{ "cells": [ { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set(style='whitegrid', rc={'figure.figsize':(10,8)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# (14.1) Pade approximants\n", "\n", "We know the Taylor series expansion fo $e^x$:\n", "\n", "$$\n", "e^x = \\sum_{l = 1}^{\\infty}\\frac{x^l}{l!}\n", "$$\n", "\n", "We first find the $b_m$ by solving the linear equation system defined be (14.7), then caulculating each $a_n$ by taking our known $b_m$ and applying (14.6)\n", "\n", "For some intuition, he linear system (14.7) for $N = M = 1$ looks like:\n", "\n", "$$\n", "c_1 b_1 = -c_2\n", "$$\n", "\n", "For $N = M = 1$:\n", "\n", "$$\n", "c_2 b_1 + c_1 b_2 = -c_3 \\\\ \n", "c_3 b_1 + c_2 b_2 = -c_4\n", "$$\n", "\n", "For $N = M = 2$:\n", "\n", "$$\n", "c_3 b_1 + c_2 b_2 + c_1 b_3 = -c_4 \\\\ \n", "c_4 b_1 + c_3 b_2 + c_2 b_3 = -c_5 \\\\ \n", "c_5 b_1 + c_4 b_2 + c_3 b_3 = -c_6 \n", "$$\n", " \n", "..." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def pade_approximants(N, M):\n", " # precalculate the factorials\n", " c = np.zeros(N + M + 2)\n", " for i in range(N + M + 2):\n", " c[i] = 1 / np.math.factorial(i)\n", " \n", " # first, let's find the b's, by (14.7)\n", " v = np.zeros(M)\n", " for i in range(M):\n", " v[i] = -c[M + i + 1]\n", " \n", " A = np.zeros((M, M))\n", " for i in range(M):\n", " for j in range(M):\n", " A[i, j] = c[i + N - j]\n", " \n", " Ainv = np.linalg.inv(A)\n", " b = Ainv.dot(v)\n", " \n", " # now find the a's, by (14.6)\n", " a = np.zeros(N + 1)\n", " for i in range(N + 1):\n", " a[i] = c[i]\n", " for j in range(i):\n", " a[i] += b[j] * c[i - j - 1]\n", " \n", " return a, b" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def pade_approximate(x, a, b):\n", " nom = 0\n", " denom = 0\n", " for i in range(len(a)):\n", " nom += a[i] * (x ** i)\n", " for i in range(len(b)):\n", " denom += b[i] * (x ** (i + 1))\n", " approx = nom / (1 + denom)\n", " return approx" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "** Pade Approximants [1/1] **\n", "\n", "a: [1. 0.5]\n", "b: [-0.5]\n", "Approximation for e^1:\n", "3.0\n", "Error:\n", "0.2817181715409549\n", "\n", "\n", "\n", "** Pade Approximants [2/2] **\n", "\n", "a: [1. 0.5 0.08333333]\n", "b: [-0.5 0.08333333]\n", "Approximation for e^1:\n", "2.714285714285714\n", "Error:\n", "0.003996114173331122\n", "\n", "\n", "\n", "** Pade Approximants [3/3] **\n", "\n", "a: [1. 0.5 0.1 0.00833333]\n", "b: [-0.5 0.1 -0.00833333]\n", "Approximation for e^1:\n", "2.7183098591549295\n", "Error:\n", "2.8030695884417867e-05\n", "\n", "\n", "\n", "** Pade Approximants [4/4] **\n", "\n", "a: [1.00000000e+00 5.00000000e-01 1.07142857e-01 1.19047619e-02\n", " 5.95238095e-04]\n", "b: [-0.5 0.10714286 -0.01190476 0.00059524]\n", "Approximation for e^1:\n", "2.7182817182817187\n", "Error:\n", "1.1017732637341737e-07\n", "\n", "\n", "\n", "** Pade Approximants [5/5] **\n", "\n", "a: [1.00000000e+00 5.00000000e-01 1.11111111e-01 1.38888889e-02\n", " 9.92063492e-04 3.30687831e-05]\n", "b: [-5.00000000e-01 1.11111111e-01 -1.38888889e-02 9.92063492e-04\n", " -3.30687831e-05]\n", "Approximation for e^1:\n", "2.7182818287356953\n", "Error:\n", "2.7665025825740486e-10\n", "\n", "\n", "\n" ] } ], "source": [ "x = 1\n", "real_e = 2.718281828459045\n", "for i in range(1, 6):\n", " N = i\n", " M = i\n", " print(\"** Pade Approximants [%d/%d] **\\n\" % (M, N))\n", " \n", " a, b = pade_approximants(N, M)\n", " print(\"a: \", a)\n", " print(\"b: \", b)\n", " \n", " print(\"Approximation for e^1:\")\n", " approx_e = pade_approximate(x, a, b)\n", " print(approx_e)\n", " print(\"Error:\")\n", " print(abs(real_e - approx_e))\n", " print(\"\\n\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# (14.2)\n", "\n", "\n", "## (a) Polynomial fitting" ] }, { "cell_type": "code", "execution_count": 375, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X: [-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7\n", " 8 9 10]\n", "Y: [0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.array(range(-10, 11))\n", "print(\"X:\", X)\n", "Y = np.array([0 if x <= 0 else 1 for x in X])\n", "print(\"Y:\", Y)\n", "\n", "plt.plot(X, Y, 'o')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 376, "metadata": {}, "outputs": [], "source": [ "def polynom_fit(X, Y, M):\n", " N = len(Y)\n", " # generate Vandermonde\n", " vandermonde = np.zeros((N, M))\n", " for i in range(N):\n", " for j in range(M):\n", " vandermonde[i, j] = X[i] ** j\n", " # get pseudo inverse\n", " vandermonde_pinv = np.linalg.pinv(vandermonde)\n", " # get coefficients\n", " coeff = vandermonde_pinv.dot(Y)\n", " return coeff\n", "\n", "def polynom_predict(x, coeff):\n", " result = 0\n", " for i in range(len(coeff)):\n", " result += coeff[i] * (x ** i)\n", " return result" ] }, { "cell_type": "code", "execution_count": 377, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.03394089901406786\n" ] }, { "data": { "image/png": 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099t+AF8UcKFLuhS8PHWLiPpMnDjRecuILl266O2331avXr3061//WpmZmZo7d6569Oihbt26OV8zevRovfrqq1q4cKGmTJmixx9/XJMnT9by5ct14403Kjk52WvjBYDLqcjfouLc+XJUXzraXl1erOLc+ZLk0UBkqh/AVwVk6PKmDz/8sMHn7rrrLm3cuLHe51JSUpwn0dfKycnx6NgAoCnKNi91BqFajuoqlW1e6tEwZKofwFcF3DldAIDGqS4vadRyX+8H8FWELgAIcmGt4xq13Nf7AXwVoQsAglxMylhZwiJdllnCIhWTMtYv+wF8Fed0AUCQqz2fyttXFZrqB/BVhC4AgFol9DcSfkz1A/giphcBAAAMIHQBAAAYEJChqyJ/iw7P/W/938v/qcNz/1sV+Vs8tu7U1FQNHjxYI0aMkM1mU25urkfWuX//fklSRkaGDh8+fNn2mzZt0jfffON8vHv3bv3617++6nEAAADvCbhzui53x+OQG5M80sebb76prl27qqCgQA888IDuuOMOxcbGOp+32+0KDQ29zBoatmDBgiu22bRpkxISEtSzZ09JUo8ePfQ///M/TeoPAACYEXCh63J3PI7zUOiq1b17d0VHR2vFihX65JNPFB0dre+//15/+MMfFBcXp1mzZun48eOqqqrSsGHDNGHCBEnSjh07lJmZKUlKTk6Ww+FwrjM1NVXz589X165ddfLkSc2aNUuHDh2SJNlsNnXv3l0ffvihPvvsM2VlZenRRx+V1WrV7NmztWLFCklSdna2Fi5cKEm64YYbNHPmTMXFxWn16tX64IMP1Lp1ax04cECtWrXS3Llz1a5dO49uFwAAUFfAhS6Tdzz+4osvVFVVpbCwMO3atUurVq3SDTfcIEl69NFH9cQTTyg5OVkXLlzQI488oh49eig5OVnPPPOMXnvtNfXt21dr167V0qVL613/pEmTNGDAAM2dO1eSVFpaqtjYWKWmpiohIUEPPvigJGnbtm3O1+zfv1+vvfaaVqxYofbt2+uNN97QSy+9pDfeeEPSpanI1atXy2q16sUXX9SSJUv0zDPPeHzbAAAAVwEXusJax6m6vLje5Z4yceJERUZGqmXLlpo7d65Onjyp22+/3Rm4zp49q+3bt6u0tNT5msrKSn333XeKi4tTVFSU+vbtK0kaOnSopk2bVqePyspK7dy5U++++65z2Y+nMBuybds2DRgwQO3bt5ckPfDAA0pLS3M+f/vtt8tqtUqSevXqpc8++6wJWwAAECgq8rdw7zRDAi50xaSMdTmnS/L8HY9rz+mqtWLFCkVHRzsf19TUyGKxaPny5QoPD3d57d69e+usz2KxeGxsVxIZ+a+7QYeGhsputxvrGwDgWy53HjTBy/MC7urFVgn91XbYBIW1bivJorDWbdV22ASjvzwtW7ZUUlKS3n77beeywsJCnTp1Sj/72c90/vx57dixQ5K0fv16lZeX11lHdHS0EhMTtWjRIuey2iNnLVu2VEVFRb199+3bVx9//LFOnTolSfrnP/+pO++801OlAQACyOXOg4bnBdyRLsk37nj82muv6ZVXXtHw4cMlXQpRL7/8stq1a6c5c+a4nEjfsWPHBteRmZkpm82mkJAQ2Ww2jR8/XiNGjNBzzz2n9evXO0+kr9W1a1dNmjRJ48aNkyRdf/31mjlzpperBQD4I5PnQUOyOH586VwzqaqqUn5+vhISElymvyRpz549io+P90g/lZWVLtOAwaax9Xty2ze3vLw8JSV59upVfxLM9VN7cNYuBXf97tZ+eO5/N3AedFvd8PT/542hGeHtfX+53HI5ATe9CAAA3BOTMlaWMNfQ4OnzoPEvATm9CAAArqz2VByuXjTDL0KXw+EweoUfJB+YdQYAGOAL50EHC5+fXmzRooVKSkoIAQY5HA6VlJSoRYsWzT0UAAACxhWPdM2ePVsbNmzQsWPHtGbNGpf7U9Wy2+2aNWuWtm7dKovFovHjx2vUqFEeGWCnTp109OhR5y0QrsaFCxcUERHhgVH5p8bU36JFC3Xq1MnLIwIAz6u92Web8mId/qwt02XwGVcMXffcc48efvhhjR3b8El1a9as0eHDh7Vx40adPn1a6enpuuOOOzzyRzs8PFw33njjVa9HunQ1Q69evTyyLn8U7PUDnvZR3hEtXrdHxWXn1DYmSg8PidfdSdf7ZT+BUktF/hadXPMnhdRclEWXbvZ5cs2fJHn2Zp+Bsr0CqQ9J2r5mpcJ2ZauNzuirdS1V3StdfYaP9Hg/TXXF6cXevXu73AeqPmvXrtWoUaMUEhKi2NhYDRw4UOvXr/fYIAHA13yUd0RvZe3SqbJzckg6VXZOb2Xt0kd5R/yun0CqpXDDYoXUXHRZFlJzUYUbFnusj0DaXoHSh3QpcLXetUxtLGdksUhtLGfUetcybV+z0qP9XA2PnNNVWFjocoNPq9WqEydOeGLVAOCTFq/bo6qLrl+jVXXRrsXr9vhdP4FUS+i5skYtb4pA2l6m+kiwHND0n7yvN2IWa/pP3leC5YDHt1fYrmxFWFxribDYFbYr26P9XA2funoxPz/f633k5eV5vQ9fFsz1B3PtUnDX743aT5Wda3C5J/u72n7caeMvtbjDUROt2NDKOsvLaqI91oe/bC9f2fc3VH6rB6I/dwai2NBKPRD9ud6rlPLy4jzShyS10Zl6l/9EZ3zm888joctqter48ePq2bOnpLpHvtzV2Du7NlYw351YCu76g7l2Kbjr91bt7daV1PsHq11MlEf7u5p+3K3dH2px1/+s66thjo9djnhccITq45C++rWH+vCH7eVL+96y7s16j0CNiP5atyc945E+JOmrdS3rDV4/qKXHPwNq70jfWB6ZXhw8eLCysrJUU1Oj0tJSbdq0SYMGDfLEqgHAJz08JF6R4aEuyyLDQ/XwEM9+dZaJfgKplqQhI7T8/F0qtUfL4ZBK7dFafv4uJQ0Z4bE+TG6vvlGHXKbl+kYd8rt9/xNLA0egGljeVNW90nXB4VrLBUeoqnule7Sfq3HFI12zZs3Sxo0bVVxcrEcffVRt2rRRbm6uMjIyNHHiRPXo0UNpaWnatWuX7rvvPknSk08+qeuv9/xVCQDgK2qvvPL2FVkm+gm8Wn6hP62L16myc2oXE6WHR/rn9kqKPKhO0Z87LwyonZbrEJkoyTN9maglvHXber/fMbx1W4/1IUl9ho/Udl06t+snOqMf5HtXL/r8F157UjBPsUjBXX8w1y4Fd/3UHpy1S/5f/9V8GbUv1V6Rv0XFufPlqK5yLrOERartsAleu3+ar37htU+dSA8AAC6pLi9p1HJfxfc7/guhCwAAHxTWOq6BI12eu+LPFL7f8RKf/+5FAACCUUzKWFnCXKeuLGGRiklp+Bti4Ns40gUAgA9iWi7wELoAAPBRTMsFFqYXAQAADOBIFwAAjVSRv4VpPzQaoQsAgEb49/tOVZcXqzh3viQRvHBZTC8CANAIZZuXutzoU5Ic1VUq27y0mUYEf0HoAgCgEQLlpqUwj9AFAEAjNHRzUn+8aSnMInQBANAI3LQUTcWJ9AAANAI3LUVTEboAwMdxewLfw01L0RSELgDwYdyeAAgcnNMFAD6M2xMAgYPQBQA+jNsTAIGD0AUAPozbEwCBg9AFAD6M2xMAgYMT6QHAh3F7AiBwELoAwMdxewIgMDC9CAAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMCHOn0cGDBzV16lSdPn1abdq00ezZs9W5c2eXNiUlJXruuedUWFio6upq9e3bVy+++KLCwtzqAgAAIKC5daRr+vTpGjNmjDZs2KAxY8Zo2rRpddrMnz9fXbp00Zo1a7R69Wp9++232rhxo8cHDAAA4I+uGLpKSkpUUFAgm80mSbLZbCooKFBpaalLO4vFosrKStXU1OjChQu6ePGiOnTo4J1RAwAA+BmLw+FwXK5Bfn6+pkyZotzcXOeyoUOH6g9/+INuvfVW57LTp0/r6aef1nfffadz585p7NixmjRpkluDqKqqUn5+fhNLAAAAMC8hIUGRkZFut/fYCVfr169Xt27d9Ne//lWVlZXKyMjQ+vXrNXjwYLfX0djBN1ZeXp6SkpK8tn5fF8z1B3PtUnDXT+3BWbsU3PUHc+2S9+tv6sGiK04vWq1WnTx5Una7XZJkt9tVVFQkq9Xq0m7JkiUaMWKEQkJC1KpVK6Wmpmrbtm2NHhAAAEAgumLoiouLU3x8vHJyciRJOTk5io+PV2xsrEu7Tp06acuWLZKkCxcu6PPPP9fNN9/shSEDAAD4H7euXpwxY4aWLFmiQYMGacmSJcrMzJQkZWRkaPfu3ZKk559/Xnl5eRo+fLjS09PVuXNn/dd//Zf3Rg4AAOBH3Dqnq0uXLsrKyqqzfMGCBc6fb7jhBr377rueGxkAAEAA4Y70AAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAaENfcAAMBfVeRvUdnmpaouL1FY6zjFpIxVq4T+zT0sAD6K0AUATVCRv0XFufPlqK6SJFWXF6s4d74kEbwA1IvpRQBogrLNS52Bq5ajukplm5c204gA+DpCFwA0QXV5SaOWAwChCwCaIKx1XKOWAwChCwCaICZlrCxhkS7LLGGRikkZ20wjAuDrOJEeAJqg9mR5rl4E4C5CFwA0UauE/oQsAG5jehEAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAFuha6DBw9q9OjRGjRokEaPHq1Dhw7V227t2rUaPny4bDabhg8fruLiYk+OFQAAwG+FudNo+vTpGjNmjNLS0rRq1SpNmzZNixcvdmmze/duvfXWW/rrX/+qdu3aqaKiQhEREV4ZNAAAgL+54pGukpISFRQUyGazSZJsNpsKCgpUWlrq0m7RokUaN26c2rVrJ0lq1aqVIiMjvTBkAAAA/2NxOByOyzXIz8/XlClTlJub61w2dOhQ/eEPf9Ctt97qXJaenq4BAwZox44dOnv2rO699149/vjjslgsVxxEVVWV8vPzr6IMAAAAsxISEhp1gMmt6UV32O127du3T++++64uXLigxx57TB07dlR6errb62js4BsrLy9PSUlJXlu/rwvm+oO5dim466f24KxdCu76g7l2yfv1N/Vg0RWnF61Wq06ePCm73S7pUrgqKiqS1Wp1adexY0cNHjxYERERatmype655x598803jR4QAABAILpi6IqLi1N8fLxycnIkSTk5OYqPj1dsbKxLO5vNpk8++UQOh0MXL17UF198oVtuucU7owYAAPAzbt0yYsaMGVqyZIkGDRqkJUuWKDMzU5KUkZGh3bt3S5KGDRumuLg4DR06VOnp6brpppv0n//5n94bOQAAgB9x65yuLl26KCsrq87yBQsWOH8OCQnRc889p+eee85zowMAAAgQ3JEeAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAvoZGPAAAY0ElEQVQAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAFuha6DBw9q9OjRGjRokEaPHq1Dhw412Pb//u//1KtXL82ePdtTYwQAAPB7boWu6dOna8yYMdqwYYPGjBmjadOm1dvObrdr+vTpGjhwoEcHCQAA4O+uGLpKSkpUUFAgm80mSbLZbCooKFBpaWmdtm+//bbuvvtude7c2eMDBQAA8GdXDF2FhYXq0KGDQkNDJUmhoaFq3769CgsLXdrt3btXn3zyiR555BGvDBQAAMCfhXliJRcvXtRvf/tbvfLKK85w1hT5+fmeGM5l5eXleb0PXxbM9Qdz7VJw10/twSuY6w/m2iXfrP+KoctqterkyZOy2+0KDQ2V3W5XUVGRrFars82pU6d0+PBhjR8/XpJUXl4uh8OhM2fO6KWXXnJ7MAkJCYqMjGxCGe7Jy8tTUlKS19bv64K5/mCuXQru+qk9OGuXgrv+YK5d8n79VVVVTTpQdMXQFRcXp/j4eOXk5CgtLU05OTmKj49XbGyss03Hjh21bds25+O5c+fq7NmzmjJlSqMHBAAAEIjcunpxxowZWrJkiQYNGqQlS5YoMzNTkpSRkaHdu3d7dYAAAACBwK1zurp06aKsrKw6yxcsWFBv+6effvrqRgUAABBguCM9AACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwACPfOE1APiaivwtKtu8VG3Ki3X4s7aKSRmrVgn9m3tYAIIYoQtAwKnI36Li3PlyVFfJIqm6vFjFufMlieAFoNkwvQgg4JRtXipHdZXLMkd1lco2L22mEQEAoQtAAKouL2nUcgAwgdAFIOCEtY5r1HIAMIHQBSDgxKSMlSUs0mWZJSxSMSljm2lEAMCJ9AACUO3J8mWbl+piebHCW3P1IoDmR+gCEJBaJfRXq4T+ysvLU1JSUnMPBwCYXgQAADCB0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwIAwdxodPHhQU6dO1enTp9WmTRvNnj1bnTt3dmkzb948rV27ViEhIQoPD9czzzyjfv36eWPMAAAAfset0DV9+nSNGTNGaWlpWrVqlaZNm6bFixe7tOnZs6fGjRunqKgo7d27Vw8++KA++eQTtWjRwisDBwAA8CdXnF4sKSlRQUGBbDabJMlms6mgoEClpaUu7fr166eoqChJUrdu3eRwOHT69GkvDBkAAMD/XPFIV2FhoTp06KDQ0FBJUmhoqNq3b6/CwkLFxsbW+5rs7GzdcMMNuvbaaxs1mPz8/Ea1b4q8vDyv9+HLgrn+YK5dCu76qT14BXP9wVy75Jv1uzW92Bjbt2/XH//4R/3lL39p9GsTEhIUGRnp6SE55eXlKSkpyWvr93XBXH8w1y4Fd/3UHpy1S8FdfzDXLnm//qqqqiYdKLri9KLVatXJkydlt9slSXa7XUVFRbJarXXa7ty5U7/5zW80b948/exnP2v0YAAAAALVFUNXXFyc4uPjlZOTI0nKyclRfHx8nanFb775Rs8884zefPNN3Xrrrd4ZLQAAgJ9y6z5dM2bM0JIlSzRo0CAtWbJEmZmZkqSMjAzt3r1bkpSZmanz589r2rRpSktLU1pamvbt2+e9kQMAAPgRt87p6tKli7KysuosX7BggfPn999/33OjAgAACDDckR4AAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABoQ19wAAb6rI36KyzUvVprxYhz9rq5iUsWqV0L+5hxX0avdLdXmJwlrHsV8ABAVCFwJWRf4WFefOl6O6ShZJ1eXFKs6dL0n8gW9GP94vEvsFQPBgehEBq2zzUucf9lqO6iqVbV7aTCOCxH4BELwIXQhY1eUljVoOM9gvAIIV04sexHkqjePt7RXWOk7V5cX1LkfzYb8ACFYc6fKQ2vNULv0xcTjPU6nI39LcQ/NJJrZXTMpYWcIiXZZZwiIVkzLWY32g8dgvAIIVoctDOE+lcUxsr1YJ/dV22ASFtW4rh6Sw1m3VdtgEjj42sx/vF8nCfgEQNJhe9BDOU2kcU9urVUJ/tUror7y8PCUlJXl03Wi62v0CAMGEI10e0tD5KJynUj+2FwAg2BC6PITzVBqH7QUACDZML3pI7VQJVy+6h+0FAAg2hC4P4jyVxmF7AQCCCdOLAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABjg1ncvHjx4UFOnTtXp06fVpk0bzZ49W507d3ZpY7fbNWvWLG3dulUWi0Xjx4/XqFGjvDHmRvso74gWr9ujU2Xn1G5diR4eEq+7k673Wj/FZefUNibKK/2Y6MNUPyb7YN/7Th+m+jG17wHAXW6FrunTp2vMmDFKS0vTqlWrNG3aNC1evNilzZo1a3T48GFt3LhRp0+fVnp6uu644w516tTJKwN310d5R/RW1i5VXbRLkk6VndNbWbskyaMfwCb6oRbf68NUP4HSh6l+TNUCAI1xxenFkpISFRQUyGazSZJsNpsKCgpUWlrq0m7t2rUaNWqUQkJCFBsbq4EDB2r9+vXeGXUjLF63x/nBW6vqol2L1+3xu36oxff6MNVPoPRhqh9TtQBAY1zxSFdhYaE6dOig0NBQSVJoaKjat2+vwsJCxcbGurTr2LGj87HVatWJEycaNZj8/PxGtXfHqbJzDS7Py8vzq3480Yc77fylFl/ow1Q/JvY92yswBVu9/y6Y6w/m2iXfrN+t6UVTEhISFBkZ6dF1tltXohsqv5UtaqdiQipVVhOtnHOJOhx9q5KSkjzaT30f9O1iojzWz9X2kZeX51Y7f6jFV/qo7cfbv2Mm9r3J7RUo+97XufueD1TBXH8w1y55v/6qqqomHSi64vSi1WrVyZMnZbdfOlRvt9tVVFQkq9Vap93x48edjwsLC3Xttdc2ekCeNqFXpR6I/lyxoZWyWKTY0EuPJ/Sq9Gg/Dw+JV2R4qMuyyPBQPTwk3q/6MNVPoPQhmfkdC6TtFUi1AEBjXDF0xcXFKT4+Xjk5OZKknJwcxcfHu0wtStLgwYOVlZWlmpoalZaWatOmTRo0aJB3Rt0I1x5arwiL67kdERa7rj3k2fPN7k66Xk+N6qV2MVGy6NL/qJ8a1cujJ+2a6MNUP6b7kJf6kMz8jgXKPjHVj6l9DwCN4db04owZMzR16lT96U9/UuvWrTV79mxJUkZGhiZOnKgePXooLS1Nu3bt0n333SdJevLJJ3X99c3/AVddXtKo5Vfj7qTrvf6hbqIPU/2Y7MObh5pN/Y4Fyj4x1Y+JfQ8AjeFW6OrSpYuysrLqLF+wYIHz59DQUGVmZnpuZB4S1jpO1eXF9S4HPIHfMQCAOwL+jvQxKWNlCXM9Od8SFqmYlLHNNCIEGn7HAADu8KmrF72hVUJ/SVLZ5qW6WF6s8NZtFZMy1rkc9avI36KyzUtVXV6isNZxbLPL+PHvGNsLANCQgA9d0qU/iq0S+nNuh5sq8reoOHe+HNVVkqTq8mIV586XJIJEA2p/xwAAaEjATy+i8co2L3UGrlqO6iqVbV7aTCMCAMD/EbpQh8krPgEACBaELtTR0FV3XI0HAEDTEbpQB1fjAQDgeUFxIj0ah6vxAADwPEIX6sXVeAAAeBbTiwAAAAYQugAAAAwgdAEAABhA6AIAADCAE+n9DN+JCACAfyJ0+RG+ExEAAP/F9KIf4TsRAQDwX4QuP8J3IgIA4L8IXX6E70QEAMB/Ebr8CN+JCACA/+JEej/CdyICAOC/CF1+hu9EBADAPzG9CAAAYABHugA4cfNdAPAeQhcASdx8FwC8jelFAJK4+S4AeBtHugA/4e2pP26+CwDexZEuwA/UTv1VlxdLcjin/iryt3isD26+CwDeRegC/ICJqT9uvgsA3sX0IuAHTEz9cfNdAPAuQhfgB8Jax/2/qcW6yz2Jm+8CgPcwvQj4Aab+AMD/caQL8ANM/QGA/yN0AX6CqT8A8G9MLwIAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAWHNPQBJcjgckqQLFy54va+qqiqv9+HLgrn+YK5dCu76qT14BXP9wVy75N36a/NKbX5xl8XR2Fd4QUVFhfbv39/cwwAAAHBb165d1apVK7fb+0ToqqmpUWVlpcLDw2WxWJp7OAAAAA1yOBy6ePGioqOjFRLi/plaPhG6AAAAAh0n0gMAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAM8InvXvSkVatW6Z133tF3332n559/Xg8++KDzuXPnzum5557Tt99+q9DQUE2ZMkUpKSn1ruef//ynFixYIIfDof79++vFF19s1F1nfcEjjzyisrIySZLdbteBAwe0atUq3XLLLS7ttm3bpvHjx6tz586SpIiICGVlZZkerkdNnTpVn332mWJiYiRJgwcP1uOPP15v23nz5mnlypWSpJEjR+rJJ580Nk5vyczM1Oeff66IiAhdc801euGFF9SjR4867VasWKHf/e53uu666yRJnTp10rx580wP96odPHhQU6dO1enTp9WmTRvNnj3b+ftcy263a9asWdq6dassFovGjx+vUaNGNc+APaisrEyTJ0/W4cOHFRERoZ/+9KeaOXOmYmNjXdo15j3hT1JTUxUREaHIyEhJ0qRJk9SvXz+XNo357PcnR48edfm8qqio0JkzZ7R9+3aXdnPnztXf//53tW/fXpJ0++23a/r06UbH6gmzZ8/Whg0bdOzYMa1Zs0Zdu3aV5N77X/KRzwBHgNm3b5/jwIEDjt/85jeOv/3tby7PzZ071/HCCy84HA6H4+DBg44777zTcebMmTrrOHz4sKNfv36OkpISh91ud4wbN86xcuVKI+P3lg8++MAxbNiwep/74osvHCNHjjQ8Iu+aMmVKnf1fn+3btztsNpvj3LlzjnPnzjlsNptj+/btBkboXR9++KHjwoULzp/vueeeetu9//77jqefftrk0LzioYcecmRnZzscDocjOzvb8dBDD9Vps3LlSse4ceMcdrvdUVJS4ujXr5/jyJEjpofqcWVlZY4vvvjC+fjVV191PPfcc3Xaufue8DcpKSmOffv2XbaNu5/9/m7WrFmOzMzMOsvffPNNx6uvvtoMI/KsL7/80nH8+PE6+9yd97/D4RufAf516MYNXbt21U033VTvUal169Zp9OjRkqTOnTsrISFBW7ZsqdNuw4YNGjhwoGJjYxUSEqJRo0Zp7dq1Xh+7Ny1fvlz3339/cw/D56xdu1bp6elq0aKFWrRoofT0dL/f15KUkpKi8PBwSdJtt92mEydOqKampplH5R0lJSUqKCiQzWaTJNlsNhUUFKi0tNSl3dq1azVq1CiFhIQoNjZWAwcO1Pr165tjyB7Vpk0b9e3b1/n4tttu0/Hjx5txRL7H3c9+f3bhwgWtWbMmoD/ne/fuLavV6rLM3fe/5BufAQEXui7n+PHjzmkUSbJarTpx4kSddoWFherYsaPzcceOHVVYWGhkjN5w6tQpff7550pLS2uwzaFDhzRy5EiNGjXKOdXm7959910NHz5cTzzxhL777rt62/z7vrZarX69r+uzdOlS3X333Q1Oj2/fvl1paWkaO3asPvroI7OD84DCwkJ16NBBoaGhkqTQ0FC1b9++zn6sb1/X9/73ZzU1NVq2bJlSU1Prfd6d94Q/mjRpkoYPH64ZM2aovLy8zvPufvb7sw8//FAdOnTQrbfeWu/zubm5Gj58uMaNG6edO3caHp33uPv+r23b3J8BfndO18iRIxv8X9xnn33m3PDBwN1tkZ2drX79+tU5x6PWrbfeqo8//litWrXSkSNH9Oijj6pDhw668847vTb2q3Wl2p955hm1a9dOISEhys7O1mOPPaZNmzYFzO+Hu/s+NzdXa9as0dKlS+tte/fdd2vo0KFq0aKFCgoKlJGRocWLF6tLly5eGzu856WXXtI111zjci5rrUB9TyxdulRWq1UXLlzQyy+/rJkzZ+q1115r7mEZ9/777zd4lOuBBx7QhAkTFB4erk8//VRPPPGE1q5d6zy/D+b4Xei6mqMwHTt21LFjx5zho7Cw0OWwfC2r1eryB+348eN1Dmn6Ane3xYoVKzR58uQGn2/ZsqXz5+uvv14DBw7UV1995dOh60q1d+jQwflzenq6XnnlFZ04ccLlf7tS3X1dWFjok/v637mz7z/44AO9/vrrWrRokdq2bVtvmx8H8e7du+v222/XN99841