MLP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MLP\n",
    "**Multi-Layer Perceptron** - каноничный вид искусственных нейронных сетей *прямого распространения*. Включает в себя один или более *скрытых полносвязных слоев*. В данном Jupyer-notebook представленная реализация MLP для решения задачи *многоклассовой классификации*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Библиотеки\n",
    "В первую очередь используется математическая библиотека NumPy, а также sklearn для загрузки датасетов и случайной перетасовки данных."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.utils import shuffle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sklearn.datasets \n",
    "import sklearn.linear_model \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#random seed, which's used in several funcs by default\n",
    "seed = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Инициализация весов\n",
    "Беря в расчет специфику функций активации и работу сети - веса должны быть случайно распределны в небольшой области нуля.\n",
    "В данной реализации используется [*Xavier-подобная инициализация*](http://andyljones.tumblr.com/post/110998971763/an-explanation-of-xavier-initialization)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def initialize_weights(mat_shape):\n",
    "    np.random.seed(seed)    \n",
    "    res = np.random.randn(*mat_shape)*np.sqrt(2 / (mat_shape[0] + mat_shape[1]))\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.24835708 -0.06913215  0.32384427  0.76151493 -0.11707669]\n",
      " [-0.11706848  0.78960641  0.38371736 -0.23473719  0.27128002]\n",
      " [-0.23170885 -0.23286488  0.12098114 -0.95664012 -0.86245892]]\n"
     ]
    }
   ],
   "source": [
    "print(initialize_weights((3,5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Деление на обучающую и валидационную выборки\n",
    "Для проведения оценки работы сети, необходимо поделить генеральную выборку, предварительно перемешав примеры."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Важно:_** в данном коде используется нотация, в которой выборка подается на вход сети в формате **(m x n)**, где m - число примеров в выборке, n - число признаков."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def __train_test_split__(data, ratio, random_seed):\n",
    "    #this func is auxiliary\n",
    "    dset = shuffle(data, random_state = random_seed)\n",
    "    return (dset[:int(len(dset) * ratio)], dset[int(len(dset) * ratio):])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_test_split(X, y, ratio = 0.8, random_seed = seed):\n",
    "    #X, y - numpy array\n",
    "    #input data should be in format m x n, where m is the number of samples for X,\n",
    "    #n is the number of features and (m, ) for y\n",
    "    assert len(X) == len(y), 'lengths of arrays are not the same'\n",
    "    TrainX, TestX = __train_test_split__(X, ratio, random_seed)\n",
    "    TrainY, TestY = __train_test_split__(y, ratio, random_seed)\n",
    "    #converts 1D-array to 2D-array\n",
    "    if len(TestY.shape) == 1:\n",
    "        TestY = TestY[:,np.newaxis]\n",
    "        TrainY = TrainY[:,np.newaxis]\n",
    "    return (TrainX, TrainY, TestX, TestY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 3,  4,  5],\n",
      "       [12, 13, 14],\n",
      "       [ 6,  7,  8],\n",
      "       [ 0,  1,  2]]), array([[1],\n",
      "       [4],\n",
      "       [2],\n",
      "       [0]]), array([[ 9, 10, 11]]), array([[3]]))\n"
     ]
    }
   ],
   "source": [
    "print(train_test_split(np.array(range(15)).reshape((5,3)),np.array(range(5)).reshape((5,))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Минибатчи\n",
    "Данная реализация обучения сети поддерживает работу с минибатчами данных, что является обобщенным вариантом *Градиентного спуска* и *Стохастического градиентного спуска*. Для этих случаев сделайте размер mbatchsize равным *размеру выборки* и *1* - соответсвенно. Во время работы алгоритма данные *транспонируются*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def minibatch_list(dataX, labelsY, mbatchsize = 32):\n",
    "    #input data should be in format m x n, where m is the number of samples\n",
    "    #and n is the number of features, y is m x 1\n",
    "    #output data is in the format n x batchsize (transposed) in list\n",
    "    assert dataX.shape[0] == labelsY.shape[0]\n",
    "    \n",
    "    data, labels = shuffle(dataX, labelsY)\n",
    "    fulls = data.shape[0] // mbatchsize\n",
    "    resX = []\n",
    "    resY = []\n",
    "    for i in range(fulls):\n",
    "        resX.append(np.transpose(data[i * mbatchsize:(i+1) * mbatchsize]))\n",
    "        resY.append(np.transpose(labels[i * mbatchsize:(i+1) * mbatchsize]))\n",
    "    if data.shape[0] % mbatchsize != 0:\n",
    "        resX.append(np.transpose(data[fulls*mbatchsize:]))\n",
    "        resY.append(np.transpose(labels[fulls*mbatchsize:]))\n",
    "    return (resX , resY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([[ 0,  9],\n",
      "       [ 1, 10],\n",
      "       [ 2, 11]]), array([[ 3, 12],\n",
      "       [ 4, 13],\n",
      "       [ 5, 14]]), array([[6],\n",
      "       [7],\n",
      "       [8]])] (3, 2)\n",
      "[array([[0, 3]]), array([[1, 4]]), array([[2]])] (1, 2)\n"
     ]
    }
   ],
   "source": [
    "x, y = minibatch_list(np.array(range(15)).reshape((5,3)), np.array(range(5)).reshape((5,1)), mbatchsize=2)\n",
    "print(x, x[0].shape)\n",
    "print(y, y[0].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Функции активации"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Сигмоида\n",
    "В [старых источниках](https://books.google.ru/books/about/%D0%9D%D0%B5%D0%B9%D1%80%D0%BE%D0%BD%D0%BD%D1%8B%D0%B5_%D1%81%D0%B5%D1%82%D0%B8_%D0%BF%D0%BE%D0%BB%D0%BD%D1%8B%D0%B9.html?hl=ru&id=LPMr0iA0muwC \"Саймон Хайкин\") можно найти так называемые *\"сигмоидальные функции\"*, к которым относятся такие популярные функции активации как *гиперболический тангенс* и *логистическая функция*(от которой подшло название *логистической регрессии*). Однако в более современных источниках все обозначают *\"сигмоидой\"* именно логистическую функцию. Её упрощённый вариант(без параметров) представлен ниже:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\ \\sigma(y) = \\frac{1}{1 - e^{-y}} \\\\\n",
    "\\end{align}\n",
    "где *y* - может быть и вектором и скаляром"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(X):\n",
    "    return 1 / (1 + np.exp(-X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Также нам потребуется производная этой функции"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid_der(X):\n",
    "    return sigmoid(X) * (1 - sigmoid(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.5        0.52497919 0.549834  ]\n",
      " [0.57444252 0.59868766 0.62245933]\n",
      " [0.64565631 0.66818777 0.68997448]\n",
      " [0.7109495  0.73105858 0.75026011]\n",
      " [0.76852478 0.78583498 0.80218389]]\n",
      "[[0.25       0.24937604 0.24751657]\n",
      " [0.24445831 0.24026075 0.23500371]\n",
      " [0.22878424 0.22171287 0.2139097 ]\n",
      " [0.20550031 0.19661193 0.18736988]\n",
      " [0.17789444 0.16829836 0.1586849 ]]\n"
     ]
    }
   ],
   "source": [
    "print(sigmoid(np.array(range(15)).reshape((5,3))*0.1))\n",
    "print(sigmoid_der(np.array(range(15)).reshape((5,3))*0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ReLU\n",
    "Rectified Linear Unit - одна из наиболее пополярных функций активации\n",
    "\n",
    "\\begin{align}\n",
    "\\ ReLU(y) = \\max(0,y) \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu(X):\n",
    "    return X * (X > 0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Также нам потребуется производная этой функции"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu_der(X):\n",
    "    return (X > 0.)*1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.  0.1 0.2]\n",
      " [0.3 0.4 0.5]\n",
      " [0.6 0.7 0.8]\n",
      " [0.9 1.  1.1]\n",
      " [1.2 1.3 1.4]]\n",
      "[[0. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(relu(np.array(range(15)).reshape((5,3))*0.1))\n",
    "print(relu_der(np.array(range(15)).reshape((5,3))*0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### One-hot encoding\n",
    "[Популярный способ закодировать](https://machinelearningmastery.com/why-one-hot-encode-data-in-machine-learning/) некоторый набор классов в *sparse-vector*, где для каждой сущности выбирается индекс в массиве и ставится 1, если этот пример соотвествует этой сущности.\n",
    "\n",
    "**_Важно:_** для бинарной классификации достаточно и обычного представления в виде серии 0 и 1, размерности m x 1, кроме случаев *классификации с отклонением*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_onehot(array, num_classes):\n",
    "    #input array should be (m x 1) or (m, )\n",
    "    if len(array.shape) > 1:\n",
    "        array = array.reshape(len(array),)\n",
    "    b = np.zeros((len(array), num_classes), dtype=np.int)\n",
