seminars/seminar3/seminar3.ipynb

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   "source": [
    "# Семинар 3\n",
    "\n",
    "## Линейная задача наименьших квадратов, решение линейных систем и QR разложение"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Кластеризация и матричные разложения\n",
    "\n",
    "- Задача кластеризации относится к классу задач обучения без учителя, в которой требуется разбить наборы объектов на группы, в которых содержатся похожие объекты\n",
    "\n",
    "<img src=\"./clustering_demo.png\">\n",
    "\n",
    "Картинка из [этого](https://towardsdatascience.com/semantic-similarity-classifier-and-clustering-sentences-based-on-semantic-similarity-a5a564e22304) поста.\n",
    "\n",
    "- Отличие от классификации - меток объектов нет\n",
    "- Классический алгоритм решения такой задачи называется *k-means* или метод $k$-средних"
   ]
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   "source": [
    "### $k$-means\n",
    "\n",
    "- Выбираем число кластеров $k$\n",
    "- Выбираем так называемые центры клатеров\n",
    "- Повторяем до сходимости\n",
    "    - Размечаем объекты на основании того, к какому центру они ближе\n",
    "    - Обновляем центр как среднее значение точек из каждого кластера\n",
    "\n",
    "- Подробности будут в курсе по машинному обучению"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "### Визуализация\n",
    "\n",
    "<img width=400 src=\"./K-means_convergence.gif\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "### Причём тут матричные разложения?\n",
    "\n",
    "- Пусть дано $N$ объектов, каждый из которых описывается $n$ числами.\n",
    "- Данные $N$ объектов уложены по столбцам в матрицу $X$\n",
    "- **Утверждение.** Алгоритм $k$-means решает следующую задачу оптимизации\n",
    "\n",
    "$$ \\| X - ZC\\|^2_F \\to \\min, $$\n",
    " \n",
    "где $X \\in \\mathbb{R}^{n \\times N}$, $Z \\in \\mathbb{R}^{n \\times k}$ и $C$ размера $k \\times N$\n",
    "- Матрица $C$ обладает следующим свойством\n",
    "\n",
    "$$ C_{ij} = \\begin{cases} 1, & x_j \\in \\mathcal{C}_i \\\\ 0, & \\text{иначе}, \\end{cases} $$\n",
    "\n",
    "где $\\mathcal{C}_i$ обозначает $i$-ый кластер, а $x_j$ – $j$-ый объект.\n",
    "\n",
    "- В каждом столбце матрицы $C$ ровно одна 1\n",
    "\n",
    "**Q:** что такое матрица $Z$?\n",
    "\n",
    "**Q:** какая интерпретация у столбцов матрицы $X - ZC$?"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Постановка линейной задачи наименьших квадратов: напоминание\n",
    "\n",
    "- Дана переопределённая система линейных уравнений с матрицей $A$, в которой строк больше, чем столбцов, и правой частью $b$\n",
    "- Задача решения такой системы в смысле наименьших квадратов записывается в виде\n",
    "\n",
    "\n",
    "$$\\Vert A x - b \\Vert_2 \\rightarrow \\min_{x}$$\n",
    "\n",
    "- Нормальное уравнение\n",
    "\n",
    "$$ A^* A x = A^* b $$"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Решение и метод вычисления\n",
    "\n",
    "- Псевдообратная матрица \n",
    "\n",
    "$$A^{\\dagger} = \\lim_{\\alpha \\rightarrow 0}(\\alpha I + A^* A)^{-1} A^*$$ \n",
    "\n",
    "- Решение записывается как \n",
    "\n",
    "$$ x = A^{\\dagger}b $$\n",
    "\n",
    "- Вычисление псевдообратной матрицы из SVD\n",
    "\n",
    "    Пусть $A = U \\Sigma V^*$ SVD матрицы $A$. Тогда,\n",
    "\n",
    "    $$A^{\\dagger} = V \\Sigma^{\\dagger} U^*,$$\n",
    "\n",
    "    где $\\Sigma^{\\dagger}$ состоит из обращённых ненулевых сингулярных чисел матрицы $A$.\n",
    "\n",
    "- Решение вычисляется с помощью QR разложения матрицы $A$\n",
    "\n",
    "$$\n",
    "Rx = Q^* b.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Сравнение методов решения нормального уравнения\n",
    "\n",
    "- Метод Гаусса\n",
    "- QR разложение"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.linalg as splin\n",
    "\n",
    "def lsqr_solver(A, b):\n",
    "    Q, R = np.linalg.qr(A)\n",
    "    return splin.solve_triangular(R, Q.T @ b, lower=False)\n",
    "#     return np.linalg.solve(R, Q.T @ b)\n",
    "\n",
    "def ls_gramm_solver(A, b):\n",
    "    gram_mat = A.T @ A\n",
    "    return np.linalg.solve(gram_mat, A.T @ b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0951368347355132\n",
      "0.09513683473549624\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "m = 10*n\n",
    "A = np.random.randn(m, n)\n",
    "x_true = np.random.randn(n)\n",
    "b = A @ x_true + 0.001 * np.random.randn(m)\n",
    "x = lsqr_solver(A, b)\n",
    "print(np.linalg.norm(A @ x - b))\n",
    "x = ls_gramm_solver(A, b)\n",
    "print(np.linalg.norm(A @ x - b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
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   },
   "outputs": [],
   "source": [
    "dim_range = [10**i for i in range(1, 4)]\n",
    "time_qr_range = []\n",
    "time_gram_range = []\n",
    "for n in dim_range:\n",
    "    m = 10*n\n",
    "    A = np.random.randn(m, n)\n",
    "    x_true = np.random.randn(n)\n",
    "    b = A @ x_true + 0.01 * np.random.randn(m)\n",
    "    t = %timeit -o -q -r 1 lsqr_solver(A, b) \n",
    "    time_qr_range.append(t.best)\n",
    "    t = %timeit -o -q -r 1 ls_gramm_solver(A, b)\n",
    "    time_gram_range.append(t.best)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.plot(dim_range, time_qr_range, label=\"QR\")\n",
    "plt.plot(dim_range, time_gram_range, label=\"Gram matrix\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.xlabel(\"Dimension\", fontsize=20)\n",
    "plt.ylabel(\"Time\", fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Свойства псевдообратной матрицы\n",
    "\n",
    "- $A = AA^{\\dagger}A$\n",
    "- $A^{\\dagger} = A^{\\dagger}A A^{\\dagger}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Закон Мура\n",
    "\n",
    "- Количество транзизисторов на интегральной схеме удваивается каждые полтора-два года"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1971</th>\n",
       "      <th>1972</th>\n",
       "      <th>1974</th>\n",
       "      <th>1978</th>\n",
       "      <th>1982</th>\n",
       "      <th>1985</th>\n",
       "      <th>1989</th>\n",
       "      <th>1993</th>\n",
       "      <th>1997</th>\n",
       "      <th>1999</th>\n",
       "      <th>2000</th>\n",
       "      <th>2002</th>\n",
       "      <th>2003</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2250</td>\n",
       "      <td>2500</td>\n",
       "      <td>5000</td>\n",
       "      <td>29000</td>\n",
       "      <td>120000</td>\n",
       "      <td>275000</td>\n",
       "      <td>1180000</td>\n",
       "      <td>3100000</td>\n",
       "      <td>7500000</td>\n",
       "      <td>24000000</td>\n",
       "      <td>42000000</td>\n",
       "      <td>220000000</td>\n",
