04-logistic-regression-training.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config IPCompleter.greedy=True\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn.preprocessing, sklearn.datasets, sklearn.model_selection\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous chapter, I introduced logistic regression and how it makes predictions. I as well pointed out, that unlike Perceptron, logistic regression returns the probability of datapoints belonging to the specific class. However, I didn't mention the training algorithm for it. That would be the content of this chapter.\n",
    "\n",
    "I also demonstrated the gradient descent algorithm in the second half of the previous chapter. There will be no surprise, that the gradient descent is the exact algorithm we are going to use in this chapter to train logistic regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression training\n",
    "\n",
    "We now should have all the knowledge we need to train logistic regression. For a reminder, the prediction of the logistic regression is:\n",
    "\n",
    "$$\n",
    "f(\\pmb{x})=\\frac{1}{1+e^{-\\pmb{x}\\pmb{w}^T}}\n",
    "$$\n",
    "\n",
    "In able to use gradient descent, we need some function, that the algorithm is going to optimize. That's why I showed a loss function. When we plug it in, we obtain the following formula.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}=\\frac{1}{2} \\sum_{i=0}^{n} \\left( t_i - f(\\pmb{x_i}) \\right)^2 = \\frac{1}{2} \\sum_{i=0}^{n} \\left( t_i - \\frac{1}{1+e^{-\\pmb{x}\\pmb{w}^T}} \\right)^2\n",
    "$$\n",
    "\n",
    "Now we want to update the weights, so we need to compute the gradient of the loss function with respect to weight (and we need to compute it for every weight). In this case, we can use the chain rule.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial w_i} = \\frac{\\partial \\mathcal{L}}{\\partial f(\\pmb{x})} \\cdot \\frac{\\partial f(\\pmb{x})}{\\partial \\pmb{x}\\pmb{w}^T} \\cdot \\frac{\\partial \\pmb{x}\\pmb{w}^T}{\\partial w_i}\n",
    "$$\n",
    "\n",
    "Then the gradient is easy to obtain (note that I mark $\\sigma(x)$ as the sigmoid function, i.e. $\\sigma(x)=\\frac{1}{1+e^{-x}}$ and $y_i$ as the prediction of the model, i.e. $y_i = \\sigma(\\pmb{x}\\pmb{w}^T)$.\n",
    "\n",
    "$$\\\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial w_i} = (t_i - y_i) \\cdot -\\sigma(\\pmb{x}\\pmb{w}^T)\\left( 1 - \\sigma(\\pmb{x}\\pmb{w}^T) \\right) \\cdot x_i\n",
    "$$\n",
    "\n",
    "> Note the minus in the second multiple. Because in the loss is $t_i - f(\\pmb{x})$ (minus in front of the prediction), the whole derivative is multiplied by $-1$. We can alternatively ignore the minus sign and then add the gradient to the weights, so the final formula would be $w_i = w_i + \\alpha \\frac{\\partial \\mathcal{L}}{\\partial w_i}$. I will stick with the proper mathematical formula - the gradient will be multiplied by $-1$ and I will subtract it from the weights. I just wanted to point this out, as the minus is sometimes forgotten.\n",
    "\n",
    "Finally, let's put it all to the code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will use the same class as in the previous chapter (`Neuron`) and I will implement the fit method. Don't forget that the gradient descent algorithm needs learning rate, I will put it in the constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, max_iters=100, random_state=None, learning_rate=0.001):\n",
    "        self.max_iters = max_iters\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        # Learning\n",
    "        for iteration in range(self.max_iters):\n",
    "            # shufle data randomly\n",
    "            permutation = self._rand.permutation(len(X))       \n",
    "            train_data = X[permutation]\n",
    "            train_labels = y[permutation]\n",
    "            # make gradient descent on each data point\n",
    "            for datapoint, target in zip(train_data, train_labels):\n",
    "                prediction = self.predict(datapoint)\n",
    "                # compute gradient\n",
    "                gradient = -(target - prediction) * (prediction * (1 - prediction)) * datapoint\n",
    "                # update weights\n",
    "                self._weights = self._weights - self._learning_rate * gradient\n",
    "                \n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm makes `self.max_iters` iterations and in each iteration, it randomly shuffles the data and performs gradient descent for each data point. That means the algorithm will make `self.max_iters * len(X)` gradient descent executions during training. Let's see how the algorithm behaves on some dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data, classes = sklearn.datasets.make_blobs(\n",
    "    n_samples=40,\n",
    "    n_features=2,\n",
    "    centers=[[-2, -2], [2, 2]],\n",
    "    random_state=42,\n",
    ")\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression\n",
    "train_data = np.hstack([data, np.ones((data.shape[0],1))])  # add bias\n",
    "n = Neuron(random_state=41, max_iters=500, learning_rate=0.01)\n",
    "n.fit(train_data, classes)\n",
    "\n",
    "# Visualize results\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "slope = - n._weights[0] / n._weights[1]\n",
    "bias = n._weights[2] / n._weights[1]\n",
    "plt.plot(\n",
    "    [data.min(axis=0)[0], data.max(0)[0]], \n",
    "    [slope * data.min(axis=0)[0] - bias, slope * data.max(axis=0)[0] - bias],\n",
    "    c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it, we have working logistic regression. What we have done is called **Stochastic Gradient Descent** - it computes the gradient for every sample and updates the weights accordingly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Batch gradient descent\n",
    "\n",
    "Let's think a little bit about the previous implementation. When we treat each data point separately, the optimum is \"put the separating hyperplane as far as possible from this data point\". In other words, when we have only one point and we want to minimalize the loss, the ideal separating hyperplane is infinitely far away from the datapoint (as only in infinity is the value of sigmoid 1 or 0, depending on the class). As a result, the algorithm can start oscillating the same way we have seen in the perceptron case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, what we really want, is the separating hyperplane that is optimal for all the data points we have. Let's look once again to the loss function.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}=\\frac{1}{2} \\sum_{i=0}^{n} \\left( t_i - f(\\pmb{x_i}) \\right)^2 \n",
    "$$\n",
    "\n",
    "We silently ignored the sum, or more precisely we used only one data point so the sum disappeared. Let's now fix the algorithm and instead of updating the weights based on the simple sample, we are going to update it based on all the samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, max_iters=100, random_state=None, learning_rate=0.001):\n",
    "        self.max_iters = max_iters\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        # Learning\n",
    "        for iteration in range(self.max_iters):\n",
    "            # predict the data\n",
    "            prediction = self.predict(X)\n",
    "            # table of gradient for each weights and gradient in the shape (samples,weights)\n",
    "            gradient = np.reshape(-(y - prediction) * (prediction * (1 - prediction)), newshape=(-1,1)) * X\n",