    "    b[np.arange(len(array)), array] = 1\n",
    "    return b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0]\n",
      " [1 0 0 0]\n",
      " [0 0 0 1]\n",
      " [0 0 1 0]\n",
      " [0 1 0 0]\n",
      " [1 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "print(make_onehot(np.array([1,0,3,2,1,0]).reshape(6,1), 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0]\n",
      " [1 0 0 0]\n",
      " [0 0 0 1]\n",
      " [0 0 1 0]\n",
      " [0 1 0 0]\n",
      " [1 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "print(make_onehot(np.array([1,0,3,2,1,0]).reshape(6,), 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Функция потерь\n",
    "Для обучения сети, необходимо определить *функцию потерь*, которую мы будем оптимизировать.\n",
    "В иностранный литературе встречается два похожих определения - *Loss function* и *Cost function*. Где Cost - сумма всех потерь за батч, разделенная на число примеров. В данной реализации вычисляется именно \"Cost\", но в соотвествии с общепринятой нотацией обозначается как \"loss\". В это же время производная этой функции вычисляется в векторном виде, т.е. сразу по *оценке y*. Также отметим, что *cross-entropy log loss, binary log loss, log loss* в случае с *бинарной* классификацией, означают одно и то же.\n",
    "\n",
    "Для задачи *много-классовой классификации* вводится суммирование по *c* - числу классов. **_Важно:_** когда вы используете бинарную классификацию, убедитесь, что массив labels имеет размерность 1 x m, не ( , m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\ Binary~Cost(y, \\hat{y}) = - \\frac{1}{m} \\sum_{i=1}^m y \\cdot log( \\hat{y}) + (1 - y) \\cdot log(1- \\hat{y})\\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\ MultiClass~Cost(y, \\hat{y}) = - \\frac{1}{m} \\sum_{i=1}^m \\frac{1}{c} \\sum_{j=1}^c y \\cdot log( \\hat{y}) + (1 - y) \\cdot log(1- \\hat{y})\\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cross_entropy_log_loss(output, labels, epsilon = 1e-9):\n",
    "    #output is c * m, so and labels is c * m\n",
    "    #result is cross-entropy log-loss, 1 * 1\n",
    "    assert output.shape == labels.shape, 'Shapes do not match'\n",
    "    #to avoid log of 0\n",
    "    eps = np.zeros(labels.shape) + epsilon\n",
    "    y = np.maximum(eps, np.minimum(1 - eps, output))\n",
    "    return -np.sum((labels * np.log(y) + (1 - labels) * np.log(1 - y))) / labels.shape[1] / labels.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9989776916432564"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummyL = make_onehot(np.array([1,0,3,2,1,0]).reshape(6,1), 4)\n",
    "dummyY = (make_onehot(np.array([1,0,3,2,1,1]).reshape(6,1), 4))* 0.95\n",
    "cross_entropy_log_loss(dummyY, dummyL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cross_entropy_log_loss_der(output, labels, epsilon = 1e-9):\n",
    "    assert output.shape == labels.shape, 'First dim is not 1'\n",
    "    #to avoid log of 0\n",
    "    eps = np.zeros(labels.shape) + epsilon\n",
    "    y = np.maximum(eps, np.minimum(1 - eps, output))\n",
    "    return - labels / y + (1 - labels) / (1 - y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00, -1.05263158e+00,  1.00000000e+00,\n",
       "         1.00000000e+00],\n",
       "       [-1.05263158e+00,  1.00000000e+00,  1.00000000e+00,\n",
       "         1.00000000e+00],\n",
       "       [ 1.00000000e+00,  1.00000000e+00,  1.00000000e+00,\n",
       "        -1.05263158e+00],\n",
       "       [ 1.00000000e+00,  1.00000000e+00, -1.05263158e+00,\n",
       "         1.00000000e+00],\n",
       "       [ 1.00000000e+00, -1.05263158e+00,  1.00000000e+00,\n",
       "         1.00000000e+00],\n",
       "       [-1.00000000e+09,  2.00000000e+01,  1.00000000e+00,\n",
       "         1.00000000e+00]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy_log_loss_der(dummyY, dummyL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Слой сети\n",
    "В нашей сети можно будет задавать произвольное число своев произвольного размера. Для упрощения работы с кодом, инкапсулируем методы связанные с одним слоев в класс *\"Layer\"*.\n",
    "При инициализации класса необходимо задать число нейронов на предыдущем слое и текущем, а также функцию активации (по умолчанию - сигмоида).\n",
    "\n",
    "*Метод forward* производит прямой прогон слоя, т.е. активирует нейроны слоя. При этом вычисляются следующие значения и производятся следующие операции:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*m* - число примеров\n",
    "\n",
    "*n* - число нейронов на предыдущем слое\n",
    "\n",
    "*l* - число нейронов в этом слое\n",
    "\n",
    "\\begin{align}\n",
    "\\ Z_{l , m} = W_{l , n} \\cdot X_{n , m} + b_{l, 1} \\\\\n",
    "\\ A_{l , m} = Activation( Z_{l , m} ) \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Метод backward* вычисляет (но не применяет) градиент данного слоя.\n",
    "\n",
    "\\begin{align}\n",
    "\\ dW = dZ \\cdot X^{T} \\\\\n",
    "\\ dX = W^{T} \\cdot dZ \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Layer:\n",
    "    def __init__(self, input_size, output_size, activation='sigm'):\n",
    "        self.W = initialize_weights((output_size, input_size))\n",
    "        self.b = np.zeros((output_size, 1))\n",
    "        self.Wgrad = np.zeros((output_size, input_size))\n",
    "        self.bgrad = np.zeros((output_size, 1))\n",
    "        self.Z = None\n",
    "        self.X = None\n",
    "        \n",
    "        if activation == 'sigm':\n",
    "            self.activation_func = sigmoid\n",
    "            self.activation_func_der = sigmoid_der\n",
    "        elif activation == 'relu':\n",
    "            self.activation_func = relu\n",
    "            self.activation_func_der = relu_der\n",
    "        else:\n",
    "            raise Exception('unknown func {}, try sigm or relu'.format(activation))\n",
    "    \n",
    "    def forward(self, data):\n",
    "        #data should be in format n x m, where m - is num of examples, n - features\n",
    "        assert data.shape[0] == self.W.shape[1], 'data dimension does not match'\n",
    "        #this will be needed for gradient calc\n",
    "        self.Z = np.dot(self.W, data) + self.b\n",
    "        self.X = data\n",
    "        return self.activation_func(self.Z)\n",
    "    \n",
    "    def backward(self, grad):\n",
    "        assert grad.shape == self.Z.shape, 'gradient shape and Z do not match'\n",
    "        Zgrad = self.activation_func_der(self.Z) * grad\n",
    "        self.bgrad = np.sum(Zgrad, axis=-1, keepdims=True) #db = sum over axis=1\n",
    "        self.Wgrad = np.dot(Zgrad, np.transpose(self.X)) #dW = dZ*X^T\n",
    "        return np.dot(np.transpose(self.W),Zgrad) #dX = W^T*dZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 10)\n",
      "(2, 10)\n",
      "[[0.   0.02 0.04 0.06 0.08 0.1  0.12 0.14 0.16 0.18]\n",
      " [0.2  0.22 0.24 0.26 0.28 0.3  0.32 0.34 0.36 0.38]]\n",
      "[[0.02849662 0.07349237]]\n",
      "[[0.22497876]]\n"
     ]
    }
   ],
   "source": [
    "dummy = np.array(range(20)).reshape((2,10))*0.02\n",
    "a = Layer(2,1,activation='sigm')\n",
    "print(a.forward(dummy).shape)\n",
    "dummygrad = np.array(range(10)).reshape((1,10))*0.02\n",
    "print(a.backward(dummygrad).shape)\n",
    "print(a.X)\n",
    "print(a.Wgrad)\n",
    "print(a.bgrad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Метрика качества\n",
    "Существует много критериев оценки работы алгоритма, мы остановимся на \"точности\" - отношение числа верно указанных классов, ко всем примерам. Точность можно считать во время обучения, на валидационной выборке и на тестовой\n",
    "\\begin{align}\n",
    "\\ Accuracy = \\frac{\\sum^n _i [y _i=\\hat{y}_i]}{n} \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def accuracy_metrics(y, labels):\n",
    "    assert len(y) == len(labels), 'length is not the same'\n",
    "    summ = 0\n",
    "    y = np.array(y)\n",
    "    labels = np.array(labels)\n",
    "    for i in range(len(y)):\n",
    "        if np.array_equal(y[i],labels[i]):\n",
    "            summ += 1\n",
    "    return summ / len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    }
   ],
   "source": [
    "print(accuracy_metrics(make_onehot(np.array([1,0,3,2,1,0]).reshape(6,1), 4),\n",
    "                       make_onehot(np.array([0,1,3,2,0,0]).reshape(6,1), 4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Основной класс нейронной сети\n",
    "При инициализации сети необходимо задать число нейронов в каждом слое, число которых соответствует мощности массива, и соответствующие функции активации. Слои хранятся в массиве *layers*\n",
    "\n",
    "*Метод propagate forward* принимает на вход данные (n * m) и производит прямую прогонку сети, при этом каждый слой запоминает значения, вычисленные при прямом проходе, для дальнейшего вычисления градиента.\n",
    "\n",
    "*Метод propagate backward* выполняет обратный проход по сети, находя по очереди все градиенты для каждого слоя. На вход метод принимает посчитанное значение производной функции потерь\n",