       "      <td>410000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   1971  1972  1974   1978    1982    1985     1989     1993     1997  \\\n",
       "0  2250  2500  5000  29000  120000  275000  1180000  3100000  7500000   \n",
       "\n",
       "       1999      2000       2002       2003  \n",
       "0  24000000  42000000  220000000  410000000  "
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "year_transistor = {\n",
    "1971: 2250,\n",
    "1972: 2500,\n",
    "1974: 5000,\n",
    "1978: 29000,\n",
    "1982: 120000,\n",
    "1985: 275000,\n",
    "1989: 1180000,\n",
    "1993: 3100000,\n",
    "1997: 7500000,\n",
    "1999: 24000000,\n",
    "2000: 42000000,\n",
    "2002: 220000000,\n",
    "2003: 410000000\n",
    "}\n",
    "\n",
    "data = pd.DataFrame([year_transistor])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1971</td>\n",
       "      <td>2250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1972</td>\n",
       "      <td>2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1974</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1978</td>\n",
       "      <td>29000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1982</td>\n",
       "      <td>120000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1985</td>\n",
       "      <td>275000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1989</td>\n",
       "      <td>1180000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1993</td>\n",
       "      <td>3100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1997</td>\n",
       "      <td>7500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1999</td>\n",
       "      <td>24000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2000</td>\n",
       "      <td>42000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2002</td>\n",
       "      <td>220000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2003</td>\n",
       "      <td>410000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year          N\n",
       "0   1971       2250\n",
       "1   1972       2500\n",
       "2   1974       5000\n",
       "3   1978      29000\n",
       "4   1982     120000\n",
       "5   1985     275000\n",
       "6   1989    1180000\n",
       "7   1993    3100000\n",
       "8   1997    7500000\n",
       "9   1999   24000000\n",
       "10  2000   42000000\n",
       "11  2002  220000000\n",
       "12  2003  410000000"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(list(year_transistor.items()), columns=[\"Year\", \"N\"])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Модель\n",
    "\n",
    "$$ \\log_{10} N \\approx  w_1 + w_2 (t - 1970)$$\n",
    "\n",
    "- Логарифмирование – очень полезный приём преобразования данных, масштабы которых сильно отличаются "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.]\n",
      " [ 1.  2.]\n",
      " [ 1.  4.]\n",
      " [ 1.  8.]\n",
      " [ 1. 12.]\n",
      " [ 1. 15.]\n",
      " [ 1. 19.]\n",
      " [ 1. 23.]\n",
      " [ 1. 27.]\n",
      " [ 1. 29.]\n",
      " [ 1. 30.]\n",
      " [ 1. 32.]\n",
      " [ 1. 33.]]\n",
      "0     11.135709\n",
      "1     11.287712\n",
      "2     12.287712\n",
      "3     14.823765\n",
      "4     16.872675\n",
      "5     18.069072\n",
      "6     20.170355\n",
      "7     21.563837\n",
      "8     22.838459\n",
      "9     24.516531\n",
      "10    25.323886\n",
      "11    27.712928\n",
      "12    28.611049\n",
      "Name: N, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "y = np.log2(data[\"N\"])\n",
    "x = data[\"Year\"] - 1970\n",
    "X = np.ones((13, 2))\n",
    "X[:, 1] = x\n",
    "print(X)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4323270736375635\n",
      "[10.38299398  0.51163732]\n"
     ]
    }
   ],
   "source": [
    "w = np.linalg.lstsq(X, y, rcond=None)[0]\n",
    "print(np.linalg.norm(X @ w - y))\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '# transistors')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.scatter(data[\"Year\"], y)\n",
    "plt.plot(data[\"Year\"], X @ w)\n",
    "plt.xlabel(\"Year\", fontsize=20)\n",
    "plt.ylabel(\"# transistors\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Предсказание на 2015 год\n",
    "\n",
    "- Микропроцессор IBM Z13 содержит $4 \\cdot 10^9$ транзисторов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.05641072680136\n",
      "9.602059991327963\n"
     ]
    }
   ],
   "source": [
    "year = 2015\n",
    "pred_given_year = w[0] + w[1]* (year - 1970)\n",
    "print(pred_given_year)\n",
    "print(np.log10(4e9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Модель авторегрессии в прогнозировании временных рядов\n",
    "\n",
    "- Дан временной ряд, например температура (и другие данные из метеорологии) в разное время, цены активов и прочее\n",
    "- Почти всегда временной ряд – это нелинейная функция.\n",
    "- Зачастую она периодична\n",
    "- Простейшая модель – авторегрессионная (AR)\n",
    "- Идея в прогнозировании $k+1$ значения по последним $M$\n",
    "- Модель остаётся линейной!\n",
    "\n",
    "$$\\hat{x}_{k+1} = w_1 x_k + \\ldots + w_M x_{k - M + 1} $$\n",
    "\n",
    "- Целевая функция – сумма квадратов невязок (опять!) \n",
    "\n",
    "$$ (x_{k+1} - \\hat{x}_{k+1})^2 + \\ldots + (x_T - \\hat{x}_T)^2 \\to \\min_w $$\n",
    "\n",
    "- Как представить эту задачу в виде $\\|Xw - y \\|^2_2 \\to \\min_w$ ?\n",
    "\n",
    "- Каким свойством обладает матрица $X$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            Temp\n",
      "Date            \n",
      "1981-01-01  20.7\n",
      "1981-01-02  17.9\n",
      "1981-01-03  18.8\n",
      "1981-01-04  14.6\n",
      "1981-01-05  15.8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x61ba77518>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "series = pd.read_csv('./daily-min-temperatures.csv', header=0, index_col=0)\n",
    "print(series.head())\n",
    "series.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3650,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x61c2bc320>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x = series[\"Temp\"]\n",
    "print(x.shape)\n",
    "train_x = x[:x.shape[0] // 2]\n",
    "test_x = x[x.shape[0] // 2:]\n",
    "train_x.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "182.0535788062525\n"
     ]
    }
   ],
   "source": [
    "mean_forecast = train_x.mean()\n",
    "print(np.linalg.norm(train_x - mean_forecast))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "120.3297552561294\n"
     ]
    }
   ],
   "source": [
    "prev_forecast = train_x[:-1].values\n",
    "# print(prev_forecast)\n",
    "print(np.linalg.norm((train_x[1:].values - prev_forecast)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1822, 3) (1822,)\n",
      "113.59510906780783\n",
      "[ 0.76670919 -0.04852799  0.26391016]\n"
     ]
    }
   ],
   "source": [