    "            # sum gradient over the samples\n",
    "            sum_gradient = np.sum(gradient, axis=0)\n",
    "            # update the weights\n",
    "            self._weights = self._weights - self._learning_rate * sum_gradient\n",
    "                \n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implementation is almost the same. We first generate all the predictions for all the data points (that mean `prediction` is a vector), then compute the gradient of loss and sigmoid (the result is still a vector) and finally multiply each value with the corresponding data point. Because `X` is a matrix, we need to reshape the gradient (of loss in respect to $\\pmb{x}\\pmb{w}^T$) to the matrix of size `(samples,features)` so we can multiply it with matrix `X` of shape `(samples,features)` (in this case the real shape is `(samples,1)`). We obtain the gradient with respect to weights for each data point (that is `gradient` variable in the shape `(samples,features)`) and we sum it over the data points. Finally, we update the weights.\n",
    "\n",
    "Note that we didn't shuffle the data this time, as it doesn't make sense. As the gradient for each data point is accounted for, the order of data points doesn't matter.\n",
    "\n",
    "Now let's train the logistic regression and see the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression\n",
    "train_data = np.hstack([data, np.ones((data.shape[0],1))])  # add bias\n",
    "n = Neuron(random_state=42, max_iters=1000, learning_rate=0.05)\n",
    "n.fit(train_data, classes)\n",
    "\n",
    "# Visualize results\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "slope = - n._weights[0] / n._weights[1]\n",
    "bias = n._weights[2] / n._weights[1]\n",
    "plt.plot(\n",
    "    [data.min(axis=0)[0], data.max(0)[0]], \n",
    "    [slope * data.min(axis=0)[0] - bias, slope * data.max(axis=0)[0] - bias],\n",
    "    c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result seems to be a bit better than in the previous case. The algorithm keeps about the same distance from the first class as from the second one. Using all the data points at once, the algorithm can find the global minimum and will not oscillate.\n",
    "\n",
    "Sometimes, this algorithm is just call **gradient descent** (instead of batch gradient descent). This makes sense as the algorithm in fact optimizes the global loss (instead of loss for individual data points). In most sources gradient descent (aka batch gradient descent) is shown first and then they start talking about its stochastic version. I decided to flip the order as from the implementation point of view, the stochastic version is easier to read (at least I believe so)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pros and cons\n",
    "\n",
    "Now, when we have seen batch gradient descent (I will refer to it as gradient descent so on) and stochastic gradient descent, we should talk about the differences and what are their pros and cons.\n",
    "\n",
    "+ Gradient descent is more stable and can result in faster convergence in some cases.\n",
    "+ Gradient descent is usually more efficient, as the operations can be vectorized (performing the same operation over multiple data at once) and thus the algorithm can be faster.\n",
    "+ Because the update is following the prediction, the algorithm can be parallelized into some level.\n",
    "+ Gradient descent can get stuck in the local optimum more easily.\n",
    "+ Gradient descent can have problems for big training sets, as the data don't need to fit into memory (nothing we would need to worry about so far). That may leads even to overflow when there are so many samples that the sum of gradients does not fit into memory (or the value would be simply too big).\n",
    "+ Stochastic gradient descent updates weights more often and thus can lead to faster convergence.\n",
    "+ Stochastic gradient descent is more computationally intensive.\n",
    "+ Stochastic gradient descent can oscillate too much and avoid the global optimum (even good local optimum).\n",
    "\n",
    "These algorithms are extremes, we update weights for every data point or for all the data points. It turns out the best approach is something between, which leads us to the following algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minibatch gradient descent\n",
    "\n",
    "Minibatch gradient descent combines the approaches above. We provide the algorithm another parameter (called batch size). Before each iteration, the algorithm shuffles the data and split them into subsets of the same size (based on the batch size parameter) called batches. The weights update is then done for each batch separately.\n",
    "\n",
    "The question you may ask is what to do with the last batch in case the number of data points is not divisible by the batch size. Well, we can ignore that batch or use it anyway. Note that the batch size should be in the order of magnitudes smaller than the data, so skipping it shouldn't have an impact on the training process. When we use it, the gradient can be noisier, but again, it shouldn't have an impact on the training process as there are plenty of batches before. I am going to use it, but if you don't want to, it is as easy as modifying the source code a little bit.\n",
    "\n",
    "Before we dig into the code, I want to point one more small change in the terminology. What we called iteration before is now called epoch - one epoch is done when the algorithm processes all the data points in the set. One iteration is then done when one batch is processed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, epochs=100, random_state=None, learning_rate=0.001, batch_size=16):\n",
    "        # use epochs instead of iterations\n",
    "        self.epochs = epochs\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        self._batch_size = batch_size\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        n_data = len(X)\n",
    "        # Learning\n",
    "        for epoch in range(self.epochs):\n",
    "            # shuffle the data\n",
    "            permutation = self._rand.permutation(n_data)\n",
    "            # for each batch\n",
    "            for batch_start in range(0, n_data, self._batch_size):\n",
    "                # get batch\n",
    "                batch_data = X[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                batch_target = y[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                # predict the data\n",
    "                prediction = self.predict(batch_data)\n",
    "                # table of gradient for each weights and gradient in the shape (samples,weights)\n",
    "                gradient = np.reshape(-(batch_target - prediction) * (prediction * (1 - prediction)), newshape=(-1,1)) * batch_data\n",
    "                # sum gradient over the samples\n",
    "                sum_gradient = np.sum(gradient, axis=0)\n",
    "                # update the weights\n",
    "                self._weights = self._weights - self._learning_rate * sum_gradient\n",
    "                \n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are not many changes. First of all, we shuffle the data as we did in the stochastic gradient descent. We then iterate over the data and use Python's slicing capability to obtain one batch (we need to index the original data by the permutations)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression\n",