    "\n",
    "*Метод update weights* изменяет веса нейронов слоев в соотвествии с оптимизирующим аглоритмом (Градиентный спуск)\n",
    "\n",
    "*Метод predict* использует выход метода *propagate forward* для *оценки класса (0 или 1)*\n",
    "\n",
    "*Метод fit* основной метод обучающий модель, последовательно выполняющий все операции, необходимые для обучения. Алгоритм имеет два критерия останова - по числу итераций и по размеру грудиента (если матричная норма получаемых градиентов меньше чем эпсилон, обучение прекращается). Эпоха - один прогон всей обучающей выборки, который в свою очередь включает один или несколько прогонов минибатчей. На каждой итерации вычислется выходное значение, потери, градент потерь, градиенты всех параметров. Затем градиенты применяются к параметрам."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Заимпортируем также метод *deepcopy* для создания полной копии объекта (используется для сохранения весов сети)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class MLP:\n",
    "    def __init__(self, input_size, layers, layers_activations):\n",
    "        assert len(layers) == len(layers_activations), 'num of layers and activations does not match'\n",
    "        self.layers = []\n",
    "        self.layers.append(Layer(input_size=input_size, output_size=layers[0], activation=layers_activations[0]))\n",
    "        for l in range(len(layers) - 1):\n",
    "            self.layers.append(Layer(input_size=layers[l], output_size=layers[l + 1], activation=layers_activations[l + 1]))\n",
    "    \n",
    "    def propagate_forward(self, data):\n",
    "        result = self.layers[0].forward(data)\n",
    "        for l in range(len(self.layers) - 1):\n",
    "            result = self.layers[l + 1].forward(result)\n",
    "        return result\n",
    "    \n",
    "    def propagate_backward(self, gradient):\n",
    "        grad = gradient\n",
    "        for l in reversed(self.layers):\n",
    "            grad = l.backward(grad)\n",
    "    \n",
    "    def update_weights(self, learning_rate, eps):\n",
    "        is_updated = False\n",
    "        for l in self.layers:\n",
    "            if (np.linalg.norm(l.Wgrad) / (l.Wgrad.shape[0] * l.Wgrad.shape[1]) > eps):\n",
    "                is_updated = True\n",
    "            l.W = l.W - l.Wgrad * learning_rate\n",
    "            l.b = l.b - l.bgrad * learning_rate\n",
    "        return is_updated\n",
    "    \n",
    "    def predict(self, inputX):\n",
    "        #support many data input types\n",
    "        X = np.array(inputX)\n",
    "        if len(X.shape) == 1:\n",
    "            X = X.reshape(X.shape[0], 1)\n",
    "        else:\n",
    "            X = np.transpose(X)\n",
    "        output = self.propagate_forward(X)\n",
    "        #case of binary classification\n",
    "        if output.shape[0] == 1:\n",
    "            return np.squeeze(np.round(output).astype(np.int))\n",
    "        return np.argmax(output, axis=0).astype(np.int)\n",
    "    \n",
    "    def fit(self, data, labels, validation=False, num_epochs = 100, eps = 0.01,\n",
    "            learning_rate = 0.1, minibatch_size = 32, visualize=False, val_data=[], val_labels=[]):\n",
    "        #input data should be in format m x n, where m is the number of samples\n",
    "        #and n is the number of features\n",
    "        if len(val_data) != 0:\n",
    "            valdata = val_data\n",
    "            vallabels = val_labels\n",
    "        else:\n",
    "            if validation:\n",
    "                data, labels, valdata, vallabels = train_test_split(data, labels, ratio = 0.8)\n",
    "        if visualize:\n",
    "            plt.plot([],[])\n",
    "            plt.ylim([0.,1.])\n",
    "        losses = []\n",
    "        vallosses = []\n",
    "        minimal_loss = 1e10\n",
    "        best_model = None\n",
    "        proceed = True\n",
    "        for i in range(num_epochs):\n",
    "            if not proceed:\n",
    "                break\n",
    "            mbatchlistX, mbatchlistY = minibatch_list(data, labels, mbatchsize=minibatch_size)\n",
    "            loss = 0.\n",
    "            for mbatchnum in range(len(mbatchlistY)):\n",
    "                prediction = self.propagate_forward(mbatchlistX[mbatchnum])\n",
    "                loss = cross_entropy_log_loss(prediction, mbatchlistY[mbatchnum])\n",
    "                loss_der = cross_entropy_log_loss_der(prediction, mbatchlistY[mbatchnum])\n",
    "                self.propagate_backward(loss_der)\n",
    "                proceed = self.update_weights(learning_rate=learning_rate, eps=eps)\n",
    "            if visualize:\n",
    "                if i % 500 == 0:\n",
    "                    print('loss on iteration {} = {}'.format(i, np.round(loss, 5)))\n",
    "                    accuracy_train = None\n",
    "                    accuracy_val = None\n",
    "                    if len(labels.shape) == 1:\n",
    "                        #binary-classification case\n",
    "                        accuracy_train = accuracy_metrics(self.predict(data), labels)\n",
    "                        if validation:\n",
    "                            accuracy_val = accuracy_metrics(self.predict(valdata), vallabels)\n",
    "                    else:\n",
    "                        accuracy_train = accuracy_metrics(make_onehot(self.predict(data), labels.shape[1]),labels)\n",
    "                        if validation:\n",
    "                            accuracy_val = accuracy_metrics(make_onehot(self.predict(valdata), labels.shape[1]),vallabels)\n",
    "                    print('Accuracy on train: {}%'.format(round(accuracy_train*100, 2)))\n",
    "                    if validation:\n",
    "                        print('Accuracy on val: {}%'.format(round(accuracy_val*100, 2)))\n",
    "                    print('-'*20) \n",
    "                losses.append(loss)\n",
    "                if validation:\n",
    "                    valpred = self.propagate_forward(np.transpose(valdata))\n",
    "                    val_loss = cross_entropy_log_loss(valpred, np.transpose(vallabels))\n",
    "                    vallosses.append(val_loss)\n",
    "                    if val_loss < minimal_loss:\n",
    "                        minimal_loss = val_loss\n",
    "                        best_model = deepcopy(self.layers)\n",
    "        if visualize:\n",
    "            train_loss, = plt.plot(losses, label=\"train\")\n",
    "            val_loss, = plt.plot(vallosses, label=\"val\")\n",
    "            plt.legend(handles=[train_loss, val_loss])\n",
    "            plt.show()\n",
    "        return best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Данные\n",
    "Для генерации обучающего множества воспользуемся уже упомянутым модулем библиотеки sklearn, а также разработанным модулем **datagen**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import datagen as dg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Метод *generate data* генерирует num_examples размеченных по num_classes классов точек в num_features-мерном пространстве в среднем удаленных друг от друга на dist_ratio радиусов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_classes = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = dg.generate_data(num_classes, 3500, 2, False, 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Нормирование\n",
    "Отнормируем данные. Это необходимо для более стабильной работы сети и не только. Например, логистическая регрессия вовсе не будет работать на немасштабированных данных. Для этого вычтем среднее по выборке и разделим на стандартное отклонение.\n",
    "\\begin{align}\n",
    "\\ Norm(X) = \\frac{X - \\mu (X)}{ \\sigma (X)} \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalize_data(X):\n",
    "    return (X - np.mean(X)) / np.std(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обратим ваше внимание, что в этой реализации сети, при *многоклассовой классификации* необходимо заранее *закодировать метки классов в one-hot encoding*. При этом размерность массива должна быть (m x c), где - m - число примеров, c - число классов. В случае *бинарной* классификации эта операция не требуется, можно подавать массив в виде (m, ) (или 1D-array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = normalize_data(X)\n",
    "onehot = make_onehot(y, num_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3500, 10)"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "onehot.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 -3.907985046680551e-17\n",
      "-2.341970033202782 1.8924137940196124\n"
     ]
    }
   ],
   "source": [
    "print(np.std(X), np.mean(X))\n",
    "print(np.min(X), np.max(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Посмотрим на визуализацию данных (проекция по двум осям)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AwZDPdyUI2zfPaCJS5pG/wrTWgx66UepzR8g89k/oYzsmbZ07D3wC47ro0/sh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e33dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#this cell contains nice dataset for binary classification \n",