    "M = 3\n",
    "X = splin.toeplitz(train_x[M-1:-1], train_x[:M][::-1])\n",
    "y = train_x[M:]\n",
    "print(X.shape, y.shape)\n",
    "w = np.linalg.lstsq(X, y, rcond=None)[0]\n",
    "print(np.linalg.norm(X @ w - y))\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x61ccf8748>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.plot(train_x.values, label=\"True\")\n",
    "plt.plot(X @ w, label=\"Predict\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37.15800015458122\n"
     ]
    }
   ],
   "source": [
    "test_X = splin.toeplitz(test_x[M-1:-1], test_x[:M][::-1])\n",
    "test_pred = test_X @ w\n",
    "print(np.linalg.norm(test_pred - test_x[M-1:-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x61afe4588>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WEpakT0K3JXRK6UKYC5T93O1O/Mg6dblL3CSrXLKE6yiI4ScrR4NSzQYAlM8axVLCkO7ss2W78eS0NbiyS1N537YDR3EagCrqlxtyWULodUgZeNCEjKJaRDge/nApCkKDcW/4HwCudKeTSUJdphw5ZH9mG0UzFaTyCG5gF6S7GynHDcXvY7x/dEYtT9fuLcGWg8altQioPAupv3FJCpd2xj4CPmvCYROHZNT+QfRP333oKBpDiBaNRISgG56N5XVRqlwopfhhzf60SIJ2WIS7sCI41LHkrRzH2tddGeGAQqGQxN9837vWRzfA8xTfrd6ncsR4t/IJzA0OS0ukc9YTerO5D+M//nfRgt+T7q6kFANLP8el7IqMEl4Hvr3QJuRZr0Mfwb2NF3wTFZKc8iPItuVX/NC+vn+VjcSy0P3CD04gdDM/9PmbCnH/p3/gjZ82J7ubCSFEHPiSOyA9nkKe6LkMo6wv/9iDv09ZqQoKbEn3AUhPeuSsT87FlgvONUGaJalFaz5HGYKCGN77QLoA8AF75YYnpg5dwlnRFbF9UaEuZ5gE5GenJPTicmHM7y+pTG4nqwOb8c5AH3yjfduUUkODeibgoPjsi45X6fZ5EnoiEL8IaWBcySxBXehrBUrIFGOia14uLp0neaAGf+nB81pleixSNBvuMhE0RRGkezOKJ2AjQph/GDGVS9a5Ldo2kIha33IAsxQ9yCZBQueF75unmUVZUXHc+hh9v9Jh38usp5MAKBEGOAMKHN2NMYG3MMb/Zpp7lTooiWBPcXm1S9slF/YSd3k4tkyXJfQaqkPPZw7If+sEDcrDxwkujWGiIHSVDj25/XMDlAph/IdKjVcRlxz6EAWhwQjQmIRLCNAQJRgXeANfBZ8XJF1Z5ZJZY0HSnbOMvl+ehJ4QRAkHFBCXqM2IeXRZpkRWuvWqpbuJcjzOf2Ue/vH5Ksv2qYcyUtQ8lF8a+8O+WKXYdgJ4uZjcGqE8QpVCxKTSP8jIbTGTnw4FxSWvL8DZL8813H9B0VQAQA4f88dfsLkQOSRG8EpC5zOMsqIWhJ4ObUBmPZ0EQJWErth2uKwK7/+6XfdQ065yMfj6dhxOPIOeRAhFYhrS33ccSfhcyYFDlYv4Xg6UVMTayxVqktKxtIOnDAqPVWHq8t06QWNn4TFUlRwEAPgUeuZscVtU4mCpXr8sgUDtobPpwDFsPlimumeqMIpSEFRGOIyZtzUtboFaSHVvfYYSeqp7UxMInQi3wICq1qCPfLYKI2dswIb9xm50mYSBb/1a7XOUiqk6a4d8AM/jXvY71Ea5zVEphsVkKu1hDLxclCqakvIIHv5sJUqzOBufhO7MFgDAsC//1O37ZuVucJyQpoJVkF5/doWubSbD1g9dEw0spZz9GxtzT1SrXBi8u2A7Xpu1CQ9O/gPpxNtzt2DuRsEpw1O5uAWZ0HkoZUDpg9dGhqZd5WLwjo9XI82m5L+risvZNhdP+adghH+S6XFpgYXXiiyNq9LnStti7cf/ug3TV+3DR3Hkjs8sxO5vuP8zdCC7DFsxoPLkxlDj8ZEFKnRcPHq+5X4GxlL2IN88+W+l2yIPIudjmrXuoCt9TBSj52zG9kJhdW1I6GkQ0bOe0CVyyKXlqm2x5H0ZpnIRoXz9fkTxnG8S6iP+qi1y6LQctBOzJWSchG4BWUIn+myLTnQu+cNn4OHPViahZ+7Cr3HTq0+MV5AseHlyU7r27aGNsiqbqFSwwwwyoUuTPaXow6xWteF5pdsig2Zla1EQGmw6GaYDjMEYpSYTcVL7kfIruozAccGJ//GqMSoJUJLEF28rwpLtRdWSgpONK5gluNM3C0/6piR8DrXbV2Yqna1oyFBCR0wq07fXn2P6qn3V6l8q0AjGhZ61ggYBL6taWJEYtrP5ABTl+mKNMxq9mTVoAme2nQbbp+OjwCuqbVQjoXcoFqR3LfGnE4aCIp+BuVwyHX4xsKghLYayBqU0Yb42a1OaemYN5ev3E+EDVUqn8Z5HlxMFKf7OIxWY4h+JF6K3mbexVLkI/6oyvhhI6JmU6iAR/Bb6u+q39Cy0UjcLXpZeJQm90H8K8qPrUBHmUCuYHZ/ucN9kDPV9j0JaB0KOP2u0WvGybpvay4WYZAVKL4wWTTQNhJ71EjrvywEAFKE+lEY0oyUQkAE6dFC54rkEaYAmog3SEjlVzmapHPh7V+Bcdr2l3l72K6cGhC7+q5LQM0Q9lkxIz0JrQGNB5QlektB5Ngg/onJps9zyPbiaWZzC3saPoWLulcbEWp1YnxcleIN3zlMaCyxSpV5O97dsDcp7Kpe4UXjqdQCAycxA/G/eVgBqHboW6SaJHmtewLaQWlKRSCwRH1sqT2J6lQsBxaszNybW0bihdx8VOuYsN4tEaH6Vu5q5H7ryTOkwPrkFqedaYY4oJHTwghHQH8yBDxz2FAu2kX6/3Iy3Av9LUU+TiwdLR4t/GRE6VH7omUjjxrEVnoQeN6RZupIn+H51TIdqJqGnG212TdVtY2RSjh+UCgZBM9XS2PkpKughehvpl8POJG5p1yXMCv1GpcrF4LVGDJa2pZUR5A+fgY9/K7DqddJxtDxsWSxYGr+XHv8Gj/q+kLcLKhdxkhNVcr5gLgKIyh5cwYiQlTHb1VAAEKBhLNleJLstKkEplclRKfRkkoRuNLY9CT0O7Coqx86i45AIg+NiXgEUwLNH/omNwTvQkexMXyctoByKjCyhxz9AJcl2/iahXmvaViByTh17Cd0qUvRW31zFNslQao1I5XEM901GELEEbVKo+cQ0uzd2e2EOrhmzEABkyVoJ6VncfWwcHvJ9I29XErpkHKVMAH5EsyLkP14Q8Ji59oDhu+YpwEWFVQoPgq4Hv05t5xKEJ6HHgT6vzcOFr82XmYDjeYV0SNA5vBohEsGPwSfT1kcrKAMqGMRcsuKFLgUIIJNrauUXE5WLAX0bGkWNaV5xZs0eRXP2t/9hqO97DGFnOexrarH5oJAs7vxX5un2mUmZLImpXGKE7gMBsHpPCRZuOZycziYRkxYXmKrHCKWg1LgMCk8pFm0VBBYeDAK8EE2c6fOaZxRNAEbGtGyANuQZUEvok3/fhfmbDOtuq6D1jhCILg1LUZNJRDmonahcVBCXrMpzGkpwYTG4wyRIJZNhRugdyU6Z0H0QC5szPjCEYtyCbbh1wu+Kk2TH2H/u23X4euVew30MeMMv+BCtB55SHCkTVly8gUE9nWDAI4CI4SvYf7QcL36/PqU2nuwndPFJMiT2sWeSbs0UihHAGPhbP/X1GgyZaFERXoTWO4KCKshV2Lf10DFcPHo+isrMc2pUH8YSuorE5eAnZ37lhApEZmcO4cUQ+ahqOGfBGAAwLTgCL/kmyL+lAg4EQEAkcp80UTHGeVyySZg5aqAjBwCOE1RJ2nshEMrYsdDr0DPhHY/xv4nNoTsM901atB0TFu7Ayt1HU9afrCd0hSe2/HciuuhUQymhx4yiievQJRgR4/u/7sD2wuOYvT6JodJEGkra/sSSKlmVIzPcJ0r3Rv75yvaS8ckwcVUauc5pROctCrtBRAwNYcGjFhGkUga8IJmaPGOSQPxCuhA1SajFgkeAK0MDoq1lQMHTmAtnxqTPpRQ9yCZczgpCV6yEolJQU3JTapD9hC4+KwYx/ZvR43vR9wEKQoNT1y8bKHNYEAtCL7DJxChxRg+yCQWhwWhAi3XnrZMjVI0vNZGOXAFR/RODSOjmNUXFbRQ63z0i+l8rB2mfgjexJPgA9hRXyEZGnhPuK9PKk208EH8qB8mOMlwRNewHBw6M7LmlNTxnk4QeNdOhg+KBjXpJlwEFT4E6QWGyTsTOlBSsn46vgs/LP+XbogbfdQpfT4Y8ncQhzYzERr69zfdTajrkEIzBTG7kh973P/N121YplnCSFHivbwYA4Ax+E7S0mhcQpL6yqmi1+mwNY5ULb+DlYgSeUszboNGvUn0Ebc99n+JkUowvV+yRjYwlon41B5lVhvDKtxbGfYw0ilswhfK2IIkgDB+IqWto9iDKGffdBw4NIgd02xlRQq+XIxB6xqy+i3cYbzdwdkglsp7QoXBts5J0Mw1EEUATCywy7vc7Gl/y4wpilggzCDG7JPw6A6U2gVdSYOq2qKgFaRX6D+C+j9U2A1+F4MlhkMgOyslh0RZBlfRP/2fa7iQVf+45igkLTT7sBGG2yojAB4hlzj7yj8ITPsW9ZolRFACiJp4f9YjxSpQBr6opmjGEroH8CgwEtVS+nRpE6DS7CN3GKKrEK2K055z1B3H7B0sR8sdem57QYzk+pOchkRtPKSYu2oEnp+nzb1cfJkZRxRKbatqq2lG9l0obvkBoTYEvlu3G8K9i/b6OiUm/vjR5t1z9v0V48fv1rp7TbOyG4ZdVLr3Zdbjf9628L5skdjOVixmIqHKRvKUyNrBI1icqJPQ02Dayn9DFB1kLFZgefFaxJTMhDULlcuwp/xTVPqnlP3xTVYFR93y0HL9sLsT17/wmb5NsTAGikNA1A12Zv+b579ZjytLdbtyKIcx06IBBoIWyIDTV57gpp0EAAMNQPPHVn/hsWazfTYhgK+B5CpbEjlu/T6233n74OJ7/bl28t5E2mE3qSpWLFtlE6O/M34aZa/c7bk8gvOO8Y8JKKB0kXlIRsS+oIo9tpdgirk49Hbo9LmFWoDbKZbc46QPPJOwqKte5CsZK5umlSuVgDSKCh31f4/PAC8I+k1Gh9XKxWpImdVzJxk/1fRmGREt/8DHVUXF5RCdpB8RVx7DwO7pzSLU1q6I8Qgrd+ez1ej3sxEUFtt1PBRqapM5VImpS1T4PlRmQWM4djIsjHYXg4QP4I8KzK0dQ3teodtDsMNeweNthdH1+NrqMmI1DxxSFrrXpjqUwf6r3XkslsorQOZ5i6vLd4I7sxPuB0XjDP0bep16uZ8bA7/PaPJw36mfDfdrSW4CC0CmVox6lbcrx0wyKKMFIJa5hFsYkf8opPE5SOaBitgw1FPepDeXnYlLPPR8t16lcfEQKrNHnxJCW3hURDnlQVIzPkHdvhBWh+2zbmE3I9UkZCJP9EjoAVIadG68ZCBGkkkuq0jU15Ev+u/5jZ0xQPGRVG5XqCb0L2Y4zyeaUpuPIKkKfvHQXhn35J6YvF2b4fHIAa/YIHh/K2ZCCIEwzo5huVVSbRk9ZMk8N+WPePBNPimqYKgQAqKXrp/yT5b+7bHoDbwbGoiezWTi9hT45qeNKPLfOy8XQCCa24dQftqRymR66xvZyz/o/xhT/SHA8RRlC8nbJgMqW7cff2O+Q5HWJ67DqrZnKJdPu0azo+U2s4JVUXhkfofMUIPJqTm90LA9H8e8fN6BSW/gjhYgReqx/bwf+h2nBESntR1YRerFY2f5oeUyyKykXtrFEoasFUInkL8cSgfS6jTwTZEKvipUlq6KCD7lyllcaPnMq1MFCgpSr1aFXo8NOofQ3V21X68lVUKhcejHrsUQs/lBFnL27c9n14CnFcZojb3t9zkbc/sFSBL4agif9U9CGZH4VIyWsXpWZyiUdS3srDBq/xHD7q/73AAAVYefuswQ8eEplQleOL2mV+878bXh3wXZ8ssT9RHxmQpBusyS4pKHsnBJZReiS9MUrpEHZk0PxiCPwIaJYmi0L2i91UwbZpVD/4o2CJipFCZ1TjKwIVVSr0ahuGMrrQv9j50++iK7L5WKgWpL7pVC59GVWyX9HSMDxVcuqorJBGABuYefil82FOF4qLJX/7vta1sWnE9EK49qhWmgNw0owpioXAYu2Hkb+8Blypsl0wS7egYsjrSyBYCeS00Ao9kkTmbQKjteDJl4QAlRGOOQPn4G1ezX2EInIo/rVBwUsUyi7iewidJHRORojLG2KUQCIatQtjYm9MSp1MPHXhnHiIUkaf/rrtfI25WSlJXQCDruOlGu2Sbr5hDrsDHFI6DEdunLwx+69koSgRUFoMN7w64s59Bu9ANexi+TfbcleVbHta9nFuCOFWRj3FJejRFxBsuDQhgjBUrdPMJZatfDDnAzNc/wLz3WSmCr4j13pdRCw0xlXhe0n2G18