    "train_data = np.hstack([data, np.ones((data.shape[0],1))])  # add bias\n",
    "n = Neuron(random_state=42, epochs=1000, learning_rate=0.01, batch_size=4)\n",
    "n.fit(train_data, classes)\n",
    "\n",
    "# Visualize results\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "slope = - n._weights[0] / n._weights[1]\n",
    "bias = n._weights[2] / n._weights[1]\n",
    "plt.plot(\n",
    "    [data.min(axis=0)[0], data.max(0)[0]], \n",
    "    [slope * data.min(axis=0)[0] - bias, slope * data.max(axis=0)[0] - bias],\n",
    "    c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is not surprising. In fact, all the algorithms look the same so far! Let's compare them on a bit more complicated example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation\n",
    "\n",
    "To evaluate the performance, we are going to stick with the MNIST dataset once again. However, to speed up the training process, I will make some modifications. Instead of using all the digits, I will focus on 4 and 9 as they are quite similar and our model can so far predict only two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = sklearn.datasets.fetch_openml('mnist_784', version=1, return_X_y=True)\n",
    "y = y.astype(int)\n",
    "one_or_seven_indices = np.logical_or(y == 4, y == 9)\n",
    "data = X[one_or_seven_indices].reshape(-1, 784)\n",
    "data[data < 128] = 0\n",
    "data[data > 0] = 1\n",
    "data = np.hstack([data, np.ones((data.shape[0],1))])\n",
    "target = y[one_or_seven_indices].reshape(-1)\n",
    "target[target==4] = 0\n",
    "target[target==9] = 1\n",
    "train_data, test_data, train_target, test_target = sklearn.model_selection.train_test_split(data, target, test_size=0.3, random_state=47)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may notice I modified the values as well. Instead of using the whole greyscale spectrum, I am going to use only black and white pictures. You can see a few examples in the following pictures. The two last lines of the code relabel the targets so class $0$ corresponds to $4$ and class $1$ to class $9$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(16,16))\n",
    "ax1.imshow(train_data[0, :784].reshape(28, 28))\n",
    "ax2.imshow(train_data[100, :784].reshape(28, 28))\n",
    "ax3.imshow(test_data[0, :784].reshape(28, 28))\n",
    "ax4.imshow(test_data[100, :784].reshape(28, 28))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will now modify the minibatch version of the code to return the losses and gradients as well. I will use it later to plot the progress. Moreover, I will allow passing test dataset to obtain real performance of the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, epochs=100, random_state=None, learning_rate=0.001, batch_size=16):\n",
    "        # use epochs instead of iterations\n",
    "        self.epochs = epochs\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        self._batch_size = batch_size\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y, Xtest=None, ytest=None):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        n_data = len(X)\n",
    "        # store gradients and losses\n",
    "        losses = np.zeros((self.epochs,))\n",
    "        gradients = np.zeros((self.epochs, int(np.ceil(X.shape[0] / self._batch_size))))\n",
    "        accuracies = np.zeros((self.epochs,))\n",
    "        # Learning\n",
    "        for epoch in range(self.epochs):\n",
    "            # shuffle the data\n",
    "            permutation = self._rand.permutation(n_data)\n",
    "            # for each batch\n",
    "            for batch_start in range(0, n_data, self._batch_size):\n",
    "                # get batch\n",
    "                batch_data = X[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                batch_target = y[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                # predict the data\n",
    "                prediction = self.predict(batch_data)\n",
    "                # table of gradient for each weights and gradient in the shape (samples,weights)\n",
    "                gradient = np.reshape(-(batch_target - prediction) * (prediction * (1 - prediction)), newshape=(-1,1)) * batch_data\n",
    "                # sum gradient over the samples\n",
    "                op_gradient = self._learning_rate * np.sum(gradient, axis=0)\n",
    "                # store losses and gradients\n",
    "                losses[epoch] += np.sum((batch_target - prediction) ** 2, axis=0)\n",
    "                gradients[epoch, int(batch_start / self._batch_size)] = op_gradient @ op_gradient\n",
    "                # update the weights\n",
    "                self._weights = self._weights - op_gradient\n",
    "                \n",
    "            # compute accuracy on the test set\n",
    "            if Xtest is not None and ytest is not None:\n",
    "                test_prediction = np.where(self.predict(Xtest) < 0.5, 0, 1) \n",
    "                accuracies[epoch] = np.sum(test_prediction == ytest) / len(ytest)\n",
    "                \n",
    "        return losses / X.shape[0], gradients, accuracies\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before I run the evaluation, I have this small helper class, that I am going to use to measure the execution time of individual configurations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TimeMeasure:\n",
    "    def __init__(self, label = ''):\n",
    "        self._label = label\n",
    "    def __enter__(self):\n",
    "        self._starttime = timeit.default_timer()\n",
    "        return self\n",
    "    def __exit__(self, *args):\n",
    "        end = timeit.default_timer()\n",
    "        print(f\"{self._label}{end - self._starttime:.3f}s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try different configurations and let's see how the gradient and loss will evolve.\n",
    "\n",
    "Note that in the standard approach people are using a test (or validation or development) set to measure the real error - generalization error on unseen data. However, in this case, we are not interested in error but rather in the behavior of the model, so it is fine not to use the test set. I will dive deeper into different datasets later on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stochastic gradient descent: 260.571s\n"
     ]
    }
   ],
   "source": [
    "sgd = Neuron(epochs=400, random_state=47, learning_rate=0.001, batch_size=1)\n",
    "with TimeMeasure('Stochastic gradient descent: '):\n",
    "    sgd_loss, sgd_gradient, sgd_acc = sgd.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minibatch of 4 samples: 77.973s\n"
     ]
    }
   ],
   "source": [
    "mbgd_4 = Neuron(epochs=400, random_state=47, learning_rate=0.001, batch_size=4)\n",
    "with TimeMeasure(\"Minibatch of 4 samples: \"):\n",
    "    mbgd_loss_4, mbgd_gradient_4, mbgd_acc_4 = mbgd_4.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minibatch of 32 samples: 20.982s\n"
     ]
    }
   ],
   "source": [
    "mbgd_32 = Neuron(epochs=400, random_state=53, learning_rate=0.001, batch_size=32)\n",
    "with TimeMeasure(\"Minibatch of 32 samples: \"):\n",
    "    mbgd_loss_32, mbgd_gradient_32, mbgd_acc_32 = mbgd_32.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minibatch of 128 samples: 12.639s\n"
     ]
    }
   ],
   "source": [
    "mbgd_128 = Neuron(epochs=400, random_state=53, learning_rate=0.001, batch_size=128)\n",
    "with TimeMeasure(\"Minibatch of 128 samples: \"):\n",