    "#X, y = sklearn.datasets.make_moons(200, noise=0.20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Разобьем наши данные уже оговоренной функцией *train_test_split* в отношении 80 на 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "TrainX, TrainY, TestX, TestY = train_test_split(X, onehot, ratio=0.8, random_seed=140)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2800, 2)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TrainX.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пришло время задать архитектуру сети. Будем использовать четырехслойную нейронную сеть (с двумя скрытыми слоями). Все активации нейронов - сигмоида."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = MLP(2, [10, 10, num_classes], ['sigm','sigm', 'sigm'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Осталось лишь запустить процесс обучения. При обучении можно выбрать отслеживание производительности (*точность*) на так-называемом validation set, т.е. на данных, не используемых в обучении сети. В конце обучения будет построен график функции потерь в зависимости от итерации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss on iteration 0 = 0.65884\n",
      "Accuracy on train: 9.64%\n",
      "Accuracy on val: 11.07%\n",
      "--------------------\n",
      "loss on iteration 500 = 0.10649\n",
      "Accuracy on train: 76.83%\n",
      "Accuracy on val: 78.21%\n",
      "--------------------\n",
      "loss on iteration 1000 = 0.04761\n",
      "Accuracy on train: 91.83%\n",
      "Accuracy on val: 92.32%\n",
      "--------------------\n",
      "loss on iteration 1500 = 0.03729\n",
      "Accuracy on train: 92.63%\n",
      "Accuracy on val: 92.32%\n",
      "--------------------\n",
      "loss on iteration 2000 = 0.03127\n",
      "Accuracy on train: 92.99%\n",
      "Accuracy on val: 92.86%\n",
      "--------------------\n",
      "loss on iteration 2500 = 0.02991\n",
      "Accuracy on train: 92.72%\n",
      "Accuracy on val: 93.21%\n",
      "--------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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Pm9nGthQNFDfft4/pWDqndDmWdDkO0LE0OCmeRh16tYxzbgbQ7lvwzKwsnkuB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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114bfd4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<__main__.Layer at 0x1149776a0>,\n",
       " <__main__.Layer at 0x1149777f0>,\n",
       " <__main__.Layer at 0x114977860>]"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.fit(TrainX,                                  # main data\n",
    "      TrainY,                                  # main labels\n",
    "      validation=True,                         # nip 20% of data for val-set\n",
    "      num_epochs=3000,                         # number of passes through the entire data set\n",
    "      minibatch_size = int(len(TrainX) * 0.8), # size of mini-batches == train without val\n",
    "      learning_rate=0.01,                      # GD learning rate\n",
    "      eps=0.001,                               # stop-criteria\n",
    "      visualize=True,                          # print performance details + graph\n",
    "     )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Примечание:_** На графике возможно будут видны осцилляции (не путать со скачками при стохастическом/минибатчевом обучении) в виде жирных линий полос train/validation. Скорее всего, это связано с нестабильностью некоторых математических операций, т.к. эти скачки наблюдаются одновременно и у train и у val, хотя данные в этих случаях разные, а общий тренд обучения остается таким же."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность классификации на общей обучающей выборке - 93.04% !\n"
     ]
    }
   ],
   "source": [
    "pred = a.predict(TrainX)\n",
    "pred = make_onehot(pred, num_classes)\n",
    "print('Точность классификации на общей обучающей выборке - {}% !'.format(round(accuracy_metrics(pred, TrainY)*100,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность классификации на тестовой выборке - 94.0% !\n"
     ]
    }
   ],
   "source": [
    "pred = a.predict(TestX)\n",
    "pred = make_onehot(pred, num_classes)\n",
    "print('Точность классификации на тестовой выборке - {}% !'.format(round(accuracy_metrics(pred, TestY)*100,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вы могли заметить, что как второй критерий останова, испольузется порог нормы градиента весов. Посмотрим, чем они равны для каждого слоя после последней эпохи обучения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.395910832083133\n",
      "0.5872807413610743\n",
      "0.6409725661904411\n"
     ]
    }
   ],
   "source": [
    "for l in a.layers:\n",
    "    print(np.linalg.norm(l.Wgrad) / (l.Wgrad.shape[0] * l.Wgrad.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision-boundary graph\n",
    "После обучения модели бывает полезно посмотреть, как именно наш алгоритм научился разбивать плоскость на классы. Для этого стоят график границ решений, подавая на вход модели разные точки и раскрашивая плоскость в соответсвующие классам цвета."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вспомогательная функция для постреония decision-boundary графика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_decision_boundary(pred_func):\n",
    "    # Set min and max values and give it some padding\n",
    "    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "    h = 0.01\n",
    "    # Generate a grid of points with distance h between them\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "    # Predict the function value for the whole gid\n",
    "    Z = pred_func(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    # Plot the contour and training examples\n",
    "    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим с помощью этой функции граф"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T1dqhIFwbVVdLSbHDDbH5SXcN1TYtSElrtda1oLVTtivXlCtmsYNeKHBpRVhs\n2M0IqNR8aX5sO5LzhKwnLFT8S/nKQuF82SZG14i4TNvGuu7DgUnMCO239npMWPOVl7WALwFGPRQn\n6lZjPMUlzXR52xt3BQLgY+8hPnrGhXqMDGEOH0CqNXR8D3P3zZgdo5gjLrLDvnqW8JtPwHKHO4Pq\ny7rC+wy+8nTET/4u5qHfyOD18W1MutOxMVw8oUQJ1/kdP+O1TRwigufB3sOG6241rMxbshmfc69H\neEnO+gR2zM7x4Bce4an3PsDK2AgSWUrZPAu7VxH1+iB66qfnY0WgZCFp0+5OiU+xbXK3bO9vu+Oa\nEvZuH9hylHTE1fARu7WEvUM+149mmkr4+p0y7hT8hC/BQjmmaJWJjIdfKTFQipVSbBmvWPNJglNL\ny6+Id2NHkdZjo7OhMBy6yUQAiSMIe/Cz+1nwMnj33FIdfvPks7iCf88RCHykEh5ijuwnu/t9lP7o\nKySuOG4AxRXlqb+NsRF8+y9CfvZXAvyMi1ZR6zJHuxHHynPfjXn9hZip64Tzx5XSSvKx+ZHObQUZ\n4Ya7DM88quTH+n8vxqfnePfnvooCwZ5hPvVPP9E5m/NKo4qJtfcQRXXx6Vcb15Swj2XgfMKFL2yp\nnJIrwmuLITuzlsmsR84TfCPsynnMVeLcG/GNtNWTERHKVjmzHHFmOSJrnJumbC0TGRgKBCM+njZf\nUlYr9S01xibspOzHMBwafIu77W+cGIwPQT5Z3I1HrUSBl2k6r3Hk0YsnscfPErznvpqoA4hn0FwG\nc+N+7LHTXd+7K8XseVdu2QKzF5Qv/bsyuw4KozthdNJw85s9jNc8SRWXnWWeHwWNoVxQludhZUG7\neioun7EcuLlzxrFa2HVQOHV07d8EAcrTBe567Amee+f9hLlsSydugEOLy6gIhdHh7g0muWm6+dor\nbhVC3L9JnsNWv7qCbMPF0dW4poTdN3BgWDnTche/d0i5WJCuddmvBmZKMTMVX/HevM+evM+BIZ8z\nlXrEAgRGuGk80yYAsVXmy/XYtZKtRxLtHqpa42Viykglira2QtHhffUsjJcMtfJibTdM4sQdA35Q\n+R2Q3qJ0NYyIHvkx3n23QSbhUg98vPtvx544B+HG71S85wbDAx/x+e5fRrXs/IuvKxdfB4h57RnL\nuz8ekBt24v2DL4XMXlAQGB6D+3/e5/TL7j1ezSP23Hdj9t1oMKbdNx+WlRPPW970Hp9zr5UJV6lI\n3ClaUAHD4xIiAAAgAElEQVQTWd78ze9zxw+f5vP/4r+n2CDeO89d5D2f+RJj03MIMLN3F9/8+C8w\nv3cqobG1RcPIokWobNo9lLBpd6R1wY8UU7g6tx255uLYx7Nwy4Syf1jZN6zcMqHszLlImO0aurgW\nzhcinpkpcnqlXjH+yGiG2yfqtd6rxKosR7bio3dfg7yn7MorN40rrXt29Lqb0Y6luGlxriPZIWeV\nG4+KCdv+k4BemgURdHoeygn32wKyZwdkkmPt10NPiY9G2H3QcMNdyV/DhcvKudcs1irf/EyZmXPO\nWrcRLM7Atz8XcefbPe55l8fIju59zV1UvvEnIXMXnGUfRZbXX4z5wZdCvvOfypx52fLYF8rs2L2G\nF1uh+in4UUx+aYV7H3ms9lymUORDf/BZdlyYxo9ivChm8sx5PvTJz2Ki5s9G4k7lHRQKXa4rWxc0\nCUFW1EXDqPtXiopZVrwF635WtLfrbxtyTVnsVXzjwhsb2ZlzG2kshINcMO1k22w13DhPrYTcOJoh\nEHeLuhK5xdXZBksfnPt0V14Z7UcPFXKRMFLdO1atKzvYk1XWJWSuW5eLbmHUvnoGLRRdGV6vEqMf\nWzCCMYbMQw9Q/tw3m08OfGTvTvT8jAsG79ND0etw/Yxw5I0ep47amtV+4Bbh0imluASZHJw/roSl\n5MkijuDW+z1uuc/jB1+OKCxYZs4n9zV3UfnGn4Zkc4BAcaUSDlh9/gLMXezhtfXwurzYcvi5l/ne\nR38OgJuefgET2aZzjUJuaYVf/N0/5pl3v41X3nQnAEE5ZMe5S1w4crC977iD+ZWQSGRCRcP6Y9vh\nmzgorklhbyWyMFcCT2BPXlkJaYuQab+c1hPj3k3w1zqxrGcSceeVYuWFShJPa4hkU08K+T6vnKkl\n61wpVT+39iHWa0xQMYf21Ky18v/3t/jvehPezde57pcLmIlRAOz8kputRvJgDP5bbsfcfNB1awzh\nN57AvnhiTWPohcl9wr0/5xNHsO+IYXhcalEuoLz2rG0S4CpxBEuzWot2eesHfY4+HTN7Ie54x2Bj\nKCwnP4frbmBEQf0iGZmZJwjbw3UMMHn+Mu/8y//M7T/4CS++5Q28+Zvf55n3vK2jsFNQNE9bjLsp\ntQ/+WhLzRq55YS9EcGKhXgfG4Cz6sQAWQ60trGY9QGmqprh2qpfb1rXoO71MwbmuOpVWaWVqZtn5\nxDPD7THEvbLW7EPP4L/rTUR/+wQUSkRf+yHR1+r9y+F9ZD7wVuzFObL/+BcBhSCoJSVVCd53H6XL\ns3Bpvv8xAIUl5fUXYooryt7DHruvby7jYDzh8N1eW/0aF/4o7NyXrLZ+ALsONiwIG9gxJbzvvwtA\n4bVnY179SfKksBFc3r8bE0VY3+fiof2UMwGZcnLMsR9F7Dtxmn0nTqNAcShPplymnMlgbIxnLf/n\nOy/wv391H1JWVz8/Wwm8jxRT2h510jeKa17YTy+5sr1VLEJoldEAbp5QiqFz680UpBLTMUghbm3L\n1YNfDNfSx5WeIJSMcS6Y8R5cMFMzK+BnXFTLeugU/dBLed/TF4m+9XSnA9DXzlL69MMEv/4hJBNg\nZxeRYUEyQfOxniG4/zbCr/6o7+Gfe83y2BdC1Dpr+dgTlt2HDA9+1Me0hATGETz+tZD7PhAQZKT