U7wVvVb0Q48ZHVUSuuxFYma/cR+FxwQ9+q+abJeyTYzH482UAAAgAElEQVTT69k/+HU7Oj47EwdTMNFmF6FLA5rGsvDFKqPHXnTUKKdHhkD2crExikqogqBy+XLFHnlbRFUKVv3xVIUjeEpB/imDQZFn5Xbxh3qfQuWiNAYWM/UNbSDXsvpyazlQfyRDfLOxMjRUtS1gQZJu4/xX5uHi0fOx+eAx/N33NeYGh6Ed2YNVe5ylAQhZRLs22mcc7Sx/A0RvQE8H7C7vNM0xBQOWULGmqPAObxb18NJ+IHa/yVYtUgqwslCp8XKRJXQ9oe/bKEzme4orkttBZBGhHyipxPhftgs/xIfHgkeICB+A0sgYsSD0dA92Kxh5ODQjRTgJMYkriLBaitNMDD7wukmOpEBA1/ZD3qzcrjWcKlQuyr41qF0LpciTf6/0dTW9bC3YfySpzvFSdDyMS//7C04XYwhOJfsce6IEiPnS3BfVF8gAYpIp0agk0wWtK60WHRl7XbcyMzrPUzDi5K+sTVrMNBDbCkiGh5P2TiRC161CLAhdcsdNhS3LdqQTQj4ghBwihKxVbBtBCNlLCFkl/ndFcrsJDP1kBY6IRtHZa4VlbAumEFezQpANUUnomVwRXXirFeEI7vloOQ6UxCRMI0I/mRRjaegBAMAAZik2hYaoqvrodOgKQu/NrsNw35QUOfJJk4i5H7oy7w4AgI8RujICMCcUBNiYHr2SxIyeWjjJgW41wScTJVSYlOqS4+4YLonxfXB/TsWe4nLFxJ1eRrcTmvJgr3qgIOBFn/xRP6yP+XkroA3cSQVhSoSuqwHLmxN6Kt+GE+b7EMD/AHyk2f5fSul/XO+RCVSGlqrj0DqxqHToFh9w+mMzhNf765ZCbKMBnFQ7iJfkPdbz67jAGwanUw8XVjMtDPV9h9mHLsA3gXcxg/+4Gv22gaxD127mxG4SXV+3HShGG6mdcgfjA0diQzNIzQnAR4wJXTnBG6bVTQBVUQ6dnp2FKE/R97TGtu0l1ZgfnDu+4iZuixczK/HqzE2yF0y6V6FWl29PduMidrWjc0gjuaCoDGik17tLofWpnMCk8c0JydtjfZGM2bxBTdQUxkbYSuiU0l8AHElBX+z6gZ5kI/7KzsBUMXpSCVbhLhQBaxiMIpwnaV2MC9IHXj83JonGm3ioggZQKbqASRGGSgkdACqpH5euewLdmG1gafK8PfYdFdQB1iXo1MarOWtjdoHGyihKhkETThHxGdbmyFY0dSChu2VTKSoLy54UUg1X50geoUtnl56rncojWaiMcNhVVI5JjP77lDA7+E9H58olVbime3MAguqwsFTv2y4XtJEldPeJ09QMrRXRKY/9JRUor9LbQEIII4hwSmi9OrqJBwkhtwNYDuAxSqmhaZ0Qci+AewGgZcuWCV+MAvgyaD5QlPk8otSc0DOF0ZuRIrQmB1A/73R5W7w9I6A4WFKO01hBT+wDL0roCkJHACHJbS9JNQ63FZbhX1NXY3JA772jVrmI/RYlq3A4tjwd5IsZu1btLcMgxTlyYR6h1xgOqsEw7qjgnLwfP6KyZK6UzNz4mO0iRdOdGuDxqavx/Z/7URCqfsKy5uQwDueJuXzAGyZgkxwL6oQPoSvZCoacrmvjNmS9vmYwEJ7Duf/+GVfV3Ya3Nce8E3gDu2gTAH2T3r9ErUXvAGgDoBuA/QBGmzWklI6nlPaklPZs3Nh+mZoolAQeAWvh2ZAZhP5R4BW8F3gd9XP98jajfOhWUH6+klqhC7MdFzKxJa3kJQMIy8Lx/tHox6xIrNMmOFhaqTDAUk3ZOX3ov5z/PWJM1HuPqqWcDox5MjFlkQEl2jKxgCLCukTodsLAvpXYErodFzErdbsSVbnwrEK3aKJDDyICSmlq0iRbYMHmeFctNlDkfzcW0IQbfXjt9ZgefDYpErDyURK91jC2T+zf4WN69SADmjLDfEJXoZQepJRyVHBheA/A2e52y+ii1ruVOnQeDPwm3gLpSGlZHo7igcl/iAEf6mEX8CnTgQJ/n7ISS3cUOTwzlVUO0oC50zcLQ3yz5RZKdQOhUVzKrsCEgOn8mzCUhKX2VIz92H5IVJ2IkiRrElXHmxBXomCTPIlPXb5b8AHfvRQAVBOqhEQI/b+R61FZ/zTFSYwp6zx2fUaoXNwmVGJD6HuPHMeT09bIwVhpXaHwJnEYEFYYGU3ohJCmip/XAUi647OPWud/6Mpsl/+2eq2pTJQj4bvV+zDjz/14bdYmaGem56bHUrtSMPhu9T5MWbrL0XmVVZrM9O+qZX8cEXrxQpbQNSYqpa5RSkEqtWWo8SrKbUI3Vb/FCbOhM+zLP/Hct+Ypem9l58j56uMBSziV3tw8l4vQuc5lizGYnYtHv7A3OiYDbhOqpGJiLCR05bfiNp8/+vkqvD5ns+aKxoNg6jLBFdPIm0nI6c6kZMKxXYsSQqZAUP40IoTsAfAcgL6EkG4Q2KkAwN+S2EcAwOzjNzpu24IcMt2XafV0i46HIeWWsjKKNobeREEQG0ARB+YQ1oRA3YAyBQNPKc58fg4a1Qrgq3P0D1yi63OPzdbtE07iLqHnptiLVSuldWR24yHftLjPw4JXG0IZ8+fCUB5373kK8AOTuX5xXysTQYiC0A1W3Nrn7DZdTlu5V7/RhD+klbKRkd4PDtEUSei2Q51SOshg84Qk9MU19GHXmO5LZ4V04wk61p9c0T+3O7NV12qZ6IuuOh8oGKKv5GIGJkleLgREFczEU4qSighKKiIqsVbyB/cTYWI5s9y45iZvQVyJoH4oVUvx2HX6MqtQV1HBXl/N3hzb+KZow+wHC6qWyi0kdKKYrPsxK7Bu3/no1Kyu42u6AeNSgdU5oaRy4Q0ldJ00nEaVi9Q/IwndBy5u+1iiyJpIUbfw+bJdKcmp4BRKKeMJ/xdgweF235y4j3UiAZipONyAZMOgICrVhDJSNCwaaO3UD9TlQCAmySoXRQsAQB1Sjg8Dr2Ig+7u8Jx4dOvUFxWN4mdQAcy8XQMyDL2JCYDR2H0l+mLkWrqtcxAmsE7PTMGnZZcwylQHa9QnFAGZvkQGPIML4MPCqbp+fcODApMRt8YQjdD5cjrsnLU93N2TsCN2q+h3Phy+oXJxL6KxB0INbiBG6uVE0TCVCt7aHUJfcDCUQl1KaOg1gMZLS4okUjYrZJrUqF2KxcqkT0SSLSoOw6rpRVGToKYGXVCH/Es5j12Ni4DXF9ZN/07HhrA/oawjzfD0ZbRTNZjzgm47icucJ9hMGpbiMWaqSLJzYY+MZkgyJZZukBpkatUimDl2pO1R5WfAxopc8bnKIjYROWCxo9bBrfUumMdhxH+IoZC2tZFjwGpWLOaH3Lfhvwn1zC65PInHaUpI9iT3zzVoM+1IwOGtTTrDE2pOFB5MS76OsIHTOxWxDuahKjfSy6Qe8G3gDD7DTZcmB4yminPWH7STyUYkezBYAzrzrkxUpSojGbdQkZa60+mD5KuQPn2F+QoZBry6nme+PE26pmpx+j0bqgXiGXMRMQre8pjaNcjqQHJVLeq4uoBezHg+w3wAAVu46KqfN1a64HvF9ZenUEAWTkqRpWUHor8zc6Or5UlJ38rgQZNGMxJbC5UlMcm+mclFK7snUoTMKHbp64MaIRiZ0m0mLEhZ+n3O1yw1Vz1r3LYn3LaE5KQR+fAIAVLpzCf1YfbCRGaSKTSx4ld7cSsrX5kpfvK3IVnhwG+5L6PGd8I8Cp/EbzvFZYCSG+b+Qf9dHKQaxc3XxLOcwG/G0/1PT8/BgUuIynRWE/tP6g/aNHIKAps0YHnUQep9oRKGTo5gk6tAlKz8FUXVGGsQNSYmc6li6x1V8GxiBo86lsyO0FpbTDpZtBlVNdXQuO1g949f9Y125BgBERJULA16ldqC1m5odohNPP1xcgLfmbnGtT25jD21k2yZeCX3aH7twyCBS00287n8H//ZPQAeijxUxytcvoRFKPQldQsTFHCQEVpVf3IcysCfC2b9RK8OKFazuSKrwlCyjKIG6pqtS5TJr7X4AQHtmr1xZKCapG69Y7uzdWpZMy6i6etF6vpXqNwcW8x/va9vHQeOX4Fhl9e6fRqvQlcRcSj8PvIAH2a+rdU4jbPB1BAAs4LsCufXl7ZH+L5kdAt6ALbYWOneVrC42HTgmV/NxDRZePUZgwaMynNxVSX0ilBLMdZACWAmp/m2ykRWEzjkgQqcgUCezvHvSckxYuMO18xuh27pRKAgNRsTBEnhRKDFjoJXuXTLWJNcoGntHfDSMt/xv41SyD9sO6ScoidCNEi4BwNVdmsm6Y62h6SOuv+p3FfzwsQQYMMqyf79tL5JLtCWKhgtHYHrwWbQmwiR1DrMRj/vdkf6V2OJrh46VH2AmfzYq+7+KGdzZ6Fs1Gkwg1/SYA3XOwK7cTqptURe/GyVmrj2AK978VZ5Ethw8hsve+CWuczgx4scrdjHg0ee1edh31H2XTWkil3ImBW0M+0bwCF2EttxTddCIlKhGyk8bDuLF76ufHc4K7Qs+AQCEo8mTHqxy1Eh51pMVWASo9eLMvhW4mv0Nr/jHG36UtUglGqPYVEIXaseKhmTNENX+DlMffAwDtLGPjqzuMAoW/gkAqAet5OvuhxolPlSI4cMktx4eiDyCAtrU0vZznKmjm9QlAik+HnYkTFghf/gMvCrash75fCXW7y9FZZRDlOPx6qxNcZ9P+cRKqPFEZVSm0QrSGPzaKMKzmpgeFOw00vjT1i22w78jg1KSNC0rCN1NSeNSdgUa09Sld1fqxKv7UTm9jhZS0FGyVC6+ymJcImZwpJSAitI1Cx4P+r7Rtb+B/QXLQg8YGkcjZwwC6jQ3ldBr56grm0Tgk6vImKGCBnADuwD/nVNN47rJF1kQugVnM/GTmhmkXDb1cv0qCrfUFNIoGA0BcryQ+bL7i3MwbGr187uMnb9N6J/4GBhCMOK7dZgj2riuZhYZZpo07K7izr7rOs6wTbzxA/F6iCUCTiTyeGsXfM719SR0CVGXrQmNUkLo+hceTtISGDAPXGnBFCKPCLpNMwl95tr92FNsXK/SCdrPuwcXs6t0289ktqIe0RcmkKAN5/64zj3wXz9O0J2KhK713qmTq9ap82DgYwjMpOR5XFfkkDD+438Xd1gUJy4pj6gKcRuByv8m1wYThQ9LnuyHBcMuUtl7LAmd53ReMByNufx+u3qf0VEJQTJ0Uwr8tP4QnvV9hBmBJ/FWYIwq0McKjEI/3rZlzNi7km8LAHg/enncEnoqLGOceJVaJD4d+lHU8oyiEtz0QwcAEAaVEQ4jLDLkJQOU5xFKQPfmBE5qa5rp0Id+8geuePPXhK8dKlXbIJzmrWAJj4hi6aoqwWdC6AdYtadHR2YXWNb8U1ZK+A1Eg5YRHpu6Co9PXY1NB8zbSBK68v+JYA7Xw3I/T3w4uW4IdXP8CPlZBH0MXr7uDMtjGD6qI0CO52VhyG4VEw8kQZOnFHVyfLjLNxOdDAo/D4/cbXoO1cpD/FVMa+Ht6LUAgBlcL4CPz+aTEgld1KE7qYuqRmocMbKC0HvmmWdP1GI+7W7bhoLB58t248NqGsnixfVV7ntESHASiWjlj11a6VLwDZwvR33g1FkiVV+5scrlGKmFDpUT1edhzCsPKCcJK7XUwVJhFVMZsVrmC8dPDz6LZ3yfWLSzxmZ6iuX+UiaWVItlCDaNvByDz2lpqYMlNKpTUXA8lZf5buZZkc7JU4ocv0UGSIvnvYXJl//2ccLq8ABtgFtvvxcdKz/AStoubpVLsimzIDQYF7KCHSVkk75Ci3G3nokL2yevwI+ErCD0l2s59ySo4u2NFVROy8njTvZHBBLIVW0P/WA+o8p5cEm8cJIrJGm5XFQZFX2OVRIsODkDowC9hK71hqAUqNRUCLeSPpWTCwFFSXkEZVVRnYFa4jvLp6i4z7t9P1q1tITVaqqMhlBO8gz3hSzIU0yLptrC8zF1JesSoVeEOVl1wFNY6oE6NjTv7xcNh8p/R3KbAAA+4Abg4g5NUIEQ6oR8caVLAOLLl1NdBCxW2sv49rptqSq+kRWEHmWC9o1E5FjUn5RACIGfZXATOx/P+T/GUPa76nTPEIfL9DN4OJr8AhOWbVxKUqWFcqzyYBwTehBR1dJVlU1QVrnYn8vHMDCjYu3xXV+Yjc7PzcKtE9TRnNIHl4poPrOCG19EL0Tnqg+QiCs1oVQn0UZ5XnYtrI7GRflMOj4703C7ERiLZGKPXt5F/pvLaYT8ysmYyvUFAHx69zmY9Y8+cefguasak2y88JuWuAR+5brotrk1odohKwg9ngo2VrnQJeSiAj6WoDaEpV5tkrhBcO/RCvy8UR/J+trszbptiUaBOoET/SExIBJXCExxDga8Y5VLCFXwKQKSVAQg6oNPJurCHka9tSKr5g1i0q6y2dIdasO4tG/Vbn3R6bV7S7ByV7FrZG9n7+h/epO4z0nAq3ToN7LzwdGYhM4kIbcsT23UHBaEnhuI1brVnqN320ZoWjcnbpXL/b5vcQpcrmtqAvOaxcaZFVMVy5gVhM4xgYSO+5XrbLj9sbLRCLDu3PqVb/2Kuz50lo7XieEyUTiR0ImCkKYu341fNhe67hsrELqzZxvQVKFhle/EL3izaAM4quDHeW0aqrZZLWeVOWGsJlTpFM9/p49JGPj2Qlw31jysO14cRwhhAz9mCoJ1z1+GR/q1Mz32/dZv4IvohYb7lCqK1/zj0SSyBzzHoxU5UC2jqNkYsZfQLa6p8t4xbqcl9ArYr9QTDcyLF1Zq2lQVszBCVhB6SV6+bttsG08BAFjIG3sGNOUPCBW8RdngHt8PCfftaLnwYh/49A/btsksUO1EQleqXIZ9+Sdu/2Cp676xLPiE3fpYVkFy+RfgychfcVFVrKD1S5HBKGROwuR7esl2EBkm90EcZit0lg6i+s9qOd8eb0evQ4+qdw335wV9lkS4Pqc7vud76bYTyuu8XOpFixBcMQ4Lgo/idCQeDW121zy1ljwZq4IcyqRjZufQ3M+9td42v1iKoRVGlDBeRXoqFxnKgdq3ajS6VI7XGNOMYSUR1y7ZjGcU2dHKqqrn5TFjzX7D7Wr3rOQRulkYvbov+jbu9EihciEU5ZHEViKsSodOMIXrh300Jo3/yJ+jKDKh/UBMvFwU6jrh/inOJhsAUOQPnyEXrnb0ubkw+b0fvQJVCBj21snZqyLGEybH8TobSW2+BP49vwEAmuKw7hinMJPE7SR01mEuFtNnryH0fSR+VVTC4CL4PPBCQoc2IiX6jZ7KRQHFiy2gTVGKWgg4KCtmRaA9lz2q+l1U5m5iIaMrJ5fQ7SckI6OoUkJfu9dgIMYJBjzun6wPMnICyuqX1GryUjw/hxKPX+EZEkAUVzO/4Yvgi7iRXQAA2FUk2E9MJahIBQpCg3ETOw9uTH9m0xEAXH6GRTZFEe2a1DIk9PJwRGd09/FVgGhYtCpfZwdLCd3iOCsJXVnb12xFolW5pCJ0XkbpPpzDWEcWR0zC/1NVncgI2UHoBtZuKyuzBCsJPVilzp3sdo50o7Ml062KdaDOOVQaS1ok5y9XHDbw7YW2qYp/3VKIAyWaoArFSZqRI5gbHOagxwbwhXSbtAbW2KU0T7ihsd5ZaXwLIox8cgAA0IJoYhvMXn+Z8Dz+zn7jCqMEfKx4Of256vb9u+3xD17UFs9fo7cNEVCd2s1Hw6ByxahqELrJbfOUWtovrPT2yu+NAFj4z4vw+1PqfDxaL5dUhM7L8OfYNomaaAmMJtxU5XfNDkIXJfTvT/qbvCnP5yAykpi3YTm1RO5mAjAzJFNCd4LS4zFCPwmC94j2tpcWWKdFuG3CUgx8e6HrfQNg+BEpP449tDHuvqC1sF2rQ/cFwGs+sI+7T1FV/DmOHDBETXDS/ZurcWMl9MIu5OLJCQhG2iu7NFdtfzQ8FGjSyegQFXwsgzaNa+u2D/V9rxNgysrKUF4luM/SOMu5OcHXK/fi/cLBpvt31DvXdB/xxxJyEQI0r5+LJnU0E3pttYpFGqo7+ZPi7mvccMAHZoReQfUrTc8PXQnKg6MEK1sOkTd1aWqeSlSCZYUXTV4TjqeYtLgA74gJiNyCclikMvDBCEr/Z0nPpy18bJRXW4vDLqqn9ip05LyNhL7+hQG4rntzXZsY1H0/ktsWeSUx99FiWluWYjkqErp4zDmVC3E1o/dkqYpExX4w2O9CWlZJQucCeXg0PFTO725GDoZQTFKzu7wu/12fqLNABhHGxn1HxUOqo3IRo03B4x++L1FfzNn/2qxNqM8Xmx5XkauOiB0XvSr2IyBM3kdpHsymU9LrftVvjqe4rGoUrg6PjPcW4sKIb9fhp/XGNjElzN6ZkduuJ6ErQCgHDgwIgOev7oQvh54LwqkDd66pegHPRO5E9OLn5G1m7kNr+XydPpmnFM99u05X7i7C8XHnklG2V77IWnBOCLO4nobbyw1mf6e4yxcLCpH8aLW3lsiUU52VxwfRAbFrs2pCf3tQd7xzS8ybSZWoykniJkJQ50gsLsEHTp5UpY9OEsQeLR6JtwL/050iIuqleRA0JdVP6saIK0MCgml8HxRQQQqNj9Bjz6Ewz7z2agiRWBHxOKv/KCE9o/OZtXjYNw0j/R84Os6nybFziNaT/yYguKnRNJxTNcb0eML6sIbPl3/nBXzYRFuiBLUc9z2awPf74eICPP21fTxL1IRfjMjb80NXgufAgwHDENxxXj565jcA4dWEfrjuGfiE6w+iWLa/Gx2Isfz1utNJGd2UOFhqnGyn3dM/4tb39TUijbD7iGBga/PUD+hK9JJ+O8Z5nmYz17+F7FmOz2EF2b/7+GEUhAbjXEZIVJZSwxNiFe4BYMNh9arpqq7NMOCMZobHEYM0BnYTy6P+L/GgbzoAoBNTAMB+AqM0VivVid3GDt3DQpph6QP3i6umuAhdMTbMSAUAWMLF1I7VIHQJ0govx2EeE78m1kNpLCREUE1UISBmyzSG8jtIRIfe/cU5OPuln+I+zslqujExri5mNA5TUscY2ULooODBqGa5Y31fxBY+tqT77u/nY9YjfeSHOTF6GSoQwtv0Jt3ZjEKvb5uw1PTqv213Vnz2glfn4bdtRbiQWY3Bvp8BAE2I+ZLUCmbDqZAKiZvMLOxOERQ/SmafEBR1N/uDeF3zgWzqplaNWUAZ+r9in3UGOyNPlEQ9Ci5nlzlqRzmBxHNIlSuBYZ/QAarfkndSlDgviq0kZ96i8o+wIhEnJFGHvmjrYVOV2WKTfZSnaEUOyN/Wxewq3MLak6SW0ItoHflvhhA5ilUryZtBaedaxHXCb9zptsccq4yi6Lh6AuJ5iue/W4e9Fiq06mRuJEmMN7FDVhB6TOWikExa9Eb/cCz3coO8AE47WW8sMkIyddmbDx5DRxJLJdqXTaywgJEe7kfuLCznBG8OJ1FzVgiKkW5UNPRpVRCGfUrCYyOI6dHv6Wtd7FkpyO27egoAYBF7juJcGnsApdhylrUvsZ0vNeWE59SMHHEl9fFevgGAmIS+hQo2gUKFOsIWioktSi0kdPCxSYiwoJTilvd/x6DxSwzbD37/d9w07jf9ef6YiAXBR3EmEys6/ZL/A0vSW8m3VUVj/z38oCogikBQhwB64jeDUnVyS+RpDIk84eg4Lab8tgX1fn8NF4+aadqmOioSQw83T+USA6EceBDVQzEjF+VH/eI1nQwlzkRn31+3FOIFg9BwAPgq8ByG+ybjpR82VCs3jATlUvOXgQsQ7fs07os8Im+trsdMUJQMP1+2U3U9K4JTLnknLNyBL5bvlnubKObwZ8rXvqqbdVpZpYRe3rwPhoSH4ZXQQ6btb+zZHMzJ1nnEtT3Xjg2J0N0CJ0rK0r28Fr0ZN1X9C+txqvOTKCT0iI2EHiN0RibELYf0xaOl9779sL4gCbNPWM1ItVQl3M9ON732Y5Gh8LMEM3AB3otege/486CkOkJiFbysVC5S//eRk3W68PjUVDE03zgRD/u+xhCLgidOMj3+wXY12WPwPXiErgAv5AdRftBR3viBS1I8BcFt5+br9hcHmhqG4NeCPQnfNmEpPlikD6G+ilmMHswWDPV9j3CUB+tKAErsXqtym4K9cBge6tce/+gvSOjVTeYfJMIy9Pfth1XXs5LClYT+4vfr8cSXf1arDwDw+OVn4L7wI/iWOxeoY03oaqmJYj7fHRWMubdT8/q5aN3YuQENAJ7yfar6TeMssmCHy7u2xC3ntMSwywRjZgQ+LKUd4/zeY605C0JnwcsTP0MElUUdGFeQslqomO3LZ8xjFngQ1M3142nmIbwUvVW3nyCmcrGS0CX16HM5w9GolrAq/duFwuSXqLrNxwmqliAipgKMk/exuupk4Mw7DPctPW8ctrb6v4T6Vx1kBaFX+upgL22kktDNLdf2ZGpk3HrLr/dwcIJP/S/hbY13xFBf9dPxao2ihBA82r89WtQXCKy6aqNzmfVg5YJaCgndUoce7w57dGnZEA/ccgM6P/SlZXY+QO3La+c/LsEqWlF5HgmXMJqcPC4Tuo/146XrzkC9XHXCubiW+CqVi/mBd/pmoa5I4CwBsPIT/Bm6B+2IvtReIm+wtoUQxIHBNV31E/RV/Gj0qfovCBOrFWwVgCQROkf8GH97D7x2Qxc8eXlHca/xccXHwyg+bm64lWILeBA8ONm4RoETgak+OQZc/ZZuOwHF2ZcOQts731Vs84yiMha3GoqB4ZdVA7l2yG9xhFKFoN5eP7wfV7N6PeHF7Cq0J7t12yWs2WMcFt+bdaeMnVR6S4JdgiszQq+k1s9Fwl/YhXjUN1WW4Jzp0I13VkUTXy1wtU/BgM5NcWqckrQE24ANm/3bCsuw5WCs7JzuDk1WgokiLuOnGYhSQrf+hCUpmmEAZttcAMBpBuPciQeJ9klexppnGT29WT3DkP4dpAV2ia6al5wuBAjVyTEfs5LKhYkbV1wAACAASURBVAeLk2qHcGPPFrb9fH/hDnR/cY5q2y+bC3FczNfUqGK7eE6CGWv2Y+WuYl30sxOBiYtD5ePp0BXoe5rw4i86LVbCqUFeAEuf6ge+UQdUnKcINa+GtDg7+E/UhV6/CABX/S9J0ZEilB47gJpYVMtCn7DsDDP6IJx3olfFpVs/i9mEp3yTASgI3aI9T4EGMHbVskOfqv8abmfYxPSgVjlR1LBu8cSXf6L/f38x3c/HWWTBDmYTdXwSnFJCd3YECypf22iMKAn9yxV7UGCgS48HklfNPReobQMSsfE8xYirOmHp0/1QK2g+yfnErIZ8NQKjAOD2D5biia8EFWGHEql+rtCZ68YuxsWj56vaO/mOzDyMjP3QPQldRrcW9VAw6kp0b1lftf2kOiEwD/6OnEuf0R2TKK3/pMxDwnMYws5MUok6LTQ5S8w+8PaXAxc/g1pX/Vu3673olXGpYs5mNqEFU6i6ntV8yKz7Cn+EhqI72aLa7mTwS1KZFokOc8fzdpwfku65u1TlaVfdnuL5Ta35zqEyijr7hH0MldMdGL0v5fN8fOpqXKVI75DItyQ9xwcuaouCUVfG+iHqyzmewscyOKm2XjBR4iAVvvkwrNspUQ/HQMDrgoO2aYzBTUnMHbk8rH7PjgjdNLAodux+thlKqX1Uu1uwHQ2EkA8IIYcIIWsV2xoQQuYQQraI/9a3OkdqoX4R8QrsjZWpL//8HCP8H+FBn/PizvcmWM5O281WDXLx76Zv4q/hx9SzO8MAfYaB1NWHwF942knYKRKnlX+y8fVj2nQzsLuE0PhOTIEY/k3xwGT7PPBWSDRPtByObnu4eYP/Y382OK9mYuXc0aHP7f42zq4cg1pBY/VCXE9BESWrNYr+ntvX8JBNB45hzgZB/WLkT6/9To4ZpJO+gjWP1dBBE8j0cL92+Oq+czH5nnNw9/mt0SDPWdGae8OP4qHwAzjKOqeYVaG/4SH2a0z5vQCjfONxKtkn71Oudm/z/YSLGDMduj1xmLVQEvqDDd9Hl6r3MipS9EMAAzTbhgOYSyltB2Cu+DujIH2YbU5KTDcLAHyloFuta+IZYISn/FMSupaOSABsC3XCXN6kkMepfXWbGIbFnLPex93hx+L2APAjitZkv7W3g9jH08hurAwNxc3sfMz4cz9ySHwV0FV9TnCgx4yidjp08+cwyv++8wtVE9ec1RZ3X3EuHrnEOCtkXB98WSxTpNYoujh0vvH5QWWvkn/5P9btt9ShJ/AIqEa//I/+7dGjVQN0OLkOnhl4umMVxI0Xnolv+d5xqyz6syvQkezE//nmY3rgX/inbwpAKV6dtUnV7nRFzIgSTiR0c/WZso2wJWNyuVBKfwGgTWJxDYBJ4t+TAFyLTIE4MKWHPemu+EPlJf/YWFIiNXYVlWOrgS9vsmDoWmU0wAmL+67qjVvuGBp3DcnL2WWYF3wMuRHzyFYpH8htPiFKsAfR1021QgFvoHZx2M0qqtazyoRud3wCopGUoGxn0XHsP1o9XbIEH0twb582CPldyHrYuo/8p1ZC33LEzJ2XIiSqDhsQ/di1NorGz+i8C6kGAGBgFyFHfLxvkSJGyrVJBe7zfYdTuL0Yt0CdksPMl92ZhG5G6FTRRtyWQRK6EZpQSvcDgPivaT5LQsi9hJDlhJDlhYWpKOBKFf+HSkc3LHKvozNMWCj4mpupLfq8Ng+XvL4g8S46QJGvKeIdxhLhXnRa4ulFb9g7yvb8iaJvWG8YdaJyuSX8JPqFR6u2NasnvNebz7Lzeohf9fTp0l0AgAtfm48xc2MS3Q6jCckh7O4zLhkuENPJchovnKgFyeTCPLWCVfxBQjp0lwg9UVCDJ0pAdUFMSkIPR3m8/6vgAdOF2W57DbNi6MqtN/YQxmdLRbHyZMIFHyprUErHAxgPAD179kx+kgMLSeNP3lk03paDZeKp1OfqxazHQVofjVCCDbRl4n00gHK2vzM8DA0aDwBsstQu5DphC22OO31CxBvnwsKudsQ8o6C2SILggVC9V+qkx4sMasPWyw2ojG3mF4g3ZIdib3EFysNR+beEKiRWrLycBm1VS/FKcM9G7kBbsk9HxFGeGIppDCjCFp+7XQqEuOGSSGq2EntiwGmYve4gYCIjNiDHcAOrFroo9D7vSkJ/79fteG3WJjRCCV7xv2ffN9PRG3uWg89picHnuMsVVkh0Gj1ICGkKAOK/h2zapxzVqRryzR9SOLx0nPDXZ4GRmBd8DFODL2Cs/00Xeqnom6Jz8/juCAbtc7XcGnkaz0djkWpKiSHRz2lLXnfTfdpPXhVa7hCnVX6I9pWT5N/JL55rff6h7Ldopqm3SQhw+rPCJKm8v0STcwlpK+wk9PjwEXcZno3eiRytCsdEMiagWM4L0alfRC/Eun0lyB8+A+2f+RFHjodTnmXTKSS1p/b53d+3Lb55oLfpcc3JYdzhU/uiUwB+jfujktB3iK6aTr3aEi2GnkwkSujfApCY5A4A5kkdUo7qj0wpAk4iSCMDyemMsTElUSiv8I9L2uOpKzqatjWDXZCJEyw6oNcpHiytRP7wGdh2WB0ZWAsVmBZ4Lq7zVyGgSpmbLD6fyl0oXsD6mQz3f4bFinwwBFROgwyoSdxJ3VYj8CC295mon/I/L1cnNCMm0bZtyD40E930osSPsWIhl3CUx69bCsFunYWC0GC0Ekv0KZEI2bs1UfMmEnqiYDWZHZXF5ivC8aUyNle5pG92dOK2OAXAbwBOI4TsIYT8FcAoAP0JIVsA9Bd/ZxicjYBJ0f66bSP9E22Pa0RKcbQ8ce8OLZSz/QMXtVEFW1gNj9xAbPB1bdnA0TFWUKZFKKuKYvXuo1i/TwgmWn9AbSDswWxGVwe6RgD4+K9n45R6+hJzyQq42EZPkS4Q13EEFN//uR8ARW9mjYrEfQlL6IwtwV2oCJqLB7WCPoyLDlRci+CB5l/p2j3n/xi3ixJrwK/+7CkFAhumAYBhHv9EUMm6ozOWVEFujJKConKUVmgqlSnSUF92+EPMDgxznCfJSEI/RnPwUfTS6nW0GrDVoVNKB5ns6meyPb2IU5wweilnMptVpzKLofzL2MXQezInBmUvJJKz46KlT/VD0McC2z9A1fzRuLdPG8PzxQM/ojhWGUHtkB/3fbICv245jDf/r5uqX3Hj1L64oF1jzHzkApwxYrZqV7Ik9NhHmdgFrmB+x9jAW9hDG8nbGpOjCZ1rE22BngY3uurZ/ohwFBVhDk3qxpcOOcfPon0TwSV3Md8JQ/G9sINSjL7jIuAl82O1uemo6BPiFpbz7XFVF+PCJPFC7qpLA6UPWaX6rXTvvbp4EsA4V61JgUV9q0bj28AzqEMqcGX4ZexFYpOzG8iKSNFEYETrhhFyBgP5d9pZtY+AyiXblNh+2F3XxUnR/vhXZIjjT+ukOiHUzfUDna9H8MHF1aobKSFAohj5/QYAwIqdggtjg73zMC3wbEKD5U++NTD4CwBC/p36uerAGq1O0y3IbmdxEkFr5iAa4yjGBoSkS81JTL+eSD70W8JP4p7wo4ZG0Xq5ATSuHUTLhrnCxBwH1j5/GabdL+iQlQVbGHC2rpFEYz7n+dj3UptU4H72m2pl8+RB8H9nu2MIdJqEzSk+DLyq+t2EFGOKfyQaIhZQeD67VnuYcd/EfwtoU7l4hxtFUKqDpHu5pB7V119JuZCVZzLK0JiIrmwNn4/bw8MRQBS/hx6Ut1MQPBe9EwDwQhptLT5wKKuK4pb3l8jh0L3+eBx+pgJ7YV6/0ggvRG5Dbu+/oYsvJn1qpXyrTHsSxt3aAyt2xlfPk1RDQn/a/0ncx5hB8tBxW7WkfG5+JaE7qLXKatIZKEfxcN8U1CYV2E6bAbhKt98J3DQWnnFKXQzodDIevbS94f4CcgryqbPSjkbf692+GWhMSnEzP1/e5sTDBVDfp5Soq7pprauLmiehd/oLKqk/ZhRLAEYfxb8NogoTmY15MChGHRxEA9V2q48glR4Id7E/IifAYtHWWJ4LqaB2n8p5cZ2rmNbC41eoXQ61/G1V3EDCgM4n4+kr7cuNKVEeR+4PLa5lFyd8bDqglNCdFGYglNekIqYqCR0QShTmD58BjqdyoJUZtBk+eReM8xICPgbjbuuB9k2Mq5E94X8a8zizQhP2kKLAn/B/HvexvIrQhXs2Km+ZStQ8Qm/QGh2qJokShhoEFMvYbrankGZZ6dM4h9lgmHI338AjwA7mleMVLoeSDj3us1cfQRLVucIRMSd4XU0lpsSs+bG72kcbxB3RagVpUpwcvRif8OkzTKUaRxAjOycSOqNRuVCY+6EfD0cxc91+w30SSqE2gJp5fyQDLdt1xn+jNzhq6zcg2wBJnIBPbRx77pI+Pd0ql5pH6DZY5Oul+m3sr84LA1wc420Y4wH9UzD+moYnJWhYixeHG5rkgHEArRrEbBmZyOCVTj2waiQGVr0c9/FWkN7lu9xARRHtDHWwdhG/8Z0QFu+XOCF0yiEvehQPs1/hm8Azho9IepbTVuiLYWihJfBUEvpL13XGmFt6Omr7nO8jV69dKxQLNIuKVMqAx7mnNnT1OvHghCJ0AmfJoFhQjJq5MSlFkc1gdKnqXH7p2YlVYFJiYfAhfOw3J107XanRfqn02lp6Ko6gjm5/tSCubBItTeYmOlVOMM0Bnwws4EVPJAeTLAMeI7ddj3/4v0I3ZjtOOrxEN9ak1df8NQW4nrWuBaBdqVVH3Rkvgj4WLRo4S097LmtcD9gNvBr9Pxyleaiscyo+ufsc+wOShPSP/CTglnNayq52WuiKABuQDgse7y7Yjt3FFUnp3+BzWmLUX85ABVH4ZROi0ydL3gpO9MxaRP15uoRWTsHygjdHc3IYF1hY/CsQn6sdANzYs4WzkP2EIDwnnjKOK8knC8eRY5oD3m0EfAw+5AQV02raxqa1IMWzCvXD1h0F0Cr46pMyPOebhLxd9o65ym9oDidkR0wp0pw35p1bzkRlywvRreo9RHy5jgz9yUIN9HIBXrrOvNK7k2d9GtmFTqQgaaG9T1/REXlBH+5ZNRn37BmOsxkhAdQPD1+AhVtibnIvXN0JLRvk4KIO8SfbIiTxiLXyKpskMiLYNBuAtOCYABguCg6MZVmzmobv/34+5m5oj/yZZ8DP2o9Z7XtbtacEN9dTj5URfkE9cSdm2Z7vOA3J80F1a90mhHQRunjPl5/RFJ2a1UWf1+ZZ1DpODWqkhG6FFvX10YpatGQKMSP4VNLqAEpRg5VsHkpozKDUvklt3HV+a/l3/bwAhl3WIeEZ/2f+TPnvr7gLHB/33cpdjtrZRU6mOgQ64hcCbVjw6NNODO4QjX3aNLNuQVsLNh1o36Q27u0jJJ7rJepvP+8ywbS91vZBQQDOnapcaTEKpio3rQVqhwTZuEer9Nb6OcEInWJAp5M0W9RQffhJGijSaRlCFKTn7rUIIXg48oD8+/nI7Y6PdepLa9fOitB7JmHgr2kn+PWf0qwZXv5LZ9W+EqQmfWm6wDIEc/7RB+NuFYzhVU3NDYV6QgeYiDt532n91lj6dIqDyEUJPVmTthPUzwtg5iMX4JXru6StD8AJR+iAT3znv3LCB/8DpzZgRBVaqBU7k+ORIknoQ87Lx1SuLwBgPc139RoE6nSvkqHwIK1nWgtRQkNyzNE17KQxq89ryr29sOEFbSGs6mFHi+uQXzkZrZudpIu8LKa18a86I129HpDeRExatGtSG3liDiCrnPhGEjpJgNCN8iCtPv1x2zqhrkMkdLtx7TaOhFqpfnc4uY47BUyqgROO0CWS2UxbIL9yMv6g6gi0qOKRrN2XWIV72z6Inbiow0l48/l/Ib9yMg6QRtYHJXgNCTyI6Hnxhu3KY17wMZWe1cz4aSuha5OGKOBnGeQEUjv4X7z9ctfPmUmEroSV5wdL1O+teYM8hOu0MmltDklfHlEIQbf0No7oTC5EY3iKIzfWNEqWcT9x1EijqDWEQWj28jlF6sxkGXiSnwNcDx4MKuIo0PCRP5ZA0yjtAWAfFZdqspPsUernq+hDEp57+rW38UNrFD25bg4q8/RFx+0gvf8IWOAf64GKYjSuHb/nU7WRJgk9E3T3WpxQEjoB1dUc1UKZHznPomRXdZAKryZtAS71/dp3oDe7Tv7bjLhZCwlcuEpqCZ0T361R9CkFycgPMB3QqlyaVW7BZ0sL4j6PNC6i8AF1TwFO7mxzRJJApHyo3vs9IQh9O4Tc2AQAThOW3dO58wzbKvXHzxpUR3cDRoma3B6K2ksoB3uqaDbVn5cUvs6aEXcS3NsyVeViBa2q7PKijxJKKiWpbiIOC0IkDWmaqDNRPjghVC4qHXCjdsivnJy+zmggBcA8fEk7V8+rHWsqFRMhKWH1m3qckvyLKCD5AKsE9Ibt8GH0UnzEXYqfk0Lo9ji1cWZ52Bi5mybibiip4qI03YR+QsiljnBCPAmJNG8719jw82VerIbHXpraPAwsQ1Aw6krc37etq+eV1A6dKifgiqqXVbYBSlIzj6c6YE4mdOWFGQYjokPEZG3OO3R7+J8OW1rPjLef2wo/P9bX8XVTASPyZhOY4aWi04dQr9p9qh5SO9AWc/Fl/kwlTghCD4iEflYr44H3Wa3b5RSg+1JM6MnCxR1OwpDz8nEcOTqXyF8vcC/ftyUcJIpy9XKGRlEF4lgjJ2pga1v5EdpVxpJA1c3AiFUj9UoiKpdlfAc8E7kTz0TucqNbiUOU0FOl/hoS+Se6VDrLmZ5qnBAql+YNcoEDQOtGxktf5TBIuaU8SfCzDEZc3Qnr95di6Q51yt5j9U9HFfUjmEAFnriQ4lLyvKRDd2Fp4NQFTksiUhzDXb1bI79RLm4+q0W1++I2tEbujXyLhFQuFAS3PPgC+h9zlioiaUgBoW/jm8pZV8PwqwqdZxJqBnvZwNf1ZuGPuuYfV6oWbV+f/22KriTg/Tt6YvoDvdGsrhDsMf2B3uKKRT/4N/HNUUqdZa5TYlD4acPt6fJyMRXEeee5Z+KZ2L84U288JwS4/dz8uEvLpQJaaXw+3zXhSjsdm9bBhe3TV0MTQEJeLspasTUJJwSho9d9wDOFQK1Y9NzVXYUCGFd1lQphCGQQ9Cd30XK8Vn5Sz69FnZAfXVvUw9zH+mL1s5eia4t6lpqHzTQ+f+StfDP8xncy3GdWNCFZkCrrmHq5UOeEzjLOiJgAOFzndF2unBTfelzQSuMtySGcbFp4xRwZc4u5Ajn/J3qT40PejQ7EEr5jsnqUNpwYhE4I4IsF1RSMuhJvDeqOglFX4u1B3UEplaVJXkzwZIVCEisft5OPLxNiOoKKACAnwAoFpWG+GiGgcX+kbZl98t8lNBe92CmKvSmW0EWe0qpcbuvVCoPPaSlUQwYUxS/M4bTgNhEC5/FYZChaV8ZsE/E/ydRBGyl6BbsUl7PLbI/7T+RG1e+M8fv2BXBq5SeYwF3h+BAKgolR56knssU99cQgdAeQhubX9YfYtuUVHiOvRW+O6zppTJUsIzfgMxygBEDz+vG72P382IXoWPkBzq4aiyiJ6RZL81pbHOU+8oLCe6kTUus3X7y2M16+7gyg7ik4ToP4d3Swav8RajCJO3SFI6DiioeAKj6nTJDQx0evxOiIvjxbohkR/8ddV90uJQ3x2r44MLpCKK8bPKtsg0foIvxibcEStgH2txts2VbpAhhvdRw3a2gmit5tG5pXoU9gBcEQggqEUIUAOjaNVSE62PjcRLuYEG4/Nx9PX9ERd5yXb9zAn4NOVRPxA3e2avPxxvpiKNThcyDI3PD/l6O34BPuEvn3/6LXYCHXKe11L1OFNXy+6T4ODIIB9cRvNwe/Ef0L9tMGNq3SC4/QofVyYW2lM16xP+BXD4r/b+/cw6SorgT+O9U9bwZmYIb3YwZmhucowoBKEAcZXoKiaBIwaIwJRo0GNKzKZ9YPYx5odrOJK6uSaIgaTdwkPhLzkE00rjEP0WDEjUZEjMbHEI2RRJmZ7r77R1V1V/Wj6Jnp6a5q7u/7mu66fXs4davq1Klzzz3nXVXJ+u7L2Db0ClakqZlZKJeLExEhXR0E02rvm0K3+a+PJHKw5/sptTRssH7BRErD3scv2VWgjHQRC9ldGq+qOl8c00w4Lde7IyexT43uc2GS5TNGurYPqELHn3tzXnfmmr8K4Qurj3a1DS73dsV9NXImx3fdGDdajhozpP9C5hit0IE1jtCyqIQpPfRXj95ul0vyo54CdsbaeLzyJJ5NkxLXBwa6RXpt2xe/qFOfVTvcHX70IzfWVTFqcHKSstR9PiDu9QgbIhv4TPcFrraXYiPYEV3q2v+5jaYF1zE1P+XnDkdySG4Uo88W+vxmd2TII7H0ZR79glfoaRk91FS50/yecvKqjP2dLsr2yfX87+ULWd46qv9C5hit0IEPzxkf/xwlxLA//9Szf0zcLpf5XV9lddcWV5/k5Fg2frbmBNWnZdQZg0r8p895eFM7912YyIEfU5LiXlnffRlvGW6F/lOO5/uxBTwaTZQ3fCzW6vKbA0wdWc3+rStSlF+hcMpXU1VGDIMh8l6f/pbznP5VNH1kk5/wcoeW0w1GIqJt25yHeH9Ce8b+26LuylTZFqbON1qhJxHNYlm8U6HHEF5Vw9mrRsfb1p+QeTLQL/pcMmjbjL51D5JvUtsm3sTG7ot8aJ/bJOSNYqTcfN9Sg1PmOux9vLTnonh6CNsCtItK+BHnMbiko4WlrX3Pr+OXczdbvCz0TlULocSTWldJDRMyKOk/x+r5XvTE+HZlgYtYeKEVehIxDN4d5V21XDkUenWFmfjLXiH4j9qpXLq4JX7y2ykFbPxioYv12H1HpIMu5VBIOVDor1TN4L7YfF9a6ADUjGd3bBJgHu9wyH2BKiTFNWZvv8UQvh5ZEe8H8MHZYxleiDzgWeB0CQoGZBlfnw5/nLnZM21c+qek52NjeSB2PDjnTkQOG7AwpqaCf1k6mfVW/VY/ohV6MiK80fpJzy7K8ag2q6GOCcMqeY9y7p91K2MuuJfK0sT3c7puYuahW+LbflHoNi9OXs8VPec7Wvqi0N3b9i760YcOgAg3R04BoEx6KEuyuGIIhghLuxJFPuY1JZSD7U+1FXo4ZHBR+6SBlrpPuI6AYbjcDMXOsc2j07b/KjYDENfNzeust49zadjgUwubCl5mzgut0C2Uw3ccDnvnaXD2FcOIT4AdqJ0F5e6Z74NU8g7V8e2Qz0Y8Fq5wX/QZbji3p6kfmfhJ8m+spdg+1efgnvxNtsyUpdCfV4m5lcuXTuaRTe1AsCxV1yS3GEiShf5XNZhsmHnoFtep0dtw3ULgfJJ2EnfFOFwufpnz6C/+Pyp54rfLf8zF3ZcAUFXnnVDJlX7WCMXT83ZFDh890Bcf9UASMcrjE2eCyhh//Wh5O/O7vpb2u8wWun+xL+onYi2IdYPutMLw3mYwm0+e4uofDhk0WMndXlbm6mBnmoRF1k39Qz5LxuVU6GKEIOx2DWWrmONGyWk3A4nUuX7G3vP3VIZ9rp/CjsgSVnZ9njkN/o4vzxat0C3+WT2RH8XMhTD1DTO4fVzmCvHK+agmIcbUmOFPXT2J+N5rV81g+YyRfP60GVy5PKEc/OZyiRhlSYo