):\n",
        "    \"\"\"Calculate the derivative of the loss with respect to logits.\"\"\"\n",
        "    num_examples = y.shape[0]\n",
        "    dlogits = logits\n",
        "    dlogits[range(num_examples),y] -= 1\n",
        "    dlogits /= num_examples\n",
        "    return dlogits\n",
        "  \n",
        "  def derivative_loss_W2(self, hidden_output, dlogits):\n",
        "    \"\"\"Calculate the derivative of the loss wrt W2.\"\"\"\n",
        "    dW2 = np.dot(hidden_output.T, dlogits)\n",
        "    return dW2\n",
        "  \n",
        "  def derivative_loss_b2(self, dlogits):\n",
        "    \"\"\"Calculate the derivative of the loss wrt b2.\"\"\"\n",
        "    return np.sum(dlogits, axis=0, keepdims=True)\n",
        "    \n",
        "  def derivative_hidden(self, hidden_output, dlogits):\n",
        "    \"\"\"Calculate the derivative of the loss wrt the hidden layer.\"\"\"\n",
        "    # Calculate the gradient as if the hidden layer were a normal linear layer. \n",
        "    dhidden = np.dot(dlogits, self.W2.T)\n",
        "    \n",
        "    # Now take the Relu non-linearity into account\n",
        "    dhidden[hidden_output <= 0] = 0\n",
        "    \n",
        "    return dhidden\n",
        "    \n",
        "  def derivative_loss_W(self, X, dhidden):\n",
        "    \"\"\"Calculate the derivative of the loss wrt W.\"\"\"\n",
        "    return np.dot(X.T, dhidden)\n",
        "  \n",
        "  def derivative_loss_b(self, dhidden):\n",
        "    \"\"\"Calculate the derivative of the loss wrt b.\"\"\"\n",
        "    return np.sum(dhidden, axis=0, keepdims=True)\n",
        "  \n",
        "  def derivative_regularisation_W(self):\n",
        "    \"\"\"Calculate the gradient of the L2 loss wrt W.\"\"\"\n",
        "    return reg_lambda * self.W \n",
        "  \n",
        "  def derivative_regularisation_W2(self):\n",
        "    \"\"\"Calculate the gradient of the L2 loss wrt W2.\"\"\"\n",
        "    return reg_lambda * self.W2"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "f8tDrHHRFdcs",
        "colab_type": "text"
      },
      "source": [
        "### Train the non linear model"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "ntVMzdM8Fg9u",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 10
            }
          ],
          "height": 207
        },
        "outputId": "efe5ed1d-3754-4288-9751-584680ff2330",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706264605,
          "user_tz": -60,
          "elapsed": 15436,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# Create an instance of our non-linear model.\n",
        "non_linear_model = NonLinearModel()\n",
        "\n",
        "# Train the model for 10000 epochs\n",
        "train_model(non_linear_model, 10000, 1000)"
      ],
      "cell_type": "code",
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration 0: loss 1.098637\n",
            "iteration 1000: loss 0.294363\n",
            "iteration 2000: loss 0.266592\n",
            "iteration 3000: loss 0.251493\n",
            "iteration 4000: loss 0.248266\n",
            "iteration 5000: loss 0.247068\n",
            "iteration 6000: loss 0.246389\n",
            "iteration 7000: loss 0.245914\n",
            "iteration 8000: loss 0.245257\n",
            "iteration 9000: loss 0.244947\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "eEseRPX_4C6g",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 54
        },
        "outputId": "ed8121b9-2f27-4675-8509-22d5d7f3ff2a",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706264807,
          "user_tz": -60,
          "elapsed": 185,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# evaluate training set accuracy of the non-linear model\n",
        "evaluate_model(non_linear_model)"
      ],
      "cell_type": "code",
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy: 0.98\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "tmcEejSmIGLc",
        "colab_type": "text"
      },
      "source": [
        "Much better! Is it possible to get to 100%? What factors about the dataset would influence this?"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "Fu5JRcMtYOms",
        "colab_type": "text"
      },
      "source": [