2\nOib3eew+ZLl40hJX3NHGc5ExB2+rC7sXwL7DBj9w545NCgdusnz7P/UWz2c8OhYR6xuBvSfOEJRC\nyiKcvONmFqZ2MHHR+dhXOZX3/tkXOXn/HUzffwvjhWXe/srzjH1ult9rOO7QYx+pbNCd0or0k2Ay\nKN547w36je/9zob320po4dhceyYqgC/KoVHl+IJsaPZpPdt1K1nySt6Dw2Pq9FQhGwuehcgo5UqU\nwdRsZfML8SAz5B5sqtGxca/J7U0aEz35EvH3ftr1WHPXYYL3v4Xw6z8iePebkWz7zBVfmCb+8rex\nC+WEFpKJY+WLv9ceZeIF8IF/GDC6o/m2R1UJixDk2vMBbKy89LizwG2sXH+74Y4HfDK5+gQACXkE\nVnnsr0POvNzb9zzIQbj2ag6ujQxElfLuixNjPPm+t3PmlhsYnZnnHX/1n9lxqbetG4wHd75hlZDI\nBu751YB3z31ircPeFnz/X37gSVW9b7XjrmmLvZvMqLodlnpPLm71ja/NzbIxd5P9jM1Z6PuGnKib\naoiigkGwbtM7PFXINpRjTnK7dLO0k8R/PQWgRCDw8e+9FfvKafTibEf/sX35NHr3jdjXL4KXXDbB\nTO3AHt4PL55OjrBJYPpMcmy58WBorP11iQhBzp1grTZZ9MYTbn+bz+1vc3/XtgcMK59Lp90OBcYn\nDWcScgiS8DMwuQ8un3Z3EGux+8KQ2ns9OrfAu/7ya12P70Qu11/Q3rOfDfk9fr/29zc+/TEe/uvJ\nNfW93bmmhd03kPPaN6oWlHygLIVCP+JsgJyvrCRmsQ6atfrn3b6rSmONmM4LueOBcl2DXg+XBaPU\nYs8NFYu8Mba8kxp0cqu0PjfIu0jfI/iFtxM/8wrx40eTj7EWjWIolYm+/xz+O+5ps3zFM3hvvoP4\nmRM9d90p3D4/LPXiVC2EJfibP3BW/sgEvOm9Pgdurh/YaJmrKmJWvwrKCYuKnSgsQGl5nS6ZVbrz\nvEpl3y6IwN4D6wtDfd//8Be8r+Hve7/8fh78w5vX1eZ24ZoWdoDrRpQTi0Js60I35FMpVNKPcDof\nxURGWYkq/oo1RLaMBi5qqxhpoouoetx6Jg7bdFfReSzDvnJgpOkhMlbqCUVVeqnJ0Y2k86vi3osb\np4tlLyLI+AjyM3cRP/FS4qQhh/dh9k+BQvyTY/gP3p3YnkyMgO/BKj7iKpP7JdGSLi5r4uPWurj1\nqutmaQ6+/8WId/6ysOeQqb2extfW4QajiZlz/U2UraLea/2tXhADR27JMT8XcfFc5zuf6w5lGB7p\nfdP1XnjyQ4/wezxS+/tq9tFf88Ke8eDmcWUpdD73vO9+zi8LS1F/Aqq46pCOfsTNSXjGwP5hpRzD\n8cW1Tg6rIS2/J31jlTEfDo4lnL1RgTxXojjUcA6WWsoTGCH42Tcivof/3nuJHnncuVpyCdaiVcwt\nB7EvnOhpWMYI7/ilgG9/LgR1gikG9t9kEjLllThyGaKNuMci9hzq3XpVdbsilUugsVJa5wbM3US9\nF+u7qS0Lx14ssv9gQC4vFBPGJgKjY1demk4++NdX7WLsNS/sULmQWr43O3PKdKk/BVtbKoRbmNw9\npAxXdnY6udhtclAyAmVtVdjGL0i/dxrt7B1p/sLVqikGeReP3qsvfDU/+QYtqMZHT0IxYeFT1fng\nD+/HXp6H2BI9/iL+W+9EGsoQqCriewTvuZdQBPv88Z763XWd4cP/NMOplyzlgrLnBsOOPabeZuX1\nxxF8889CFmfahW5huj9hFhFOHYv5/l9HLlHXwO0/Yzh0h0cUwitPxZx4rvfVHDF0DJkc2+EzN91s\nefdi3Z89FTK1x6eYUEp5ZNT0VcJ4UDQK/T2/GjD/Gw9tW6FPhb0DGQ+uG1ZO15I5VrvQKrWc12DO\n5nwYqUTYLZRYNSpmz5ByviBE1rlrqku8B4eVU8tS8Z6v/YthoFYmoK08blh0MemtrGOhc13n9oiM\nDhF89F3o5TniJ19C5yobqitE330WvvvT2lsW//hFEMG//zbneimFxK+dhXKEjA7h3X8b9oXjPSfz\nBFnhyD3tboXGOvRiYGkuucHxXQ3Hdaie2UhYVk781F1FNnZ3WaUVmNhdTQ5TluYsl3usfdZNqGcv\nV4RZIJMRpnb7nD3VWz39yxeTXTEjY4N1wayFZz8bwmfrQn/osY/w6aPZbbMYmwp7F8azMBIoL81J\nT99hrf2/P4t5tqTsHXLJj627t7X24FXuLkYyykLZlUHIGmUi67ZC2xn1f6fR2sdQUBF0E9QTi2wM\nUcmZbuWlitVeMeVsXLHkvfX52wcVFpkwUZjr97gFx32TeHfcQPkvH3XlAsDtbg5NH1v8oxecwGd8\nKFWEyjMuczbj47/3PqJvPLG+cVaHa139l1vfYjj6w3qsOri39J53uq9pWAbPuFIIcVRxpFnwAqVa\ndSGO4NyrlrOv2Kb2Tz5vueU+y/njlp9+J+7NfSKQzdOxFHDzi3ATyqULfWyS0uFLNXM5Ymp38y10\nXCkXsBmWPDhr/n1QW4y998vv5/LO4S1r0afCvgqecXVkZordFjOrrP2ii6y7S3ALr53bOTLqwtsE\nV+9mIluZTtRt+ze7TlE3wK3hiiu65WfrAmnEiVx5qZKm36g+QT3errUsaj+bLfR7Xh9UrVrxDHiG\nzN9/H0Qx8dHXXRJTOWwXGtW6qIObAGILUUT8zKuV9yTAf9udeLddj5YiF33z9Mt9rTYaT3j+exFn\nXrFtH/2NbzRMXecs7b/7jIsjLCzCzv2GqKRcPqMMT7h66kHG7W968fX2vlXh9Rdjjv4wecPr9jfM\n1YXvSdQb+kja5KNfGie2Usly+kSJwoobdC5vOHhDlmyfoZCD5skPuUXYRot+K4l8Kuw9sCevlKL+\nF1P7ofpV7Pydc7746ZKwvORCNafyii8wXRSWwmoNpFa/++rjFRQjMKYxhykxgm0WdaiHRngZZ7nX\nHveqGTUN3a4iao3Pd9rVZjU6iX+Pk0I1zt274xDe4X1EP3ze+eFLPSiTgk7PY+65ieAd94DvIcYg\nwyAP3o3ZP0n48PdXb6eBu97hEYXK/KXmK+C1Zyx7D8ccuNk9vzTrHj/3av24pVltW3Rte70GLp/R\n3vcUUYjXItKd1uP7oOqKsVZ59aVCk9AXViyvvlTgtruGVt2IZCPZaguxqbD3gAjsHVZemU9ezBwE\nx+dl1RSSUgyFGEAoWVhebBplwhmrR9YIyq0U2aMN355OAdi1+ugNwu4lRGsMMj6uE53Eu09LXzwP\nRvL4f+/N+O9+M+E3n8D+9DVnjdvur8F/4K628gMS+Jgj+5GdY+jMQts51lpUBa9FlE6/ZHnlqWbV\nDbJw14OmsomGcuAWw0s/WmMKm8LcpSufZb7eujTGwJ797j1dmIsT21OFubmInZNB+5NbhFah3+gY\n+lTYeyTrwUQG5suNLhnn884ZWI47if7qi64Acfc8WLKmWoCsNVxxdUxlObUxN1Zxi6QTROymZRGr\nkyirNn9zpbKRQT8iuwELpWuhurtS8L77ifdPYU9dBFOJfkl6O0aGkKSQSHC1v/fsbBJ2a5Wffjui\nXITDd3v4WedSG58yRKHyo4ejJsvUnQNBzhUIA7j1/rUJu/HgwY9Wwi670C36ZSMQgVvuyBNk3P66\nxWKy28haKA+mGt+G0RpDf6WzYlNh74P9w25hcabo9Gkso0zmYSWE5SXo3U1TL1TQvWSBmzj2DysX\nV7r73juR9eDImBJZ576JFcK5kBDYScxE4pRS8aG3hjUCRGXnUw9yDYcniPWALOqNRkTw7jyMd+dh\nwr99ouMNmXfX4Y7bzAGw2OycfvKRiN0HDftvNrUCX1GohCV1CUQJN0lx6BY9j9zjvqY//Y7t+2bI\nePAL/8QnP2xWPXd8qrd67IOiOp5q9uwNN+UIMobF+Ygzr5cJw+TBGgNDQ5sfObMernRWbCrsfSAC\nO7KwI9t8wY0ErszvQsuFOOLDclsGqbO+J7KKVbhc7BZxI4wGyljGTSb9GimCsnfI+c8zXkLoYjfC\nAvg5V7GqkcbiXlWqO0RscdHuGVXnM++0IXPgYyZGEp/S2KIrRezpi5WmlOKyMnNWedN76pUXAfxA\niEIlN0LnCaTh+NdftP17uATOvwaH74bcCBQWOx86eUCYu3jl3TVVJnZ6BBlDEAjjO3w8TyisxJx8\nrdS1KkWQEUbHt7ewtzJoiz4V9gEg4koTrESwUBY8UcazLhb8xKJUygM4o8wIXD+qZDyX6Xq5SyU9\ngzIcuCt8Kq8Vn3pvrp2c5+LdR4I+Bb2RqOgs92rp3W5WuDakVm4DgVdbDRHs4C4CvNtuIH7ueHsJ\nAWuxKyXk0hwahsjwEDLs7mDszALxq2cwN19HdOw05QK8+nTM1HXJ74kfCMZLrpnuBXDTG+um/Frc\nJDaCU0djDt/tttD78VeS/dYAp17cOFEHmJuJMSZmx6TPay8VnMNQpaOoez7s2Omze1/7nrxXG60W\nfb+LsamwDwgRGA6oCXGVw6NO8AuxKxkw2rAbXGCctb8UtodSCm4v0bGKG3ckgPGMMl92zzZTLezl\nQiCrlRjXLOi1QSREvKyKVpYWtvYXL3r6KGbfLsy+yXaRqHyE5sAU3ptuJn7qmMub94wLd1SIH3uG\n2Gp9T82RvJsAohjv9kP4P/82zFsWOPm/fo1Xn7FM7jfJuyDFSn7EsPeIcPYVxfOdgCtw4xsM+26s\nC/u+Gw1njtlE6z437ObUJIvc84WwpOy/0XDoTsuJnyYrZ3md5Xr7RdW9rc2JSp3dL4eO5AZeP2a7\nUF2Mvb/H41Nhv8LUBT/5+etGlHPLwly5fkH74lw1U3ln4Vc5MOys/ELNveP+vyev5HznT/fNAAS9\nGsPeL42x7K1mV1I45CaKv3/7YUqffhj/rXfg3XerE2hbUZps/cPyH7wHs2cH4cM/gEwA48Mws9Be\nurehBk38wgn8d74RxkdZMeMUl6c5+4oljsFvyRQ1AhIIP/MLAT/5dsjkXg8bw+7rhZEd7rilOeXY\nkxFhUV1tlsYAJoF3fNRnz2GDKizPKz/4UtTkUjl11LKyGBJk4NKpjbXKB4Vq/2V8r2VSYd9kjMCB\nEWVfRQvNKkEmN4wqiyEslqubcqvbto8BCDq4BdPWGPbVaPWvV10zUcmtAGaGALMxYZA9IkM5Mv/V\nuyl/5ftET76EOTAF2Qz+W25HMoHb7LpigUePHyXzD34OmRyvvYb4ueNE33g8uXHPoEsr+FMTvP50\noWaBP/rZkAc/6pMfqXzWXj2T0s8IN9zh8+QjEe/6WMC51yw/fDjkxjd6PPlIjI0TXDECD/1GQH5U\narXbxybh7/1qUCv9W2X6zNZ439eCGJic8jct63Q7kgr7FsH0GPQi4twzY5n6F3Uggl5lLaKehIhr\ny89CXK7Hu28hF43ZN0n2Hz6Ezi8jRpCxYVCl/OiTSBCgC8vYY6cJPvZeZGqibmmL4N19hOjpl+Fy\nwj6oVpGxYTS2+Jn6652/rHzlD0PGJgU/Cw98OGBkon7a0Jgwe0H54d+ERGWYPgPTZzpkNwh88B8F\nDI01758qIohRrr/D8OrT2ysksBO79gTs3rt1Y9a3Ium9zTZmamZ5sKIOgxXeaox7UhLTFkFEMBMj\nNVEHhXKZ+McvYo++DrkMZs+O9o03RAh+/m2uSFgjvod3760ucclabnqjtAUWLcwoNoKRiXqb1iqX\nzzjT/uJJZfKA8NaHvI65Yp7vzk9aRAwywtBo/fGhoc2fTP1A2LPfJ5fvM4FMIJs1V/1i6aBJhX2b\nMnBBr7KW/dBW+9J1S2JaL4Ny7VTbiWP8t95VG6/kOq81mF0TZD72HuS6XU7gR4fw3vkG5N7b0GKZ\n8Gs/5IYjZa6/zWB8F+ViPPADeNsv1G+Wra3UYv+Os87f/hGfO9/uc92tXsebuGyejin1YUmZPute\nz8iYx+FbconHbRRDw8Jtd+XZvTfLTbf1v7l5Y4hoSm+krphtxhUT9CpxySlQ1W++nlrrG8Gg+q+2\n4/mYiVH8Dz9I9J9/hM4udEwgFhFkz06yv/Ke2mMaxdiZWVb+9O/wxCIivPWhgDsesFw6bcnmhL03\nGmwEi7MWzxcun7E8952YhWll72Fh1/X1JKa9RwznX2vPwDzyxmSbTFW5eKpe3dH3YHlxc10yK8vK\nqy8VOXJLDmOEkVHDUo9jMgaGR1L7s19SYd8mXHFBr6IKpSW3q7Hx66t8bcfZzjVl1tLnZpUfSFr4\nBfwbD+D9449AFKPlELJBj+6ASvVNa5v2NB3daRiecCGPnud+wjJ8/Y/KhOV6scz9N9VFHeCtD/l8\n6y9CFqa1aQF1eFSwsTZZ7arKxZOW7/5lPWxmbjZmfm49G5gOhmLBculCyO69ASNjXs/CfuSWXOqG\nWQMD+WaKyAdE5CUReUVEfmsQbabU2TBRr1GJaCkvQ7gCpUW3wUb1sdKi+3e9BdCSwiKTjrmSdElQ\nEhFX1CvnEmJUtbaZdJcG0cUlzj4v2JiaGNvYVWPwGkypoVHhg5/IcOcDHlMHhJ27fIaHPOK43kc2\nL/zcr2X42V/2mdxXH+sz34opLrsa6ABRWSkX4Tt/1b55xVYIRFKFmcshLz1X4PyZ1ctGisD1R7Lk\n8tdm3Pp6WbfFLiIe8Pu4GvSngcdF5Muq+sJ6207ZDFHvgG34MornFMra7vGZ3aiqTVioROIkfIHX\nEx65Hmu/w3lVcW/vSmubdUTfeprnf/c4ceixMquM7a3sjnRJ2HNrTKbF3Z3NC7e91SdnPE4fC3n6\n22U+cHOmydoH2LHHMNuQyFNchq/8YZnr7zDs3CcsXFZOPGfXVmp3g3C12rt/njsnfTwfdk4FZLKp\nC2atDMIV8xbgFVV9DUBE/gL4MJAK+zrYMoLeSmPy0mrC263uevXcIAfllfp2e61+/fXchjeuE3Rr\nq4/NQTq5BaInjhI/fxzv1v3EoTsmLArTJ+rHz54y5Mdtk9UOEBWVF58qsLTgxvmjr0S89YO+86uL\ns/h//DdR094m4Na5jz9rOf5sx+FuKEMjhsLyGurZVPA8OHBoDYlxKW0MQtgPAKca/j4NvHUA7aZs\nOSR5A45WahEmIfUa7knNSWVh0nOunSAHJGyvV22z02LuatUlG0W75bmqBS5J5/VKGFF46hRxbpyJ\nNx4BXks8bOGCMDIljO9zZReqnqjvfd7WRB3g1IuWs6+U2X29wUZKuGw4cH0ePRhy8WyZKHI3TK1l\nfjeboWHDoSM5lhdjTp902VHWugVQP4Byl20fRWDHZLrkNyg27J0UkU8AnwC47uD22BB2s9i61nqf\nl0trAHcngpwzS6uWeydxjaPkhdxeqUwMahUtxy4ZNvASasU0TxQaWy595qfkb5ti5P79bVUfo8WQ\n899aRnWJi1+7QG4ISoXmGxZjIJMT5k56LJxTMsNKVIaFC3DpXLvixWF9l6T8kEVVmZwK2Dnp14b3\n6kvF2pZxq7zkNSECEzsNi/O2tkeq50HUYUIRwPddpcbRcY+FuZgwVIaGDeWy5fSJcse+hkYMe/Zv\n3XyH7cYgnFhngIMNf19XeawJVf2Uqt6nqvdN7koueZqyxUnyg0NdORoXQ6ux66vFsNeOMa70QFxu\nV6Lq36bLzk59MPf1Vzn7734Mkpzg0ybqn32Oua+8wvl//2OKx2ZcuYGG58/93z+unOba8wMYGq03\n5/nubz+olBCIhfKCYfGSIY5X3yi9UFCOPldgZTl2CVXG9bP/YGbVl37LnXn2Hwz6vhGZ2Olz8x15\nrjuU57a7h7j1rjx3vGGIm24fSmxLBMZ31Cd+Y4SJnT679gQMj3hE5e6vct+BTK0sQsr6GYSwPw7c\nLCKHRSQDfAz48gDaTdlqeEFnEa2GgMDa3BlVcbeRM1e1wVfRKP7rRYTsDeMc+BdvQ/zV2xPPkL1+\nDAAtWU79H9/i7O/+yNVdjy3Tf/UCxZemW7oQXN1w93cuXxf96vMA2Zybq4LVaqCo25Tj+LEicVQX\nyKFhj5tu75x8ZAxkMobJXRnueMMQh2/KMr6jt/dw156AmUshp0+WWJyP8X0hipTpS2WGR03ldVD7\nd9fegHyXzS+CTPd+04XSwbJuV4yqRiLyT4Gv49by/0hVn+92jndxnvFPPtz0WPAr7679fnnn8HqH\nta25vHN467ljpFoYOEmE1PnITbA+V0m1n6oLp5NpuM749vxtUz3HRmtssYUG34NC4acXKR6bIXvD\nBPPfOJF4nojgeUrsJc9HIoLnu0qP+6/P8HqXzSUaumZ+LmLnVN3Flct57JzymZ2O2taqd0z6hGXL\n+bMhi/MRYmB8wkdMcv33xnNfOVqotTc/GyFCzR1TJZMVxic8rHX7ky4tFJjcFTC+o929NTbhYbz6\n3N/I1G6/bQ/YlPUxEB+7qn4V+Op62gg/92jt9/Eux83/xkPr6WbbUJ3ctozAawdRr26wAcAAMhx7\nKRbWiyh3Ef9+El40six862TzY1aJizGn//VjxAvJK4Kqboes7CrZ/EEGJnb4+LcIF8+FlEoWI1As\nJoRVWhK3i9t3XYZS0bKyXN86b3jEkMsJR5+rlxMmhulLq6+4tk4wSfuOApSKyuxMTBRq7ZxCocTy\nks+B65ujW4wRbrwlz8nXipRL1TwB2LXHbZyRMli23TJ0q6XfyNVi9W+UmKsqLK/A4pLbRGJsrEtt\nFO2+Dyokm2O9D6ZeBXK9mYbryMhRVTR2i6viGy7/+XOUjs81H1OOWfzRaQpHLwOdJ4o4gkw2+XlV\nl6GarZROCbIeQ8PubieKYl56rtgmqMbASMJGE8YIR27JUyxYSkVLNmcoFWNeP955sbITVa9XJzFv\nJWzxnauF2emIXXva49BzecOtdw4Rli2KcxOlXBm2nbB3o1erP/iVd2+48E/NLDeNrxv95Jg0Tmb9\noKpw9hysNIRvzC+gU5PIjonkc4pLYDJ1NQIkKoI2CPpaxVmk8+Jsv1QSiXodgVY2v1BVorkiFz/9\nE0zWY+XZi8kWuRFM3l/V8u8mjq3nBhlXCAyF4THD2A6Phdm41oYxLnJkqEvdlFzekMu750++trbt\nkAZRxUEElpfijn7z1fztKevnqhL2Xgk/92hX4b8ifQ6qISPIziFkNAfliPCL34XS6rfX/ofeBsUS\n+D4MD8PKSrOog/v98jQ6Ouos+MqmzgAax3DylHO0GlMpdhKi+/YiI8OotS4OTkHWWqa3X0XpknjU\nTXSrQt56rIhgsj7LT55zuyl1Gef8w690bb8q0i6OW1edBEQEP6OoBWMMt9+TczsiLVnOny4zMuYx\nMVr680sAACAASURBVOETRb29R1V3R79kc9UM0fXhp5tibCrXpLBvWzzBu3UP+B7iGdQq3uQI9vUZ\ndLFUS2sn8NzvlQ2bzZFd6IlT9YVHVXSphJkYau9DFc6dc5OAKhoEMDQECwtNpW1rK2nnL6CjI7BQ\n2Wxzaje6d7Rna7mp3zhM3pKvUcC7bbnXa1flmLgQ4Y1kwGsOeTSBcXsTdgvPi1b3U3g+DI9VaqX1\nOEbBLbRWJx4RGB3zGL0jj1qlWFi1iRp+IEQJ/vjV2HddDmPgxCvO4u921+H5lVo4Ld0Y48oFp2we\nqbBvBXKVMrmrWN5m9xgEXs2Klsq2S+aGSZfJWI6QoPKFEkGXSxDGyEimdg5U3BTj+TbLFap+90I9\nCScM0bm5juKkUYwsLNa/3db2dj+f5Ae3EWhAbRu96nGNlSQrjyeNPbmbhNcYK+f/4AkKL1xm4oM3\nsevv31UfQmjxx7KEl1b6WmRtpOk8oz2NtZoB6/kdJgLpz5Lesy/gzKlyx9Isvg9DIx5LC87dk8sL\n+w5ka4J8+z1DLC7ElAqWixfCtiiaqb0+e/dlWFyIOX3CRfQoEATCDTemFRk3m1TYNxEZyTpRNlLf\ntTqMsdPL6IWFti+lTOQbBLrhcRFn7mVb/L4j2frzrcdTF5O29kzy8ckH0yzS87Ow70Dn45sbrv+u\n6hKUSkvg5+ohj9WqVp5pObW7cBSPz5I9NNH2WgDEcy4XLcfMfvUYk790OybjoZElXiwRzfRhGq9C\nY1XIxjE3vvfVGHfP72xh97sevHMqcDdfp8uJNzl7D2TYMdk5M9gYYXzChwnX1ux0SLGoDA0LEzuD\nWnji2LjP7fd4FAuu9nw21yHpK2VDSYV9swg8zJEppEWwyPiYPaPoSBb7yqWmp9R2XxDsJOD90Fco\nYJLaRBGcOokePNSUXCStIp5U26VaNyYqup8qwVBfLhe1ioYWjSySaXcJiG9Yee6i+6NsOfE/f8Md\nvxKiVrEIq+eDro+q4Lf6+jtVj1xLwNHkroAdkx6Xzodcvuji3I2BPfu7i3orfiDs2tt53UREuiYn\npWw8qbBvErJzKDnXB5xVPpRxPysNIWuFMprvdcOHHsawxnZq4lMMnSWdabmM5mdhaQFGx93zO3eh\nvk/tBau6PUETB0W7+8BWasT06qs2Qu7wBDa2tNa/VVWWf3IBu1z3a0TnmsNLq6lYvbp7VqOTZ6qj\neyuh3/LaglwwxrBnf5bd+zLYuPo2phb11U4q7BuFZ5ChAI0sFEJXfKpT7RNwIXV7RrHHp8E3yGgO\nGRms77KTcDU+nnSMiGCXitjj08hQBnPDZPudRxzD3Ixr49x57OUyjI3A7ALsGMW7/24kSLj8EkzT\nn3z8Ee78f9+PP5rpqQwAgC3HaGixgYdpGJuWYy5++ulVz+9kPdfa6cNv7m5aev/cnAC7c9VCseDW\nwoOME+Y4rqcO9Ipz9fR3Tsr2Jf2oNwDZM4bZO1aLUqEcYS8tobFtF8TqOSIwmkMOjGOmRp3ZN8Ai\nSVXRSRQodYuidBBRVUWGMnh37kcXCsTHL2N2jyHDGReO2ehLji328hJ6YREuVGqqzMyhN14PO8ed\nuDduuoELR332s3WL2vPh5X/+t+z5+B3s+NmDmJyf6DtvRDzDud/9EZO/cgfZQxNglXixzPl//zjR\ndG8+9EFMomtpI4qgvFT/2xgYGQWkwWefg5WGNeuUlEZSYb/CyFgOs2fUCVFFjDTrI5PDUIzQvN/Z\ncjeC2TVaEYfBW+odrU4Be3ERs3888XmppicCjOUwgH31khvvjVOQz9Ta0fmCE/VGrBJ//XvI9fuQ\ng3ugUMYeOwkLS02CLgL5kUpRx5Ui03/0FJf/4nlu/uQHmsS99XXYMKZ0cp6VZy+y8uxFvIkcJusR\nXhhcRm/X96/hmLXQGoGSG6Im6vV2lUzOlQcGN/l5ngtKGkQcesr2JhX2K4zsGm2zysUYyAfERy8g\nUyOYShnjJJfH6nts9u8Lbq0ymITpsbSyGAPjeWfdRxZ77BLkAiTjocUQygmrfpVJTk+eRU+ebXrq\nnl8NauKeG3KiXov6AVgp8er/8i2u+2f3kj8y4YpyvTSNvzNPMJVHgeUnznHhD5+qtRnPFbkS2zlf\nKV91Nk+tYFY1yTfp2ggylRBJr7n2miqsLLVPECnXDqmwX0k8SYzKqD9vMGOd/eaDWrxbE0kbUHTB\nHNzh1gMAiqET9VZ8gzm4AxmrqhXO7bNcwp6ec4uxFUSSY7pFhPjsPK/9T39HZtRDrCvUpap4Ixm0\n4lvfynT7XKuPV0V7tc8gqNVMazxOyQ85cU+5NkmLNlwhZO8Y3l37IeMlW90ieEemoIvw95qAM+jI\nvMba4Yn9JR0/lu+8BmAEc2gn3l37kfE8YsT9SOXfkSzeLbtr78U9v9o9FE+kImhlF9JYHYNdDlcV\n9V7ugNZDNWZ9tf5XG0e3z6D1mKTJr48gopSrkNRivwLIRB6z+/9v70yDJEnP+v57Muvuc3p67pnd\n1a52xa4UMoeMOeRQrLQCgdbglSzAQTiCwARYARE4Qg4MoW/+AjYWBAEYpBA2EUY2tgOvkSVkHUjy\ngoPDAoQsaXcl7TE7Mzs9Pd3TXV33kfn4w1vZXUdmVdbVVV39/iJ6eqoqjzezs/755PM+x0qH7zw0\nZjlmhEfUNsyb4N85wLmw2ndC8ShCY/Rve18xUsV5+DySSUDDx9/Ko/fKADj3bxhB72OlqoBzbgX/\nlqmkmIjQ9qAOS3v05ETGPyEG3RBtqKHlOLDCPgXkfIhfPWISUls9OAdFeaiv0PRQ1zGWcUso/Jfv\nIS1/eD/xGFZQosIcI3EEJ9fyC6QdnKtn0JUMWm30FfXDbTuCLpn1m1Ulne3dnzlXpilylPAPIrSE\nQsRnk2bY5K9x8gzCarhYTg9W2KeAJIbIwlPA91FtfYmF3kzNFt7zd3CurCNnWsW7/NZNZCkVKljj\nJiAF4ZiDthV6E3AdOJNDYoqLqkLFBGcXbka7U5qNo8JTwx5evxteWNr/cdJ+Ux4lfr59HVWolgfv\n89s++j0TL199/c1PD7W8AgfuEkltkvPDm5ZYhscK+xTQgwpsLg8U28MvYyvqQ4s1/O0C7n0baMI5\nKpmrJv7dff0lQI7CDR0gRNTNJscUKMU8ITij1/7oiGaJs8uKmTw9eDla2MQxk6r1KqSzkxPiWbtI\nAkH3PONqSvapfBx2HTXq5pLw/f5Zqj/7zp8+evHBIcfo+YiC70r0XbVt+4m6R6LuUc8k8Lvcjr/2\n8d/kevoCf7zxd6lJEhXhQm2Xd9z7c5aswI+NFfYpoPVmqJ51W2NHwtdaeiWDu5zGv76HrKZhY6lj\nckzpFaBpCNLhuNLJWH7pSSXyOFfWqW5V8GvR20wkzU8wrEFZsvNC7Lh3VWqV/sIOnRZ6s95avtW9\nMJWCSqmzR2mHoA+J0/S58MoBuaJ5omokXbbvW6W6FO4PE0+5eD1PtlhHRRBVDs5m2bm8fHhD+Bdv\n+ymufe0eTtvldStznt968CluPLLRc+P405/6eui+/uoHPjXycS0yVtingHN+daTElcASd+4/g+73\nZkeOIlrjit2xCqUI7tV1nOwOfqXXHdMd0tf73vwzUNxbhm21DJlc500L6LHUARKprqcjgeyyUswb\nd8ubP/jwOAPm8ov7pCtHxkqq7nH5xX1eed0GzZCornM3C2SLdSParTGu7laop10ONnOgyuarhR43\nnQDJuk+60qSWa7tpqPK2X32AbKlBM+FQWkujwZzUO8c4tjF58qnd0Pff/hO/f8wj6cUK+6RxJDIV\nH2IKkWJqw0xgsu0kCZ+IkLyQ4zU/c42bv3eb2u2jgihRXY+6159n4v7toXfic5Tj3bgm44k6kK40\nSdW83idQX1nbqbB7uTORTXxlOV/tsMQBHIX1u2UONnNs3C6SKzTCvXS+srpbYSftmkABVS69nCdb\nqCMKKqA3hVuvXaeeHXEGfUJ87Omz4e8P+XT05FO7vO9zf9DzfnsW9rBYYZ80voKnpgtPF0NZz+5w\nIjVNUTtOF4c4gqSFi+86z/XfvHn0fsz9R81jzLvogxlrs9VrJaoJdlxEhHoBzlf22c6G97CNQ6Lu\nEZYo4QDJVmOYTKnBxlaRVNWjnnIiJ8xdT3EbPus7lcipFwdY2auylK9x85ENcgc1soX64Y1C1Jyn\nq1/f46XHzqLDBCrMKR97+iwf4yd7P3hnyMJ/9T9jbdMmKE0BrTUiE3li4fSZnJoBkxLFYeLIE0su\nyTP97Y7u7alqq4GTHv6c1LopMqFv5ndtPx+9D19xmq2OV6qs3i1z/7M7vObLd7nwcp5EzSNZbSIh\nQUq+QGUpSbZY5/ILe2SLDRJNn1w5vAuYApXlJOny4LKUjpqbwLmbBVbv9Vr/ghH4C68UQte3WIt9\nKkh3J6M+HGaOCke/mW8Lc5ib1uHxtcRDXSfWsYkjseKw28fieVAtQW75SBgTyfk+l+0E9V+CidOo\n1oVxJmLBXEpXSzu973s+528UWD4w0SeNpEsjKeRKR3705XyNpYMaor2BTcEZL5zNcvkb+6HCGywX\nXNa+I+xeWmbjdilWCKwAuUKdeibcIg8+Hynu9RRgLfZpMODCbbcoD0XP8/Hvmjqs8y5E3b7ugRPF\ngnkKCSlRHGXFq6809/v3gA3222yYKJBK0RQOEyc63X7eaR9zv6Q2GPwE5AP30is97196KX8k2mom\nQ9tFHY6s4tDoLsBzBd91SFej/0bt67764Bq+Iyzla/EjYAUONjKRXyeB0KcJixX2qaC7JZMpGrmA\n+TmsleI64DitgmEnQ4iGEc12kT3MtvX8vsJU3YoXyxyMwWvpS2Qz6BNGnKiqZr1/bZoGDv/74us7\n3ktWm2TKjUgre9B7Adq6SXsxymKoA6mqR6bcPIpmiYHnCNVsEt8Jb1RYz7jokHNRpwUr7FPA38qb\n5J4o4RJ6G0Y7gqzl0Gq4f35Ricqi9O4WBxbUCpb1feNyCUrcRi3X/nteiHOMUbgJqJSPttNOA4ff\nffit3FrqjNwIJjxjja3P+8max/1f3aGcSzDIaFYE3xWaSSe0l2zUflxPufxSHmkZSdq2vO8Idy+v\nmDkAz7f1E7qwPvZpoCaL1IlI1460xgT8V+7hPnLhpBjuHcSNnhER1IkWdc1XyDpVVu93OLg++Fk7\nkQAnfeSmiBqH72nkpOQsomeC2jejTJSKCDimPG/w2hw7bD71IO/ZeoJGSEGdbKkRu8xD5L5bvxMN\nn5WGmQxtmx4KpbyaRgUaCYdU3e9x+0Ttx20T9WbCoZFxqaVdI/ov7nes30i57FxZpryaHum4Fglr\nsU8J3a+gXnwHoKqalPpKA+/67txZlnGYiCg2vMO67kuXoidkjaWuPQ2a+7mI+gmozsDoM2I83vrd\nPnkR+KWvPngo6rl8jcsv7HHt+V02Xi2y1ifUsJ1BQk3r8/afsG14Dtx+cN24YEQ4ONvnsWrAvlzP\nZ/vqKn7CYTlfw8EIWLD/VN3jYivm/bRjhX1KaL6CFmuxBdqkk7dqizuOiYefE8KOIe5xRbkawopd\nqe/j7x51h8iclUM/cve65nenqPejozRDSJikOMZPf9w31PbSCJNARHjqlb8E4MxWiYvX8+SKDdJV\nj/WdcmxrfVLPLfubWZb3quTyVVDF9UY/TlE4s1VkfbvcM0cQ4CicvW07jFhXzBTxX9xBLppG1rHE\nJ5tGNpdgCD/ocTFKkpL6Co2miUjLhGcJdgiaCOI4h75UEaFageWQuinjFCbrdtcEvxPJ441IClwn\n7WOYBGdrRZymz8Z2Z2ihowMDtiZGsJ+NbVMaY223ggqxBnD49+96X4CVfG3gzSlVbXaUMljZq7Yi\nbLIUzmRORXikFfZpkk4g6finWBzBuXIGLRnrZhIZn5PKGu2wdj3f/KSjU7qNYCskE5jaVjFLHpxb\nhr0yVKaXWdS3Vk8Ek/pbtFOrmvmBSd9MdlPLrNyrhIpolMtkGlLXs82I8MmB67XhKHhAv3xTUVi7\nWyJXbB7VrAHS5QJLBzW2Hhg9E/ekYF0x0yKbxH3dBWQ9N9QX17SKy0S3mRtAlNtiHHpqtDiCt1UI\ndbO0T0KK4xy1wItItAnZGbJ25Id9448maYS4Y8ZlWFfSJES9UYdywcTcFw+gUQtqy0e7uiLj/CM+\nr+PyjPMYZ2+XwtcLee9YRD3GfuL+hZ0BywqwcadCtlTvcNk4Ckv5Ohde2mdpv7rQkTRjCbuIvEdE\nviIivoi8aVKDWgScq2cQ1xnYGSmMQBRheEE7FldCqwpjkFzVkXA1LkHCVhu1iklCmtg+hiBOvH7c\nMXmeqZfuNTlUpnrEPF9YvZvOfUKjrq3GI8alsyc5PpZ+E88nrkV+sad9dbSe00Yi7tiiJmvbcXyN\nTF5aOahz4cYBV76xN1dzWZNkXIv9y8C7gGcmMJaFQnLhBbWHEaZ5zZwUkaObloLul8HXyYxXQPc6\n2/+88UeTVMtQ7a1kPBZxYuQHfT7M5HgyxHMV9l73eu1jCfZZq5jSvtUylArwSX09H8x9L88lrx2t\nGzXuPvtbFJnzHNNHt5vgLcc3lSvXdid8Uc0JY/nYVfVZWIxMv4nj+SZkY4rMQ2MJcR1Yy03ksVZV\n8bcLUPdCP2/WQTMAvRUchy1x3AwaYvdZZpjM2ljLOcHy4CYBbaulPoDAZaO+sfL9rlNUdjP4Eu96\na/9LTcPnPssrMjg2N4Yl7igs71fJn8tNd1Az4Nh87CLykyLyBRH5wk5p8Vtf+duFnjh29Xz0Xhn1\nxy9wMS2XxEjbFYaaE1BVtNbsOD/qqwkPfTXfd91KkY4Kjr6vI/ng1Tty74QxKfdL+/K+B8k0LK1C\nJmPq2jgxvoEiguOa8VYrvaIOcH/1Dun04KxOX2DnyjKF1YjuR5zI3LgO2mPrte0nDF1Qo3TgZSUi\nnxGRL4f8/OAwO1LVD6nqm1T1TZtLi58ZptuFw5ox2vTN7/0y/iv38F/cHal0QIcv25+OtR42yRln\nnWGqWWqpjv/sFv6tffxiDb9Uw7+1h/+Nuz3LJ3/48Y7Xvm8mIEvBz4HxwQcx6HHH67jGjTHSTaF9\ngjgqe7ZtLMHvRBLSmWAOZbgiZSLSt2TCQ5WbXL7o9aT3B+Lmi/nZO5+jnnFZOYhodDEms5bJsBBJ\nBZpubzEDxdSbT1XmL7x4XAa6YlT1ieMYyCLi39qHrTykEsa90LJQtVDFe3YL56FzyGqmZ7320qzt\ndPhbnXilW8OYVvr8oPGoKv7dInrLpILrbgndDY/eAPjA4++GbeDxd8PjkYsB8C/P7XLw7/6Y23/m\n0+2qCRtHUDSsVjE1VxxnuHMZJehRnw/rKopa3nF7LfaGuDyfu4+/PVhimd6nYcGI+suvPweq3P9s\neEu3eSMqnn1oBLavrXLxxgFOK0EqsOiTDZ8r39jj+qNnexpun2RsHPu08TQyJlvvldCllPFTd3wA\nfqGK5ivIUsqETLa5OsYWCVW04UGqs2781OPmlVjJV/n3PsmHnxvuqe5f3z0L7/khsm8v852/8wxr\nt/Ph/uNWUlB7NEpQ7tdNDL7hxX0i6Pe6H8M+PZSdNP/l/BNUnRSre7VIl4Pjgwqcu1XE9XTmlnU/\nBs0BDLutZtKlsppi675VLr2c7wiBFEBUWblXIX8+vLbTSWQsYReRp4BfB84BHxeRL6rq905kZKcA\n3Suj6zlYSRsftZrUQP+lHbRgLC/ZOD9SyGQ/xHEgJaFPBaHjjCn47U8UoclIjiBJJ1J8kj/8OL+0\nvQHPDdxVJJX1HJ993zs4/9xtvvnpvyKbrxxWB3QzLvW9BvUqHeqhakIRw0r+dh9L3HM2Do06JFNh\nTTZ6rfU/W31Da+LUGAdRfyW/ZTus7FXnWtRhcu4cxVSB3HpgFURINsLnthyFVC18wv6kMm5UzNPA\n0xMay6nEf2kHWU4jy2kzubpXhmbbBdjwhrKkw4QojPZ0+vZ1DkVLzT9+voKzHh41EOXSidqnqqLF\n8MDtQ1GPga9HQThhXQR9hVcfucSdn3+SXN6EYlbO5HoW/IlvqnH9zebyHSYDtPucBcc2Cu3rqRq/\nv9c0ETSJROc2q+XuteGF7JVDUe87ZjW12Met7HjS2N/MUs8Ymatlw+XOd6Cam21j7EljXTFzgBZr\naDE8UsjfLuKuZGI1tx7VlRJmkfrbBfReCepNWM2G7n9o69VTtFDtefvQlz6Apg+Fem+EQ9ppPXLr\n4UPPIYVsjpVUeHmQDz+Xhg//CADf8R/+hMtfeTX2oXQTx30T9jTgNU1N9bYacIBp8ee6JixS/SCC\np3fbCfwQr3rIGMRYpZWlpCnd2/5ZcAwxtnOSEGBju8zabgUv4VDLuNQyCdLV5qE7RjEx78X1xQro\nWJzZgkWlVMO/tT+Sb3dkFCjXjD9cwb+5H9nxqK91HtTSVkV9H++