3vXxihHlVpU/ClLxP8S0fm+i2oothYFjL/L/Us5aOruuJVI9j5VHux3V7n760upWfx2ZzWtfnuDt6EjdZcffjhlayf+sKpo/2V2yyS6FLCMIVru8z1YtNhyBQUWN99ievkzhHRWBd7BpO6vo3V5/4vIKVK3+P8vaJq/gTp3/PZ5t+KXQR2S8iz4jIbhHZlSuhColYkyPnnLUuYx+XhS4h1swdz8aOZj55YsKP2lBXxU3rZrPuuAlc4Gj3i8vlkbZtbOk5BxGDT3dMBrwXFg0aXJvxbyXfo4JkodvuFTAtt71qLM0jUlMB2H0WTzMt8d2qCRBfxiI7ibksdEGVuBV6Gb1IoSzxf3zLmeXb4/mVBGG3TOUN3CGo2aZGtvHzeZxMLtTLQqXUTKVUWw7+VsFIufmmice2H91cPvSQQUnIYGNHS1bha6OGVBy2Tz54rX4BO6LLMAyYWG8qsCihjD701YtPTN/etQUR4UeXzOd/LlsAJOKV/WzQxC10JYjlMwqJ4pvnzuHGs2al9LeHpW5QGV/50NEp3/uRE5rrUnzooej7rj7l0hsLPRis7P5i3D2YLnClt/5/3yQhywL/O8LyRMROvWqfAWkUuoq/O8u5ZTfjHf3Ew7zW2enKdVJIYnFtK2b0AxAhxOjOR9P2L0tKcfC1yOkcUDU8pcwQzRk+XAbtRcLlIlBlWt1vqFoWTklkzzy5dSS8YH523ucWTu5dhs1Csf3sNjr//k/YZm6LEUJC7lWyfU0DAGa4ph85SCUHVSUi6YudFEsRm3T0d88U8JCIPCki56frICLni8guEdl14MCBfv53A0fESq1aEsqs0MvpBmDKwcfjbUYou3tiaOwsxs3KPl3nQJNQUCo+KehluYSSkr+MHtfEnVEz8iXZEo+7XHxsoreONX3BMQzeP/4zXNi9gSdlhqvPjWsTlrpzMtt2vxwuZ0yhqSgNMaEuEWGFCN2NHZl/cBjmNdVBiTlfVF0zjOvOOKq/IuYc541XSD9ntS82ig2LzKLsi6YMZ9EU7xv0f0b8m2Uymf5a6B9QSr0mIsOBnSLynFLKZeIppbYD2wHa2tp8e4VHoqZoYTsPdhqFHhKrCLEzF0ZAK46X2FZ5NKHQvXyLhgiXdrTAY+b23MYaxvytgr+8836Kk/Gi9ib2dv6D04/xpwUHsHFRE9xtWuq1w+opaT2de+a7V/g6wxmdI2PH15f5XKEDLg1nSIhBVYn0yBEJE1aZXS4/rFnHKe+YOd73bzUXUzHkRFi2lbkzz/JTYiIuXzaZ0pDBjsf3x9tEUkNSXlbcswAADrtJREFUz+y6ml1qMvsXtwBw67lzPP9uw6G7ci7rQNKvM1Ip9Zr13gncC8z1/oV/6bGqI4Q9LHSbQ0biopCAKnR7PyMxhZSZPvQSj8fvkCFs6GhONCi4a/2xbF4+JV44w2bkkHLuWn9cSrufsFMfxBBChnDD2mOYOS41e+Da7qtY0PUfifPCQcuI6pQ2X2MYVA9KnLv3NGSO5AL4Uc3ZqY0iZgWwcn+52C5qb+ITJ0xMmQJKrl61S00hOLMBvafP2khEqkSk2v4MLAH25EqwfGP70Es8LHSb+yZsTmwEdOVd2Aq36YnGoMxUTGWWSykdyb7IvzcuZ8KwKldkT5CwUx8czp/669h0/qxGJM4LoKaylO1nz+Yb5wQrDsAQg5LSRIbBaCh9uoIvjbuZc7svd03+BxER6XPB8M2RT7Iz6p4cnz3B/7Hq/TliI4DHRORp4HfAg0op7zSFPsZW6NlY6AdLE6lRsy1V5jfC1okeiSooNy3TcskcwmZfGBtqbuC87k3EKoZl7BsE4iUHs7TWSpLcK0umj6S2KjkNr88xBBxKPF30xuKu63mlvMVMjRtAhX76zETysdkTaunr5fk91c76nk3x7Z9uPIEvrp7h8Qt/0OcjppTap5Q62npNV0p9IZeC5ZtI1J4UTbXQ7z/6Jm7j1Ph2Tyjx2Gr0I9lRIbH3MxKLQW0jj0en8a89H8vY3350fbmkiV/EZjmiZAKKMo93tiFpJekqggQMQwRC3onYXlBj42Gn9oTirZHleZEvF2zsaOHZa5ay55qlHDdxGBsXtaT0Ob8PybWmjBxMWdj/13ow/QUDwKqZY7jv93/hE3bqW8fJ3nTsCladfhZssfyGjtu+CqjLZd6kYbRNqOXyZVPAMDir57Oe/e3JJdtSH1wezP2O03UQgDdV5gVTTkoC+iTmJFV9e+9TKCTxScGPD4hEuccwxLUe5IzZYzlj9ljYYm5v7GhmY0eqki8Wgn+W5oihVaXcf/F8xtam5kROKVbhsN6NgF7oVWVhvnfhvKwn9mwL/bozjuLSjhYm1acprBwkpp3GrZHlXB9Zk1V3P9SC7S8pIXxJ25clVWQ6sSV9qocgk6nwTDJBfQANuJmVH5J1triyLfr/MSwX2JZ50/BB7miXoFJaybWRNFEcRUyKPk9Sbp3U2l8AiXmWI5GA6nNtoWdDqoXuSM5VpAr9zsgilnRdF9/ua7RA0Fk4uXis1GSFrpKOabdd6EQl+j9xVUc8bXCQ2TXqLN5S2YeZ+nlRnBdaoWeBfSHc1nonq7o+F8/9AWYWwmJkj2rkJZVIPHWkKvTt57TxzJYlhRYjJ6S6G5IUOua6gTPbzAVhbROGUl9dFk8bHGR+2biR2V23ZEpVlEIw1blW6Flh67LOymaeVk0uC90IFZeF/mDztQD8ITbRdVL7Le1vvigJGVSX+3eBVG9IuSdLskIPM7dhKO0t9ezfusK3hZD7wtq545lYX8UH23q/erkvUTGFojjNy5xjp1o1VZzLzZJlcq6g8OywJVz2zDi6KHWlODhSLfRiIrW4itueaxo9jBsuOD5/AuWR0TUV/OIz7Vn3tz0uF7ZP4oplU7w7+whtoWdBXJdZB7msJHEfNPyS4DxHRJWiC3PBjNNC1wo9+BzOQo9QHE8iuSRoZ31xaaMBwrZs4grOcEa5FNdDTjSaUOPORTdaoQefVK+ZuyFqBGzlax4ImqdRK/QssHWZPfPtnFwqtiiXqGt236HQg3Zma1JIcbkkW+iGttA7B00utAj9Qiv0LEipwGMUbxx6NJZ+fj+g66c0DlINdPdB1S4X+MHR32DOoW3x7aAFAxSXv2CASD2mjiiXIlHoW1e3UltVyqN/Sl+ERFvowSdVOWkLPZkeo4ID1HLuvAa6ItFARbiAVuhZkVL02JVKtTgugjVzxwPwyPOdab8vVh96ZWlx3JCzIVmfR4F/lAxlUM/bPBidi5LiOJdzwaCyMFtOnV5oMXqNVuhZYFs2tsvFmSe6blD6nNJB5Zjxtdz9u1fY8bE5VJeH4Ztme2rIW/B58NPzqa8uruPnRbKFHlPCHdO+wUu7fsI90YXM1361wKMVehbY1qkdhx5zPJqWlRTXRfDB2WP5QFMdY2oqCi3KgDN9tL+q7uSbmIJ3ykdzT3QhELyIjoEgqCtEbbRC9+CS7ot5WY3gVnHnh444fOjhIrNqRMSlzO+MLOJnsTncUUCZNLkh2UKPqkQtXY2boN7ctEL34IexeUAibLHK8re+152ovVkMhQ+8+GwkKJmwNYcjJTmXknhhF/P74j6XjwSKy7wcIGyXS0Wpef9736XQ9RBqgkGyha5E4qUXze/zLZEm12gLPQtsy6V1jOlznTyymn2xkTwWa+XDRW6ha4LP1ug6RqpO5qVEuRgul4s+k2HqqMEATLPeg4ZW6FlgW+jzm+t4eFM7DcMqabznKwCsKzIfuqb4uC22ku5ojEeSniZjhFwWuna5wOJpI3hkU3tgUwZrhZ4FzkfRxqQDXQylyTTFjV3QOzkiKyYhs0i4hT6VTYKqzEH70LMiaMt/NRontkIvTbLQoxJi8/KplIbtdn2eBx2t0LMgnULfeekCrj/zqAJIo9H0DtupklDcJlHCjBxSzh3nzQVg3NDiX3tQ7GiXSxakW/bePKKa5hHZ1ygMKkOrSnn7n92FFkPTD+wVzmVhd5qDmFWc5diJw7jl7Nm0F1H91CMVrdCz4Ej2LT68qd0VpqkJHufOa2DH4/tT1kxEHA/oS6ePzLdYmgFAK/QsOJJn/4dUlDCkQidtCjJXr5zGVSumppzHEaU9rsWGVugaTZFjGIKRZsKzRyv0okMfUY3mCKVHHTmpg48UtELXaI4w9jZ+BNAul2JEH1EPVrSOKrQIGk3O2dO6meZDt6MTLRYfWqF7cMPaY3ju2mWFFkOjySlGKEQP4aSC4JpiQE+KehAyhFCR1AzVaGzKrAVGyStHNcGnX0dURJaJyPMisldErsyVUBqNZuBYNGU4F7ZP4uqV0wotiibH9NlCF5EQsA1YDLwKPCEiDyil/i9Xwmk0mtwTDhlcsWxKocXQDAD9sdDnAnuVUvuUUt3Ad4BVuRFLo9FoNL2lPwp9DPCKY/tVq02j0Wg0BaA/Cj3deviUaXMROV9EdonIrgMHDvTjv9NoNBqNF/1R6K8C4xzbY4HXkjsppbYrpdqUUm319Tqbm0aj0QwU/VHoTwDNItIoIqXAGuCB3Iil0Wg0mt7S5ygXpVRERC4GfgaEgNuUUs/mTDKNRqPR9Ip+LSxSSv0Y+HGOZNFoNBpNP9BLxTQajaZIEJXHfA4icgB4uY8/rwP+mkNxBgotZ+4Igoyg5cwlQZAR8i/nBKXUYaNK8qrQ+4OI7FJKtRVajsOh5cwdQZARtJy5JAgygn/l1C4XjUajKRK0QtdoNJoiIUgKfXuhBcgSLWfuCIKMoOXMJUGQEXwqZ2B86BqNRqPxJkgWukaj0Wg8CIRC90shDREZJyIPi8gfReRZEdlgtW8Rkb+IyG7rdbLjN5stuZ8XkaV5lHW/iDxjybPLahsqIjtF5AXrvdZqFxG5wZLzDyIyK08yTnaM2W4ReVdENvphPEXkNhHpFJE9jrZej5+IfNTq/4KIfDQPMn5ZRJ6z5LhXRGqs9gYRed8xpjc7fjPbOlf2WvuRLvFeruXs9TEeaD2QQc7vOmTcLyK7rfaCjacnSilfvzDTCrwITARKgaeBaQWSZRQwy/pcDfwJmAZsATal6T/NkrcMaLT2I5QnWfcDdUlt1wNXWp+vBK6zPp8M/AQzg+ZxwG8LdJzfACb4YTyBBcAsYE9fxw8YCuyz3mutz7UDLOMSIGx9vs4hY4OzX9Lf+R1wvCX/T4DleRjLXh3jfOiBdHImff/vwNWFHk+vVxAsdN8U0lBKva6Uesr6fBD4I9454FcB31FKdSmlXgL2Yu5PoVgFfMv6/C3gNEf77crkN0CNiIzKs2yLgBeVUl4Lz/I2nkqpR4G30/z/vRm/pcBOpdTbSqm/ATuBnFUdTyejUuohpVTE2vwNZhbUjFhyDlZK/VqZ2uh2x34NmJweZDrGA64HvOS0rOwPAXd7/Y18jKcXQVDoviykISINwDHAb62mi63H3NvsR3EKK7sCHhKRJ0XkfKtthFLqdTBvTsBwH8hpswb3xeK38YTej1+h5T0P00K0aRSR34vIL0XkBKttjCWXTT5l7M0xLvRYngC8qZR6wdHmt/EMhELPqpBGPhGRQcD3gY1KqXeBm4BJwEzgdcxHMyis7B9QSs0ClgOfEpEFHn0LOsZipl8+Ffhvq8mP4+lFJrkKJq+IXAVEgG9bTa8D45VSxwCXAXeJyOACytjbY1zoY78Wt8Hht/EEgqHQsyqkkS9EpARTmX9bKfUDAKXUm0qpqFIqBnydhBugYLIrpV6z3juBey2Z3rRdKdZ7Z6HltFgOPKWUehP8OZ4WvR2/gshrTb6uBD5iPfZjuTDesj4/iemPbrFkdLpl8iJjH45xwY69iISB1cB37Ta/jadNEBS6bwppWH60W4E/KqW+4mh3+ptPB+xZ8geANSJSJiKNQDPmhMlAy1klItX2Z8yJsj2WPHakxUeB+x1ynmNFaxwH/N12LeQJl/Xjt/F00Nvx+xmwRERqLZfCEqttwBCRZcAVwKlKqfcc7fUiErI+T8Qcu32WnAdF5Djr/D7HsV8DKWdvj3Eh9UAH8JxSKu5K8dt4xsnX7Gt/XphRBH/CvAteVUA55mM+Pv0B2G29TgbuAJ6x2h8ARjl+c5Ul9/PkabYbMxLgaev1rD1mwDDg58AL1vtQq12AbZaczwBteRzTSuAtYIijreDjiXmDeR3owbS6Pt6X8cP0Y++1Xh/Lg4x7MX3N9vl5s9X3DOtceBp4CjjF8XfaMBXqi8CNWAsOB1jOXh/jgdYD6eS02ncAFyT1Ldh4er30SlGNRqMpEoLgctFoNBpNFmiFrtFoNEWCVugajUZTJGiFrtFoNEWCVugajUZTJGiFrtFoNEWCVugajUZTJGiFrtFoNEXC/wNV2kUDTuv3KwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(test_x.values, label=\"True\")\n",
    "plt.plot(test_pred, label=\"Predict\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Полиномиальная регрессия"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x6275c17f0>"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "num_points = 10\n",
    "x = np.linspace(-2, 2, num=num_points)\n",
    "y = 5 - x - 10 * x**2 + x**3 + x**4\n",
    "y_noise = y + np.random.randn()\n",