    "    mbgd_loss_128, mbgd_gradient_128, mbgd_acc_128 = mbgd_128.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Batch gradient descent: 21.716s\n"
     ]
    }
   ],
   "source": [
    "bgd = Neuron(epochs=400, random_state=47, learning_rate=0.001, batch_size=train_data.shape[0])\n",
    "with TimeMeasure('Batch gradient descent: '):\n",
    "    bgd_loss, bgd_gradient, bgd_acc = bgd.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5L8tAuoOCd2Jk0hL2UoQKffSTJ4vFO/kB8agwDlXWZXNqGy4OdSbOXZFqFsfrGQ6Vc9S6xEMJFkWTYC19I530pXspBBP47qkRvip8WlxodKPEcgHcoEukoQESiyBRi1c0eAWPUHzsnGAEJ9lAsQi5vmGM6xCprcBxHHzfx/d9Rg53MNzai58/NZ3gyNNtuOFu6jauJpQYDbD5kQxDhzrIdA8Sq6sAINXeix2bLOoXPVJdQ+RTebxCkd7WEXJZSzTuEC8PYX1Lb1cW1zFEEgHcWJxE0iER88nlDcF4hFhtGcYYsgMp0n2pU+nVQDTkYy2kM5Z0fxaLJVYeORmST7zmSGr0pHAIahpjZIfz+J4lm/FOm35QVe0SjgUZ6s2SOn0VMFwHquqCLK5LnHovz0MoHmbRpjXEF1e/4rm58vG7MQY3mcRNJjn/KxV5dZoDLSIyS3zfZ2fnMbrTgziFEUL9+3DOWPt0vOFCnhf6j9Gabidd6CVcHCJHkdxpc3cN1oyO4k5WAIMDVNsAkXF3+RecCJlQNcnoImKhClzH4fKqJTTGK+jIjHDtsqsoL2+gN5UiWV6HHckxdKQLr1AkEAmRXFJLsDxOYTjN8JEuitlTH/lHKpNE68oZPtpN17ZDdO7ppr+ncPImp1gMkpVhinmfgd4Cnn/qZigY/XQ8P26AOxSEipowYOnvyVEovPq8YmNG24+/0WoiJ25uKq90iVdESA/mSI8U8X2oXhTBWsgOZfHSGVJeBJ9xhY7vh1MLY9hxM5AdLJHo6DzjbNaedlp5pUv10kqiFVFat7UxMugRjTm4AUMg7FC7spZYdZKh430c296NtRBPBqhdWU3NmibiTTU4jiFSXV7yUViRhUZzoEVESixfLHKwv4N9Pe0c7T3EQO8ulkfLuaqylmCmF3yPzmyKLYNttOaG6Mz3UPD7MVNYocDFsJggiwPl5OOrILqY2vKlNJc3UFdWhx+pABNgKDNAW/d+CsUsZYEAt1RUgl9goFBkSf0qhjxoP9RGQ7wCBnKk+7L4wTg4AfyCR6p7CGMN8XgSExi76cgHumH45QHM0SzPFrdRKLw4LVMCYlFYsjpJsqGcQrpAz8FehvtyOI5h8fI40YoY6b40vn/iJixDtCJCpCKGX/TpPTTaHgPV9VFqV9dTvqSaQPz0j8xzAyN0bDtKLpXDcRzi1TESiyqIVpeR7hkEINFQhTM2Amwch0RjNeHKya8x4BV9MsMFoskg+YERUu29YC2RqiSxxdUnR2mtb8mMjP4WEE0ET86rPpdLfv3cz18+6SpF5EJoBFpEZJJ608Ps7m7lYM9xWjteYGf/AUyhi6biICmbp58i3liUdOzoGOSJtWetMdixUUkHQ7UNUO/GWF65lvqyJfhOkHx5C8Vw1au+ftB12dS0ivJ4JcVcEd8/dcd9cCwoFrO501YtACgMpRhu7cHL5sn0jtC5o42e9uzJ5a/OxnDuUFxW5hAMuwRCDvHKGG7IxQ25JOorCERDFNJ5Up0DeAUPJ+CSWFROMDb6Ybq1lmz/CNmBDPG6JNVrl1C+ovEcryYiMjs0Ai0iMgHf93nhyA62H92Ck+vH8fLkizl6U20cSHfQ6Y/uIBD10wRsgRZCVBCgNVhBPFjGimCCxeEkTdEymisaWbTsejb397J7oAsvkABjSJgQ14YaSBDCDQdILKklEAnjFYqkjnUxeKSLkfZ+RrqGKeaKY8tUxbAWRnpGeG7gMOmU94opCgHX4jjmtGkNryYYgJrGKDUranFDAcIVMRINVSeXpnKCDvGGGgBSx7vxvdOjdLSmbEojsiIiC40CtIhcdPzsEL/c/jDPHHmGgUwHpjgExREGvSFyvDKBBnBpMHFeE0zQHIyyqHwpTWvfTKysHhJ1EBsdNR4+0sHBB7Yy1DnMrkyRXWwl7HqsMj6ZYpZM2ieThec5dlr/jhmdKjs+proOBAJj83QPpIDRebvxhEtdU5x4dRwnMDYVwLNkBtIUCx7xqjhu6PR1Xt1QgMSiSoKxMMFElMp1zZO+2ats+eKJG4mIXGQUoEVk3ssW8hxo28PgQCsFz6N1pI/24Tb6ho/j+0VCToCaYJTOoX0MFLrwbYERfEIYagjgOlF8N86K6BqWVa7g6iVXEU42YENxgsEwi6qacNxTobT7xf28+P9tZbi/lWLhVOzN5kb/HY1AOOKAMQxmw3jWIRIoUF4TYnF1jER92eioc67ASNcQXq6IEzDEa8soa6omubSO6KKqkyE3PzK6GcGJlSNERGR2KUCLyLyUH2zj6T1P8OD+X3AgtRvHP33HqxNbAAcxDOJzCJ+kiVMbXY4fLOPm2vXcdcWdxCqaTm5mke0dYrhziEIRquvrCTgwfLST1m3bKKZz5NM5Ond30t1RIOhCWVWQZFXg5KoKscooK95yDcmm2mm9VgVnEZG5RQFaROakbCHPgb5Ojg104aa7qXEtiyJRjnXu5dmDP+fl7FEy+IRwuDrSTHPNFSQql+NgaEpW0FK9hFhFIwRGb1wbGhrG685x/Nm9tG7tIh6HfdtfpO3wk2AcHBeGh0+NJhtjXrHlL4yuw7t8fSWXvudmzQMWEblIKUCLyJzSPdTH/S/8Fz8+9FN8r4+oPzK2c92oSDpELFvG0ui1rF10GVcvu5aIE6Vz2xHS29P41qd9aJAj2X7gJQCKRUtu3K7DZeUufUMOnd05yqsiBAM+Xt5n5YYKKpvKcPwivUeHIOCe3N43XJHACbokmuvnzGYRIiIyOxSgRWRmFLL4hQzPHXielw88SsNwgPrBBH2FDEfSA/SlR3BHwPg+rufw5vxSyllDIBDFBmLkjaFQsFBIEHCDuI6Dvxuef2THyZcIBUc3qYjEHOLlQUYncoAbdEjUxEkuKqdydSOVa5opFjxy6SLx8rPvU7ZkJt4TERGZlxSgReS8HRvo5fnjeznc307rcAcDQ4cxfcdZta+aeDqBwRAsRAlYcJ1BMk4RvAABr5xOv4xOAMK4VLAIcIyDYxxc16UiESIQCZ/IwMQB1zVUL62krLHy1HZugBNwqL1iObH6V19D+UyBoEug3J24oYiIyBkUoEXknHzfJ9szSMdze+g/2I3v+3QOD3Kkr43CSBaHAiYwyFLjsT5XTqBwDeBinGHAx7hpio5P0ask6oeIBINULaogXxukrw7qyqpYU7uE8rIEieb6kxuCiIiIzFUK0CILmJcrYL3Tt5vLDYww3Nozul1zZz/dezoJhFwi5aMrPWQHM2TTBdqKfeQGcphUGIfQ6K56fp6cn8W3HhECVDqGuIniefUYJ0Q4YqhfV8ny111G5ZqmUy8aiIKr/9yIiMjCoP+jiSwAxXSWjuf2kO4eOnmsa08nna3Zc27HDKO70llrKXojWAt5P0uqOIDjBbHOCJnIbkaiI/RXdNNZ202tG+DWYBWvrVtLvPFKWHId1Kwq7QWKiIjMIQrQIvNMMZ1l6FAHfXvb6NzVznBvlnTa4p+RlAOuZcnqMqLl49YQzqcImDT5eJEtHS/SazsJ1nkcLYzQU8jh4+M5WeqN5e5QA9etuYO0u5jW3sOk3HUEatexcfWNOLGq0+Ygi4iIXEwUoEXmAJvPkzl2nPRggeGOQQqpLPH6cgYOd9N7qI/0UB7Ps3ge5MftNB0MWMorHMpqPLqT3QzHenH9NJ4bw0/AsB2iq5AiU0gRKA4xbIbpMUXSaR/KHZKmjKFCgRoT4ep4BQEc1pY1cfOKGwiseROE4kSB6ll7Z0REROYeBWiRWZTPFWl/dh97f/Asg+mz/3WMRiBeFsQJGoYLGQYYpNPuozN6iL6qbhzjnZqmUTB4xsX1POgDzwQI4hA1YYpOhFBiDVWJFi6N13LH+jtZ27B8xq5VRERkoVCAFpkBvu/TvWUfA4e66DvUTV97Gs+DQnF0t7tI0GH1TS0ka2IkGyoIJSKMtPWRXFJDT6Cfv33oH+jKteLaHCGbp9nCmvAibPQqCsEybLiKK5quZs3Sy3HcIPhFsBYTCFMbS2rjDxERkWmkAC1SIsV0luGjXQwe6uTAY/vp7x9dDSPgWqrqwoSiQYIRh7ql5TTctpFAWQKAPd1tPHH4JRy/G+/Jh3hxeAcecLdTwaL4UjbUr6F+xc2w9EbNQxYREZkFCtAiF6CYzTF8uJOho10Mt/XTc6iPwd4CvrV43qlwGwzApTc30njDGhJNdTiB0zfwaBvs5YeP/5BtrU/TPbKdqB0Ba7HGIRRu4eObfp+rLrlBgVlERGQOUIAWmYLBA8c58NOtZIay5DNF+nsKp61+EQlD3ZIYgZBLMBoisaicsiU1VFyyhFAi+or+OkcG+duHvkhb508J+SNU4vKWQBXXL38r4YpmapffRLy8fgavUERERCaiAC1yFr7v07V5LwDGGNpfOETXgT6GhnwMEA6D60LTqiRVy2spW1JD+bJFhKvKXrW/g72dHDyymVzXSwSGDtE30s7jhW7SeNzqlHHz+g+zdvkmnNo1EAjN4NWKiIjIVChAi4xTTGdpf2Y3+x7cRV/v6Tv4lZU5rL66hhVv3kh8cc2Efd2/6zn+7cVvkfeyhAvtJItduHZ0Dbq8EyFvwlSFmviD5bdw+ZW/CmWLS3JNIiIiMr0UoOWiZ62l76X9HPjlTo4fGMbzIejCutcsJtlQSTFXYNG1lxCtKZ9Uf77v8/ln7ue7+/6D2kCCW4sdVBSHqIyvorL5JsoXXw2Rcloq66iOJUt8dSIiIjLdFKDlota/bS8vfO1R+nNRjIGG5ihLNq2g4bo1BGKRSfXhFwt0HdvCwd42Dg9181Tny7SmdvNaE+ITwSLxZBVs/GNYqpsARUREFgIFaLno+L5P3/bDtD61h4PbunFDSdbcuoTlt68nVju5UWaAza37+fyz36TQ9ziOP3TyeBDD+wO13L10E05lM6x5K8S1l5+IiMhCoQAtFwXf92l9aCuDR3po393D0LAPQFVNmGs/dieJhoop9fUPj3+bx/d/i3pvkE0ECS5+K/W1a1leUc/yygYiNcvB1V8vERGRhUj/h5cFr5jO8tQ/3E9Xew6AWGx0Tealt19BrL5qSn1tbTvIl5/9Ft09D3CbDx9cciOVV/8m1K8rRekiIiIyBylAy4Li+z6p1h68XJ7jT++h9eUO0imL58Oa6+pZ9fbrCZcnptTns0f3cN9jf8dg5gAFP0UAw91uJe96w1/hLN1UoisRERGRuUoBWhaMvh2H2fqtZ+jrLZ48Vlbm0LQqweKrl9F48+WT7iuVy3HPk/fyQueLDIxsp9pPsya8hLry63nzkkupXXEzVC4txWWIiIjIHKcALfNepmeQl+95mKP7Rgi4lkuuqSNalaRixSJqLl8+pb583+c72x7ixy9+DgptLCLILU6Mt9z4P6lc/yslugIRERGZTxSgZd7J9Q8zdKiD4dYeBlv7OLKjD88zLL0kyfr33Ua05uy7AU7kmaN7+Nenv0Zh6ClavCJvXXoXN218J0QqIKnttEVERGSUArTMWb4/ulJGqrWHtqd30bGrg4GeAoXi6e2qa0NseM/1VK5pPq/XOTbQy2ce/xr7uh6hwRvkN9wkd97xFwRabrjQSxAREZEFqKQB2hjzBuCzgAt8xVr7t2c8Xwl8DVgBZIEPWmu3l7ImmR/antrB5m+/QL5wauORSBjqlsRI1iVJLq6krLmW5NL6SW94cibf97n3yW/x891fIeCn+DWT4FeXvIaya38HqldM16WIiIjIAlOyAG2McYEvAHcArcDzxpgfWmt3jmv2Z8BWa+3bjDFrxtrfXqqaZH7Y//0n2fbzQ0Qjhub1NYTiIRo2rqR8dROO40zLa+xqP8hXH/wUnemXWEqCD67/MCvW3QGVLdPSv4iIiCxcpRyBvhbYb609CGCMuQ+4CxgfoNcBnwaw1u42xrQYY+qttZ0lrEvmqPxIhu33PMTBl/uprHJ5zR+9mXDV+c1nfjW9qSG++PN/ZFf3LwnbAneUb+A3fuXvCcQqp/V1REREZOEqZYBuBI6Ne9wKXHdGm23A24EnjDHXAkuBJkAB+iLi+z67v/UIe58+TtEzNC6Lce1/fytuODhtr5Eu5PjGM9/n6d1fxvqDXBls4Ndv+mOaVt08ba8hIiIiF4dSBmhzlmP2jJkv+7YAACAASURBVMd/C3zWGLMVeBl4ESieeZIx5sPAhwGam8/vRjGZe3KDI3Rt2U/r8wc5fihNdU2QtW++nLrr1lz4VA1rITdEa9suvvPyT9jS8zx4fSy3QX71st9lw6bfBMedngsRERGRi0opA3QrsGTc4yagbXwDa+0Q8AEAY4wBDo19cUa7LwFfAti4ceOZIVzmob4dh3nqS0+QHd1dm+XrK9nwu2887+Cczaa494l7aB9qJeBlKB/eR2e+n8Mmj8Wy1iS4tf5mbrjl93AqlkzcoYiIiMirKGWAfh5YZYxZBhwH3gX8xvgGxpgKIG2tzQMfAh4bC9WyQA23drPvB89xZGc/rgvXveNSqi9rIVY39TnIA5kUX/jZ35EZ2MFgvp0B8kQYDeBZJ0YgupR1VZdy9/o3csnSKzTiLCIiItOiZAHaWls0xnwceIDRZey+Zq3dYYz56NjzXwTWAt8wxniM3lz426WqR2ZPfihFz0uH6HzpCIde7se3UNcQ5srfvpVkU+159fnAvhf5xpOfxs0dpMYkcMJNvHfVW7lz/WshEIZ4zTRfhYiIiMiokq4Dba39CfCTM459cdz3TwOrSlmDzK7U0Q4e/sdfkM2PTolf1BTh8vfeSFlLw5T78n2fh3c8wi9f+DcO5Y9R53u8t+F2rn3zp8DVnkAiIiIyM5Q6pGSybZ08/pmfUfCCbLz7EqrXLz3vEedULsdf/uCTdAw+ScS63FG2nnevfT2xy96u8CwiIiIzSslDSmLwwHGe+twvSBfDXPe+jTRtOv8PGtqG+vjkj/4SO/I0t0dX885f+Qzx8kXTWK2IiIjI5ClAy7Tp33OMvfdvpuNQioIHrhvk+t/cyOJrzy88D2bTPLL9Qb7/0pdxit38VqSF297xfyBSPs2Vi4iIiEyeArRcsHRXP9u/+ShH943gGKhvilDRVEHjjWupWNl4Xn3e88Iv+cHWLxAvtpK0AT7S8Bo23PQxhWcRERGZdQrQct5832fPfY+y58lWPM+w9JIkl77n5vNakm58n3/y839jb+v3uMxL88ba67ni9j8nXl4/jZWLiIiInD8FaDkvvu/z0pd+xv6tfVTXBNnw3huoXHMBu0QW8wx27eEfn7mPI72P8hYb5Dev+W8Er3wvmLNtaikiIiIyOxSgZcqGj3ax7Z5H6Tieo3FZjOv++O7z3kHQ933+64Ufc2DbF9ld7CaHzx2BRXzw9j/FablxmisXERERuXAK0DIlA/uO88i/PITvG1ZeWcPlv/P68w7PAF9++N947MC/E8WhpuJG7l55M5uueNPoZigiIiIic5ACtExafiTD0//PIxgMr/2D26hYdX43CJ7w5HP38dT+r7PareBPf+2rhCqWTFOlIiIiIqVz/kOHclHxfZ9nPvMjUmnL1e+47ILD8/P7NvPvL36WqJPkd9/+dYVnERERmTc0Ai0T8n2fLZ+9n672HGuvX0TTrVdcUH8PH3yZrzz6p1QCv3fHZ6iturAwLiIiIjKTFKDlnNJd/Tz7uQfo7Smy9JIka9/32gvq775tj/KdzZ+m2Rvm9zd8lGUtG6apUhEREZGZoQAtryrXP8xjf/cT0mnL+luaWP3rN1/QDYMHezv5z+c/xZriMH942Xupvub901itiIiIyMxQgJazSnf28fRnHyCVsmz6jctpvPnyC+rP933+9Wd/QcLr50OX/zbV139E6zuLiIjIvKQALafxfZ/d33qEPU+14ftwxZ3LLzg8A9z7+DfoGXmR15ddwXKFZxEREZnHFKDlpGI6y+Of/i96uwtU1wa58v03UrGq6YL7ffbQdn6x58u0OGW8++5/UngWERGReU0BWk568d8eoLe7wKU3LeaSd996QfOdT8hmhvnKQ5+g3Bb52B2fIhAtm4ZKRURERGaP1oEWfN/n4A+f5sie4dGVNt7z2mkJzwy28oPvfIBssYu7V7yDRcs2XXifIiIiIrNMI9AXuY7ndvPifZtJpSGRMFz5kTunpd+BI8/z4sOf4oF8F4nym3jd6/5oWvoVERERmW0K0Bexnd98iJ1PthEJw4Y7l9Fy59UEYpEL7nf3nsf43COfoM9xGYqs5R9u+4NpqFZERERkblCAvkgde2grO59so3ZRkE3/482EyxPT0u/uw1v5l0f+lIIJ8oHr/4bb195AwHWnpW8RERGRuUAB+iI0sK+VLd97mUTc4YY/votg/MJHnQE6Bnv4l1/8ER4+H7vlH7jqkhumpV8RERGRuUQ3EV5kBva18tjnHsYYw/W/e+u0hWff9/nr//of5PxBPnDFxxSeRUREZMHSCPRF5OCPnuGln+7DGMPNH7+Z8hWN09b3N579PoPZ3by96jpu2PTeaetXREREZK5RgL5IHHlgMy/8aD9lZS6bPnorZcsXT1vfA5kUP9/5dVpsiLvv/PNp61dERERkLlKAvgj4vs+un+8hFoXb//oduOHgtPWdyuX4gx//Da7XxTua34JT1jBtfYuIiIjMRQrQF4EjP9vCSMpy5RtXTFt49n2fB/e/xH2bv0R25AXe41Zz5Ws+Mi19i4iIiMxlCtAXgb0P7yUWhWVvvnba+vz0Tz/DS23/RYWf572xFbzpzX8Dyfpp619ERERkrlKAXuD6dx9leNiy7jWLcQIXvh6z7/t876lvs+v4d9nkVvM7r/k4iVV3QCA0DdWKiIiIzH0K0AvckUe2A9By+xUX3Ne9Wx/mnm1fpT63lwaT4CPv+HdiZRp1FhERkYuLAvQC5vs+x3f3UVUdINZQfUF9ZQt57t3+XS4pdHFHoJbr3/I5hWcRERG5KClAL2DdW/aSycLq11z4es/f2vYIgdwh3mcCXHfrJ6BuxTRUKCIiIjL/aCfCBcovemz77gsEA9B8+4YL6qvoefxoz/dZUxzimhW3wLKbp6lKERERkflHAXqB2v3tRxka8ll/xwrClckL6uurmx/ATe/kzeEanGt/B4yZpipFRERE5h8F6AXIyxXY90wb1TUBlr31ugvqqzc9zI9238sav8At130YYlXTVKWIiIjI/KQAvQC1PbWDggfLb16J41zYj/ifn/oPwoV23pdYirPqjmmqUERERGT+UoBegFqfO4jrQONr1l9QP4PZNM8ff5hNnsfq9XdprWcRERERFKAXHC9XoOtomrrGCIFY5IL6+ubWB4kW2nhDpBJWvX6aKhQRERGZ3xSgF5i2J0enbzRd03JB/RQ9j0f3fZ91xRTrLn2b5j6LiIiIjFGAXmD2PbSHUMBe8PSNLz55H4HMbl6XaMa54l3TVJ2IiIjI/KcAvYB0bNlPX0+BFVfVXdD0jSN7H2XL7n9lLQFuvf3PIXhhU0FEREREFhLtRLhAWGvZef9LBB2P1b9243n3s3n3U9z76J9RMAHefcdncRoun8YqRUREROY/jUAvEMce30VfR5qVG6oJliXOq4+nD2zjnx/7BFks77/+r1i17MpprlJERERk/tMI9AJQzOR46ftbiYc9Lnnf686rj+HMCF9/+JNU2AJ/cfs/smjlTdNcpYiIiMjCoAC9AOz5jyfJZnyu//UrCESnNl/Z930+98wP2bn3W2S8Ht695kMKzyIiIiLnoCkc85zv+xx5sY3ycofG2zZM+fzv73qG/9z7HZK5Nu6q2sRtt3y0BFWKiIiILBwagZ7nurfsJZ2Gy29fcl7nP3jwWapsnk/HGwjd/N+muToRERGRhUcj0PPcwYd24jrQ8saNUz43Xcixu387NxhLqKwB6taVoEIRERGRhUUj0PPYSGs37YfTLG6JE0pEp3z+T/duwS32cavNwYrbwJgSVCkiIiKysGgEeh7bds+jAKx7x3VTPtf3fR7a/j1aCu1sqF8DK++Y7vJEREREFiQF6Hmq47ndtB/LsuyySsqWL57y+f/nmfvpG3yKmyOLCb3uf0H4/NaOFhEREbnYKEDPU7t/vI1gAC59/2unfO7W9sP8ZPfXucx3ec9tn4RI+fQXKCIiIrJAKUDPQ8NHOujpLNC8rvK85j7/+4s/osLr4yN163GarilBhSIiIiILlwL0PLT/x1sAWPmWqYff7pEhdnc9xg2+oXr928HRHwERERGRqVB6mme8QpGjO/upXRQk2Vw35fO/sfUXxAtdvD6xGJbfUoIKRURERBY2Beh5pnvrfgpFaL6mZcrnFj2Pxw/9jHV+ntWXvQ0C4ekvUERERGSBU4CeZ9pfOAxAw6a1Uz73h7ufg9whXhusgtV3TnNlIiIiIhcHBeh5pvtgP+VlEKkum/K5P97xfRZ7w9yw7q1aeUNERETkPClAzyOZ/hGGBn1qWyqmfO729iMMDT7DDYEqwhveXYLqRERERC4OCtDzSPszewBLw1XLpnzu15/4PEk/w+uu+iBEpj56LSIiIiKjFKDnkfaXjxM0HrUbVk7pvC2t+zk+8DQ3hBpYdPnbSlSdiIiIyMVBAXqeKBY8uo6lqF0cxolMbfWMe574PEk/z93XfQTcQIkqFBEREbk4KEDPE+3P7sUreDRd1Tyl8548sovO4c3cFG6kZs0bSlSdiIiIyMVDAXqeaH3+EK7xWHzT5VM67+tPf5kKP89dV/8WOG5pihMRERG5iChAzwNe0aPr8BC1dS6BssSkz3v44Mv0jmzjDreK8kvuKGGFIiIiIhcPBeh5oOPFQxRyRRqvWDKl8+7f+XMqvRHesPatEIqVqDoRERGRi4sC9DzQ+uQeHHwaX3vlpM9JF3Ic6nqCKwiTWPumElYnIiIicnFRgJ7jPM+n4+AgtfVBQhWTX7/5J7s3E/B6uaZsGVRNfd1oERERETk7Beg5rvO53RTyPk1Xt0zpvIf2P0SVn+VqrbwhIiIiMq0UoOe41qf34RhofO2GSZ/TPTJEa//zXEmU8LLXlLA6ERERkYuPAvQc13NsmMqaIKFEdNLn3Pfyw0S8AW6pWg0VU7vxUERERETOTQF6Dhtp7SadgdoVVVM67+kDP2aZV2Dt+rtKVJmIiIjIxUsBeg7reH4fAIuuWjHpc548vAsvs5Pro4tg1etLVZqIiIjIRUsBeg7r2tNO0IWq9S2Taj+Sy/HVR/+Gcj/PTdf8DgRCpS1QRERE5CKkAD1H+b5Pb1uGyrowjjO5H9O//vB/U8zu4p2111Gt1TdERERESkIBeo4a3HecXB7qVtdOqv3B7jZ29/2SS2MtvO6uf4JJhm4RERERmRqlrDnq2GM7AGi86dJJtf/Bc9/G4vO2q34b3GApSxMRERG5qClAz1Ftu3spr3BINk08Al30fF7ofJxlRFm9+rYZqE5ERETk4qUAPQcN7GtlJGVpXL9oUu1/vOd5Cl4PN1auhWCkxNWJiIiIXNwUoOego49sB6D51ssm1f7Rg0+Q9PPccsnrSlmWiIiIiKAAPSd17u+jrMwhMYnpG77vc6x3CysJEW68cgaqExEREbm4lTRAG2PeYIzZY4zZb4z5k7M8X26Mud8Ys80Ys8MY84FS1jMf5AZHGBr0qW0pn1T7PT1tFAudrA1WQtXkN1wRERERkfNTsgBtjHGBLwBvBNYB7zbGrDuj2ceAndbaK4Bbgc8YYy7q3T86n9+LBeovXzqp9g8eeIGYn2J907Vauk5ERERkBpQycV0L7LfWHrTW5oH7gLvOaGOBpDHGAAmgDyiWsKY5r3N7K46BuqtWTqr9rtanqPIty1beUuLKRERERARKG6AbgWPjHreOHRvv88BaoA14Gfh9a61fwprmvN7WYcorXQKxiVfTSBdydA5t5xITwdH8ZxEREZEZUcoAbc5yzJ7x+E5gK7AY2AB83hhT9oqOjPmwMWazMWZzd3f39Fc6R2R6BhkZsdQur5pU+/t3PYfrD3Bl5RoIJ0tcnYiIiIhAaQN0K7Bk3OMmRkeax/sA8J921H7gELDmzI6stV+y1m601m6srZ3c1tbzUdcL+wCoW988qfYP7v05NX6ea9a+vpRliYiIiMg4pQzQzwOrjDHLxm4MfBfwwzPaHAVuBzDG1AOXAAdLWNOc1ruvEwPUXL5swrYdw/10DG5ho4kTWnZT6YsTEREREQACperYWls0xnwceABwga9Za3cYYz469vwXgb8G/t0Y8zKjUz4+aa3tKVVNc13/8SGSSWdS85/ve/lRYv4gN9ZeDYm6GahORERERKCEARrAWvsT4CdnHPviuO/bAM0/APyix9CAR+PKyc1lfvbwgyz1fFave1OJKxMRERGR8bRw8BzRv/sYng9Vyyee4721/TAjmX1schPQvKn0xYmIiIjISQrQc0TPjiMA1F428QYq/7HjYRL+CDc3boRoRalLExEREZFxFKDniN5DPQQDkFzWcM52vu/zYtsTXOZB9bIbZqg6ERERETlBAXqO6O/IUFETxJlgO+6XOo9iCx1sDMShceMMVSciIiIiJyhAzwHDrd1kslCzvGbCts+17iLuj7C6ogXKzj1aLSIiIiLTTwF6Duh8fnQDlfoNE6//vKNjF5V+luZlN5a6LBERERE5CwXoOaB7bwcB11K1vmXCtm0DO1hGEGfRpaUvTEREREReQQF6DuhrT1NVG55w/nPnyCCZfBsrTRiqV81QdSIiIiIyngL0LDs5/3nFxPOfnzyyk7CfZUWyESJlM1CdiIiIiJxJAXqWdb+wH4C6yyde//nF9j1EbZbVjRtKXZaIiIiIvAoF6FnWe6ALx0DluokD9P7ubSyzhoTmP4uIiIjMGgXoWdbfnqK8wsUNBs7Zrjc9TH/mIGtMBKpXzlB1IiIiInImBehZVMzmGB72qVicnLDtgwe2EfbTXBoug4qJR6tFREREpDQUoGdR78uHsRaqV9ZP2Pa549sp8zOsa7wK3HOPVouIiIhI6ShAz6KeXa0A1F4x8QYqB3pfYo21hBqvLHVZIiIiInIOCtCzqP9IH+EQxBefewm7g32dZHPHWOtEYdFlM1SdiIiIiJyNAvQsGuzNUV4dnrDdwwe3EvVTXBav0/xnERERkVmmAD1LcgMjZLJQ2Tjxhihb2ndQ7WdZ0XwdGDMD1YmIiIjIq1GAniV9O48AULG89pztfN/nWP9LrLUuzuIrZqI0ERERETkHBehZ0negE4DqCTZQeanzKH6hi3VOFBZdPhOliYiIiMg5KEDPkoHWAcIBn2h91TnbPXJobP5z1QqInbutiIiIiJSeAvQsGerJkqwMYiaY07yjaxcNfp7GpdfOUGUiIiIici4K0LOgkMmTSlvKF028A2Hf4G6WEoAGTd8QERERmQsUoGdB355jYC1VLede/7lzZJBCsYNmJwJ162aoOhERERE5FwXoWdC78zgAVeuaz9lu8/F9hPwszWXNEIzORGkiIiIiMgEF6FnQd7iHcMAn0dJwznYvdx4gZHNcskijzyIiIiJzhQL0LBjoylJRG57wBsKDvfuotVBZu3KGKhMRERGRiShAz7BU1wDZrE9Vc+WEbXuG97OEIJQvmYHKRERERGQyFKBnWM+2gwDUrG06Z7vOkUGyhR6WmhBUnHuutIiIiIjMHAXoGda7tx0DVF++/JzttrYfJGRztITLIFY9M8WJiIiIyIQUoGdYf+sQyaQhEIucs92u7iMEbY7mquUwwVxpEREREZk5CtAzyMsXGBwoUrk4MWHbg/3HqLBFamt0A6GIiIjIXKIAPYMGdh7Gt4aqlYsmbNs5fJhGa3AqNf9ZREREZC5RgJ5BPTuPAVBz+bJztvN9n+HsMZpMECqWzkRpIiIiIjJJCtAzqO9wD8GgQ1lz7Tnb7elpw3gjLHFCUKkALSIiIjKXKEDPoIHODOU1oQk3UHmp4xBhm6UpVgfh5AxVJyIiIiKToQA9Q7JdvaRyLpXNVRO23dd3jLCfY2n9mhmoTERERESmQgF6hvS+NLqBSvUliydse7j/MHXWI6EVOERERETmHAXoGdK3vxOMoWb9xHOa+0cO0YhuIBQRERGZiyYM0MaYtxhjFLQvUP/xQaIxl0hZ9JzthnMZ0oUOmoxuIBQRERGZiyYTjN8F7DPG/L0xZm2pC1qIrLUM9hUprz337oMAL3UcJuRnaQrGIDHxetEiIiIiMrMmDNDW2vcCVwIHgK8bY542xnzYGKPlISYpfayTnOdS1Vw5YdudXUcJ2xzNVSvB0cC/iIiIyFwzqYRmrR0CvgfcBzQAbwNeMMb8XyWsbcHo2XEEmNwNhPv7DhPzczQ1XFbqskRERETkPExmDvRbjTHfBx4CgsC11to3AlcAf1Ti+haE3oM9GAPVayfelrtrYB8NOARqtQKHiIiIyFwUmESbdwD/bK19bPxBa23aGPPB0pS1sAy0DZFIOARi4QnbDqYPczUhqFoxA5WJiIiIyFRNZgrH/wKeO/HAGBM1xrQAWGsfLE1ZC4df9Bga8CivO/fqGwD/f3v3HiVldef7//3tqupL9YW+gQIdLySKCjQIjUFJIsbggBokwgkaQoKcxGNOiOZk6S8krslE5xjJ5UwyjpnDMBkWemLIzzij8lNDIipBDF4gB7URDKitNCD0hb5Xdddl//7opqeFbvopuqqru/m81mJRz1P7eerbm2fhx82uvasb64nHGhjnz4WC/qd7iIiIiMjg8xKgfwfEexzHus6JB/VvfUA0BqMvOKvftjsP7uvcwrtoAvSz3beIiIiIpIeXAO13znUcP+h6nZm6kkaWo292foFwzPT+p2S8eeSvZLp2Jo6/NNVliYiIiMhp8hKga8xswfEDM7sBqE1dSSNL3bu1ZGc68j42pt+2B2oqGe18jDpby22LiIiIDFVevkR4G/CImT0IGHAA+EpKqxohnHPU17RTOiYL62dKRjwe52jb+8whE/LHDlKFIiIiIpKofgO0c+4dYJaZ5QHmnGtOfVkjQ+N7R4h0OEonlPbbtqqhhkiskfMysiBfOxCKiIiIDFVeRqAxs+uASUD28ZFU59y9KaxrRKh9swqAMVPP67fta9V/xe8ifDw4GgL9r9ghIiIiIunhZSOVNcAS4Ft0TuH4L8C5Ka5rRGg+3IDhKPhEWb9tK4++Q5aL8Ini81JfmIiIiIicNi9fIrzCOfcV4Jhz7h7gcuBjqS1rZGitayU70+HL6n/RkqrGA4x3RvYorf8sIiIiMpR5CdDhrt/bzGwcEAHOT11JI0dbUwc5eZ5mydDQXsNYF4M8zX8WERERGcq8BOj/z8wKgZ8CfwGqgA2pLGqkaGuNk1uY3W+7eDxOqOMopeaH/P43XBERERGR9Dnl8KiZZQDPOecagH83s6eAbOdc46BUN4y1N7YSjTpyS/P6bftBQy0Z8TCjM/yQpwAtIiIiMpSdcgTaORcH/leP43aFZ2+a3j8CQN7Zo/pt++6xDwm4CGMsoAAtIiIiMsR5mcLxRzNbZP3tBCIf0VJdB0BeWf9rQL/fcAS/6+DsrHzI7j9wi4iIiEj6ePmG23eAXCBqZmE6l7JzzrmClFY2zLV82ABAwTn9jygfaDrSOQJdOB70/ykiIiIiQ5qXnQjzB6OQkaa1roWAz5FZ2P8c6COttRTjyB41fhAqExEREZGB6DdAm9lnejvvnNua/HJGjtaGMDm5Pk9t60K1fCIe0/xnERERkWHAyxSOu3q8zgYuA3YCn01JRSNEqCVG0egsT22bwx8ymgytAS0iIiIyDHiZwvH5nsdm9jHgJymraARoP9ZMuB3yz+5/mng40kEkWt+5BnTemEGoTkREREQGwssqHCeqBiYnu5CRpG73+wAUf6L/EeV36jtX4BiTEYB8jUCLiIiIDHVe5kD/E+C6DjOAacDrqSxquKvfdxiAksn973he1XAEv4sw2p8FwZJUlyYiIiIiA+RlDvSOHq+jwAbn3EspqmdEOFbdQHYW5JT2P4XjYFMNAddBad65kOHtS4ciIiIikj5eAvRjQNg5FwMwM5+ZBZ1zbaktbfhqqmunoNjbFwg/bKnrXAO66JwUVyUiIiIiyeBlDvRzQE6P4xxgc2rKGf7a65sIhaGozNs+M0db6yiMx8gsGJviykREREQkGbwE6GznXMvxg67XwdSVNLzVHv8C4QXeAnFj2xFKnOkLhCIiIiLDhJcA3Wpm048fmNkMIJS6koa3Y/s/BKD4kvM8tW9rP0KR+bSJioiIiMgw4WUO9LeB35nZoa7jscCS1JU0vDUebiIr09sXCOPxOOFIPSVaA1pERERk2PCykcprZnYRMBEwYK9zLpLyyoap5row+YUBT20/bGnAXJhi80OuArSIiIjIcNDvFA4z+yaQ65yrdM69CeSZ2X9PfWnDT6w9Qmubo2BMnqf2VceO4ncRSjILIJCd4upEREREJBm8zIH+unOu4fiBc+4Y8PXUlTR8New7iHNQeE6xp/YHGmsIuAgl+gKhiIiIyLDhJUBnmJkdPzAzH5CZupKGr2P7O6eJF10wzlP7Q821+F2Eswo/lsqyRERERCSJvHyJ8A/Ao2a2hs4tvW8Dfp/SqoapxgP1mEHBBG8B+khrLTkuSmHh+BRXJiIiIiLJ4iVAfxe4FfgGnV8i/L90rsQhJ2g62kpuruHL8vYlwoaWg4wigwxN4RAREREZNvqdwuGciwMvA+8CFcDVwJ4U1zUsNTdEKCjx/mXAprbDlOCD3NEprEpEREREkqnPEWgzuxC4CbgZqAP+XwDn3FWDU9rwEqptpCMCBWO9beEdj8dp7jjK2ZapNaBFREREhpFTTeHYC7wIfN45tx/AzP7HoFQ1DB3bewCAognedhR8p/4IuBDjLQDB0lSWJiIiIiJJdKopHIuAD4EXzOxfzexqOudAe2Zm88zsbTPbb2arenn/LjPb1fWr0sxiZuZtDbghpuG9owAUTSzz1H730ffxuwjjgqXg16ImIiIiIsNFnwHaOfe4c24JcBGwBfgfwFlm9r/N7Jr+bty13N0vgfnAJcDNZnbJCZ/xU+fcNOfcNOB7wJ+cc/Wn/dOkUeOhBgJ+CJ7lLf/vq6vG7yKcoyXsRERERIYVL18ibHXOPeKc6nZzjQAAIABJREFUux4oA3YBJ40m9+IyYL9z7l3nXAfwW+CGU7S/Gdjg4b5DUnNtmPxRXhY16fRB0yFGOUdRobcl70RERERkaPCykUo351y9c+5fnHOf9dB8PHCgx3F117mTmFkQmAf8eyL1DBXxaIyWljgFY4KerznccojxDsgZljNWRERERM5YCQXoBPU2X9r10fbzwEt9Td8ws1vNbIeZ7aipqUlagcnS9N5h4g5GfcxbGI7H4zSEDzOWDMjVFwhFREREhpNUBuhqoOcE3zLgUB9tb+IU0zecc2udcxXOuYrRo4femsnH/noQgKKPe9tfprqpDhdvZbwvUyPQIiIiIsNMKgP0a8AFZna+mWXSGZI3ntjIzEYBVwJPprCWlGo8UAdA4QXetuSuPPIBfhelLCNLI9AiIiIiw4z3b70lyDkXNbOVwB8AH7DOObfbzG7ren9NV9MvAH90zrWmqpZUa6lpJScb/EFvuxAebq7F5yKM8QcgpyjF1YmIiIhIMqUsQAM4554Bnjnh3JoTjtcD61NZR6q1NHYQzA94bl/T1oCfKEX+PMguTGFlIiIiIpJsqZzCcUaIx+O0tTnyir2NPgPUhRrIdY5gXilk6I9AREREZDhRehugtkN1xONQcPYoz9fUhxooBH2BUERERGQYUoAeoMb3jgCQX+Y9DDd3NFHs4voCoYiIiMgwpAA9QE3VnStwFJx/tudrmjsaKHFRjUCLiIiIDEMK0APUcrQJnzmC47yNJsfjcdqjDRRhGoEWERERGYYUoAeouS5EMGhkePwyYE1bM+baKTK/RqBFREREhiEF6AFqa4qSW5jpuX11Yy1+F6UwwwfBkhRWJiIiIiKpoAA9ANH2COGwI6806PmaD1uO4XcRijP8msIhIiIiMgwpQA9A68E6wJE7xvsSdh8213UGaH8OZHu/TkRERESGBgXoAWg5VAtA7lnedxM82tqA30UoKTgbzFJVmoiIiIikiAL0ALR+2ABA3njvc5nrww3kEicn/6xUlSUiIiIiKaQAPQCttS0YkDt+tOdr6kMNFLk45Hq/RkRERESGDgXoAWg71kZWpsOXGfB8TUv7sa4ArS8QioiIiAxHCtADEGrqICfoS+iatvYaivBpBFpERERkmFKAHoBQW5ScgizP7TuiUdqjxyg2HwQ1Ai0iIiIyHClAn6ZYR5T2dggW5Xi+prqpDj8dlFhAI9AiIiIiw5QC9Glq7VrCLjg63/M17zccxe8ilPoyIahtvEVERESGIwXo09RysDNA5yWwBnR1Yw1+F6U4WAIZic2dFhEREZGhQQH6NLUe6VwDOnec95HkD1s6dyEcUzg+VWWJiIiISIopQJ+m1poWAPLKxni+5mhbPbkuRkHBuFSVJSIiIiIppgB9msINITID4MvyvgZ0XWstJVoDWkRERGRYU4A+TeHWDrKyLaFrWsJHKCJDS9iJiIiIDGMK0Kcp3BYlK+hP6Jq2SC1F5tcItIiIiMgwpgB9mtrDjuy8TM/tW9vbicaaKTG/1oAWERERGcYUoE9DrD1CJAo5o7xvovLesSP4XbQrQGsEWkRERGS4UoA+DW01nUvYZRfmer7mg8Ya/C5CcXYh+L1v/y0iIiIiQ4sC9GloO1wPQLAkz/M1h5trO3chzDsrVWWJiIiIyCBQgD4NodomAHJGj/J8zZHWegIuwmhtoiIiIiIyrClAn4bQsc5NVIJnF3m+prbtGHkuTk7B2FSVJSIiIiKDQAH6NIQb2jAgu9T7CHRT21EKMa3AISIiIjLMKUCfhlBTmMxMyMjw3n2hcA2jyFCAFhERERnmFKBPQ3tLhKzsxLouFKlnFH4IlqSoKhEREREZDArQpyHcFiM71/suhB3RKO2xZgrNB9nep32IiIiIyNCjAH0aOtoT24XwUFM9GUQpzvBBVkEKKxMRERGRVFOATlC0LUwkBtkJ7EJ4oLEWn4tRGMgHn/eRaxEREREZehSgExQ6vgvhqKDnaw411+EjSnG292XvRERERGRoUoBOUNvRRgByir3vQnikpZ4MF6M0V18gFBERERnuFKATFD7WDEB2cb7na2rajhEgRkm+lrATERERGe4UoBMUPtYKJLaNd13oGKMcZOQUpqosERERERkkCtAJCjeGAMgZ7T0MN7Q3UOycVuAQERERGQEUoBPU3hwm4ANfVsDzNW3t9YzCB9kK0CIiIiLDnQJ0gsItETKzErumPdpIARkagRYREREZARSgE9QeipCZ7fPcPhqLEY23kG8agRYREREZCRSgE9QRjpMd9D5942hrIxkuRp5pF0IRERGRkUABOkEdHZCZwDbeR1ub8LkoBRkagRYREREZCRSgE9DREiIWh+wC79t417Y24iNGgfkg0/va0SIiIiIyNClAJyB0pB6AnCLv23jXtjXiczHyM/PB509VaSIiIiIySBSgExCq69yFMKsw1/M19aEmfEQp0CYqIiIiIiOCAnQCQrWdATqn1PsuhA3hZjJcjMLcklSVJSIiIiKDSAE6Ae2Nndt4B0u9fxmwMdxCDo7sYFGqyhIRERGRQaQAnYBwYxsA2Qls493c0UJ+3EG291FrERERERm6FKATEG5uJ+CHDL/3jVSaO5opIK41oEVERERGCAXoBETbY/gTXEgj3NFAHqY1oEVERERGCAXoBEQ7Yvj8ltA17ZFG8tAuhCIiIiIjhQJ0AmKROIFAYl0WiTV3buOtEWgRERGREUEBOgGRSBxfAgG6uT1E3LVTQIZGoEVERERGCAXoBMSiDn+m9y8Q1rQ24XNR8jUCLSIiIjJiKEAnIBoFf5b3AH20pQEfMQoy/JCZn8LKRERERGSwKEAnIBaDQJb3ZTg6R6Bj5GflgS/B5TtEREREZEhSgPYoFokSd+DPDni+pj7UhI8o+VneN14RERERkaFNAdqjaHPnLoSJBOi6tkYyXIzC3OJUlSUiIiIig0wB2qOOljAAgZxMz9ccCzcRIEZBbmmqyhIRERGRQaYA7VGkawQ6EPQeoBvamyhwkJEzKlVliYiIiMggU4D2KNLWOQLtz8nyfE1zezOjXFxrQIuIiIiMIArQHnVP4cjL9nxNqOMYeWRoDWgRERGREUQB2qNoqAOAQDCxAF2ATyPQIiIiIiOIArRH0bZ2ADLzvQfoSKyZAvNBtuZAi4iIiIwUCtAeRUIRAPy5QU/tG8NtxF07+WRAlnYhFBERERkpFKA9ioY7p3Bk5ud4av9hcwM+F2VUhl9zoEVERERGEAVojyKhKBkGvixvG6kcaTmGjxgFGX7I0hQOERERkZFCAdqjaEcEn897+5q2RnwuSkFWAWSom0VERERGCiU7j6LtMfx+7+1rW7umcARLUleUiIiIiAw6BWiPIh0xfH7z3L4u1IiPGMV52sZbREREZCRRgPYoFonjD3jvroZwM0EXJztXAVpERERkJFGA9iiaYIBuDDcyyjmtAS0iIiIywihAexSNuIQCdGtHIwUAOYUpq0lEREREBp8CtEexmMOf5f1bhO0dx8hDuxCKiIiIjDQK0B5Fo4Y/y/s6duFoY+cuhArQIiIiIiOKArQH8WiMuAO/x01U4vE40VgLeaYALSIiIjLSKEB7EGluAyCQ4y1AN4bbMBchz3yQrTnQIiIiIiOJArQHHa1hAPzZmZ7aH21twkeMXPNDVkEqSxMRERGRQZbSAG1m88zsbTPbb2ar+mgzx8x2mdluM/tTKus5XVmFeVw6/+OcXfFxT+1ru7bxzs3M0zbeIiIiIiNMAptTJ8bMfMAvgblANfCamW10zr3Vo00h8M/APOfcB2Y2JlX1DERmXg4fv+Fyz+3r21rwuSh5WsJOREREZMRJ5fDoZcB+59y7zrkO4LfADSe0+RLwH865DwCcc0dTWM+gaQg34yNGXnZxuksRERERkSRLZYAeDxzocVzdda6nC4EiM9tiZjvN7CsprGfQHAs143NRCvNHp7sUEREREUmylE3hAKyXc66Xz58BXA3kANvN7GXn3F8/ciOzW4FbAc4555wUlJpcDe2dI9CjckvTXYqIiIiIJFkqR6CrgY/1OC4DDvXSZpNzrtU5VwtsBaaeeCPn3FrnXIVzrmL06KE/qtsSbibHQSA7P92liIiIiEiSpTJAvwZcYGbnm1kmcBOw8YQ2TwKfNjO/mQWBTwJ7UljToGhrbyAHg8zcdJciIiIiIkmWsikczrmoma0E/gD4gHXOud1mdlvX+2ucc3vMbBPwBhAHfuWcq0xVTYMl1NHIGDIUoEVERERGoFTOgcY59wzwzAnn1pxw/FPgp6msY7C1R5oJKkCLiIiIjEja5SMF2mMt5JIBmXnpLkVEREREkkwBOgXaY63k4dMItIiIiMgIpACdZB3RKNF4mDzzQSCY7nJEREREJMkUoJOsPtRMBjFyTVM4REREREYiBegkq21tJsPFyPUFwJ+Z7nJEREREJMkUoJOspq2RDOLkBTT6LCIiIjISKUAn2bFQCz4XIzdLuxCKiIiIjEQK0El2LNREBjEKskeluxQRERERSQEF6CRrCLeQQZzCnMJ0lyIiIiIiKaAAnWTHwk0EXJz8HI1Ai4iIiIxECtBJ1tjeTJ6DjGzNgRYREREZiRSgk6y5vZkCnNaAFhERERmhFKCTLNTRQB4Z2sZbREREZIRSgE6ycKSxM0BrG28RERGREcmf7gJGmvZYMwXm0xQOERERIRKJUF1dTTgcTncpcgrZ2dmUlZURCAQ8tVeATqLW9nZi8TD55tMUDhEREaG6upr8/HzOO+88zCzd5UgvnHPU1dVRXV3N+eef7+kaTeFIoiOtDWQQJx8FaBEREYFwOExJSYnC8xBmZpSUlCT0rwQK0El0tKUBHzFGZShAi4iISCeF56Ev0T8jBegkqmltJMMdD9CaAy0iIiLpd9999zFp0iTKy8uZNm0ar7zyCr/4xS9oa2s7rfv98Ic/5Gc/+9mA61q/fj2HDh3qPv7a177GW2+9NeD7DgbNgU6i2rZGfC5GQaAAAtnpLkdERETOcNu3b+epp57iL3/5C1lZWdTW1tLR0cGSJUv48pe/TDCYvlXD1q9fz+TJkxk3bhwAv/rVr9JWS6I0Ap1E9aEmfEQpyi1OdykiIiIiHD58mNLSUrKysgAoLS3lscce49ChQ1x11VVcddVVAGzYsIEpU6YwefJkvvvd73Zfv2nTJqZPn87UqVO5+uqru8+/9dZbzJkzhwkTJvDAAw90n1+4cCEzZsxg0qRJrF27