FXvX+wOPvjjUkX+EgRNQBaj7U\n/ZYl3/VZU2GvBntVOKh1Pgy18/W3fBPNZFccuCu98x8MdwNVVRoNqNeg2ezM0g1a+qGdoh7geVCv\nBpE74dt/tPgSfvcUSshyjm/a2Xlu5zInxYAfNalKMA070jWPlXyddLVJYT1N05XDCKJEU3ng2V1W\nFihZyVrsJwDdLeF7Ps59G6FCM3EESCbM71warTXwXtjBuXYGMoMbdavqYTaqZlNQrpvEo66J07ii\nrtHzz7EJLPqDOqymoDsAYvfBc3zxqW/l7/zh3wCwdd9Z/uL7v4X82RXW7xb45s99hdc+fwu/7uH7\nw0XReE2TXBUgTriQj8LBv3kD1V9zyZSOTlCUu2Xz1SKpqhfa5GLeBT4IWwx+B8RJppK239Lyp3sJ\nB9c7Oheup5y7VcBPOJTWTr71boX9hKD7FXx3H+fyekdC0DQqEooIspHDubR29K3wFX8rj1xe73HL\n9OzHV/zbB5ERMO3+9KYP1aaxtpMOZBKdbhNPjftlkiU9yg0Ia7Lzyrc/yM1vvZ/EvTJ3VpYPk1f2\nLqzx+R/6Dl5+6Q7+5hK+I7ztVz9JIiJDtgPtFHWYnKjf/6dP8Ue/uAkPwcqucTkka16osAuQ7hL1\n7s/nnXZxD1CBWsohXfNjH0Om3DzcXjuOwsZW0Qq75XjR3RLebglSLiQc3IfDW+iptpzNY7hmJJfq\nFGsXnMvraKUO2aMQTfVNCV91HbO/agPvxl4sUa81odS2WNODmmdENwgSKtQY2FNzWJp9bhJ+wuXu\n2kqP60Mdh5cfusRaytxsPvvP3sp3/cf/w9Je+ehP4IC2NZJQbblapsQ//MXLAKxtlzm7VUT0ZAj0\nOPQkICl4Sdf448bYTkCiPumrbTZYYT+J1D2oe+jdIpxfDo1KUUb3uZuSBxJ+09gtoYkqztklEPB3\nS+h2sXUjoe8zvfzQ4/yr2xuoGqO/HKL9PlCum91P6zvWL3pU1Qh36GfAfsv6Lpzf4Mb7/gGvfeE2\nj/7Jc2QOKtz5pkt87S2vI12qg8BPPPsZ/t9/mnxW4/1/+tShqDuez2ZL1OPgM97E2rh1ZCa9vcCH\nnt/MsrpbOTwP/bbZ77N6err1nY4LK+wnGP/OAe655Z4rVX3ffGNCIlkGZof6Cq3kpR4EcB10u4C3\nXQhZOXqsd556gl+/sRbLl1vvV9xjAriEP9CoQmEIX74CX3/oEncfu9Rxs6itmfDQX7n0j+Ct5r33\nfe4P+NJHxm8e0i7qgPGtxzhXCjSSgoqQat0xw1wbx80kEpCquYSZQNbO94Nji7sPBXavLI85ovnA\nCvtJxvPxb+7hXF0/Uilf0WIVWQkpVeCHmzMaxAh6Pv6Ne+ApzoOb4TeGwnAF3A6SGT7x95/gS1vT\n9Vs6xHfZNBSKDVjpqqxc96OjZvpR98zcQD8+0FYWYRSR/9l3/rT5zy92vu/FmEwP9C7VUHwUz4Hq\nUpKlwnTqxRw3mVKjZ/4gEPV62iUdI/lIgbuXl6kuhZfbPmlYYT/h6G4Jr1TH2ciZ+jH5ClqoGWFe\nSR827DALK/6tfZwrba3BpLXOTrEjll6LNVhOH/nSg+SpanxBqjkuv/X3vo+DyvQjeYbV44Zv/Pdu\na8LWkdFbzQa6kXLjFbkMRL49QSqMb/vo9/DmDz7cf9+5BCrRkTDQeR93APHBS7nU0x7pIX3Tx02c\nJ4qwSeHgdbLuxXY/HZztU2XthGGFfRGoNvC7yt36L+/iXD0DZ1pZow0P/8Y9tFDD2yub4mMi6EH1\nsDhZx/ov7iBncsjGkqkts1tC88PF+X75HW/nYG9+UyUaLa9T1TMhkDJgjiAKT818QbkZHkoZRZAg\n1S3wh9b5B2NsRITtqytcuFEYqgPR8r0qXkJm7orpR5w/xcCxCxTX0izna2bayA9fr5ZNjNyOch6x\nwr6o+Ir/yj24cc8U/W4Xb1/R/cEirXvlnm5Gw/Cxg5NTVKnUgGzCWPLjEBUn349A4D/29NmR9lnc\nyNJMOpy7WTj0n0N/0XMU3EYrgWzAsu0MWm7SN4qxt+VDcT3DvYtLJuPWV87eNpPNjrae9Bzh7tWV\n8Qc7R1hhX3RavvPj5gOPvxv3BJW59lqROimnNxon40B1iFN4UIf19HAG4KiiHlBdSXPjUTOPcfmF\nPXLFaJdZt/jOlRBPcFvBcV68nqeeSfDqg+utBKQMqztlMuUG9WyS/GaWZmoxomECrLBbJk6QUZp2\nTfLRvGc1BjgCyykzgdr0jWvG96EyQuG/ahNmVVfqYCNLptToKE8Li1sTppvu4xQ1/U0vXM9z+6Ez\neEmHvUuLEf0Sxfw6QC0nkvYyAY603BInREmCwKJEa0I16Ywm6hAdC38cFNfS1LKJwxoyimm0UVxP\nU09Hl03uJs5ywxzmcZ6SsMnUXKmBM0rY0wnECrtlYuTf+2TPe65jMknXT0AUWXe26TgaMNObmSPc\neugMO5eXKS8lKa2muP2aNXYvLpMckHqvbT8+4MnR61FoX3ecUzKJm4LCYW3+Rce6YixjsZ/KHaD7\nLgAADMxJREFU8tmrj/I3F16D/K2ZgAxzVzoOrCSHSwA6TsJEZ1QhEiA962+WIxxs5jjYPKqlv749\neCJcgKZjqkEKHCrqKDVm4gr6oOXCKlGGLRvcRBppl1StNwTSSzh4ydNhy8768rOcYPKpDL/xxieo\nJFvO5FbiT8aDXIiFnnRhTcwys3RVhKGY8r4JMaKcHMO8XE0Z67/mG3dUQsYq23OsKOD6w9/UFGPd\nO22VJRoZFwUy1Xj+rKiImu7EoygE44baubzMta/v4Xg+Tiv3TsX0PT0xf4gxscJuGQkF/ttDb2qJ\neueXpepD0jNC3o3rGKGbN2EPaKppajEOhXpnwlQw1zDrMOniWpqzt4tT2/7ulRUKZ7M4Tb9VnMth\ndadM6tVi34ncYU5Lv2V9B0prabyUyyuv22D1XoVssUEj5ZI/l6Ux88eo4+P0HKllojxz6bW8tHae\nqK9aoQHrTriYzammT4xu17yvUKyHlwo+Tpp9ClwpoA7UUi7ZmBZ2N5u3i3gJh7Nbpu675wp7m1lq\n2VbXIn96f3vFlFcotkru+gmH/fNL7J+f0g7nnNPhcLJMDAU+f/kRPvXAGwc+1tY8E0LfPSkZZskv\nOk01HZwKdZPtOiui+n42XaGaTZKpeSOJr2AmJi+9nD9M8U94yuadMr4IW1dXOopyDWuptxM2PhW4\n+fCZ2T8WzQlW2C1D8Teb9/H5q48S52tZaUK+Dvu1TjFLOafzwmtqq0ZNwzT7CBg3OWkYdi8v97TS\n88VYuNlSo6Om+7DRMGH14IMwwzMxJm6HIXgqCkI5tx5YM3XZLYB1xViG5LPXHqXhDnfZKEbMltVU\nAxaBtbSxXvs1vVhkqt5R8bHjpLKc4tWHzrDRcpc00i75sxnOR9SaabSiSJKNeKUKwhDMBOokDtUX\n2Dufw/GUbKlBI+2ydy5HfVbZYHOKFXZLbJ5bv8heZvSMvWITpFVmwJVWbRZvuHT9RaLhw6c/enzW\nekB1KcmrD505fJ0p1k0bwC6fmWAs+ZuPbCCeogK5Yp1LL+UPP+9eflyiImOCyJbSWpq9C0unJrpl\nVKywW2LhIfzeo9899nYC6WgO2dRiEZkXaaplE0j3RAjGOi63itZrqzZ/NZdEGd6V5rngevHi3nvG\nAZTWUuxeWqZ5iiJbxuE0ujotI/Bv3/KuWP7WjHVzxmZecmXUdbh3YanD9+4Dvivk2xKcAFzPH1o1\nfODu1VVUBvvsy0tJ/LblfIFmyuXutVUr6kNgz5RlIB94/N2HdawHMYNCkieSjDtf3oT9C0s0MgnW\n75ZxGz6l1RT753M9mZqNlGvcNjFu84qJttl+YM349hMOl1/Y75thWl1JsXN1hbWdMomGT3klReFM\n9vCJwRIPK+yWvuTf+yQ8ZxKL3BiJRY1TOhk6LEnneKNh4lBaS1NaGxBsHzT2eOXgMAom0i8usPXg\nOrXWxGZ1OcWrrz3D2VsHZCohk6kChTMZmimXnaur4x/QKcYKu6UvH37u6Iu+3Kr1ckrqKE2VcRt6\nzJLSeoZbKZf1u2UStSaOp6TqncXFFFObpTtuvrqU5NYjZ8kU61x6Od9Ri+bOtZWFq4s+K6ywW0LJ\nv/fJDlEHY7WvpczEZ63Z25DCEp9yHZJpn0ZtThztQ1LLJblz/5p5ocrmzQKre1XzUgQEbr9mLdLf\nVF1O8dJjm63YeaWynEJtctHEsMJu6SH5w4/3iHqAiCmQlUyZZtDW9TIavg8r6w3u3ZlxnYFJIMLO\ntVXy53Nkiw28hENpJUZxHEeorJyAes4nECvslh5+aXsj1nLpBDROecjiyAg06ifTWo+ikU6cqkJb\n88xiXVmWsWnvgDSIpHNyuiPNE74PzbpDYc+KoGU6WGG3HDKMqINxyyzbTO6hqZRcvvKXq8xPipJl\n0RhL2EXkl0XkORH5kog8LSLrkxqY5XgZVtQDHAdy1vCMjefB83+9Qq1ioz8s02Nci/3TwBtU9Y3A\n14BfGH9IluNmVFEPCBo/WwajPuRWmrMehmXBGevrqKqfUtXgKv1z4Or4Q7IcJ2ENqEfBJgbGQwSq\nZWutW6bLJO2sHwc+EfWhiPykiHxBRL6wU6pNcLeWUekX1jgs855Xkp6DJwrfg1IhQblgfVeW6TLw\nChORzwAXQz56v6r+YWuZ9wNN4CNR21HVDwEfAvi2a2ds9PMcEDesMQ4JB9Ku6Zo0ke2J2V7KhWoT\nKmNud9rJVCnHZJP2u7B3t1K8+NWl6Q7EYiGGsKvqE/0+F5EfA54E3qYaUvvTMpeM61cPI5cwQlxr\nlWcdVeQF47dv+mYb6YRpp1f3TMnwWoRI9ytNNe0Lc9CN49aLaa4/P3ote4tlGMZ6JhSRdwA/B7xF\nVSfb+8oyNaYh6tCWlRq4PfqIcD8UKLYlPpWbsJKCoEmO0wi34EcVb4feBtSTZndrATJMLSeGcT2P\nvwGsAJ8WkS+KyG9PYEyWKTItUQ8jl5zcpGqxftTgZ9KtLact6ikHinkb8G85Psay2FX1tZMaiGX6\nHKeog7HgV1PG99zwoq33lJiaM/0sbgUO6kft9E4Sz/yvyc1lWCxxsNPzp4TjFvUAEeN3V6KFvR7T\nh+KpcdHMQYBLbFIO+J6NBbUcLyfpO2IZkUnFqo/DJGu4n5RqwUkHnvmEtdYtx4+12E8Bk4pVH4dF\nLRYWTLw6mEielNN6LfBH/2O+OiRZTg9W2BecWblgukm0KkE2Fygg1gHW0r29JOxjsGXW2GtwgZkX\nUQcjfispyLon66JLCGQiBrycmq+G1BZLgLXYF5R5EvUAEcgmzU+5AdWu6JaEY5KSZo1rOruRbrlW\nRCCrrege39yY0on+DYLmrVG15XRhhX0BmUdR7yaXNPHotVYJuXQrNr0wRWHvl5nazmqIJR5E98x7\nTRyLBaywLxwnQdQDko7pnRqgGl98u+mXPZpouYEAKs3eJ4V2VibgXrHWumXWWGFfIPLvfRKem/Uo\nRkcElpKd5QTisJw0lvReNfymkEseiXUuaaJXPN+4UkSO3D9Jx/rMLYuBFfYFYZIleGdJyoV1x1R0\nVDXFtaIs+KDoWODrXkub0gNB5I1gbhSJrslPR8Bpc6lY94pl0bDCviBMsgTvrHHkqOBXrpVt2ujy\nswRWevd6q2mTDKUY98xxW+DWDWOZB6ywLwAnya8+LEHDbK8VlSJ0Wulh9PvMYjkNWGE/4SyyqAeI\nmAnQbpfKvGGtdcu8MOdfFUs/ToOoWyyW4bHCfkKxoj5fWGvdMk9YYT+BWFG3WCz9sMJ+wpiHEryW\nTqy1bpk3rLCfMBYhVt1isUwXK+wnCOuCsVgscbDCfkKwoj6fWDeMZR6xwn4CsKJusViGwQr7nGMn\nS+cXa61b5hUr7HPMohT2slgsx4sV9jlmkQp7WSyW48MK+5xi/erzjXXDWOYZK+xziBV1i8UyDlbY\n5ww7WTr/WGvdMu9YYZ8j7GSpxWKZBFbY5wg7WWqxWCaBqI7SE37MnYrcBa4f+46j2QR2Zj2IOcKe\nj07s+ejEno9OjvN83K+q5wYtNBNhnzdE5Auq+qZZj2NesOejE3s+OrHno5N5PB/WFWOxWCwLhhV2\ni8ViWTCssBs+NOsBzBn2fHRiz0cn9nx0Mnfnw/rYLRaLZcGwFrvFYrEsGFbYLRaLZcGwwg6IyC+L\nyHMi8iUReVpE1mc9plkjIu8Rka+IiC8icxXKdZyIyDtE5HkR+YaI/PysxzNLROTfi8i2iHx51mOZ\nB0Tkmoh8TkS+2vqu/OysxxRghd3waeANqvpG4GvAL8x4PPPAl4F3Ac/MeiCzQkRc4DeB7wMeA/6x\niDw221HNlN8F3jHrQcwRTeB9qvoY8B3AT8/L9WGFHVDVT6lqs/Xyz4GrsxzPPKCqz6rq87Mex4z5\nduAbqvqiqtaB3wd+cMZjmhmq+gxwb9bjmBdU9baq/nXr/wXgWeDKbEdlsMLey48Dn5j1ICxzwRXg\nRtvrm8zJF9cyX4jIA8C3AH8x25EYErMewHEhIp8BLoZ89H5V/cPWMu/HPF595DjHNivinBOLxdIf\nEVkG/gD456p6MOvxwCkSdlV9ot/nIvJjwJPA2/SUBPcPOicWbgHX2l5fbb1nsQAgIkmMqH9EVf/7\nrMcTYF0xmMgH4OeAH1DV8qzHY5kb/i/wsIi8RkRSwI8AH53xmCxzgogI8DvAs6r6K7MeTztW2A2/\nAawAnxaRL4rIb896QLNGRJ4SkZvAdwIfF5FPznpMx01rQv1ngE9iJsb+q6p+Zbajmh0i8p+BPwNe\nJyI3ReSfznpMM+a7gX8CvLWlG18Uke+f9aDAlhSwWCyWhcNa7BaLxbJgWGG3WCyWBcMKu8VisSwY\nVtgtFotlwbDCbrFYLAuGFXaLxWJZMKywWywWy4Lx/wECTHRdlX8xHAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114967dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(lambda x: a.predict(x))\n",
    "plt.title(\"MLP\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для сравнения посмотрим как с задачей справилась [логистическая регрессия](https://www.coursera.org/learn/vvedenie-mashinnoe-obuchenie/lecture/8G3Xu/loghistichieskaia-rieghriessiia)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QXKqDqgNnMxTyLqqCtRXf+ELcHMLQ+TSHX+sin3NwHGXbzglczzKTeq7Rd9+onlZS1lW3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11494db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression classifier\n",
    "clf = sklearn.linear_model.LogisticRegressionCV()\n",
    "clf.fit(X, y)\n",
    "# Plot the decision boundary (the method is in the main code link provided in the end)\n",
    "plot_decision_boundary(lambda x: clf.predict(x))\n",
    "plt.title(\"Logistic Regression\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ирисы Фишера\n",
    "Протестируем работу сети на классическом датасете *\"Ирисы Фишера\"*. Для этого загрузим их, используя sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = sklearn.datasets.load_iris(return_X_y=True)\n",
    "X = normalize_data(X)\n",
    "onehot = make_onehot(y, 3)\n",
    "TrainX, TrainY, TestX, TestY = train_test_split(X, onehot, random_seed=55, ratio=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kAEcxHT+YqRsSgDG0ldlPwzD467NL2L6pAJ9fIgCnS3DBRT25/vZ5AOzcmsUL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\n5hSoewcF5xsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114e4cf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Воспользуемся такой особенностью данной реализации как сохранение весов модели, показавшей себя лучше всего на валидационной выборке, во время обучения. Для этого возвращаемые методом fit слои сохраним в переменную best_layers.    **Внимание:** Такой подбор параметров (по сути числа итераций) неизбежно приведет к переобучению на валидационную выборку. При использовании данной особенности обязательно проверьте качество на отдельной тестовой выборке."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Важно:_** В этот раз мы будем использовать для валидации не часть подаваемых данных (TrainX), а ту часть, что мы получили ранее (TestX). Таким образом у нас будет всего две выборки - Train и Test, без Validation. Для этого в качестве аргументов val_data и val_labels подадим TestX и testY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss on iteration 0 = 0.70101\n",