        "### Visualize the nonlinear model's decision boundary\n",
        "Lets see what the decision boundary of the non-linear model looks like"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "gb3KwDN84P8z",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 514
        },
        "outputId": "e8e4b681-a79f-41ed-824c-4d66e7545206",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502706265384,
          "user_tz": -60,
          "elapsed": 531,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# Plot the decision boundary of the non-linear model on the dataset X\n",
        "plot_decision_boundary(X, non_linear_model)"
      ],
      "cell_type": "code",
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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Ok0gO+ggjAGEk0tvRSkvlReKzF4x8kcqIQ1YaNHjcrkA2d0K2Z3qAmTukZrM5iIgJ9wpa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\n3vPQ7Xbzxn/u5ZV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UscNkSmI05y7XYYkJIzU/lQOnr2DWaFi/Zj4pSTGUfHGGa7Hh5OYO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\nwr/7d08yMRHlwBufsGVtLdWVc/+C/vH/00rpeRc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eWewpss8Ci3mNuk4fxZfIryycziQI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WbUYT5c3VmNU+lMRyesSIc7bMmSAkaThM+GB7A2Y5FmpQu0W4ZwqaMLsLmg0WvwudK1UCvDszIW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\nEcSwRURERBRB/x8NPCRJfWPGTwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0xff0ae50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "RsR2U3klH5SU",
        "colab_type": "text"
      },
      "source": [
        "# Using TensorFlow\n",
        "\n",
        "The above models worked well, but it was a little tedius to implement the gradients by hand. Let's re-implement the above models using TensorFlow and see how it compares."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "OGrFDQ1KGmv8",
        "colab_type": "text"
      },
      "source": [
        "### Create a session\n",
        "\n",
        "TensorFlow makes use of \"[sessions](https://www.tensorflow.org/versions/r0.12/api_docs/python/client/session_management)\" to encapsulate the environment and manage the resources within which graphs are executed. Sessions are also used to run the graph operations you are interested in. There are different ways to create sessions, but we will make use of the [interactive session](https://www.tensorflow.org/versions/r0.12/api_docs/python/client/session_management#InteractiveSession), which sets a default environment that will be shared across all code cells, and avoids the need to explicitly pass around a reference to the current session object."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "COL_PqgMmx5Y",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "# First we need to import TensorFlow.\n",
        "import tensorflow as tf\n",
        "\n",
        "tf.reset_default_graph() # Clear the graph between different invocations.\n",
        "sess = tf.InteractiveSession() # Create and register the default Session.\n"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "yiseUdITmzT0",
        "colab_type": "text"
      },
      "source": [
        "### Define hyperparameters\n"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "MMTIs4bYKgCX",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 232
        },
        "outputId": "7b6c83e3-3660-4dee-d5b3-69828f02c7a8",
        "executionInfo": {
          "status": "error",
          "timestamp": 1502727861859,
          "user_tz": -60,
          "elapsed": 1144,
          "user": {
            "displayName": "Stephan Gouws",
            "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
            "userId": "102606466886131565871"
          }
        }
      },
      "source": [
        "### HYPERPARAMETERS\n",
        "learning_rate = 1e-0\n",
        "reg_lambda = 1e-3\n",
        "training_iterations = 200  # 'epochs'\n",
        "batch_size = X.shape[0]  # The whole dataset; i.e. batch gradient descent.\n",
        "display_step = 10  # How often should we print our results\n",
        "###\n",
        "\n",
        "# Network Parameters\n",
        "num_input = 2 # 2-dimensional input data\n",
        "num_classes = 3 # red, yellow and blue!"