    "plt.scatter(x, y_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.60000000e+01 -8.00000000e+00  4.00000000e+00 -2.00000000e+00\n",
      "   1.00000000e+00]\n",
      " [ 5.85520500e+00 -3.76406036e+00  2.41975309e+00 -1.55555556e+00\n",
      "   1.00000000e+00]\n",
      " [ 1.52415790e+00 -1.37174211e+00  1.23456790e+00 -1.11111111e+00\n",
      "   1.00000000e+00]\n",
      " [ 1.97530864e-01 -2.96296296e-01  4.44444444e-01 -6.66666667e-01\n",
      "   1.00000000e+00]\n",
      " [ 2.43865264e-03 -1.09739369e-02  4.93827160e-02 -2.22222222e-01\n",
      "   1.00000000e+00]\n",
      " [ 2.43865264e-03  1.09739369e-02  4.93827160e-02  2.22222222e-01\n",
      "   1.00000000e+00]\n",
      " [ 1.97530864e-01  2.96296296e-01  4.44444444e-01  6.66666667e-01\n",
      "   1.00000000e+00]\n",
      " [ 1.52415790e+00  1.37174211e+00  1.23456790e+00  1.11111111e+00\n",
      "   1.00000000e+00]\n",
      " [ 5.85520500e+00  3.76406036e+00  2.41975309e+00  1.55555556e+00\n",
      "   1.00000000e+00]\n",
      " [ 1.60000000e+01  8.00000000e+00  4.00000000e+00  2.00000000e+00\n",
      "   1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "deg = 4\n",
    "V = np.vander(x, deg+1)\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.           1.         -10.          -1.           4.02412184]\n",
      "4.364259793084321\n"
     ]
    }
   ],
   "source": [
    "w = np.linalg.lstsq(V, y_noise, rcond=None)[0]\n",
    "print(w)\n",
    "x_test = np.linspace(-3, 3, num=20)\n",
    "y_pred = np.vander(x_test, deg+1) @ w\n",
    "y_test_true = 5 - x_test - 10 * x_test**2 + x_test**3 + x_test**4\n",
    "print(np.linalg.norm(y_pred - y_test_true))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x6276fd438>"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x_test, y_pred, label=\"Predicted\")\n",
    "plt.plot(x, y_noise, label=\"Train\")\n",
    "plt.plot(x_test, y_test_true, label=\"Test\")\n",
    "plt.legend(fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Томография сетей \n",
    "\n",
    "- Дана сеть из $n$ рёбер\n",
    "- Каждое ребро вносит некоторую задержку $d_i$\n",
    "- Чтобы выяснить характеристики сети, то есть найти вектор $d$, по сети запускают большое число сигналов по различным маршрутам и измеряют время прохождения сигнала $t_i$, $i=1,\\ldots, N$ по известному маршруту\n",
    "- Маршрут описывается бинарной матрицей $P$ размера $N \\times n$ такой что\n",
    "\n",
    "$$p_{ij} = \\begin{cases} 1, & j \\in \\mathcal{P}_i\\\\ 0, & \\text{иначе}, \\end{cases} $$\n",
    "\n",
    "где $\\mathcal{P}_i$ – путь $i$.\n",
    "\n",
    "- Необходимо по матрице $P$ и вектору $t$ определить вектор $d$, описывающий сеть\n",
    "\n",
    "**Приложения**\n",
    "\n",
    "- Дорожные сети\n",
    "- Компьютерные сети"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Решение линейных систем, обратная матрица"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Напоминание основных фактов\n",
    "\n",
    "- Линейная система имеет вид\n",
    "\n",
    "$$ Ax = b,$$\n",
    "\n",
    "с квадратной $n \\times n$ матрицей $A$\n",
    "\n",
    "- Для любой матрицы существуют PLU разложение\n",
    "\n",
    "$$ A = PLU, $$\n",
    "\n",
    "$P$ – матрица перестановки, $L$ – нижнетреугольная матрица, $U$ – верхнетреугольная матрица.\n",
    "\n",
    "- Сложность $\\mathcal{O}(n^3)$\n",
    "- Если $A \\succ 0$, то матрица раскладывается на факторы $A = LL^*$ – разложение Холецкого \n",
    "- Обратная матрица $A^{-1}$ существует для невырожденных матриц и $AA^{-1} = A^{-1}A = I$\n",
    "- Тогда $x = A^{-1}b$ или $x = U^{-1}L^{-1}P^*b$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Push-through identity\n",
    "\n",
    "- Дано $A \\in \\mathbb{R}^{m \\times n}$, $B \\in \\mathbb{R}^{n \\times m}$ и $I + AB$ обратима\n",
    "- Покажем, что и $I + BA$ обратима\n",
    "- Также покажем, что $(I + BA)^{-1}B = B(I + AB)^{-1}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Формула Шермана-Морисона-Вудбери\n",
    "\n",
    "- $(I+P)^{-1} = I - (I+P)^{-1}P = I - P(I+P)^{-1}$\n",
    "- Ранее доказанное утверждение $(I + BA)^{-1}B = B(I + AB)^{-1}$ \n",
    "- Применим к $(I + UV)^{-1} = I - UV(I + UV)^{-1} = I - U(I + VU)^{-1}V$\n",
    "- Формула Шермана-Морисона-Вудбери\n",
    "\n",
    "$$(A + UCV)^{-1} = A^{-1} - A^{-1}U (C^{-1} + VA^{-1}U)^{-1}VA^{-1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Моделирование миграции населения\n",
    "\n",
    "- Пусть $x_t \\in \\mathbb{R}^{100}$ распределение населения по возрастам в год $t$\n",
    "- Динамика этого распределения описывается во времени как \n",
    "\n",
    "$$ x_{t+1} = Ax_t + u $$\n",
    "\n",
    "- Что такое $u$?\n",
    "- Какой вид имеет матрица $A$ ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Определение миграционной политики\n",
    "\n",
    "- Дан вектор $x_1$, матрица $A$ и желаемое распределение $x_T = x_d$\n",
    "- Необходимо найти такой вектор $u$, чтобы желаемое распределение было достигнуто"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Определение координат по дополнительным измерениям\n",
    "\n",
    "- Дано положение 4 объектов в пространстве $a_1$, $a_2$, $a_3$ и $a_4$\n",
    "- Известны расстояния между ними и искомым объектом $x$: $r_1$, $r_2$, $r_3$ и $r_4$\n",
    "- Как определить положение $x$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Выигрыш от LU факторизации при решении систем с многими правыми частями\n",
    "\n",
    "- Дан набор систем $Ax = b_1$, $Ax = b_2, \\ldots$\n",
    "- Посмотрим на выигрыш в скорости при использовании однократной факторизации матрицы $A$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "n = 1000\n",
    "time_factor = []\n",
    "time_full = []\n",
    "A = np.random.randn(n, n)\n",
    "t = %timeit -o -q -r 5 splin.lu_factor(A)\n",
    "factor_time = t.best\n",
    "lu = splin.lu_factor(A)\n",
    "num_rhs = 10\n",
    "for i in range(num_rhs):\n",
    "    x_true = np.random.randn(n)\n",
    "    b = A @ x_true\n",
    "    t = %timeit -o -q np.linalg.solve(A, b)\n",
    "    time_full.append(t.best)\n",
    "    t = %timeit -o -q splin.lu_solve(lu, b)\n",
    "    time_factor.append(t.best)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plt.plot(np.arange(1, num_rhs+1), factor_time + np.cumsum(np.array(time_factor)), label=\"Factor\")\n",
    "plt.plot(np.arange(1, num_rhs+1), np.cumsum(np.array(time_full)), label=\"Full\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.xlabel(\"Number of rhs\", fontsize=20)\n",
    "plt.ylabel(\"Time\", fontsize=20)\n",
    "plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Резюме\n",
    "\n",
    "- Решение задачи кластеризации как вычисление матричного разложения\n",
    "- Приложения задачи наименьших квадратов\n",
    "- Приложения и свойства обратных матриц и систем линейных уравнений"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}