FoBYLMby5cuZPHkyU6ZM4ec//zmPPfYYO3bsYOnSpUybNo1QKMScOXPYsWPHKT93qNAIdBIdCzcRcHFycxSgRURE5KM2vPoBH9Sf3rSJvpxTHOTmy87p8/1rrrmGe++9lwsvvJDPfe5zLFmyhNtvv51/+Id/4IUXXqC0tJRDhw7x3e9+l507d1JUVMQ111zDE088wezZs/n617/O1q1bOf/886mvr+++7969e3nhhRdobm5m4sSJfOMb3yAQCLBu3TqKi4sJhULMnDmTRYsWUVVVxcGDB6msrASgoaGBwsJCHnzwQX72s59RUVHxkZpramr6/NyhQiPQSdTY3kw+joxgYbpLERERESEvL4+dO3eydu1aRo8ezZIlS1i/fv1H2rz22mvMmTOH0aNH4/f7Wbp0KVu3buXll1/mM5/5TPfSbsXF/zlAeN1115GVlUVpaSljxozhyJEjADzwwANMnTqVWbNmceDAAfbt28eECRN49913+da3vsWmTZsoKCg4Zc2n+tyhQiPQSdTc0UyJc5CtAC0iIiIfdaqR4lTy+XzMmTOHOXPmMGXKFB566KGPvO+c6/U651yfq1McnxJy/P7RaJQtW7awefNmtm/fTjAYZM6cOYTDYYqKinj99df5wx/+wC9/+UseffRR1q1b12e9p/rcoUIj0EnU2tHMKBeH7FHpLkVERESEt99+m3379nUf79q1i3PPPZf8/Hyam5sB+OQnP8mf/vQnamtricVibNiwgSuvvJLLL7+cP/3pT7z33nsA/U6laGxspKioiGAwyN69e3n55ZcBqK2tJR6Ps2jRIv7+7/+ev/zlLwAfqaGnRD83HTQCnUTtkQbyMI1Ai4iIyJDQ0tLCt771LRoaGvD7/XziE59g7dq1bNiwgfnz5zN27FheeOEF7r//fq666iqcc1x77bXccMMNAKxdu5Ybb7yReDzOmDFjePbZZ/v8rHnz5rFmzRrKy8uZOHEis2bNAuDgwYPccsstxONxAO6//34Ali9fzm233UZOTg7bt2/vvs/o0aMT+tx0sL6G7YeqiooKd/wbmkPNvPVfYlH7Ib4+/8dwzifTXY6IiIik2Z49e7j44ovTXYZ40NuflZntdM5VnNhWUziSpDHcRjweYpT5IEcj0CIiIiIjlQJ0khxqqu9cAzrDrznQIiIiIiOYAnSSHG6ux+diFGb4FKBFRERERjAF6CQ53FKPz0Up8ueAX9t4i4iIiIxUCtBJUtPa0LWNdwkM8bULRUREROT0KUAnSV1bAwEXpyi3NN2liIiIiEgKKUAnSX24gQIgI6co3aWIiIiIdPP5fEybNo2pU6cyffp0/vznP5+yfUNDA//8z//c733nzJnDUF1aONUUoJOkqb2JQue0hJ2IiIgMKTk5OezatYvXX3+d+++/n+9973unbO81QJ/JFKCTpKWjiSIX0wocIiIiMmQ1NTVRVNT5r+UtLS1cffXVTJ8+nSlTpvDkk08CsGrVKt555x2mTZvGXXfdBcBPfvITpkyZwtSpU1m1alX3/X73u99x2WWXceGFF/Liiy8O/g+UJtrKO0lCkXoK0RJ2IiIi0oed6+FYVXLvWXQezFh+yiahUIhp06YRDoc5fPgwzz//PADZ2dk8/vjjFBQUUFtby6xZs1iwYAGrV6+msrKSXbt2AfD73/+eJ554gldeeYVgMEh9fX33vaPRKK+++irPPPMM99xzD5s3b07uzzdEKUAnQUc0SiTW3LkLoQK0iIiIDCHHp3AAbN++na985StUVlbinOP73/8+W7duJSMjg4MHD3LkyJGTrt+8eTO33HILwWAQgOLi4u73brzxRgBmzJhBVVVV6n+YIUIBOgkONXWuAT0qwwfZmgMtIiIivehnpHgwXH755dTW1lJTU8MzzzxDTU0NO3fuJBAIcN555xEOh0+6xjmH9bFEb1ZWFtD5RcVoNJrS2ocSzYFOgkPN9WQQpci0jbeIiIgMXXv37iUWi1FSUkJjYyNjxowhEAjwwgsv8P777wOQn59Pc3Nz9zXXXHMN69ato62tDeAjUzjOVBqBToIPW47hczGKfArQIiIiMrQcnwMNnaPJDz30ED6fj6VLl/L5z3+eiooKpk2bxkUXXQRASUkJs2fPZvLkycyfP5+f/vSn7Nq1i4qKCjIzM7n22mv50Y9+lM4fKe0UoJPgSOsx/C5KsT8PAjnpLkdERESkWywW6/V8aWkp27dv7/W93/zmNx85XrVq1UdW3wDYsmXLR+51Js2B1hSOJKhra8BHTNt4i4iIiJwBFKCToD7USC6QFSzut62IiIiIDG8K0EnQ0N5AoUPzn0VERETOAArQSdDU0UQxcS1hJyIiInIGUIBOgpaORori2sZbRERE5EygAD1A8Xic9mijdiEUEREROUMoQA9QTVsz5jq0iYqIiIgMSWbGsmXLuo+j0SijR4/m+uuvB2Djxo2sXr36lPc4dOgQixcvBmD9+vWsXLkyoRq8rBu9fPlyHnvsMU/3i8ViXHrppd0/w2BTgB6gj27jrQAtIiIiQ0tubi6VlZWEQiEAnn32WcaPH9/9/oIFC05a4/lE48aN8xxue5PsjVf+8R//kYsvvjip90yEAvQAHWquw0eU4gw/5OhLhCIiIjL0zJ8/n6effhqADRs2cPPNN3e/13NEefny5dx+++1cccUVTJgwoTs0V1VVMXny5O5rDhw4wLx585g4cSL33HNP9/mFCxcyY8YMJk2axNq1a4HOTViO74a4dOlSAB5++GHKy8uZOnXqR0bHt27detJnn6i6upqnn36ar33ta8nomtOinQgH6Gj3Nt4BjUCLiIhInx7762NUN1cn9Z5l+WUsvnBxv+1uuukm7r33Xq6//nreeOMNVqxYwYsvvthr28OHD7Nt2zb27t3LggULuqdu9PTqq69SWVlJMBhk5syZXHfddVRUVLBu3TqKi4sJhULMnDmTRYsWsXr1ah588EF27doFwO7du7nvvvt46aWXKC0tpb6+PqHP/va3v81PfvITmpubvXZT0mkEeoBq2xrwuwhFmfkQCKa7HBEREZGTlJeXU1VVxYYNG7j22mtP2XbhwoVkZGRwySWXcOTIkV7bzJ07l5KSEnJycrjxxhvZtm0bAA888ABTp05l1qxZHDhwgH379p107fPPP8/ixYspLS0FoLj4Pzei6++zn3rqKcaMGcOMGTM8/+ypoBHoAaptayDoouSOGq9tvEVERKRPXkaKU2nBggXceeedbNmyhbq6uj7bZWVldb92zvXaxk7IPGbGli1b2Lx5M9u3bycYDDJnzhzC4fBJ1zrnTrre62e/9NJLbNy4kWeeeYZwOExTUxNf/vKX+fWvf93nz5MKGoEeoIb2RopdjIxR49JdioiIiEifVqxYwQ9+8AOmTJky4Hs9++yz1NfXEwqFeOKJJ5g9ezaNjY0UFRURDAbZu3cvL7/8cnf7QCBAJBIB4Oqrr+bRRx/tDvE9p3D05/7776e6upqqqip++9vf8tnPfnbQwzNoBHrAmsPH+LiLQr4CtIiIiAxdZWVl3HHHHUm516c+9SmWLVvG/v37+dKXvkRFRQVTpkxhzZo1lJeXM3HiRGbNmtXd/tZbb6W8vJzp06fzyCOPcPfdd3PllVfi8/m49NJLWb9+fVLqGizW19D8UFVRUeF27NiR7jK63fjrW7m8dQ93/c1qOG92ussRERGRIWTPnj1pXW5NvOvtz8rMdjrnKk5sqykcAxSJ1FOID/LPTncpIiIiIjIIFKAHoCHUiou3Umg+yB+b7nJEREREZBAoQA/A3ppqAi7CmOwiyNQSdiIiIiJnAgXoAXjn2GECroOzCsrSXYqIiIiIDBIF6AF4v6EzQJeVfjzdpYiIiIjIIFGAHoAPGw9Q6OLklZyX7lJEREREZJAoQA9AU0sVpS4AheemuxQRERGRXpkZy5Yt6z6ORqOMHj2a66+/HoCNGzeyevXqU97j0KFDLF7cuZPi+vXrWblyZUI1/OhHP+q3zfLly3nsscdO2SYcDnPZZZcxdepUJk2axN/93d91v3fXXXdx0UUXUV5ezhe+8AUaGhoSqjERCtAD0Bo+zGjzQ5ECtIiIiAxNubm5VFZWEgqFgM5dBMePH9/9/oIFC1i1atUp7zFu3Lh+w+2peAnQXmRlZfH888/z+uuvs2vXLjZt2tS94+HcuXOprKzkjTfe4MILL+T+++9Pymf2RgH6NB1rayEab6IkUADZo9JdjoiIiEif5s+fz9NPPw3Ahg0buPnmm7vf6zmivHz5cm6//XauuOIKJkyY0B2aq6qqmDx5cvc1Bw4cYN68eUycOJF77rmn+/zChQuZMWMGkyZNYu3atQCsWrWKUCjEtGnTWLp0KQAPP/ww5eXlTJ069SOj41u3bj3ps3syM/Ly8gCIRCJEIhHMDIBrrrkGv79zk+1Zs2ZRXV09wF7rm7byPk1v1x4ky4UpLbgo3aWIiIjIMHDs0UeJHEhuqAt8rIyiL36x33Y33XQT9957L9dffz1vvPEGK1as4MUXX+y17eHDh9m2bRt79+5lwYIF3VM3enr11VeprKwkGAwyc+ZMrrvuOioqKli3bh3FxcWEQiFmzpzJokWLWL16NQ8++CC7du0CYPfu3dx333289NJLlJaWUl9fn9Bnx2IxZsyYwf79+/nmN7/JJz/5yZParFu3jiVLlvTbL6dLI9Cn6Z26agKug7GlF6a7FBEREZFTKi8vp6qqig0bNnDttdeesu3ChQvJyMjgkksu4ciRI722mTt3LiUlJeTk5HDjjTeybds2AB544AGmTp3KrFmzOHDgAPv27Tvp2ueff57FixdTWloKQHFxcUKf7fP52LVrF9XV1d1Bvqf77rsPv9/fPdqdChqBPk0Hj74FznHO+CnpLkVERESGAS8jxam0YMEC7rzzTrZs2UJdXV2f7bKysrpfO+d6bXN82kTP4y1btrB582a2b99OMBhkzpw5hMPhk651zp10fSKffVxhYSFz5sxh06ZN3dNLHnroIZ566imee+65Pj8jGTQCfRpa29t57dA2ziWTgjEagRYREZGhb8WKFfzgBz9gypSBD/49++yz1NfXEwqFeOKJJ5g9ezaNjY0UFRURDAbZu3dv95f7AAKBAJFIBICrr76aRx99tDvE95zC0Z+ampru1TVCoRCbN2/moos6p9Nu2rSJH//4x2zcuJFgMLU7RGsE+jT88pUncNEPWZx9NuSPTXc5IiIiIv0qKyvjjjvuSMq9PvWpT7Fs2TL279/Pl770JSoqKpgyZQpr1qyhvLyciRMnMmvWrO72t956K+Xl5UyfPp1HHnmEu+++myuvvBKfz8ell17K+vXrPX3u4cOH+epXv0osFiMej/PFL36xezm+lStX0t7ezty5c4HOLxKuWbMmKT/viay/4fGhpqKiwu3YsSNtn98YbmP5b5Yys6OG7191N0ycn7ZaREREZGjbs2cPF198cbrLEA96+7Mys53OuYoT22oKR4J+//ofyY1W87mzZsCF89JdjoiIiIgMMgXoRDjH2289RJ7zM/1zd0MKJ6eLiIiIyNCkAJ2A5j3P8H5HNWOLr8CfPybd5YiIiIhIGihAe1X1Eq/8+Z9ozsjhiqnL+m8vIiIiIiOSVuHw4J13X+ORZ7/LmxkZhHKmcNXHtfaziIiIyJlKAdqD0rGX8Nfsc5l+zjxuqbgev8+X7pJz1LV9AAAMtklEQVREREREJE00hcODUTm5PLzs//C9q5Zxdn5RussRERER8czMWLbsP6efRqNRRo8e3b1+8saNG1m9evUp73Ho0CEWL14MwPr161m5cmVCNfzoRz/qt83y5ct57LHH+m23YsUKxowZ07374HF33XUXF110EeXl5XzhC1/o3nAlEonw1a9+lSlTpnDxxRdz//33J1R7bxSgPcrIUFeJiIjI8JObm0tlZSWhUAjo3EVw/Pjx3e8vWLCAVatWnfIe48aN8xRu++IlQHu1fPlyNm3adNL5uXPnUllZyRtvvMGFF17YHZR/97vf0d7ezptvvsnOnTv5l3/5F6qqqgZUg1KhiIiIyAg3f/58nn76aQA2bNjAzTff3P1ezxHl5cuXc/vtt3PFFVcwYcKE7tBcVVX1kRHfAwcOMG/ePCZOnMg999zTfX7hwoXMmDGDSZMmsXbtWgBWrVpFKBRi2rRpLF26FICHH36Y8vJypk6d+pHR8a1bt5702Sf6zGc+Q3Fx8Unnr7nmGvz+ztnJs2bNorq6GugcgW9tbSUajRIKhcjMzKSgoCDBHvyolM6BNrN5wD8CPuBXzrnVJ7w/B3gSeK/r1H845+5NZU0iIiIi6bD7xYM01YaTes+C0mwmfXp8v+1uuukm7r33Xq6//nreeOMNVqxYwYsvvthr28OHD7Nt2zb27t3LggULuqdu9PTqq69SWVlJMBhk5syZXHfddVRUVLBu3TqKi4sJhULMnDmTRYsWsXr1ah588EF27doFwO7du7nvvvt46aWXKC0tpb6+PqHP9mLdunUsWbIEgMWLF/Pkk08yduxY2tra+PnPf95rAE9EygK0mfmAXwJzgWrgNTPb6Jx764SmLzrnrk9VHSIiIiJnuvLycqqqqtiwYQPXXnvtKdsuXLiQjIwMLrnkEo4cOdJrm7lz51JSUgLAjTfeyLZt26ioqOCBBx7g8ccfBzpHqfft29fd7rjnn3+exYsXU1paCvCRMOvls/tz33334ff7u0e7X331VXw+H4cOHeLYsWN8+tOf5nOf+xwTJkw4rftDakegLwP2O+feBTCz3wI3ACcGaBEREZERz8tIcSotWLCAO++8ky1btlBXV9dnu6ysrO7Xzrle29gJuzGbGVu2bGHz5s1s376dYDDInDlzCIdPHnF3zp10fSKffSoPPfQQTz31FM8991z3Z/zmN79h3rx5BAIBxowZw+zZs9mxY8eAAnQq50CPBw70OK7uOneiy83sdTP7vZlNSmE9IiIiImesFStW8IMf/IApUwa+n8Wzzz5LfX09oVCIJ554gtmzZ9PY2EhRURHBYJC9e/fy8ssvd7cPBAJEIhEArr76ah599NHuEN9zCsdAbNq0iR//+Mds3LiRYDDYff6cc87h+eefxzlHa2srL7/8MhdddNGAPiuVAbq3/7U48X8l/gKc65ybCvwT8ESvNzK71cx2mNmOmpqaJJcpIiIiMvKVlZVxxx13JOVen/rUp1i2bBnTpk1j0aJFVFRUMG/ePKLRKOXl5fzt3/4ts2bN6m5/6623Ul5eztKlS5k0aRJ33303V155JVOnTuU73/lOQp998803c/nll/P2229TVlbGv/3bvwGwcuVKmpubmTt3LtOmTeO2224D4Jvf/CYtLS1MnjyZmTNncsstt1BeXj6gn99OZ3jc043NLgd+6Jz7m67j7wE45/pcfM/MqoAK51xtX20qKircjh07klytiIiISPLt2bOHiy++ON1liAe9/VmZ2U7nXMWJbVM5Av0acIGZnW9mmcBNwMYTijrbuiaomNllXfX0PSlHRERERCTNUvYlQudc1MxWAn+gcxm7dc653WZ2W9