      ],
      "cell_type": "code",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[1;32m<ipython-input-1-9f1ac3bd53be>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mreg_lambda\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1e-3\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mtraining_iterations\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m200\u001b[0m  \u001b[1;31m# 'epochs'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mbatch_size\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m  \u001b[1;31m# The whole dataset; i.e. batch gradient descent.\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      5\u001b[0m \u001b[0mdisplay_step\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m  \u001b[1;31m# How often should we print our results\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;31m###\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;31mNameError\u001b[0m: name 'X' is not defined"
          ]
        }
      ]
    },
    {
      "metadata": {
        "id": "4NgyMmZeRtZX",
        "colab_type": "text"
      },
      "source": [
        "### Graph input placeholders\n",
        "\n",
        "Graphs provide an abstract definition of what computations we want to perform on our data. TensorFlow provides [placeholders](https://www.tensorflow.org/api_docs/python/tf/placeholder) as a means for injecting data into our graph at execution time, through a process called \"feeding\"."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "9gDraGrsRw-4",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 181
        },
        "outputId": "565fc4b2-7e8a-46db-dacb-27eebed4fdfd",
        "executionInfo": {
          "status": "error",
          "timestamp": 1502706392889,
          "user_tz": -60,
          "elapsed": 399,
          "user": {
            "displayName": "Ulrich Paquet",
            "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
            "userId": "117228953648657363788"
          }
        }
      },
      "source": [
        "# placeholders for the inputs and labels. We will 'feed' these to the graph.\n",
        "x_tf = tf.placeholder(tf.float32, [None, num_input])\n",
        "y_tf = tf.placeholder(tf.int32, [None])"
      ],
      "cell_type": "code",
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[1;32m<ipython-input-76-5abfc02f5cd5>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mx_tf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplaceholder\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat32\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnum_input\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0my_tf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplaceholder\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mint32\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;31mNameError\u001b[0m: name 'num_input' is not defined"
          ]
        }
      ]
    },
    {
      "metadata": {
        "id": "eyfHfdka9NKY",
        "colab_type": "text"
      },
      "source": [
        "### Define helper functions\n",
        "Let's create some helper functions that we can re-use in the Tensorflow models. We need fewer than before because Tensorflow already provides lots of useful functions out the box! "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "CRWJAimx9MXm",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "def cross_entropy_tf(predictions, targets):\n",
        "  \"\"\"Calculate the cross entropy loss given some model predictions and target (true) values.\"\"\"\n",
        "  targets = tf.one_hot(targets, num_classes)\n",
        "  return tf.reduce_mean(-tf.reduce_sum(targets * tf.log(predictions), axis=1))"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "YocWzSZFXMQL",
        "colab_type": "text"
      },
      "source": [
        "## Linear model"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "YlhRC4-gWSUU",
        "colab_type": "text"
      },
      "source": [
        "We construct a linear model with the same architecture as above. Notice how TensorFlow provides out-the-box many of the functions we had to previously define ourselves. There is another major difference between the TensorFlow code and Numpy code that may not be immediately apparant. In TensorFlow, when we call functions like tf.nn.softmax() we are not performing a computation, rather we are defining an operation in a calculation graph that gets run later. "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "UcS63poGGTYr",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "class TFLinearModel(object):\n",
        "  def __init__(self):\n",
        "    # Initialise the variables\n",