ehy2q16uTJk7Lb7QoNDZXdbldRUVGd/Vi7r3v27Cmp7v96/d3s2bP1/fffa/78+fUe1XT3PeFvavdzRESExowZU+/FAe5+9vurkydP6ssvv9Tvf//7ep9v166d8+e77rpLVqtVBw4cUJ8+fUwN0Wvcff/Xtm3uz4Cgml4cPHiw/vGPf0i6NJ22e/fuOle5SNKgQYO0adMmlZaWqqamRllZWRoyZIjp4XrEV199pYqKCvXv37/BNkVFRXI4HJKk06dP69NPP61zhaO/OXnypPPnrVu3KiQkxOWPTq3BgwcrOztb58+f1/nz55Wdne23+/rHNm/erFdeeUULFy5Up06dGmz34+107Ngxff311+rWrZuJIXpMXFyc4uPjlZOTI0nKyclRfHx8nSO7gwcPVlZWlmpqalRaWqpNmzZp0KBBzTFkj5szZ47y8/M1b948RURE1NvG3feEPzl79qwqKiokSQ6HQ2vXrlV8fHyddu5+9vurlStXasCAAQ0eufrxvt+zZ4+OHTumG2+80dTwvMrd97/kG58BFkftX9sAkZOTo9///vcqLy9XeHi4oqKi9Je//EU33XSTzp49q6lTp2rPnj0KCQnRb37zGw0cOFCS9Mc//lHt27fXL3/5S0nSe++9p3feeUfSpf8ZTJs2zS8Pw7/44otq06aNJk2a5LL8x/UuWbJEy5YtU1hYmOx2u9LT0/XYY48104g945FHHlFJSYksFotatmypyZMn67bbbpMkvfDCC0pNTdU999wj6dLl1NnZ2ZIuHQF4+umnm23cnvIf//EfCg8Pd/ngWbRokWJiYlzqnzNnjv73f//X+bv96KOPauTIkc017Cb77rvvNHXqVJWXl6t169aaPXu2fvaznykjI0MTJ05Ujx49ZLfbNXPmTH366aeSpIyMDOfJ1f7swIEDstls6ty5s1q0aCHpX7f+SEtL09tvv60OHTpc9j3hr44cOaKnn35adrtdNTU16tKli1588UW1b9/epfbLffYHgkGDBumFF15w+c/1j3/3p0yZom+//VYhISEKDw/XxIkTNWDAgGYccdPMmjVLGzduVHFxsWJiYtSmTRvl5uY2+P6X5HOfAQEXugAAAHxRUE0vAgAANBdCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADDg/wcP4krRMoYNOQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.013509963284611574\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.007418481265720188\n" ] } ], "source": [ "for rank in [5, 10, 15]:\n", " coeff = polynom_fit(X, Y, rank)\n", " predict = np.array([polynom_predict(x, coeff) for x in X])\n", " \n", " plt.plot(X, Y, 'o')\n", " plt.plot(X, predict, 'o')\n", " plt.legend(['Data', 'Prediction'])\n", " plt.title(\"Polynomial Fit with %d terms\" % rank)\n", " plt.show()\n", " \n", " error = np.mean((predict - Y) ** 2)\n", " print(\"Mean squared error (in sample):\", error)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## (b) RBF" ] }, { "cell_type": "code", "execution_count": 378, "metadata": {}, "outputs": [], "source": [ "def RBF_fit(X, Y, M):\n", " N = len(Y)\n", " \n", " # centers\n", " c = np.linspace(-10, 10, M)\n", " \n", " # build matrix like in (14.26)\n", " mat = np.zeros((N, M))\n", " for i in range(N):\n", " for j in range(M):\n", " mat[i, j] = np.abs(X[i] - c[j]) ** 3\n", " \n", " # get pseudo inverse\n", " mat_pinv = np.linalg.pinv(mat)\n", " \n", " # get coefficients\n", " a = mat_pinv.dot(Y)\n", " \n", " return c, a\n", "\n", "def RBF_predict(x, c, a):\n", " result = 0\n", " for i in range(len(c)):\n", " result += a[i] * np.abs(x - c[i]) ** 3\n", " return result" ] }, { "cell_type": "code", "execution_count": 379, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.029756141390931794\n" ] }, { "data": { "image/png": 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uAAAaqUZ3eXHCsHD5+1oclvn7WjRhWLjb+jxw4IBuvfVWzZ49W71799bq1au1atUqtWvXTsXFxVU+5q233lKbNm20cuVKffLJJ+rWrVu1bQEAQMPX6ELXgKgb9eyo7moT2FRektoENtWzo7q77NOLP7Rp0yZ9+OGHio+PV2FhoX70ox/Jy8tL27Zt0/fff29vFxAQoMLCQvvvhYWFateunXx8fPT1119rz549bhkfADijMH2rjs1/Uv967WEdm/+kCtO31vWQgEan0V1elC4HL3eFLEmaMmWK/ZYRYWFhevfdd9W9e3f96le/UmJioubPn6+uXbuqS5cu9seMHj1ab775phYvXqxp06bp6aef1osvvqi//e1vuvnmm9WrVy+3jRcArqYwfauy1yyUrezy2faygmxlr1koSWoR0a8uhwY0Ko0ydLnTp59+Wu26e+65Rxs3bqxy3cCBA+2T6Cukpqa6dGwAcC3yNifZA1cFW1mx8jYnEboAF2p0lxcBALVTVpBTq+UArg2hCwA8nE/L4FotB3BtCF0A4OECB46Tl4+/wzIvH38FDhxXRyMCGifmdAGAh6uYt5W3OUllBTnyaRmswIHjmM8FuBihCwCgFhH9CFmAmxG6AKCeK0zf2mjOQjWmWuA8jvtlhC4AqMca0z20GlMtcB7H/T9qDF3z5s3Thg0bdPLkSa1evVqdO3eu1MZqtWru3Ln67LPP5OXlpYkTJ2rUqFFuGbAz3JmoBw0aJD8/P/n5+am8vFxPP/20hg8fft3bXLhwoTp37qyEhAT9+te/1k033VRt+02bNqlt27bq1q2bpMtfQ7RkyRL993//93WNA0DtbEk7rqXrDio776JaBzbVhGHhLr8xs6l7aDXGWs7mXVSbdTluqcXE/jLVz67VK+WzL0U36LzOqbnKusepd8wIl23f5H3gTBz761Fj6Lrvvvs0YcIEjRtX/adYVq9erWPHjmnjxo3Kz89XXFyc7rrrLnXo0MGlg3XG1RK1981RLunj7bffVufOnZWRkaExY8borrvuUlBQkH291WqVxWK5yhaqt2jRohrbbNq0SREREfbQ1bVrVwIXYNiWtON6J3mfikutkqSzeRf1TvI+SXLpi3xpQba8qlnuKo2tls9XrtAkvzQFBhYprzxA61dGSRrpslpM7S8TtexavVIt930oP6/LtbTSeZXs+1C7JJcFLxPHXTKzv65XjaGrZ8+eNW5k7dq1GjVqlLy9vRUUFKTBgwdr/fr1euKJJ1wyyNq4WqIOdlHoqnD77bcrICBAK1as0Oeff66AgAB9//33+u1vf6vg4GDNnTtXp06dUnFxsYYPH66nnnpKkrRnzx4lJiZKknr16iWbzWbf5pVnvbKysjR37lx99913kqTo6Gjdfvvt+vTTT7V9+3YlJyfrscceU2hoqObNm6cVK1ZIklJSUrR48WJJ0k033aQ5c+YoODhYn3zyif7+97+rZcuWOnLkiFq0aKH58+erTZs2Lt0vgCdYuu6g/U23QnGpVUvXHXTpC/w5W3O18jpf5XJXaUy1pK37RA832WYPEUGWIj3cZJvWrPPRgKhnXNLH0nUHFeF1RNE37FWg9+U399SLkVq6zs+l+8tELT77Uuzbr+DnZZXPvhTJRaHLxHGXzOyv6+WSOV2ZmZlq3769/ffQ0FCdPn261ttJT0+vtMzHx0dFRUVOb6OsmuRcsbw226pKeXm5Ll68qKKiIu3evVvFxcUqLy/XV199pY8++kg33nj5Cff000/riSeeUFRUlEpLS/Xkk0/q1ltv1Z133qlf/OIXeu2119SzZ09t3LhRSUlJ9m1euf1f/vKXuueee/Tmm29KkvLy8hQYGKh+/fopPDxcY8aMkXQ5xJWXl6uoqEjffPONfvvb3yopKUlt2rTRH//4R82aNUvz5s2TJO3fv18ff/yx2rVrp1dffVXvv/++nn322SprLSkpUVpa2nXtr/qkMdVyLTy5fnfUfjbvYrXLXdnf6qIeGhOww+GNscRm0SdFPWRzoh9nxtJQanFG//Iv5GepHCL6W79QWtpPXNLHTUX/dKgjyFKkMQE79FGRlJbmuhvKXm8tzhy7VqochiTpBp132bE3cdwlM8f+etWrifQRERHy93e8Qd/BgwcVEBDg9DZ8WrauMnj5tGwtSbXaVlW8vb01bdo0+fv7q3nz5po/f76ysrIUFRWl2267TZJ04cIFpaWl6dy5c/bHFRUV6eTJk/rRj36kZs2aqX///pKkESNG6LXXXlPTpk0VEBAgb29vNW3aVJK0b98+ffDBB/Lx8XEYu4+Pj/z9/e2/N2nSRN7e3goICND+/fs1YMAAdezYUZI0fvx4xcbG2ttGRUUpLCzM/vP27dur3Sd+fn7q3r37de2v+iItLU1RUa4909mQeHL97qq9zbqcKsNKm8CmLu1vwbocfVQkRTd1PKtyLOCOGvtxtvaGUIuzvl1X9R/Wgd5FCnNRH17r3q7y7NCDAV/pzqipLulDur5anD32X65rXmXwOqfmLjsmJo67ZObYVyguLq7yRFFNXBK6QkNDderUKfscox+e+TIpcOA4hzldkuvvrFwxp6vCihUrHIJLeXm5vLy89Le//U2+vr4Ojz106FCl7Xl5VXW12z2uDLUWi0VWq/UqrQFUZ8KwcId5PZLk72vRhGHhbuinRGnnbnHo51kX9tOYarE2DZTPpbwql7vKDVVcKrva8mtlopay7nEquWJOl3T5LFRZ9ziX9WHiuEtm9tf1csnXAA0dOlTJyckqLy9Xbm6uNm3apCFDhrhi07XWIqKfWg9/6t9ntrzk07K1Wg9/yujHUps3v/wXwrvvvmtflpmZqbNnz+qWW27RpUuXtGfPHknS+vXrVVBQUGkbAQEBioyM1JIlS+zLcnNz7dsvLCyssu8+ffroH//4h86ePStJ+utf/6q7777bVaUB+LcBUTfq2VHd1Sawqbx0+azQs6O6u3zCrol+GlMtoUMmqNzb8Y/dcm9fhQ6Z4LI+fP995cTZ5dfKRC29Y0aooPsjyrc1l80m5duaq6D7Iy799KKp/18m9tf1qvFM19y5c7Vx40ZlZ2frscceU6tWrbRmzRolJCRoypQp6tq1q2JjY7Vv3z7df//9kqRnnnnGPrepLtSHOyv/7ne/0xtvvKGYmBhJl0PUa6+9pjZt2uitt95ymEhf3VnB3/3ud0pMTFR0dLS8vb0VHR2tiRMn6sEHH9SMGTO0fv16+0T6Cp07d9bzzz+v+Ph4SdKNN96oOXPmuLlawDMNiLrRyKeiTPTTWGq58iuNSguy5duytctvxGniiopk7uuZeseMcNmk+eqY+P9l4thfLy/blR+dqyMV10arm9MVHu6aU5BFRUXXPaerIatt/a7c93XNk+c0SZ5dP7V7Zu2Se+uv73dY59i7t/6r5ZarqVcT6QEAaAjqwxUVNDwumdMFAACAq2sQoaseXAH1OOxzAABcq96HriZNmignJ4cQYJDNZlNOTo6aNGlS10MBAKDRqPdzujp06KATJ07Yb4FwPUpKSuTn5+eCUTVMtam/SZMmdfLdmQAANFb1PnT5+vrq5ptvdsm20tLSGs0d1q+Fp9cPAEBdqveXFwEAABoDQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAM8HGm0dGjRzV9+nTl5+erVatWmjdvnjp27OjQJicnRzNmzFBmZqbKysrUp08fvfLKK/LxcaoLAACARs2pM12zZs3S2LFjtWHDBo0dO1YzZ86s1GbhwoUKCwvT6tWr9cknn+if//ynNm7c6PIBAwAANEQ1hq6cnBxlZGQoOjpakhQdHa2MjAzl5uY6tPPy8lJRUZHKy8tVUlKi0tJShYSEuGfUAAAADUyNoSszM1MhISGyWCySJIvForZt2yozM9Oh3aRJk3T06FHde++99n9RUVHuGTUAAEAD47IJV+vXr1eXLl30wQcfqKioSAkJCVq/fr2GDh3q9DbS09NdNZxqpaWlub2P+syT6/fk2iXPrp/aPZcn1+/JtUv1s/4aQ1doaKiysrJktVplsVhktVp15swZhYaGOrRbtmyZXn/9dXl7e6tFixYaNGiQvvjii1qFroiICPn7+9e+CielpaV59Nk3T67fk2uXPLt+avfM2iXPrt+Ta5fcX39xcfE1nSiq8fJicHCwwsPDlZqaKklKTU1VeHi4goKCHNp16NBBW7dulSSVlJRox44duvXWW2s9IABoKArTt+rY/Cf1r9ce1rH5T6owfWtdDwlAPebUpxdnz56tZcuWaciQIVq2bJkSExMlSQkJCTpw4IAk6aWXXlJaWppiYmIUFxenjh076qc//an7Rg4Adagwfauy1yxUWUG2JJvKCrKVvWYhwQtAtZya0xUWFqbk5ORKyxctWmT/+aabbtKf/vQn140MAOqxvM1JspUVOyyzlRUrb3OSWkT0q6NRAajPuCM9AFyDsoKcWi0HAEIXAFwDn5bBtVoOAIQuALgGgQPHycvH8dPWXj7+Chw4ro5GBKC+44sRAeAaVMzbytucpLKCHPm0DFbgwHHM5wJQLUIXAFyjFhH9CFkAnMblRQAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAp0LX0aNHNXr0aA0ZMkSjR4/Wd999V2W7tWvXKiYmRtHR0YqJiVF2drYrxwoAANBg+TjTaNasWRo7dqxiY2O1atUqzZw5U0uXLnVoc+DAAb3zzjv64IMP1KZNGxUWFsrPz88tgwYAAGhoajzTlZOTo4yMDEVHR0uSoqOjlZGRodzcXId2S5YsUXx8vNq0aSNJatGihfz9/d0wZAAAgIbHy2az2a7WID09XdOmTdOaNWvsyx544AH99re/1R133GFfFhcXp/79+2vPnj26cOGC/uu//ktPP/20vLy8ahxEcXGx0tPTr6MMAAAAsyIiImp1gsmpy4vOsFqtOnz4sP70pz+ppKRETzzxhNq3b6+4uDint1HbwddWWlqaoqKi3Lb9+s6T6/fk2iXPrp/aPbN2ybPr9+TaJffXf60ni2q8vBgaGqqsrCxZrVZJl8PVmTNnFBoa6tCuffv2Gjp0qPz8/NS8eXPdd9992r9/f60HBAAA0BjVGLqCg4MVHh6u1NRUSVJqaqrCw8MVFBTk0C46Olqff/65bDabSktLtXPnTt12223uGTUAAEAD49QtI2bPnq1ly5ZpyJAhWrZsmRITEyVJCQkJOnDggCRp+PDhCg4O1gMPPKC4uDh16tRJDz/8sPtGDgAA0IA4NacrLCxMycnJlZYvWrTI/rO3t7dmzJihGTNmuG50AAAAjQR3pAeQAtIAAAAaCElEQVQAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAKdC19GjRzV69GgNGTJEo0eP1nfffVdt23/961/q3r275s2b56oxAgAANHhOha5Zs2Zp7Nix2rBhg8aOHauZM2dW2c5qtWrWrFkaPHiwSwcJAADQ0NUYunJycpSRkaHo6GhJUnR0tDIyMpSbm1up7bvvvqsBAwaoY8eOLh8oAABAQ+ZTU4PMzEyFhITIYrFIkiwWi9q2bavMzEwFBQXZ2x06dEiff/65li5dqj/+8Y/XNJj09PRrelxtpKWlub2P+syT6/fk2iXPrp/aPZcn1+/JtUv1s/4aQ5czSktL9etf/1pvvPGGPZxdi4iICPn7+7tiSFVKS0tTVFSU27Zf33ly/Z5cu+TZ9VO7Z9YueXb9nly75P76i4uLr+lEUY2hKzQ0VFlZWbJarbJYLLJarTpz5oxCQ0Ptbc6ePatjx45p4sSJkqSCggLZbDadP39er776aq0HBQAA0NjUGLqCg4MVHh6u1NRUxcbGKjU1VeHh4Q6XFtu3b68vvvjC/vv8+fN14cIFTZs2zT2jBgAAaGCc+vTi7NmztWzZMg0ZMkTLli1TYmKiJCkhIUEHDhxw6wABAAAaA6fmdIWFhSk5ObnS8kWLFlXZfvLkydc3KgAAgEaGO9IDAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGCAT10PAADcoTB9q/I2J6lVQbaObW+twIHj1CKiX10PC4AHI3QBaHQK07cqe81C2cqK5SWprCBb2WsWShLBC0Cd4fIigEYnb3OSbGXFDstsZcXK25xURyMCAEIXgEaorCCnVssBwARCF4BGx6dlcK2WA4AJhC4AjU7gwHHy8vF3WObl46/AgePqaEQAwER6AI1QxWT5vM1JKi3Ilm9LPr0IoO4RugA0Si0i+qlFRD+lpaUpKiqqrocDAFxeBAAAMIHQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADDAx5lGR48e1fTp05Wfn69WrVpp3rx56tixo0ObBQsWaO3atfL29pavr6+mTp2qvn37umPMAAAADY5ToWvWrFkaO3asYmNjtWrVKs2cOVNLly51aNOtWzfFx8eradOmOnTokB599FF9/vnnatKkiVsGDgAA0JDUeHkxJydHGRkZio6OliRFR0crIyNDubm5Du369u2rpk2bSpK6dOkim82m/Px8NwwZAACg4anxTFdmZqZCQkJksVgkSRaLRW3btlVmZqaCgoKqfExKSopuuukmtWvXrlaDSU9Pr1X7a5GWlub2PuozT67fk2uXPLt+avdcnly/J9cu1c/6nbq8WBu7du3SH/7wB73//vu1fmxERIT8/f1dPSS7tLQ0RUVFuW379Z0n1+/JtUueXT+1e2btkmfX78m1S+6vv7i4+JpOFNV4eTE0NFRZWVmyWq2SJKvVqjNnzig0NLRS27179+qFF17QggULdMstt9R6MAAAAI1VjaErODhY4eHhSk1NlSSlpqYqPDy80qXF/fv3a+rUqXr77bd1xx13uGe0AAAADZRT9+maPXu2li1bpiFDhmjZsmVKTEyUJCUkJOjAgQOSpMTERF26dEkzZ85UbGysYmNjdfjwYfeNHAAAoAFxak5XWFiYkpOTKy1ftGiR/efly5e7blQAAACNDHekBwAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMAAQhcAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGCAT10PAGgMCtO3Km9zksoKcuTTMliBA8epRUS/uh4WAKAeIXQB16kwfauy1yyUraxYklRWkK3sNQslieAFALDj8iJwnfI2J9kDVwVbWbHyNifV0YgAAPURoQu4TmUFObVaDgDwTIQu4Dr5tAyu1XIAgGcidAHXKXDgOHn5+Dss8/LxV+DAcXU0IgBAfcREeuA6VUyW59OLAICrIXQBLtAioh8hCwBwVVxeBAAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAMIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAXwMENBCF6Vv5fkcAaMAIXS5k4k2RN17PVJi+VdlrFspWVixJKivIVvaahZLE8QeABoLLiy5S8aZYVpAtyWZ/UyxM39qg+kD9lLc5yR64KtjKipW3OamORgQAqC1Cl4uYeFPkjddzlRXk1Go5AKD+IXS5iIk3Rd54PZdPy+BaLQcA1D+ELhcx8abIG2/tFaZv1bH5T6rV+td1bP6TDfZSbODAcfLy8XdY5uXjr8CB4+poRACA2iJ0uYiJN0XeeGvnyjlwXlKDngPXIqKfWg9/Sj4tW0vykk/L1mo9/Ckm0QNAA+LUpxePHj2q6dOnKz8/X61atdK8efPUsWNHhzZWq1Vz587VZ599Ji8vL02cOFGjRo1yx5hrbUvacS1dd1Bn8y6qzbocTRgWrgFRN7q0jxYR/XTwaI589qXoBp3XOTVX2e1xutmFb4om+qhQsc+y8y6qdWBTt+wzd/dxtTlwrg4rJvZXWvHNWnruoct92JpqQvHNGuDSHszUYaofE897AKgNp0LXrFmzNHbsWMXGxmrVqlWaOXOmli5d6tBm9erVOnbsmDZu3Kj8/HzFxcXprrvuUocOHdwycGdtSTuud5L3qbjUKkk6m3dR7yTvkySXvgBvSTuud7b5qrh0pH2Z/zaLnm1/3GX9mOjD3o+b95mJPkr/fYarquWu1Fj2l9HnSiOpBQBqo8bLizk5OcrIyFB0dLQkKTo6WhkZGcrNzXVot3btWo0aNUre3t4KCgrS4MGDtX79eveMuhaWrjtof+GtUFxq1dJ1BxtcP9RSO+dszWu1/Fo1lv3F/y8AcK8az3RlZmYqJCREFotFkmSxWNS2bVtlZmYqKCjIoV379u3tv4eGhur06dO1Gkx6enqt2jvjbN7FapenpaU1qH5c0Ycz7RpKLTVZXdRDYwJ2yM/rP2++JTaLPinqIRvH3i19OKOh7K/GwtPq/SFPrt+Ta5fqZ/316o70ERER8vf3r7lhLbRZl1PlC3CbwKaKiopqUP1cbx9paWlOtWsItThjwbocfVQkRTfdq0DvIuWVByj1YqSOBdzBsXdDH85qCPursXD2Od9YeXL9nly75P76i4uLr+lEUY2XF0NDQ5WVlSWr9fLZAqvVqjNnzig0NLRSu1OnTtl/z8zMVLt27Wo9IFebMCxcfZp+p1k3LNf/BC7VrBuWq0/T7zRhWLjL+/H3tTgs8/e1uLQfE32Y6sdUH+m2W5V47iH9Im+CEs89pHTbreyvOuzDVD+magGA2qjxTFdwcLDCw8OVmpqq2NhYpaamKjw83OHSoiQNHTpUycnJuv/++5Wfn69NmzYpKanu75Qe5X9UHQJ2yLu8VJIUZCnSmIAdCvGPlOS6CbUVk3Pd+YksE31U9NPs1B7HT0l2j1PvBlbLlX2czbuoNm7cXxX9NORjb/L/l7v7MXXsAaA2vGw2m62mRt9++62mT5+ugoICtWzZUvPmzdMtt9yihIQETZkyRV27dpXVatWcOXO0bds2SVJCQoJGjx7t1CAqTtO54/LisflP/vu7Ch35tGytmyb/P5f2Vd85e7r1h1+uLF2+H1hDvi8Up9o9t35q98zaJc+u35Nrl8xdXqxtbnFqTldYWJiSk5MrLV+0aJH9Z4vFosTERKc7NoWvzqk9k/e3AgDAUzT6O9Lz1Tm1R1AFAMD1Gn3o4qtzao+gCgCA6zX60HXld9bZJL6zzgkEVQAAXK9e3afLXVpE9FOLiH4eP7HQWRWBNG9zksoKcuTTMliBA8cRVAEAuA4eEbpQexVBFQAAuEajv7wIAABQH3CmC3WmMH0rlzABAB6D0IU68cMbsJYVZCt7zUJJIngBABolLi+iTlztBqwAADRGhC7UCW7ACgDwNIQu1AluwAoA8DSELtQJbsAKAPA0TKRHneAGrAAAT0PoQp3hBqwAAE/C5UUAAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgE8vAjCOLzsH4IkIXQCM4svOAXgqLi8CMIovOwfgqQhdAIziy84BeCpCFwCj+LJzAJ6K0AXAKL7sHICnYiI9AKP4snMAnorQBcA4vuwcgCfi8iIAAIABhC4AAAADCF0AAAAGELoAAAAMIHQBAAAYQOgCAAAwgNAFAABgAKELAADAAG6OCsCuMH0rd4oHADchdAGQdDlwZa9ZKFtZsSSprCBb2WsWShLBCwBcgMuLACRd/i7EisBVwVZWrLzNSXU0IgBoXAhdACRJZQU5tVoOAKgdQhcASZJPy+BaLQcA1A6hC4AkKXDgOHn5+Dss8/LxV+DAcXU0IgBoXJhID0DSfybL8+lFAHAPQhcAuxYR/QhZAOAmXF4EAAAwgNAFAABgAKELAADAAEIXAACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwABCFwAAgAGELgAAAAN86noAkmSz2SRJJSUlbu+ruLjY7X3UZ55cvyfXLnl2/dTuuTy5fk+uXXJv/RV5pSK/OMvLVttHuEFhYaG+/vrruh4GAACA0zp37qwWLVo43b5ehK7y8nIVFRXJ19dXXl5edT0cAACAatlsNpWWliogIEDe3s7P1KoXoQsAAKCxYyI9AACAAYQuAAAAAwhdAAAABhC6AAAADCB0AQAAGEDoAgAAMIDQBQAAYAChCwAAwIB68d2LrrRq1Sq99957+vbbb/XSSy/p0Ucfta+7ePGiZsyYoX/+85+yWCyaNm2aBg4cWOV2/vrXv2rRokWy2Wzq16+fXnnllVrddbY++PnPf668vDxJktVq1ZEjR7Rq1SrddtttDu2++OILTZw4UR07dpQk+fn5KTk52fRwXWr69Onavn27AgMDJUlDhw7V008/XWXbBQsWaOXKlZKkESNG6JlnnjE2TndJTEzUjh075Ofnp2bNmunll19W165dK7VbsWKFXn/9df3oRz+SJHXo0EELFiwwPdzrdvToUU2fPl35+flq1aqV5s2bZ///XMFqtWru3Ln67LPP5OXlpYkTJ2rUqFF1M2AXysvL04svvqhjx47Jz89PP/7xjzVnzhwFBQU5tKvNc6IhGTRokPz8/OTv7y9Jev7559W3b1+HNrV57W9ITpw44fB6VVhYqPPnz2vXrl0O7ebPn6+//OUvatu2rSTpzjvv1KxZs4yO1RXmzZunDRs26OTJk1q9erU6d+4sybnnv1RPXgNsjczhw4dtR44csb3wwgu2P//5zw7r5s+fb3v55ZdtNpvNdvToUdvdd99tO3/+fKVtHDt2zNa3b19bTk6OzWq12uLj420rV640Mn53+fvf/24bPnx4let27txpGzFihOERude0adMqHf+q7Nq1yxYdHW27ePGi7eLFi7bo6Gjbrl27DIzQvT799FNbSUmJ/ef77ruvynbLly+3TZ482eTQ3GL8+PG2lJQUm81ms6WkpNjGjx9fqc3KlStt8fHxNqvVasvJybH17dvXdvz4cdNDdbm8vDzbzp077b+/+eabthkzZlRq5+xzoqEZOHCg7fDhw1dt4+xrf0M3d+5cW2JiYqXlb7/9tu3NN9+sgxG51u7du22nTp2qdMydef7bbPXjNaBhnbpxQufOndWpU6cqz0qtW7dOo0ePliR17NhRERER2rp1a6V2GzZs0ODBgxUUFCRvb2+NGjVKa9eudfvY3elvf/ubHnrooboeRr2zdu1axcXFqUmTJmrSpIni4uIa/LGWpIEDB8rX11eS1KNHD50+fVrl5eV1PCr3yMnJUUZGhqKjoyVJ0dHRysjIUG5urkO7tWvXatSoUfL29lZQUJAGDx6s9evX18WQXapVq1bq06eP/fcePXro1KlTdTii+sfZ1/6GrKSkRKtXr27Ur/M9e/ZUaGiowzJnn/9S/XgNaHSh62pOnTplv4wiSaGhoTp9+nSldpmZmWrfvr399/bt2yszM9PIGN3h7Nmz2rFjh2JjY6tt891332nEiBEaNWqU/VJbQ/enP/1JMTExmjRpkr799tsq2/zwWIeGhjboY12VpKQkDRgwoNrL47t27VJsbKzGjRunLVu2mB2cC2RmZiokJEQWi0WSZLFY1LZt20rHsapjXdXzvyErLy/Xhx9+qEGDBlW53pnnREP0/PPPKyYmRrNnz1ZBQUGl9c6+9jdkn376qUJCQnTHHXdUuX7NmjWKiYlRfHy89u7da3h07uPs87+ibV2/BjS4OV0jRoyo9q+47du323e8J3B2X6SkpKhv376V5nhUuOOOO/SPf/xDLVq00PHjx/XYY48pJCREd999t9vGfr1qqn3q1Klq06aNvL29lZKSoieeeEKbNm1qNP8/nD32a9as0erVq5WUlFRl2wEDBuiBBx5QkyZNlJGRoYSEBC1dulRhYWFuGzvc59VXX1WzZs0c5rJWaKzPiaSkJIWGhqqkpESvvfaa5syZo9/97nd1PSzjli9fXu1ZrjFjxuipp56Sr6+vtm3bpkmTJmnt2rX2+X0wp8GFrus5C9O+fXudPHnSHj4yMzMdTstXCA0NdXhDO3XqVKVTmvWBs/tixYoVevHFF6td37x5c/vPN954owYPHqwvv/yyXoeummoPCQmx/xwXF6c33nhDp0+fdvhrV6p8rDMzM+vlsf4hZ4793//+d/3+97/XkiVL1Lp16yrbXBnEb7/9dt15553av39/gwpdoaGhysrKktVqlcVikdVq1ZkzZyodx4pj3a1bN0mV/+pt6ObNm6fvv/9eCxcurPKsprPPiYam4jj7+flp7NixVX44wNnX/oYqKytLu3fv1m9+85sq17dp08b+8z333KPQ0FAdOXJEvXv3NjVEt3H2+V/Rtq5fAzzq8uLQoUP18ccfS7p8Oe3AgQOVPuUiSUOGDNGmTZuUm5ur8vJyJScna9iwYaaH6xJffvmlCgsL1a9fv2rbnDlzRjabTZKUn5+vbdu2VfqEY0OTlZVl//mzzz6Tt7e3w5tOhaFDhyolJUWXLl3SpUuXlJKS0mCP9ZU2b96sN954Q4sXL1aHDh2qbXflfjp58qS++uordenSxcQQXSY4OFjh4eFKTU2VJKWmpio8PLzSmd2hQ4cqOTlZ5eXlys3N1aZNmzRkyJC6GLLLvfXWW0pPT9eCBQvk5+dXZRtnnxMNyYULF1RYWChJstlsWrt2rcLDwyu1c/a1v6FauXKl+vfvX+2ZqyuP/cGDB3Xy5EndfPPNpobnVs4+/6X68RrgZat4t20kUlNT9Zvf/EYFBQXy9fVV06ZN9f7776tTp066cOGCpk+froMHD8rb21svvPCCBg8eLEn6wx/+oLZt2+qRRx6RJH300Ud67733JF3+y2DmzJkN8jT8K6+8olatWun55593WH5lvcuWLdOHH34oHx8fWa1WxcXF6YknnqijEbvGz3/+c+Xk5MjLy0vNmzfXiy++qB49ekiSXn75ZQ0aNEj33XefpMsfp05JSZF0+QzA5MmT62zcrvKTn/xEvr6+Di88S5YsUWBgoEP9b731lv7v//7P/n/7scce04gRI+pq2Nfs22+/1fTp01VQUKCWLVtq3rx5uuWWW5SQkKApU6aoa9euslqtmjNnjrZt2yZJSkhIsE+ubsiOHDmi6OhodezYUU2aNJH0n1t/xMbG6t1331VISMhVnxMN1fHjxzV58mRZrVaVl5crLCxMr7zyitq2betQ+9Ve+xuDIUOG6OWXX3b44/rK//vTpk3TP//5T3l7e8vX11dTpkxR//7963DE12bu3LnauHGjsrOzFRgYqFatWmnNmjXVPv8l1bvXgEYXugAAAOojj7q8CAAAUFcIXQAAAAYQugAAAAwgdAEAABhA6AIAADCA0AUAAGAAoQsAAMCA/w9Np+tN5QHSDwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.008629484686481507\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.0027021660450248395\n" ] } ], "source": [ "for rank in [5, 10, 15]:\n", " c, a = RBF_fit(X, Y, rank)\n", " predict = np.array([RBF_predict(x, c, a) for x in X])\n", " \n", " plt.plot(X, Y, 'o')\n", " plt.plot(X, predict, 'o')\n", " plt.legend(['Data', 'Prediction'])\n", " plt.title(\"RBF Fit (r^3) with %d centers\" % rank)\n", " plt.show()\n", " \n", " error = np.mean((predict - Y) ** 2)\n", " print(\"Mean squared error (in sample):\", error)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## (c) Out of sample performance" ] }, { "cell_type": "code", "execution_count": 380, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Error for Polynomial Fit (5 terms):\t 0.037418004376817283\n", "Error for Polynomial Fit (10 terms):\t 0.03497768433217678\n", "Error for Polynomial Fit (15 terms):\t 4.391779493179244\n" ] } ], "source": [ "x_out = np.linspace(-10.5, 10.5, 22)\n", "x_vis = np.linspace(-10.5, 10.5, 1000)\n", "y_out = [0 if x <= 0 else 1 for x in x_out]\n", "\n", "colors = sns.color_palette()\n", "ranks = [5, 10, 15]\n", "\n", "plt.plot(x_out, y_out, 'o', color=colors[0])\n", "plt.title(\"Out of sample performance (Polynomials)\")\n", "plt.ylim(-1, 2)\n", "\n", "errors = []\n", "\n", "# polynom fit\n", "for i in range(3):\n", " rank = ranks[i]\n", " coeff = polynom_fit(X, Y, rank)\n", " predict = np.array([polynom_predict(x, coeff) for x in x_out])\n", " y_vis = np.array([polynom_predict(x, coeff) for x in x_vis])\n", " \n", " plt.plot(x_vis, y_vis, color=colors[i + 1])\n", " \n", " error = np.mean((predict - y_out) ** 2)\n", " errors.append(error)\n", " \n", "plt.legend(['Ground Truth', 'Poly (5)', 'Poly (10)', 'Poly (15)'])\n", "plt.show()\n", "\n", "print(\"Error for Polynomial Fit (5 terms):\\t\", errors[0])\n", "print(\"Error for Polynomial Fit (10 terms):\\t\", errors[1])\n", "print(\"Error for Polynomial Fit (15 terms):\\t\", errors[2])" ] }, { "cell_type": "code", "execution_count": 381, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Error for RBF Fit (5 centers):\t 0.0326876099147709\n", "Error for RBF Fit (10 centers):\t 0.010861016784034101\n", "Error for RBF Fit (15 centers):\t 0.01543128976687474\n" ] } ], "source": [ "plt.plot(x_out, y_out, 'o', color=colors[0])\n", "plt.title(\"Out of sample performance (RBFs)\")\n", "\n", "errors = []\n", "\n", "# polynom fit\n", "for i in range(3):\n", " rank = ranks[i]\n", " \n", " c, a = RBF_fit(X, Y, rank)\n", " predict = np.array([RBF_predict(x, c, a) for x in x_out])\n", " y_vis = np.array([RBF_predict(x, c, a) for x in x_vis])\n", " \n", " plt.plot(x_vis, y_vis, color=colors[i + 1])\n", " \n", " error = np.mean((predict - y_out) ** 2)\n", " errors.append(error)\n", " \n", "plt.legend(['Ground Truth', 'RBF (5)', 'RBF (10)', 'RBF (15)'])\n", "plt.show()\n", "\n", "print(\"Error for RBF Fit (5 centers):\\t\", errors[0])\n", "print(\"Error for RBF Fit (10 centers):\\t\", errors[1])\n", "print(\"Error for RBF Fit (15 centers):\\t\", errors[2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## (d) Curvature regularizer\n", "\n", "I'm going to try and use sympy to derive, integrate and solve, so first let's do it step by step for a 5 term polynomial" ] }, { "cell_type": "code", "execution_count": 382, "metadata": {}, "outputs": [], "source": [ "from sympy import *" ] }, { "cell_type": "code", "execution_count": 383, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x^{4} {a}_{4} + x^{3} {a}_{3} + x^{2} {a}_{2} + x {a}_{1} + {a}_{0}$" ], "text/plain": [ "x**4*a[4] + x**3*a[3] + x**2*a[2] + x*a[1] + a[0]" ] }, "execution_count": 383, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# prepare polynomial\n", "degree = 5\n", "x, a = symbols(\"x a\")\n", "f = Indexed('a',0)\n", "for i in range(1, degree):\n", " f = f + Indexed('a',i) * (x ** i)\n", "f" ] }, { "cell_type": "code", "execution_count": 384, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 4 x^{3} {a}_{4} + 3 x^{2} {a}_{3} + 2 x {a}_{2} + {a}_{1}$" ], "text/plain": [ "4*x**3*a[4] + 3*x**2*a[3] + 2*x*a[2] + a[1]" ] }, "execution_count": 384, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = diff(f, x)\n", "df" ] }, { "cell_type": "code", "execution_count": 385, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 12 x^{2} {a}_{4} + 6 x {a}_{3} + 2 {a}_{2}$" ], "text/plain": [ "12*x**2*a[4] + 6*x*a[3] + 2*a[2]" ] }, "execution_count": 385, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ddf = diff(df, x)\n", "ddf" ] }, { "cell_type": "code", "execution_count": 386, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 80 {a}_{2}^{2} + 32000 {a}_{2} {a}_{4} + 24000 {a}_{3}^{2} + 5760000 {a}_{4}^{2}$" ], "text/plain": [ "80*a[2]**2 + 32000*a[2]*a[4] + 24000*a[3]**2 + 5760000*a[4]**2" ] }, "execution_count": 386, "metadata": {}, "output_type": "execute_result" } ], "source": [ "right = integrate(ddf**2, (x, -10, 10))\n", "right" ] }, { "cell_type": "code", "execution_count": 387, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 21 {a}_{0}^{2} + 1540 {a}_{0} {a}_{2} + 101332 {a}_{0} {a}_{4} - 20 {a}_{0} + 770 {a}_{1}^{2} + 101332 {a}_{1} {a}_{3} - 110 {a}_{1} + 50666 {a}_{2}^{2} + 7913620 {a}_{2} {a}_{4} - 770 {a}_{2} + 3956810 {a}_{3}^{2} - 6050 {a}_{3} + 335462666 {a}_{4}^{2} - 50666 {a}_{4} + 10$" ], "text/plain": [ "21*a[0]**2 + 1540*a[0]*a[2] + 101332*a[0]*a[4] - 20*a[0] + 770*a[1]**2 + 101332*a[1]*a[3] - 110*a[1] + 50666*a[2]**2 + 7913620*a[2]*a[4] - 770*a[2] + 3956810*a[3]**2 - 6050*a[3] + 335462666*a[4]**2 - 50666*a[4] + 10" ] }, "execution_count": 387, "metadata": {}, "output_type": "execute_result" } ], "source": [ "left = 0\n", "for i in range(len(Y)):\n", " left += (Y[i] - f.subs(x, X[i])) ** 2\n", "left = simplify(left)\n", "left" ] }, { "cell_type": "code", "execution_count": 388, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[42*a[0] + 1540*a[2] + 101332*a[4] - 20,\n", " 1540*a[1] + 101332*a[3] - 110,\n", " 1540*a[0] + 101348.0*a[2] + 7916820.0*a[4] - 770,\n", " 101332*a[1] + 7918420.0*a[3] - 6050,\n", " 101332*a[0] + 7916820.0*a[2] + 672077332.0*a[4] - 50666]" ] }, "execution_count": 388, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lambd = 0.1\n", "I = left + lambd * right\n", "system = []\n", "for i in range(degree):\n", " dIda = diff(I, Indexed('a',i))\n", " system.append(dIda)\n", "system" ] }, { "cell_type": "code", "execution_count": 389, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{a[0]: 0.415934776553056,\n", " a[1]: 0.133926172914499,\n", " a[2]: 0.00359861417898801,\n", " a[3]: -0.000949811572734460,\n", " a[4]: -2.97154546527246e-5}]" ] }, "execution_count": 389, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = solve(system, dict=True)\n", "sol" ] }, { "cell_type": "code", "execution_count": 390, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error (in sample): 0.03394155818872691\n" ] } ], "source": [ "coeff = np.zeros(degree)\n", "for i in range(degree):\n", " coeff[i] = sol[0][Indexed('a',i)]\n", "\n", "predict = np.array([polynom_predict(x, coeff) for x in X])\n", " \n", "plt.plot(X, Y, 'o')\n", "plt.plot(X, predict, 'o')\n", "plt.legend(['Data', 'Prediction'])\n", "plt.title(\"Polynomial Fit with Curvature Regularization with %d terms\" % degree)\n", "plt.show()\n", "\n", "error = np.mean((predict - Y) ** 2)\n", "print(\"Mean squared error (in sample):\", error)" ] }, { "cell_type": "code", "execution_count": 391, "metadata": {}, "outputs": [], "source": [ "def polynom_regularized_fit(X, Y, degree, lambd, integ_domain=(-10, 10)):\n", " x, a = symbols(\"x a\")\n", " f = Indexed('a',0)\n", " for i in range(1, degree):\n", " f = f + Indexed('a',i) * (x ** i)\n", " \n", " df = diff(f, x)\n", " ddf = diff(df, x)\n", " \n", " right = integrate(ddf**2, (x, integ_domain[0], integ_domain[1]))\n", " \n", " left = 0\n", " for i in range(len(Y)):\n", " left += (Y[i] - f.subs(x, X[i])) ** 2\n", " left = simplify(left)\n", " \n", " I = left + lambd * right\n", " system = []\n", " for i in range(degree):\n", " dIda = diff(I, Indexed('a',i))\n", " system.append(dIda)\n", " \n", " sol = solve(system, dict=True)\n", " \n", " coeff = np.zeros(degree)\n", " for i in range(degree):\n", " coeff[i] = sol[0][Indexed('a',i)]\n", " \n", " return coeff" ] }, { "cell_type": "code", "execution_count": 395, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Error for Lambda = 0:\t\t 0.023773381091605296\n", "Error for Lambda = 0.01:\t 0.015278746396171095\n", "Error for Lambda = 0.1:\t\t 0.01561114723230335\n", "Error for Lambda = 1:\t\t 0.022923101989995476\n", "[0.023773381091605296, 0.015278746396171095, 0.01561114723230335, 0.022923101989995476, 0.04207856962142806]\n" ] } ], "source": [ "degree = 15\n", "\n", "plt.plot(x_out, y_out, 'o', color=colors[0])\n", "plt.title(\"Out of sample performance (Polynomials with Curvature Regularization)\")\n", "plt.ylim(-1, 2)\n", "plt.ylim(-0.5, 1.5)\n", "\n", "errors = []\n", "\n", "lambdas = [0.01, 0.1, 1, 10, 100]\n", "\n", "for i in range(len(lambdas)):\n", " lambd = lambdas[i]\n", " \n", " coeff = polynom_regularized_fit(X, Y, degree, lambd)\n", " predict = np.array([polynom_predict(x, coeff) for x in x_out])\n", " y_vis = np.array([polynom_predict(x, coeff) for x in x_vis])\n", " \n", " plt.plot(x_vis, y_vis, color=colors[i + 1])\n", " \n", " error = np.mean((predict - y_out) ** 2)\n", " errors.append(error)\n", " \n", "plt.legend(['Ground Truth', 'Lambda = 0', 'Lambda = 0.01', 'Lambda = 0.1', 'Lambda = 1'])\n", "plt.show()\n", "\n", "print(\"Error for Lambda = 0:\\t\\t\", errors[0])\n", "print(\"Error for Lambda = 0.01:\\t\", errors[1])\n", "print(\"Error for Lambda = 0.1:\\t\\t\", errors[2])\n", "print(\"Error for Lambda = 1:\\t\\t\", errors[3])\n", "\n", "print(errors)" ] }, { "cell_type": "code", "execution_count": 394, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.022923101989995476" ] }, "execution_count": 394, "metadata": {}, "output_type": "execute_result" } ], "source": [ "errors[4]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion:\n", "**15 Terms Polynomial with Curvature Regularizer ($\\lambda=0.1$) is comparable with 15 RBF ($r^3$)**" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Error for Lambda = 0:\t\t 4.581968127894955\n", "Error for Lambda = 0.01:\t 0.0191014567704912\n", "Error for Lambda = 0.1:\t\t 0.02070527358918754\n", "Error for Lambda = 1:\t\t 0.021831414018453114\n" ] } ], "source": [ "# Different integration domain\n", "\n", "degree = 15\n", "\n", "plt.plot(x_out, y_out, 'o', color=colors[0])\n", "plt.title(\"Out of sample performance (Polynomials with Curvature Regularization)\")\n", "plt.ylim(-1, 2)\n", "\n", "errors = []\n", "\n", "lambdas = [0, 0.01, 0.1, 1]\n", "\n", "for i in range(len(lambdas)):\n", " lambd = lambdas[i]\n", " \n", " coeff = polynom_regularized_fit(X, Y, degree, lambd, integ_domain=(-20, 20))\n", " predict = np.array([polynom_predict(x, coeff) for x in x_out])\n", " y_vis = np.array([polynom_predict(x, coeff) for x in x_vis])\n", " \n", " plt.plot(x_vis, y_vis, color=colors[i + 1])\n", " \n", " error = np.mean((predict - y_out) ** 2)\n", " errors.append(error)\n", " \n", "plt.legend(['Ground Truth', 'Lambda = 0', 'Lambda = 0.01', 'Lambda = 0.1', 'Lambda = 1'])\n", "plt.show()\n", "\n", "print(\"Error for Lambda = 0:\\t\\t\", errors[0])\n", "print(\"Error for Lambda = 0.01:\\t\", errors[1])\n", "print(\"Error for Lambda = 0.1:\\t\\t\", errors[2])\n", "print(\"Error for Lambda = 1:\\t\\t\", errors[3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Seems sensitive to the choice of intergration domain**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# (14.3)" ] }, { "cell_type": "code", "execution_count": 355, "metadata": {}, "outputs": [], "source": [ "# for M = 4, we know from Table (6.1) that the relevant bits are 1 and 4\n", "lag = np.array([1, 0, 0, 1])\n", "state = np.array([1, 1, 1, 1])\n", "\n", "def lfsr():\n", " global state\n", " x = np.dot(lag, state) % 2\n", " state[0] = x # replace the oldest element with the newest\n", " state = np.roll(state, -1) # roll the state so the newest element is now in its proper position\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate dataset\n", "\n", "Every X is the history of the last $k$ bits seen. And $y$ is the new bit.\n", "For LFSR of max order 4, no reason to set $k$ bigger than 4. \n", "\n", "I generate a dataset which contains a subset of the existing LFSR, and test on the remaining" ] }, { "cell_type": "code", "execution_count": 396, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training:\n", "(11, 4)\n", "(11, 1)\n", "Testing:\n", "(4, 4)\n", "(4, 1)\n" ] } ], "source": [ "x_dim = 4 # how many bits are in each x\n", "training_size = 11 # size of training dataset\n", "testing_size = 4 # size of testing dataset\n", "\n", "X = []\n", "Y = []\n", "\n", "x = []\n", "for i in range(x_dim):\n", " x.append(lfsr())\n", "\n", "for i in range(training_size):\n", " y = lfsr()\n", " \n", " X.append(x.copy())\n", " Y.append(y)\n", " \n", " x.append(y)\n", " x.pop(0)\n", " \n", "X = np.array(X)\n", "Y = np.expand_dims(np.array(Y), axis=1)\n", "\n", "print(\"Training:\")\n", "print(X.shape)\n", "print(Y.shape)\n", "\n", "X_test = []\n", "Y_test = []\n", "\n", "for i in range(testing_size):\n", " y = lfsr()\n", " \n", " X_test.append(x.copy())\n", " Y_test.append(y)\n", " \n", " x.append(y)\n", " x.pop(0)\n", "\n", "X_test = np.array(X_test)\n", "Y_test = np.expand_dims(np.array(Y_test), axis=1)\n", "\n", "print(\"Testing:\")\n", "print(X_test.shape)\n", "print(Y_test.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## DIY neural network\n", "\n", "After messing around with building my own NN from scratch, I resorted to using one of the many codes lying around the web. The ReLU and Dense layers are copied as is from https://towardsdatascience.com/building-neural-network-from-scratch-9c88535bf8e9\n", "\n", "To keep it simple, I implemented a Sigmoid layer (to keep the output between 0 and 1). And a simple squared error loss." ] }, { "cell_type": "code", "execution_count": 397, "metadata": {}, "outputs": [], "source": [ "class ReLU():\n", " def __init__(self):\n", " # ReLU layer simply applies elementwise rectified linear unit to all inputs\n", " pass\n", " \n", " def forward(self, input):\n", " # Apply elementwise ReLU to [batch, input_units] matrix\n", " relu_forward = np.maximum(0,input)\n", " return relu_forward\n", " \n", " def backward(self, input, grad_output):\n", " # Compute gradient of loss w.r.t. ReLU input\n", " relu_grad = input > 0\n", " return grad_output * relu_grad\n", " \n", "class Dense():\n", " def __init__(self, input_units, output_units, learning_rate=0.1):\n", " # A dense layer is a layer which performs a learned affine transformation:\n", " # f(x) = + b\n", " self.learning_rate = learning_rate\n", " self.weights = np.random.normal(loc=0.0, \n", " scale = np.sqrt(2/(input_units+output_units)), \n", " size = (input_units,output_units))\n", " self.biases = np.zeros(output_units)\n", " \n", " def forward(self,input):\n", " # Perform an affine transformation:\n", " # f(x) = + b\n", " \n", " # input shape: [batch, input_units]\n", " # output shape: [batch, output units]\n", " return np.dot(input,self.weights) + self.biases\n", " \n", " def backward(self,input,grad_output):\n", " # compute d f / d x = d f / d dense * d dense / d x\n", " # where d dense/ d x = weights transposed\n", " grad_input = np.dot(grad_output, self.weights.T)\n", " \n", " # compute gradient w.r.t. weights and biases\n", " grad_weights = np.dot(input.T, grad_output)\n", " grad_biases = grad_output.mean(axis=0)*input.shape[0]\n", " \n", " assert grad_weights.shape == self.weights.shape and grad_biases.shape == self.biases.shape\n", " \n", " # Here we perform a stochastic gradient descent step. \n", " self.weights = self.weights - self.learning_rate * grad_weights\n", " self.biases = self.biases - self.learning_rate * grad_biases\n", " \n", " return grad_input\n", "\n", "class Sigmoid():\n", " def __init__(self):\n", " pass\n", " \n", " def sigmoid(x):\n", " return 1 / (1 + np.exp(-x))\n", " \n", " def forward(self, input):\n", " return sigmoid(input)\n", " \n", " def backward(self, input, grad_output):\n", " # Compute gradient of loss w.r.t. ReLU input\n", " grad = sigmoid(input) * (1 - sigmoid(input))\n", " return grad_output * grad\n", "\n", "def forward(network, X):\n", " # Compute activations of all network layers by applying them sequentially.