f7a4DFwDfMLAqEgJtcqobERURERESSIKXrQDvnngGeOeHcmh6vHwQeTGUNIiIiIiLJpJ0IRURERFJI/7g+9CX6Z6QALSIiIpIi2dnZ1NXVKUQPYc456urqyM7O9nxNSqdwiIiIiJzJysrKqK6uRsvwDm3Z2dmUlZV5bq8ALSIiIpIigUCA888/P91lSJJpCoeIiIiISAIUoEVEREREEqAALSIiIiKSgJRt5Z0qZlYDvJ+mjy8F+txmXE6i/kqM+isx6q/Eqc8So/5KjPorceqzxKSjv851zo0+8eSwC9DpZGY7etsPXXqn/kqM+isx6q/Eqc8So/5KjPorceqzxAyl/tIUDhERERGRBChAi4iIiIgkQAE6MWvTXcAwo/5KjPorMeqvxKnPEqP+Soz6K3Hqs8QMmf7SHGgRERERkQRoBFpEREREJAEK0B6Y2Twze9vM9pvZqnTXMxSZWZWZvWlmu8xsR9e5YjN71sz2df1elO4608nM1pnZUTOr7HGuzz4ys+91PXNvm9nfpKfq9Omjv35oZge7nrNdZnZtj/fO9P76mJm9YGZ7zGy3md3RdV7PWC9O0V96xnphZtlm9qqZvd7VX/d0ndfz1YdT9JmesVMwM5+Z/V8ze6rreGg+Y845/TrFL8AHvANMADKB14FL0l3XUPsFVAGlJ5z7CbCq6/Uq4MfprjPNffQZYDpQ2V8fAZd0PWtZwPldz6Av3T/DEOivHwJ39tJW/QVjgeldr/OBv3b1i56xxPpLz1jv/WVAXtfrAPAKMEvP12n1mZ6xU/fbd4DfAE91HQ/JZ0wj0P27DNjvnHvXOdcB/Ba4Ic01DRc3AA91vX4IWJjGWtLOObcVqD/hdF99dAPwW+dcu3PuPWA/nc/iGaOP/uqL+su5w865v3S9bgb2AOPRM9arU/RXX870/nLOuZauw0DXL4eerz6dos/6csb3mZmVAdcBv+pxekg+YwrQ/RsPHOhxXM2p/5I9Uzngj2a208xu7Tp3lnPuMHT+xwoYk7bqhq6++kjPXd9WmtkbXVM8jv9TnvqrBzM7D7iUzhEvPWP9OKG/QM9Yr7r+aX0XcBR41jmn56sfffQZ6Bnryy+A/weI9zg3JJ8xBej+WS/ntHTJyWY756YD84Fvmtln0l3QMKfnrnf/G/g4MA04DPyvrvPqry5mlgf8O/Bt51zTqZr2cu6M67Ne+kvPWB+cczHn3DSgDLjMzCafovkZ31/QZ5/pGeuFmV0PHHXO7fR6SS/nBq2/FKD7Vw18rMdxGXAoTbUMWc65Q12/HwUep/OfUY6Y2ViArt+Ppq/CIauvPtJz1wvn3JGu/yDFgX/lP/+5Tv0FmFmAzjD4iHPuP7pO6xnrQ2/9pWesf865BmALMA89X5707DM9Y32aDSwwsyo6p8t+1sx+zRB9xhSg+/cacIGZnW9mmcBNwMY01zSkmFmumeUffw1cA1TS2U9f7Wr2VeDJ9FQ4pPXVRxuBm8wsy8zOBy4AXk1DfUPK8b9Eu3yBzucM1F+YmQH/Buxxzv1Dj7f0jPWir/7SM9Y7MxttZoVdr3OAzwF70fPVp776TM9Y75xz33POlTnnzqMzaz3vnPsyQ/QZ8w/WBw1Xzrmoma0E/kDnihzrnHO701zWUHMW8Hjnf4/wA79xzm0ys9eAR83svwIfAP8ljTWmnZltAOYApWZWDfwdsJpe+sg5t9vMHgXeAqLAN51zsbQUniZ99NccM5tG5z/TVQH/DdRfXWYDy4A3u+ZcAnwfPWN96au/btYz1quxwENm5qNz8O1R59xTZrYdPV996avP/o+esYQMyb/DtBOhiIiIiEgCNIVDRERERCQBCtAiIiIiIglQgBYRERERSYACtIiIiIhIAhSgRUREREQSoAAtIjKMmFnMzHb1+LUqifc+z8wq+28pInJm0zrQIiLDS6hra2AREUkTjUCLiIwAZlZlZj82s1e7fn2i6/y5Zvacmb3R9fs5XefPMrPHzez1rl9XdN3KZ2b/ama7zeyPXTuoiYhIDwrQIiLDS84JUziW9HivyTl3GfAg8Iuucw8CDzvnyoFHgAe6zj8A/Mk5NxWYDhzfYfUC4JfOuUlAA7AoxT+PiMiwo50IRUSGETNrcc7l9XK+Cvisc+5dMwsAHzrnSsysFhjrnIt0nT/snCs1sxqgzDnX3uMe5wHPOucu6Dr+LhBwzv3P1P9kIiLDh0agRURGDtfH677a9Ka9x+sY+q6MiMhJFKBFREaOJT1+3971+s/ATV2vlwLbul4/B3wDwMx8ZlYwWEWKiAx3GlkQERlecsxsV4/jTc6540vZZZnZK3QOjtzcde52YJ2Z3QXUALd0nb8DWGtm/5XOkeZvAIdTXr2IyAigOdAiIiNA1xzoCudcbbprEREZ6TSFQ0REREQkARqBFhERERFJgEagRUREREQSoAAtIiIiIpIABWgRERERkQQoQIuIiIiIJEABWkREREQkAQrQIiIiIiIJ+P8BYxAoCGyV4xIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(sgd_loss, label=\"Stochastic\", alpha=0.7)\n",
    "plt.plot(bgd_loss, label=\"Batch\", alpha=0.7)\n",
    "plt.plot(mbgd_loss_4, label=\"Minibatch 4\", alpha=0.7)\n",
    "plt.plot(mbgd_loss_32, label=\"Minibatch 32\", alpha=0.7)\n",
    "plt.plot(mbgd_loss_128, label=\"Minibatch 128\", alpha=0.7)\n",
    "\n",
    "plt.yscale('log')\n",
    "ticks = [0.028, 0.04, 0.056, 0.08, 0.112, 0.16, 0.225, 0.32, 0.45, 0.64]\n",
    "plt.yticks(ticks=ticks, labels=ticks)\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.title(\"Loss evaluation\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(sgd_gradient.sum(axis=1), label=\"Stochastic\", alpha=0.7)\n",
    "plt.plot(bgd_gradient.sum(axis=1), label=\"Batch\", alpha=0.7)\n",
    "plt.plot(mbgd_gradient_4.sum(axis=1), label=\"Minibatch 4\", alpha=0.7)\n",
    "plt.plot(mbgd_gradient_32.sum(axis=1), label=\"Minibatch 32\", alpha=0.7)\n",
    "plt.plot(mbgd_gradient_128.sum(axis=1), label=\"Minibatch 128\", alpha=0.7)\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.ylabel(\"Gradient\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.title(\"Gradient evaluation\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(sgd_acc, label=\"Stochastic\", alpha=0.7)\n",
    "plt.plot(bgd_acc, label=\"Batch\", alpha=0.7)\n",
    "plt.plot(mbgd_acc_4, label=\"Minibatch 4\", alpha=0.7)\n",
    "plt.plot(mbgd_acc_32, label=\"Minibatch 32\", alpha=0.7)\n",
    "plt.plot(mbgd_acc_128, label=\"Minibatch 128\", alpha=0.7)\n",
    "\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.title(\"Test accuracy\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What may we see in the plots? First of all, the stochastic and minibatch with small batch sizes are almost identical - green and blue lines lays on each other, and it is very hard to distinguish them. Small batches behave identical to stochastic gradient descent - however, the running time is over three times faster.\n",
    "\n",
    "The batch version, when we use only a single update in each epoch, has gradients at the beginning much bigger and decreases under minibatch around 170th epoch - it probably converged to better local optima, as we can see in the loss evaluation loss. This is the main advantage of batch gradient descent - it always decreases the loss. This doesn't mean the algorithm is better (it may overfit). From the \"test accuracy\" plot, all the algorithms reached almost the same value.\n",
    "\n",
    "Minibatch versions with bigger batch sizes have faster training with respect to epochs. We can see that in the first 100 epochs in the loss evaluation and test accuracy plots. The speedup is even in real time, as we can see from running times. The minibatch version runs over ten times faster compared to the stochastic version! That is a huge speed up and it is usually a good tradeoff, as we may train the network much faster. Note that although the minibatch with batch size 32 ran the around same amount of time as the batch version, in reality, the difference would be much bigger. MNIST dataset is not very big and it can fit fully into the memory. For bigger datasets, this doesn't need to be the case.\n",
    "\n",
    "The last thing, that we do not see here is, that the minibatch version with a reasonably big batch size is more stable compare to the stochastic one. Its a bit visible in the test accuracy plot, where the minibatch curve is a little bit smoother. We will see this more significantly later on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is one more thing I want to point out. In the implementation, we sum the gradients of examples. It is this line: `op_gradient = self._learning_rate * np.sum(gradient, axis=0)`. There is a discussion, whether we should sum the gradients or mean them. First of all, it doesn't really matter for the functionality, as with proper learning rate, the resulting value is the same. There are two views - if we use the sum, we may increase the batch size and the neural network will train at the same speed (with respect to epochs). In reality, it would be training a bit faster, as there are fewer iterations in the epoch. However, the batch size needs to fit into the memory and we must be careful about the batch size. If we use too big, the gradient can explode and the result will be the same as if we set the learning rate too big. On the contrary, if we mean gradients over examples, with the bigger batch size the network will train at the same speed, but this time with respect to iterations. As there would be fewer iterations in the epoch, the network would need more epochs to train into the same level, and thus it needs more time. On the other hand, there is no problem with the gradient.\n",
    "\n",
    "Once more, the operation doesn't really matter, as with properly scaled learning rate the resulting gradient values will be same. Both Pytorch and TensorFlow uses sum, so I will stick to it as well."
   ]
  }
 ],
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