        "    # Tensorflow variables can be updated automatically by optimisers.\n",
        "    self.W = tf.Variable(W_init, dtype=tf.float32)\n",
        "    self.b = tf.Variable(tf.zeros([num_classes]), dtype=tf.float32)\n",
        "\n",
        "  def predictions(self, X):\n",
        "    \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
        "    logits = self.get_logits(X)\n",
        "\n",
        "    # Compute the class probabilities.\n",
        "    probs = tf.nn.softmax(logits)\n",
        "    \n",
        "    return probs\n",
        "  \n",
        "  def loss(self, probs, y):\n",
        "    \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
        "    data_loss = cross_entropy_tf(probs, y)\n",
        "    regulariser = reg_lambda * tf.nn.l2_loss(self.W)\n",
        "    return data_loss + regulariser\n",
        "    \n",
        "  def get_logits(self, X):\n",
        "    return tf.add(tf.matmul(X, self.W), self.b)"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "tZMShhHyOYAq",
        "colab_type": "text"
      },
      "source": [
        "Remember, up until now we've been defining (constructing) a computation graph. Now we can run this graph multiple times, feeding in our data, in a training loop. The training loop is a bit more complex than before, but by wrapping up our models in classes, we can again benefit from re-using the same training loop on multiple models."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "CLlW9MiUHutE",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "def train_tf_model(tf_model, epochs, report_every):\n",
        "  \n",
        "  # Get the op which, when executed, will initialize the variables.\n",
        "  init = tf.global_variables_initializer()\n",
        "  \n",
        "  # Get the model probabilities\n",
        "  probs = tf_model.predictions(x_tf)\n",
        "  \n",
        "  # Get the model loss\n",
        "  loss = tf_model.loss(probs, y_tf)\n",
        "  \n",
        "  # Create a Gradient Descent optimizer with our hyper-parameter learning rate \n",
        "  optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
        "  \n",
        "  # Now we create an op that computes the gradient of the loss with respect \n",
        "  # to the model parameters and performs one update to all of the parameters \n",
        "  # in the direction of their gradients. \n",
        "  optimizer_step = optimizer.minimize(loss)\n",
        "  \n",
        "  # Actually initialize the variables (run the op).\n",
        "  sess.run(init)\n",
        "\n",
        "  # Training cycle.\n",
        "  for iteration in range(epochs):\n",
        "      avg_cost = 0.\n",
        "      total_batch = int(X.shape[0] / batch_size)\n",
        "\n",
        "      # Loop over all batches.\n",
        "      for i in range(total_batch):\n",
        "\n",
        "          batch_x = X[i * batch_size : (i + 1) * batch_size, :]\n",
        "          batch_y = y[i * batch_size : (i + 1) * batch_size]\n",
        "\n",
        "          # Run optimization op (backprop) and cost op (to get loss value).\n",
        "          _, c = sess.run([optimizer_step, loss], feed_dict={x_tf: batch_x,\n",
        "                                                             y_tf: batch_y})\n",
        "          # Compute average loss.\n",
        "          avg_cost += c / total_batch\n",
        "\n",
        "      # Display logs per iteration/epoch step.\n",
        "      if iteration % report_every == 0:\n",
        "          print \"Iteration:\", '%04d' % (iteration + 1), \"cost=\", \\\n",
        "              \"{:.9f}\".format(avg_cost)\n",
        "\n",
        "  print \"Optimization Finished!\""
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "jQt4FzSbHvKq",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 2
            }
          ],
          "height": 374
        },
        "outputId": "0fe15e6a-5268-41f7-f174-8ff463ff2e90",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502560289590,
          "user_tz": -60,
          "elapsed": 384,
          "user": {
            "displayName": "Stephan Gouws",
            "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
            "userId": "102606466886131565871"
          }
        }
      },
      "source": [
        "# Intialize our TensorFlow Linear Model\n",
        "tf_linear_model = TFLinearModel()\n",
        "\n",
        "# Train the model for 200 epochs\n",
        "train_tf_model(tf_linear_model, 200, 10)"
      ],
      "cell_type": "code",
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration: 0001 cost= 1.096919417\n",