      "Accuracy on train: 34.17%\n",
      "Accuracy on val: 30.0%\n",
      "--------------------\n",
      "loss on iteration 500 = 0.06098\n",
      "Accuracy on train: 96.67%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 1000 = 0.04287\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 1500 = 0.03856\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 2000 = 0.03651\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 2500 = 0.0352\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 3000 = 0.03424\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 3500 = 0.03348\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 96.67%\n",
      "--------------------\n",
      "loss on iteration 4000 = 0.03287\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 100.0%\n",
      "--------------------\n",
      "loss on iteration 4500 = 0.03235\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 100.0%\n",
      "--------------------\n",
      "loss on iteration 5000 = 0.0319\n",
      "Accuracy on train: 99.17%\n",
      "Accuracy on val: 100.0%\n",
      "--------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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NythyhXvk3pf5HmE7LZPrVghzA6plvGY7537nTx8DMjd3zjfGkh+7/8/0a/CO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114b8e2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = MLP(4, [8, 3], ['sigm', 'sigm'])\n",
    "best_model = deepcopy(a) # we'll use it later to assign weights of layers of the best model\n",
    "best_layers = a.fit(TrainX,\n",
    "                    TrainY,\n",
    "                    validation=True,\n",
    "                    num_epochs=5500,\n",
    "                    minibatch_size = len(TrainX), # now we won't nip anything\n",
    "                    learning_rate=0.005,\n",
    "                    eps=0.001,\n",
    "                    visualize=True,\n",
    "                    val_data = TestX, # replace nipped part from TrainX to TestX\n",
    "                    val_labels = TestY\n",
    "                   )\n",
    "best_model.layers = best_layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность классификации на общей обучающей выборке - 99.17% !\n"
     ]
    }
   ],
   "source": [
    "pred = best_model.predict(TrainX)\n",
    "pred = make_onehot(pred, 3)\n",
    "print('Точность классификации на общей обучающей выборке - {}% !'.format(round(accuracy_metrics(pred, TrainY)*100,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность классификации на тестовой выборке - 100.0% !\n"
     ]
    }
   ],
   "source": [
    "pred = best_model.predict(TestX)\n",
    "pred = make_onehot(pred, 3)\n",
    "print('Точность классификации на тестовой выборке - {}% !'.format(round(accuracy_metrics(pred, TestY)*100,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Оптимизация гипер-параметров сети"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В процессе построения модели возникает множество параметров сети, которые можно варьировать и тем самым менять качество работы сети. Часто для поиска этих параметров в небольших моделях используют полный перебор вариантов в определенных границах, например ищут лучшее значение скорости обучения между 0.0001 и 1.0. При этом выбриается метрика качества и оценивается ее значение на отложенной выборке (validation set). Значения гипер-параметров лучшей модели сохраняются. Неизбежно при большом числе параметров происходит переобучение на validation set и для контроля следует смотреть качество на test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Составим словарь: \n",
    "- parameter - значение параметра сети, которое мы будем варьировать и искать лучшее значение,\n",
    "- start - начальное значение, end - наибольшее значение,\n",
    "- points - число значений между (включительно) этими границами, \n",
    "- log (еще не имплементировано) - поиск по логарифмической шкале, вместо обычной,\n",
    "- int - целочисленное значение.\n",
    "\n",
    "В итоге наш перебор составит: (число разных параметров сети * число точек из диапазона). Обычно это довольно много и ресурсо-затратно. Помните: каждый раз нам придется обучить с этими параметрами сеть и оценить ее производительность."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid_dict =[\n",
    "{\n",
    "    'parameter': 'learning_rate',\n",
    "    'start': 0.001,\n",
    "    'end': 1.,\n",
    "    'points': 5,\n",
    "    'log': False,\n",
    "    'int': False\n",
    "},{\n",
    "    'parameter': 'minibatch_size',\n",
    "    'start': 1,\n",
    "    'end': 256,\n",
    "    'points': 5,\n",
    "    'log': False,\n",
    "    'int': True\n",
    "},\n",
    "#     {\n",
    "#     'parameter': 'eps',\n",
    "#     'start': 0.001,\n",
    "#     'end': 0.01,\n",
    "#     'points': 2,\n",
    "#     'log': False,\n",
    "#     'int': False\n",
    "# },\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'end': 1.0,\n",
       "  'int': False,\n",
       "  'log': False,\n",
       "  'parameter': 'learning_rate',\n",
       "  'points': 5,\n",
       "  'start': 0.001},\n",
       " {'end': 256,\n",
       "  'int': True,\n",
       "  'log': False,\n",
       "  'parameter': 'minibatch_size',\n",
       "  'points': 5,\n",
       "  'start': 1}]"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Опишем функцию выполняющую перебор значений. Она основывается на значении функции потерь на отложенной выборке после обучения на 50-ти эпохах. (Число эпох можно и нужно менять, сейчас задано небольшое число для ускорения перебора)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "def grid_search(model, dictionary, data, labels):\n",
    "    data, labels, val_data, val_labels = train_test_split(data, labels, ratio = 0.8)\n",
    "    num_parameters = len(dictionary)\n",
    "    minimal_loss = 10e9\n",
    "    minimal_dict = {}\n",
    "    linspaces = []\n",
    "    #we'll be saving to this dict best values\n",
    "    for dic in dictionary:\n",
    "        minimal_dict[dic['parameter']] = None\n",
    "        linspaces.append(np.linspace(dic['start'], dic['end'], dic['points']))\n",
    "    iterator = product(*linspaces)\n",
    "    for i in iterator:\n",
    "        model_copy = deepcopy(model)\n",
    "        feed_dict = {}\n",
    "        for j in range(num_parameters):\n",
    "            if dictionary[j]['int']:\n",
    "                feed_dict[dictionary[j]['parameter']] = int(i[j])\n",
    "            else:\n",
    "                feed_dict[dictionary[j]['parameter']] = i[j]\n",
    "        model_copy.fit(data, labels, num_epochs=50, **feed_dict)\n",
    "        val_pred = model_copy.propagate_forward(np.transpose(val_data))\n",
    "        val_loss = cross_entropy_log_loss(val_pred, np.transpose(val_labels))\n",
    "        if val_loss < minimal_loss:\n",
    "            minimal_loss = val_loss\n",
    "            minimal_dict = feed_dict\n",
    "    return (minimal_loss, minimal_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = MLP(4, [10, 5, 3], ['sigm','sigm','sigm'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "mloss, mdict = grid_search(a, grid_dict, TrainX, TrainY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13150557014410855 {'learning_rate': 0.25075, 'minibatch_size': 1}\n"
     ]
    }
   ],
   "source": [
    "print(mloss, mdict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss on iteration 0 = 0.35927\n",
      "Accuracy on train: 35.83%\n",
      "--------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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HzprumusuEgoK7tnoeCs01Qbbc1fxMJFQUXDPRk210N4WcM9dZX9FwkTBPRs1BDxTBqAw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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114e512e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a.fit(TrainX, TrainY, num_epochs=10000, eps=0.001, validation=False, visualize=True, **mdict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Последний этап оценки качества сети - это ее показатель на тестовой выборке."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pred = a.predict(TestX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = make_onehot(pred, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность классификации на тестовой выборке - 96.67% !\n"
     ]
    }
   ],
   "source": [
    "print('Точность классификации на тестовой выборке - {}% !'.format(round(accuracy_metrics(pred, TestY)*100,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}