            "Iteration: 0011 cost= 0.917309999\n",
            "Iteration: 0021 cost= 0.851534605\n",
            "Iteration: 0031 cost= 0.822352290\n",
            "Iteration: 0041 cost= 0.807593584\n",
            "Iteration: 0051 cost= 0.799452126\n",
            "Iteration: 0061 cost= 0.794682562\n",
            "Iteration: 0071 cost= 0.791764617\n",
            "Iteration: 0081 cost= 0.789920688\n",
            "Iteration: 0091 cost= 0.788726211\n",
            "Iteration: 0101 cost= 0.787937403\n",
            "Iteration: 0111 cost= 0.787408412\n",
            "Iteration: 0121 cost= 0.787049174\n",
            "Iteration: 0131 cost= 0.786802888\n",
            "Iteration: 0141 cost= 0.786632478\n",
            "Iteration: 0151 cost= 0.786513925\n",
            "Iteration: 0161 cost= 0.786430955\n",
            "Iteration: 0171 cost= 0.786372602\n",
            "Iteration: 0181 cost= 0.786331296\n",
            "Iteration: 0191 cost= 0.786302209\n",
            "Optimization Finished!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Ltr_n567HPEj",
        "colab_type": "text"
      },
      "source": [
        "**NOTE**: Our final cost (0.786) matches the final cost reached in our Numpy implementation above. This is not by accident, but because we used exactly the same initial values for the parameters, the same optimizer with the same update rules on the same data. (The exact value may be different if you changed some of the HyperParameters)\n",
        "\n",
        "Notice how much less code we had to write for the TensorFlow model compared to the Numpy one earlier! TensorFlow is designed for deep learning and provides a number of common functions. In fact, it's possible to define a linear model like this in even fewer lines in TensorFlow, but we wanted to make this example as clear as possible!"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "1OFoR4Oz8CNF",
        "colab_type": "text"
      },
      "source": [
        "### Visualizing the linear model's decision boundary\n",
        "\n"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "i38AYE4F8Bal",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 494
        },
        "outputId": "a900b1bd-3e9c-4917-a590-14193c09dcc2",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502560157929,
          "user_tz": -60,
          "elapsed": 687,
          "user": {
            "displayName": "Avishkar Bhoopchand",
            "photoUrl": "//lh5.googleusercontent.com/-OainnMWSi6A/AAAAAAAAAAI/AAAAAAAAAOQ/eI7Z19q5v7E/s50-c-k-no/photo.jpg",
            "userId": "105781587643595215149"
          }
        }
      },
      "source": [
        "# Here we wrap the TensorFlow model so that it behaves more like a Numpy model \n",
        "# which the plot_decision_boundary function expects. Don't worry too much about \n",
        "# the details, it's just so we can visualise the decision boundary!\n",
        "\n",
        "class TFModelWrapper(object):\n",
        "  def __init__(self, model):\n",
        "    self._model = model\n",
        "  \n",
        "  def get_logits(self, x): \n",
        "    return tf.get_default_session().run(self._model.get_logits(x_tf),\n",
        "                                        feed_dict={x_tf : x,\n",
        "                                                   y_tf : np.zeros(x.shape[0])})\n",
        "  \n",
        "wrapper = TFModelWrapper(tf_linear_model)\n",
        "plot_decision_boundary(X, wrapper)"
      ],
      "cell_type": "code",
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PP8wencz0vAw2vbGdD98t5KN3drHykcm+JPppk7I5eOBcwP0H9p9l2iT/pVdF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\ngg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x1027fa10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "GRGbrnuyrNzh",
        "colab_type": "text"
      },
      "source": [
        "## Using a nonlinear classifier\n",
        "\n",
        "Let's replicate the nonlinear model in TensorFlow. TensorFlow saves us from writing more code as the model becomes more complex. In particular, this is because we don't have to implement the derivatives ourselves!"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "LrNH71Jv31RB",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "class TFNonLinearModel(object):\n",
        "  def __init__(self):\n",
        "    # Initialise the variables\n",
        "    # Tensorflow variables can be updated automatically by optimisers.\n",
        "    self.W = tf.Variable(non_linear_W_init, dtype=tf.float32)\n",
        "    self.b = tf.Variable(tf.zeros([num_hidden]), dtype=tf.float32)\n",
        "    self.W2 = tf.Variable(non_linear_W2_init, dtype=tf.float32)\n",
        "    self.b2 = tf.Variable(tf.zeros([num_classes]), dtype=tf.float32)\n",
        "\n",
        "  def predictions(self, X):\n",
        "    \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
        "    logits = self.get_logits(X)\n",
        "\n",
        "    # Compute the class probabilities.\n",
        "    probs = tf.nn.softmax(logits)\n",
        "    \n",
        "    return probs\n",
        "  \n",
        "  def loss(self, probs, y):\n",
        "    \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
        "    data_loss = cross_entropy_tf(probs, y)\n",
        "    regulariser = reg_lambda * tf.nn.l2_loss(self.W) + reg_lambda * tf.nn.l2_loss(self.W2)\n",
        "    return data_loss + regulariser\n",
        "    \n",
        "  def get_logits(self, X):\n",
        "    hidden_output = self.hidden_layer(X)\n",
        "    logits = tf.add(tf.matmul(hidden_output, self.W2), self.b2)\n",
        "    return logits\n",
        "  \n",
        "  def hidden_layer(self, X):\n",
        "    linear = tf.add(tf.matmul(X, self.W), self.b)\n",
        "    return tf.nn.relu(linear)"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "RI0a_no65COO",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 10
            }
          ],
          "height": 204
        },
        "outputId": "0db5bbc8-2228-4a68-89e7-1873c8af19f6",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502560198777,
          "user_tz": -60,
          "elapsed": 16655,
          "user": {
            "displayName": "Avishkar Bhoopchand",
            "photoUrl": "//lh5.googleusercontent.com/-OainnMWSi6A/AAAAAAAAAAI/AAAAAAAAAOQ/eI7Z19q5v7E/s50-c-k-no/photo.jpg",
            "userId": "105781587643595215149"
          }
        }
      },
      "source": [
        "# Create an instance of the TensorFlow Non Linear model\n",
        "tf_non_linear_model = TFNonLinearModel()\n",
        "\n",
        "# Train it for 10000 epochs\n",
        "train_tf_model(tf_non_linear_model, 10000, 1000)"
      ],
      "cell_type": "code",
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration: 0001 cost= 3.389798164\n",
            "Iteration: 1001 cost= 0.244746178\n",
            "Iteration: 2001 cost= 0.244569406\n",
            "Iteration: 3001 cost= 0.244453162\n",
            "Iteration: 4001 cost= 0.244375437\n",
            "Iteration: 5001 cost= 0.244325101\n",
            "Iteration: 6001 cost= 0.244291067\n",
            "Iteration: 7001 cost= 0.244269177\n",
            "Iteration: 8001 cost= 0.244246393\n",
            "Iteration: 9001 cost= 0.244226977\n",
            "Optimization Finished!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "7CKPywnwrUWo",
        "colab_type": "text"
      },
      "source": [
        "## Visualizing the Nonlinear Model's Decision Boundary"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "51oCM2Y_hh1b",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "height": 494
        },
        "outputId": "8d1a15af-61aa-4e3d-d757-1652e9b0fc48",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1502560215531,
          "user_tz": -60,
          "elapsed": 716,
          "user": {
            "displayName": "Avishkar Bhoopchand",
            "photoUrl": "//lh5.googleusercontent.com/-OainnMWSi6A/AAAAAAAAAAI/AAAAAAAAAOQ/eI7Z19q5v7E/s50-c-k-no/photo.jpg",
            "userId": "105781587643595215149"
          }
        }
      },
      "source": [
        "wrapper = TFModelWrapper(tf_non_linear_model)\n",
        "plot_decision_boundary(X, wrapper)"
      ],
      "cell_type": "code",
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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L557z7A3buXs1e945yO4ty3C5XBw+Xka/1Y5Bp2FNYT6Xr9axp7QSvV6Pw+bg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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x102b9950>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "pY8YwfFVo51Y",
        "colab_type": "text"
      },
      "source": [
        "This decision boundary looks very similar to the one obtained earlier, which is of course the goal, congrats!"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "qiseJLFuzyuM",
        "colab_type": "text"
      },
      "source": [
        "# Acknowledgements\n",
        "\n",
        "* http://cs.stanford.edu/people/karpathy/cs231nfiles/minimal_net.html \n",
        "* https://aqibsaeed.github.io/2016-07-07-TensorflowLR/\n",
        "\n"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "Cd5a1rucbH0x",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        ""
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    }
  ]
}