\n", " # Return a list of activations for each layer. \n", " \n", " activations = []\n", " input = X\n", " # Looping through each layer\n", " for l in network:\n", " activations.append(l.forward(input))\n", " # Updating input to last layer output\n", " input = activations[-1]\n", " \n", " assert len(activations) == len(network)\n", " return activations\n", "\n", "\n", "def squared_error_loss(y_true, y_predict):\n", " return (y_true - y_predict) ** 2\n", "\n", "def grad_squared_error_loss(y_true, y_predict):\n", " return -2 * (y_true - y_predict)" ] }, { "cell_type": "code", "execution_count": 398, "metadata": {}, "outputs": [ { "data": { "image/png": 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TDOVkptCLGAAAxJXc3FwtWbJEd911l6fJwYMPPqh+/fppyZIlWrhwoVasWKHMzEwtXbo0yruVbE6n0xmJB+3Zs0cLFy5UfX2958MXFhZqzpw5uvPOOzVmzBjdeOONOnjwoCUbvGzZMhUXF2v27NmqqamRzWZTenq6FixYoAsuuECSdOTIEd177706dOiQkpOTdf/99+vLX/5yUPs6ceKEdu3apaKiog7T/91h4aObJUn/5weXRvzZAAAAwYp2zNSdIhYQx6po/8f97Z/e10efHtFTiyZF/NkAAADBinbM1J2YVBdlIwb21dHjDTp09GS0twIAANArERBH2SVjB0qS3th2MMo7AQAA6J0IiKMsNytVowtz9I9tB9XLq1cAAACigoA4Blz2pUH6ovqE9lXWd3wzAAAAwoqAOAZcMnag7HabXqdsAgAAIOIIiGNA3/RkXVCUq9e3HaBsAgAAIMIIiGPE1780SIfrzqhiX3SGhAAAAPRWBMQx4qLzC5SUYNf/vv9FtLcCAADQqxAQx4i0lER9bdxAbXrvgE43NEV7OwAAAL0GAXEMmXJpoc6cbdZr75IlBgAAiBQC4hhSNDRLxcOyVLb5MzkcHK4DAACIBALiGHPtxEIdOnpK7+88HO2tAAAA9AoExDHma2MHKjszRes2fxbtrQAAAPQKBMQxJsGw61tfG673Kw7ri+oT0d4OAABA3CMgjkGTLx6upERDz722K9pbAQAAiHsExDGob3qySi8ZoX+8f0AHDpMlBgAA6E4ExDHqhivOUVKioT+/TJYYAACgOyVEewMIrG96skovLdTzmz7Vv37zXA3Nz4z2lrqd4+xpHXvrr8q6bJpsRutfzfptryo5f4SSC0Z6rp09tFvH310vp9MR1Nrp512qPkVf8fzcXF+jEx9tUr9LbpTNZvNcP/bPv6lP0VeUmF3guXZ674c68eHGrnw0AAC6Tfqor6nPqAujvY0ejYA4hl1/+Tla/+Zn+tPLO3XfzK90/IYe7sy+7Tr21gtKK75QKQPP8Vyv3bha6aMnWgLik5+8oZMfv6HE7PwO120+flSOMyctAfGpne+o7h9/Usa4K5WQkSVJcjQ2qPa1VXKaTcq65EbPvSe2vaJTO99VYr/ccHxMAADCqim/MNpb6PEIiGNYZp8kXTtxpJ59dZduOnhchYP6RntL3cppNru+cf/pdd0Z4Jo9NV1Dblve4bqHVv+X//sdzS1/to7Jdt8T6FlJ/Qdp8JzfBPdBAABAj0INcYy77vJzlJ6aqNUbyqO9lW7ndJgtf/oGpKb/NYcpm90IbmEjQWpZ28M0rX9Krff4BcSmZOffjgAAxCsC4hiXnpqom648V+9VHNb2PUejvZ3uFSBD63Q6JUfgDLF3nXF7bPaEgO/3e5b7mk/wLUfwzwIAAD0PAXEPcM2lhcrpm6JV68tdAWKcai2ZCJS19cnwOkxX5jcINsNop2TC9L/m8yynacpmBJmNBgAAPQ4BcQ+QnGjoO1eP0s79dXrnk6pob6fbtJu19cvwNgWfITYSApRhtP2sQDXMZIgBAIhfBMQ9xDe/MkSDctO1esMOmY74zBIHqiFur67YFmxdr5EQOMMsSd7rmu5n+d7bTA0xAABxjIC4hzAMu773rRJ9UX1Cm7Z+Ee3tdI9A2eB2s7bBlTGEXEPchWcBAICeh4C4B/namAKdO6Sf/vhyhRqbzI7f0MN4MrPedb2mf62v554ulUyYlj9dzwh8qM7pMCmZAAAgjhEQ9yA2m02zrjlPR+rOaMNb+6K9nbBzmk0tf3qXTLSTtQ2yjMFmD3CoLkDmud0aYkomAACIWwTEPcy4c3N1QVGu/t+ru3S6oanjN/Qk7nphS5Dqn8mVXIFy0FnbQH2IA2WDHYGfJbM56Gw0AADoeQiIe6BZ3zpPJ043au0/9kR7K2EVsA+wOzh2+AT/ZrMU5GCOgG3XQq0hDnYICAAA6HEIiHugc4b008VjCrT29T06eSZ+ssTOANPj2u8NHMpgDt8Ms39HCU8gTA0xAAC9CgFxD/Wdq4t1qqFZf3s9frLEIWVtHSF0fjASXNPuvIeaBKohbqdemZIJAADiFwFxDzViYN/WLPHpxmhvJywClUy03wotMah1PdldRwfBr+lfw+x6HxliAADiGQFxD/adq4t1uqFZa+IlSxwoSA3Qik1SaDXELfdZWqy1l412+JZnUEMMAEA8IyDuwUYM7KuvjS3Q317/TPWnen6WuLWGt/3A1f1zKKObfdfwdK/oIGvsdJiS00GGGACAOEZA3MNNnzRKDY3Nen7jp9HeSpc5A7Zda2dYRrBZW3cPYe/Mr6eGOMC1AKOjGd0MAED8IiDu4YblZ+qK8UNUtvkz1Rw/E+3tdE2gMob2BnN0KUMc5AG+lu/JEAMAEL8IiOPA9Emj5HA69aeXd0Z7K10SsMWaVys2S5eIkEY3G5b1Lc8KkA221hqbljUAAED8ISCOA3nZaZp88XC9suVzHTxyMtrb6bRAfYBbs7VOyemwXA96dHOIGeJAz2d0MwAA8YuAOE786zeLlJRg1zMvVkR7K53mDND2LGALNs9BtxBriL0zz4G6VwQaE+1+PhliAADiFgFxnMjKSNE1l4zQmx8eVFXNqWhvp3PaqeG1vO5wlzGEO0Pc1OZ91BADABC/CIjjSOmlhbLZbCrbvDfaW+kUZ4CsrTPQ9+4MbqgBcUf1wo5ArdjcwXdwQ0AAAEDPQ0AcR/r3S9Wl4wbp5Xf263RDU7S3E7L2MrTe34da19s6mCPIGmKzdcxz67MomQAAIF4REMeZqV8v1JmzzXr5nc+jvZXQBcrQthcQB1vG4L4vUCmGd39jR4AaY/d9lEwAABC3CIjjzLlDsjS6MEfr3tgj03R0/IYYErgPcIADbu4/gx3d7CmZCG50s/e97uCcDDEAAPGLgDgOTb2sUIfrzuifH1dFeyshaS1Z8A5cm/xeDzVD7C6t8Lzf6fC0cOuwo4UZ2gE+AADQ8xAQx6Gvji5Qfk6a1vxjd7S3EpKAo5sd/kMyQu8y4TOYI1D7NflmpjtZngEAAHocAuI4ZNhtunbiSFXsr1PF/tpobydorX2Gw3uozreGuK31rZlp3/IMAmIAAOIVAXGc+uZXh6pPSoLW/mNPtLcSvEA1xO0edAuyhtjTZSK4wR+u69Z7Gd0MAED8IiCOU6nJCZp00XC9tb1Sh2tPR3s7QWnNygYuY/C0ZXOEWEPc0kPYty7Yb/22puKF8CwAANDzEBDHsdJLCyVJ6zZ/FuWddCyog24+wzSC7vzgvs+3S4VkrSe2ZKZ9stWUTAAAELcIiONYblaqLh07sGcM6ggwMU7qqA9xcNPjfEc3d9RqzXKdQ3UAAMS9iP2W37t3rxYuXKhjx46pX79+Wrp0qYYPH26559FHH9WGDRtkt9uVmJio+fPna+LEiZKk+++/X2+//baSkpKUlpamn/zkJxozZowk6Xvf+54OHTqk9PR0SdLMmTN14403RuqjxbSpXx+p1z84qFe3fK5rLxsZ7e20KZiDbp7vQ+5D7O4yEUINsU+9MX2IAQCIXxELiBcvXqzp06dr6tSpWrt2rRYtWqTVq1db7hk7dqxuvvlmpaamqqKiQjNmzNDmzZuVkpKiyy67TP/5n/+pxMREbdq0SfPnz9err77qee9//dd/6YorrojUx+kxioZmqWR4tv72xme65tJCGXZbtLcUkCXr65PBtRmJcppNnuA15D7EbWSIXesGfpZvyQQZYgAA4ldESiZqampUXl6u0tJSSVJpaanKy8tVW2ttCTZx4kSlpqZKkoqLi+V0OnXs2DFJ0hVXXKHERNf/i/yCCy5QVVWVHI6eNYktWqZ+faSqa0/rnY8ro72VNnnqgpOS/TK4tqTklnt8D7oFW0PsbrvmzjC3PsvaxaLtZzG6GQCA+BWRgLiyslJ5eXkyWgIYwzA0YMAAVVa2HaCtWbNGQ4cOVX5+vt9rzzzzjC6//HLZ7a3bX7ZsmaZMmaJ77rlH1dXVAdesr6/XgQMHLF9Hjhzp4qeLfRedX6C87DStieUWbO7OEYkpktPhOmQnSWaz65q6MKnOZpPsRmuXCrP1WX4ZYp9nUUMMAED8i8nf8lu2bNHDDz+sJ5980u+19evXa926dXrmmWc815YtW6aCggKZpqnHHntMd999t/70pz/5vXfVqlVavny55VpRUZGWLFkS9s8QSwy7TVMmFur/W/uxdn1ep6KhWdHekh93AGpPTJYpubK5CXY5zWava9YgNZTODza70Vpy4fB61ul6rz2Ynmf5ZaOpIQYAIG5FJCAuKChQdXW1TNOUYRgyTVOHDx9WQUGB373btm3TvffeqxUrVqiwsNDy2iuvvKLf/va3Wrlypfr3729ZX3JlnmfOnKnly5fL4XBYMsiSNGvWLF1//fWWa42NjaqrqwvXR41ZV311qP74UoXW/mOP7v3ehGhvx4931tb9sy0hUU6H2XrNb1hGCAGxkeB/UC4xRU5H6397p9kse4rrYKY8z2rpzkFADABA3IpIyUROTo5KSkpUVlYmSSorK1NJSYmys7Mt93300UeaP3++HnnkEY0ePdry2qZNm/TQQw/piSee0ODBgz3Xm5ubdfToUc/P69evV1FRkV8wLEmZmZkaPHiw5Ss3NzecHzVmpaUk6ptfHaq3th/SsRNno70dP54MsbuG1+tQm923rrczZQxGgleG2Wx9ls9UPN9nyWFKRoKr7AIAAMSliJVMLFmyRAsXLtSKFSuUmZmppUuXSpLmzJmjO++8U2PGjNH999+vhoYGLVq0yPO+ZcuWqbi4WD/+8Y+VmJioO++80/PaypUrlZycrLlz56qpyZXJGzBggH7zm99E6mP1KFdfOEx/e/0zbXrvC11/+TnR3o6VuzQh0TcgbfZc83R+6EQZg82e4J9hTkwOUEPsH5DbGMoBAEBci9hv+pEjR+q5557zu/6HP/zB8/3zzz/f5vv/+c9/tvnaCy+80LXN9RLD8jM1aliWXtmyX9d9fWRMZT1ba4hd5RHyCl7tvkGy+8+QSyasAbXd6wCfzWaX09Hseb73mGcO1AEAEN+YVNfLXHXhMH1RfVIV+2KrbtqdkfVre2aasiUkSTZ7aw2wp+1aKAFx66E6T+eIlmfJq7Y44LVg27sBAIAeiYC4l5l4wSClJht6+Z390d6KhW+G2FIvbE9wZXg9ZQxNkmySLYS/vl41xK1dJlqf5XQ6JdNsveZoLdkIpZsFAADoeQiIe5nU5ARNvGCw3vjwoE43NEV7O63MtmqIW0oW7EZrqYTDlAwjpJIPmz1QlwmvemGnQ5LT6/lkiAEA6C0IiHuhqy4cqrONpt744GC0t+LRXg2xzTCsNcBmc8h1vdb3e9UQt6zXZobaQQ0xAADxjoC4FyoemqUheel67d0vor0VD6f3OGV5B6Su4Nc1WMMdJJuhd36wG54uFfKpV5bD9K8rdlhLNgAAQPwiIO6FbDabrhg/RDv21ary6Klob8fFa1KdZG17Jnu4M8Q+zzKbvQ7qJbYc4Gs9gEeGGACA+EZA3Etd/uUhstmk/30vNrLErV0m/A+62YwE16G4lqDVddAttLpeV5cJnxriJP+SCZvhPsDn7mjRzNhmAADiHAFxL5WblaoxI/tr03sHXIFnlPnVEJtm60E3d5eJljHKncoQ2/37ENssGWKv6Xd2gz7EAAD0IgTEvdgV44eosuZUTPQkdgboMmHJ2tp9SyZCzNp6lUzI3crNXRtsNluGfdi8W7SZzSENAAEAAD0PAXEv9rWxBUpKNLQpFsom3L2B3WUMXgfdZBiukgevwRydqSFuHf3c2rnCvZ4nILcbrgN83m3fOFQHAEBcIyDuxdJSEnXR+fl644ODamo2o7oX397A8s4Q2901xNYMbyhsljKIZk+tsPtn/xriLmSjAQBAj0JA3Mt9Y8IQnTzTpK07qqO6j9aA2H3QrckyotkyWMPR2S4TXofq7IbnYJ7TESD49tzbRA0xAABxjoC4l7vg3Fz1y0jWxq3RLZvwa4XmMP2ztl1ou2bNMJuWDLHM5tYOFj7Pck3FIyAGACCeERD3coZh19e/NFhbd1Sr/lRj9DbiMD39hqWWANkdwLqzuQ6vzg8+x5UqAAAgAElEQVShtl3zzTB7Hapzmqang4XNaKkh9i6ZoIYYAIC4RkAMXTF+sJpNpzZ/GL1Rzp6srzsb206GWJ3o/BAow9x6qK7ZWp7hM+aZkgkAAOIbATFUOKivhuVnRLVswntEs+Q+6OYdpHoN1uhE5wfX+71bqRmtQbXZGnzLc4CPwRwAAPQWBMTwjHLeub9Oh46cjMoevEc0u3/2PuhmMxK9sradOOhmd/UWdjqdnlZq7u4RTrPJc4jOt+dxZ7LRAACgZyEghiTp618eLJtN2vTegehswF2a4JUh9j7oJrvR2pfYYboyvCHwBNBOR2vJhLuG2GG2TqprCcq9O1LQdg0AgPhGQAxJUv9+qRp3Tq7+9/0vojLK2XPQzWZzZXMdPgfduthlwpJ5dli7TPj2IbaMbmYwBwAAcY+AGB6XXjBIVTWntfdQfcSf7R3kuqbS+Rx0s3vVEJudCFLddcDuMc12I+ABPrkn2DlayysomQAAIL4REMPjwtH5stukt7YfivizPQfdJM+kOO+DbpYMcScHc7if01oy4V+eYbMnegJyd5s3ukwAABDfCIjh0S8jWSUjcvTP7ZWRf7h3aYK7ZMG7jMFI8PzsmTQXAmv3imZPrbD3NdezDM8BvtZDfdQQAwAQzwiIYXHxmALtrzqhQ0cj223CWjLhGp3sKZmwG67OD+5Ddl2pIXa0rOtzgM/p8KkhdpiWtm8AACB+ERDD4qLzCyQp4lliS0Bsd5dMuA/VtbRIczo8I51Dztp6T8Bzl0x4DvC1ZqM9rd9Ma8kGAACIXwTEsMjLTlPhoL56O9JlEy2jm6XWqXLuDK3noJtaAlqnQzYjMaTlPVleR7OlBtlVL2zNBntGNzvIEAMA0BsQEMPP18YUqGJ/nWqOn4nYMy2t1NwH6Dw1vImtGd6msy33dLWGuLU8w1MvbLN79SH2zlBTQwwAQDwjIIafi8a4yibe+aQqYs/0LoOw2Q1XKzRPhtbwBLCOpoaWa53tMmFaB3u0ZIMtI5p9a5jJEAMAENcIiOFnaF6GBvbvE9GyCaejdUSyJWsrdw1xS0Db6MoQh1xDbPcqmfA7wNdsGdHsGd1MDTEAAL0CATH82Gw2XTymQNt3H9XJ042Reah7dLNaA2J3H2DvjhCOlpKJLvch9i6ZcB/U8+qDLDnlaGrs1LMAAIB09uxZLV68WFdffbWmTJmin/70p5KkvXv3atq0aZo0aZKmTZumffv2RXejIiBGGy4eUyDT4dSW8uqIPM+3hth7epylZ3BLyUSo0+OsAbFX8N2SDfYe0ewOjJ2dLM8AAADSL3/5SyUnJ+ull17SunXrdNddd0mSFi9erOnTp+ull17S9OnTtWjRoijvlIAYbTh3SJayM1P0z48jUzbhquF1B6lGa5cJr4NuknfJRIgBsWUqnddgD+/yDO+AXF7ZaAZzAAAQklOnTmnNmjW66667XG1OJfXv3181NTUqLy9XaWmpJKm0tFTl5eWqra2N5nZF6gsB2e02XXR+vl599ws1NDYrJal7/6r4jW42rQfdunqoztOlotlaBmGzG65aYYc1ayx5d7TgfyYAALhVVVXp+PHjlmuZmZnKzMz0/PzFF1+oX79+Wr58ud555x316dNHd911l1JSUpSXlyej5Xe+YRgaMGCAKisrlZ2dHdHP4Y0MMdp08ZgCNTaZ2rbzSPc/zCsgdXd+kCVr6y5j6GTbNXfWt9EaULfWEDe1Bt9t3AsAAKTZs2fryiuvtHytWrXKco9pmvriiy903nnn6YUXXtA999yjefPm6fTp01Hadfv4TY82nT+yv9JTE/X29kO6uKUVW3fxPegmM9BBN68gNdSSCZ8+xr4H+Lzrij0jnZs6V54BAEA8W7lypVJTUy3XvLPDklRQUKCEhARPacS4ceOUlZWllJQUVVdXyzRNGYYh0zR1+PBhFRR0b5zRETLEaFOCYddXR+drS3m1mk1Htz7LtxWaXzcIe9cOuvm+P2ANsXdAbnkWNcQAALjl5+dr8ODBli/fgDg7O1sXXnih3nzzTUmuzhI1NTUaPny4SkpKVFZWJkkqKytTSUlJVMslJAJidOCi8wt06kyTPtlT023PcDqd1tHN9oSWYRmmV29i16hmR2Pn2q55Dsr5vN89BMRSQ+xzLzXEAACE7v7779djjz2mKVOm6Ic//KGWLVumzMxMLVmyRP/zP/+jSZMm6X/+5390//33R3urlEygfV8qylWCYdfWimqNK8rtnoc4WgdwSJIMwzMYw7+MwSfDG6TWg3LukgufA3ze5Rlt3AsAAII3ZMgQPf30037XR44cqeeeey4KO2obGWK0KyU5QeePzNF7Fd3Xj9hpWkck29x9iL27TPi2QutkH+LW97syzpbRzT4H+PzuBQAAcYmAGB0aPypPX1SfVHVt95wM9R7RLHkNy7DUFXfxoFsbXSoso5t9gm/PvWSIAQCIawTE6ND4UQMkqfuyxA5XhliWMgbTlTm2+9b1du1QnW+XCu9nWeqKu/AsAADQsxAQo0ODB6RrQHaa3ttxuFvW980Qy2646oq9yxj8hmWEWkNsSDa7V9s1rwN8niEg1gN8vvcCAID4RECMDtlsNo0fNUAf7T6ipmYz7Os7fQ7Vedf7+l/rfNbWZiR43i+vdZ0Oa3mGwvAsAADQcxAQIygTRuWpodHUJ5+Fv/2aJ0Ps2we48azfYA5nYxeGZdiN1vd7H6AzrVPxPD2L3W3XGMwBAEBcIyBGUMae018Jhl3vVXRD2URLlwkFygb7DOYIV4bYUkPsMOV0mAE6WjRIdkM2m60znwoAAPQQpL4QFO/2a7dce35Y127NELfU6rrrhRsbWut3w9D5wWY35PQ5KNduR4vGBnoQAwAQo5qamvThhx+qoqJC9fX1yszM1KhRozRu3DglJobWMpWAGEEbPypPT/ztYx2uPa0B2WlhW9e/hri1D3CgumLvn0NhMxJkNpxy/eA1ulkOU06zqXUiXYAaZgAAEBvq6ur0+OOP669//av69u2rwsJC9enTR6dOndLTTz+t48eP6/rrr9ecOXOCHgnNb3sEbfyoAXrib672a//ytRFhW9edIZZvvXDT2dZaYZtdks0vwxsSI8Grc4RPvXBToyVr7Hl+anrozwEAAN1m+vTp+va3v621a9cqLy/P7/Xq6mqtW7dOM2bM0IYNG4Jak4AYQfO0X6s4HNaAWAEGc0iSnI7WumKbrfUAnNS5kgkjwbWm97OM1mf51hC7rvE/EQAAYsnatWuVlJTU5ut5eXm69dZbNXPmzKDX5FAdguZuv/bhp+Ftv+ZsGczhCT69sr/eNbzePYk7c9DNO7j1C4jlnzX2fR0AAERfW8FwfX29tm/frpqamnbvC4SAGCHpjvZr/qObAwekrZ0hOnfQzfI+nwN8lu8tQTKH6gAAiHUvvviirr32Wv3iF79QaWmpVq1aFdL7SX8hJN7t1y4oGhCWNd2H6uRbsiD5BKf+Wd2QBFzLP/hu6/kAACA2VFdXW+qHn3nmGZWVlSk9PV1Hjx7VlClTNGvWrKDXI0OMkKQkJ+j8Qlf7tbDxHd0cIEiV5JXV7WSG2B4o2xwgG9xygM/3PQAAIDbMmzdPTzzxhMyWWQYZGRl6/fXXtX//fr322mtBd5dwi1hAvHfvXk2bNk2TJk3StGnTtG/fPr97Hn30UV1zzTWaMmWKbrjhBr3xxhue186cOaO7775bV111lSZPnqxNmzYF9RrCb3zJAH1RfVKHa0+HZT1ny1/mgHW9AconOpshDlwvHCBIdh/g68KzAABA9/njH/8oh8Oh73znO9q6dat++tOf6uWXX9Ztt92mjRs36te//nVI60Xst/3ixYs1ffp0TZ06VWvXrtWiRYu0evVqyz1jx47VzTffrNTUVFVUVGjGjBnavHmzUlJS9MQTTyg9PV2vvPKK9u3bp+9+97t6+eWX1adPn3ZfQ/i5+hF/Erb2a/41xP6Bq+t7w+/1kHhnln0GfliutTzXaTZ3OhsNAAC6T0JCgubMmaNvfetbevDBB5Wenq5FixaFnBl2i0iGuKamRuXl5SotLZUklZaWqry8XLW1tZb7Jk6cqNTUVElScXGxnE6njh07Jkn6+9//rmnTpkmShg8frvPPP1+vv/56h68h/Lzbr4WFp4a47c4P3t93OUNss8tms3frswAAQPeqqalRbW2tHnzwQU2aNEk333yz/vjHP8rpdIa8VkQC4srKSuXl5cloycAZhqEBAwaosrKyzfesWbNGQ4cOVX5+viTp0KFDGjRokOf1goICVVVVdfiat/r6eh04cMDydeTIkbB8xt7EZrPpgnNz9fGeozIdof+l89WaIQ5QIxywC0TXuky0WZIRsMaYDDEAALFm5cqV+ta3vqWf//znuuaaa9TQ0KA///nPqqys1He+8x1t3749pPViMv21ZcsWPfzww3ryySfDuu6qVau0fPlyy7WioiItWbIkrM/pDcac018vv7Nfew8e1zlD+nVpLU8f4nZ6A1te72TJhM1omWvewfre93CoDgCA2PPYY49p3bp1GjBggKqqqnT77bfrW9/6ln70ox9p9+7d+tnPfuZXmtueiPy2LygoUHV1tUzTlGEYMk1Thw8fVkFBgd+927Zt07333qsVK1aosLDQc33gwIE6ePCgpzaksrJSF154YYeveZs1a5auv/56y7XGxkbV1dWF7bP2FmPP6S9J+mj3ka4HxO4McaCSCUsGt4sH3dzvD1RL7PW65R5KJgAAiDk5OTnatWuXsrKyVFFRof79+3teO+ecc0IKhqUIlUzk5OSopKREZWVlkqSysjKVlJT4FT5/9NFHmj9/vh555BGNHj3a8trkyZP17LPPSpL27dun7du3a+LEiR2+5i0zM1ODBw+2fOXm5ob98/YG2ZkpGpKXrg93H+36Yi1dJgJ2duiGGmJrVjjR7/VwPAsAAHSfX/3qV1q9erWmTp2qNWvWdPn/2x+x3/ZLlizRwoULtWLFCmVmZmrp0qWSpDlz5ujOO+/UmDFjdP/996uhoUGLFi3yvG/ZsmUqLi7WLbfcooULF+qqq66S3W7Xz372M6Wnp0tSu6+h+4w9J1evvfu5mk2HEozO/9vKaTZZDrpZMrVGgHriTvch9s8QtzkVzwiQTQYAADFh1KhRevzxx8O2XsQC4pEjR+q5557zu/6HP/zB8/3zzz/f5vvT0tL0yCOPhPwaus+Yc/pr/Zt79ennx1QyonNtTiTXpLq264b9M7hd7jIRTA2xPbFLzwIAAN3jtdde05VXXhm2+yQm1aELxoxsrSPuCqdpth2khnEwhwK9v42OFrZAfYoBAEDUbdiwQaWlpXrsscf0/vvvq66uznMmbNu2bXr88cdVWlqqv//970GvyW97dFpmnyQVDuyrj3Yf1bSriju/kOmTIfbu7BBocEYXRzd3NPjD+zpdJgAAiC2//vWvtXPnTj377LNasGCBDhw44JoyK2no0KG67LLL9Nvf/lbnnntu0Gvy2x5dMuac/trw1l41NplKSuxcoOp0mG12fuiO0c0dtXXzfi4lEwAAxJ7i4mLPmbMzZ86ovr5emZmZngFvoaJkAl0y9tz+amp2aMe+2o5vboPTN0Nss0uBJskFaMsWitYyiA4Gf0he5RUcqgMAIJalpqYqLy+v08GwRECMLho9Ikd2m/TJZzWdXsPpaPYrg2gvm9vpMoaAa7bRZcLT0YIMMQAA8Y6AGF3SJzVRwwf27VJA7FtDLKm1dtiSwQ2Q4Q1BhzXE4TzABwAAegwCYnTZ6MIcVeyvU1Ozo1Pvd5qmpb2a1EGGOBI1xATEAAD0GgTE6LLRI3LU2GRqz8FjnXq/02z2G4DReqgtwOjmzpYx2AN0qeimjhYAAKD7rVq1SrW1nT/H5EZAjC47r9A1lKO8s2UTjma/fr/tjVkOa4bYZvMEveE8wAcAALrfP//5T1155ZX6/ve/rw0bNqixsbFT6xAQo8uyMlI0KLePPu5kQOzqMuGTifVkc8PYh7iNMoiAI509B/jIEAMAEKt+//vfa+PGjbrsssu0atUqXXLJJfrJT36id999N6R1CIgRFueNyNGOvbVyOJwhv9fpMP2D1O6oIW6jc4RnPUsvZDLEAAD0BFlZWfrud7+rZ599Vk8//bS2b9+umTNn6hvf+IZ+//vf69SpUx2uEXRA/NRTT2nHjh2SpA8++ECXX365vvGNb2jbtm2d/wSIG+ePzNHJM036vPpEyO911RD7Zm39M7RdHpZh+Nclu64nSPYEz5Qby3MJiAEAiHlvv/22fvzjH2vmzJnq37+/li5dqmXLlmnHjh2aM2dOh+8P+rf9ypUr9e1vf1uSa2Te7Nmz1adPHz344IN67rnnOv8JEBfOG5EjydWPeHhBZkjvdZrB1hCHv8uE5Aq+g8lQAwCA2LJ06VKtX79eGRkZmjp1qtatW6e8vDzP6+PGjdNXv/rVDtcJ+rf9iRMnlJGRoZMnT2rnzp1auXKlDMPQ0qVLO/cJEFfystOU0zdFn3xWo2suGRHamx3+XSY89cLeAak9QGlDCALVCkuujLFv1jhQhhoAAMSWs2fPavny5Ro7dmzA1xMTE/WXv/ylw3WCDogLCgr0/vvva/fu3ZowYYIMw9DJkydlMNoWcnVrGD0iRx9/ViOn02kpP+iI7+hmqbsyxC29jgM8q63BIGSIAQCIXd///veVkpJiuXb8+HE1NDR4MsUjR47scJ2ga4gXLFigO++8U//3//5f3X777ZKkTZs2acyYMaHsG3HsvMIc1dY3qLr2dEjvc5qm/0E398+21r+i7ixup7O2bfUxthsBRkcH6HIBAABiyu23366qqirLtaqqKt1xxx0hrRP0b/uvf/3r2rx5s+Xa5MmTNXny5JAeiPh13ghXP+Id+2qVn9Mn+Dc62sgQG9aDbq1ZW+tUu2C1WUNsJFJDDABAD7R3714VFxdbrhUXF+uzzz4LaZ2gM8S7d+/W0aNHJUmnTp3SI488oscee0zNzc0hPRDxa2h+plKTE7RjX2gTY1yjm/1LFgIdfnO/1hltB8RtP4uAGACA2JWTk6P9+/dbru3fv1/9+vULaZ2gA+If/vCHqq+vl+Q60ffuu+/qgw8+0KJFi0J6IOKXYbepeFiWduwNNSD2H8xhsxv+rdi6OCzD84xAQ0B8SyO6Wp4BAAC63Y033qh58+Zp06ZN2r17tzZu3Kg777xTN910U0jrBJ3+OnjwoAoLC+V0OvXKK69o/fr1SklJ0ZVXXhny5nsr89Rx2ZJSZE9M9lxzNDeqsfIzOZ2OsDwjKWeQjD59A77mOHtGZ6v3huU5bbkwp16v7v1cx3bnKDkpuL9ebR2qC3sZgyegDv5Z9CEGACB2zZ07VwkJCVq6dKmqqqqUn5+vm266Sf/+7/8e0jpB/7ZPTk7WyZMntWfPHhUUFCg7O1vNzc06e/ZsyJvvrQ49/VP1GXWRsi+f7rl2/O21qnv9z2F7RsrwMRr43SUBX6t5bZVObHslbM8K5DxJ52VItc++FNL77MnWmmOjT1/Z06z9jI2Wn4200Poce56RlCYZCX7/YDD69PULiI20vpLNLiM1o1PPAgAA3c9ut+vWW2/Vrbfe2qV1gg6IS0tLNWvWLJ06dUozZsyQJJWXl2vw4MFd2kBv4jh7Ruap45ZrZsNJ2RJTlH/TfV1ev/b1P8tx5mTbzz9zUgl9c5V7ze1dflZbGhqb9Yuntujy8UN05YQhwb3JblfyoCLLpazLpqnvRVMt15IGDNOQ25YrMbugU3szUtM15D8eUUJmf8v1/pPnSk7ryOnUwgs05Lb/VkJmTqeeBQAAIqOxsVF79+5VXV2dnF6/zy+++OKg1wg6IP7P//xPbd68WQkJCbroooskuXrP/vjHPw5hy72bzTBcU9m8mc2yJSYpdUTghtKhSHj/JTUePdDm606zWfbkPmF5VltSJTXmHtc7tckq7cJz7Empsiel+l3vbDDseX+/PL9rRmq63zWbzabErPwuPQsAAHSvrVu36u6771ZjY6NOnjyp9PR0nTp1Svn5+XrttdeCXiekAslLL71Uhw4d0rZt25SXl0cP4hDZjAQ5HdaA2Gk2+/fF7SwjQXKYbb7sDNDerDuMGp6t/33vgEyHU4Y9+AEdAAAAoXjooYd06623avbs2frKV76iLVu2aPny5UpN9U+qtSfoLhOHDx/WjBkzdPXVV2vevHm6+uqrNWPGDFVXV4e8+V7Lbkg+GWJXkBqeTgY2e4J/Btqb2ezfYaEbnDc8W2fONuvzqvpufxYAAOi99u3bp5kzZ1quzZ07VytXrgxpnaAD4iVLlmjUqFHasmWLNm/erC1btmjUqFFavHhxSA/szWxGomsqm7dAPXg7vX6C//penI7wPas9o4a7BnSUh9h+DQAAIBQZGRk6edJ1fio3N1e7d+9WfX29Tp8ObWpu0AHxe++9p/vuu09paWmSpLS0NC1YsEDbtm0L6YG9mc3uX0PsNJv9xgZ3aX1H2xnisJZntCMvO03Zmckh9yMGAAAIxVVXXaV//OMfklw9iWfOnKkbbrhBkyZNCmmdoKOjvn37as+ePRo1apTn2meffabMzM61wOqVjAQpUA1xJ0cRB1y/nZKJgBPhuoHNZlPxsGzt/JyAGAAAdJ+f/OQnnu9vueUWjRs3TqdOndLEiRNDWifo6MhdsPztb39bAwcO1KFDh/TCCy/orrvuCumBvVmgLhNOR3PYpqEF7GLhzdEUtmx0R0YNy9Lb2yt1/ORZ9U1P7vgNAAAAITBNU5MmTdKGDRuUlJQkSZowYUKn1gq6ZOJf//Vf9dvf/lZ1dXXatGmT6urq9Otf/1pVVVWdenBv5Krx9W+7Fq5paB0dqgs0Ea67FA3NkiTt+rwuIs8DAAC9i2EYMgwjLEPiQoqOLr74YkuT48bGRt18881kiYNksyfI6dMWzXXQLUxZWyNBcjrkdDpks/n/WydSJROSdM7gfrLbbdq5v05fOY9+vgAAIPxmzpypu+++W9///veVn58vm6213euQIUEOCFOIAXEgTp8JX2hHgAyxa1hGaL3y2uIJdk1TSggUEDdLEThUJ0kpyQkalp+hnWSIAQBAN3nggQckSW+++ablus1m044dO4Jep8vRkXckjvbZ7EaAQ3Vm2Do/uGuRnY5m2RTgoF44s9FBKB6WrTe2HZDD4ZSdAR0AACDMKioqwrJOh5HY22+/3eZrTU1NYdlEbxGwhtjRFL4a4pZ12qojjmQNsSQVD+2nF9/ep4NHTmpIXkbEngsAABCKDqMj73YWgRQUFIRtM/Eu0OAMV4Y4TFlbuzsgDjycI5wdLYLhPli3c38dATEAAAi76dOnt1mt8MwzzwS9TocB8caNG4PfFdpnb6sPcXgzxL7P8H5WuLLRwRg8IENpKQna9XmdvvnVoRF7LgAA6B1uuukmy89HjhzR888/rylTpoS0TuSiIwTOEIdxnHJ7JRNOpzOsY6KDYbfbVDQki4N1AACgW1x//fV+1yZNmqQf//jHuuOOO4JeJ+g+xOi6gIMzwtj5wX1gLmANsdMhyRmR0c3eioZlaV9lvRoa2xkYAgAAECZ5eXnauXNnSO8hQxxBNiNBTt+SCUcYD7p5Sib8a4jdQXIkM8SSVDw0Sw6HU3sOHNfowpyIPhsAAMS3v/zlL5afGxoa9PLLL+uCCy4IaR0C4kiyG5LZLKfT6SkAd9UQh2l0s72dLhPuaxFsuya1Hqyr2FdLQAwAAMJq7dq1lp/T0tL0pS99SbNnzw5pHQLiCLIZLb2BnQ7J1lreEPYa4kAZ4pZrkS6Z6JeRrIH9+2jHvtqIPhcAAMS/p59+OizrUEMcQZ7BGS3ZWvdBN4WpFVrr+v79oaNVMiFJ543IUfneWjkcTDUEAADhs2bNGr/hHBUVFVqzZk1I6xAQR5JntHJL+YL7oJsRYKpcl9YPlCGOZkCcrROnG3XwyMmIPxsAAMSvhx9+2G8mRn5+vh5++OGQ1iEgjiC/DLE7axuuDHF7k+rc1yI4mMPtvJba4fK9NRF/NgAAiF8nT55Uenq65VpGRobq6+tDWoeAOIL8anw9B93CVEPczqG6aJZMDOzfR/3Sk1W+lzpiAAAQPiNHjtRLL71kufbKK69o5MiRIa3DoboI8s3gth50C1eG2LCs6809ECTSh+okyWazqWRENhliAAAQVvfcc4/mzp2rv//97xoyZIg+//xzvf3223r88cdDWocMcST5BsThztr61ih7iWaGWHIdrKuqOa2a42ei8nwAABB/JkyYoLKyMo0ZM0ZnzpzR2LFjVVZWpvHjx4e0DhniCPJkgh3uDHF4g1RPjbIjQA2xO2sc4T7EbueNyJYk7dhXq0vHDYrKHgAAQHxpbGxUbm6u5s6d67nW1NSkxsZGJSUlBb0OGeII8jv0Fu4a4pZuFYFriJsse4i0wkF9lZxk6JPPKJsAAADh8e///u/65JNPLNc++eQT3XLLLSGtQ0AcQa2H3kzLn+GqIZani0XsDOZwSzDsKh6axcE6AAAQNrt27dK4ceMs18aOHevXm7gjBMSR5M7OOrqnhtjms743Z5iz0Z1x3ogc7Tt0XKcb/AeHAAAAhCojI0NHjx61XDt69KhSU1NDWoeAOILa7DIR7tHNAfsQh/dZnVEyIlsOp7Tr87qo7QEAAMSPq6++Wj/60Y+0a9cunTlzRjt37tR9992nf/mXfwlpnYgFxHv37tW0adM0adIkTZs2Tfv27fO7Z/Pmzbrhhht0/vnna+nSpZbXFixYoKlTp3q+Ro0apddee02S9N///d+6+OKLPa/df//9kfhIIfO0RfOtIQ5TGYPf+l48B/iiMJjDrXholmw2aed+AmIAANB18+fP18iRI3XTTTfpy1/+sqZNm6YRI0bohz/8YUjrRCxduHjxYk2fPl1Tp07V2rVrtWjRIq1evdpyzwwYYcoAACAASURBVJAhQ/SLX/xCL774ohobGy2vLVu2zPN9RUWFZs2apYkTJ3quXXfddbrvvvu690N0kaeG2OGuIQ7zQTef9b1Fu+2aJPVJTdTgARmqICAGAABhkJycrMWLF2vRokWqq6tTVlaWbDabHA5HSOtEJENcU1Oj8vJylZaWSpJKS0tVXl6u2lrrAathw4appKRECQntB21/+ctfNGXKlJDaacQEnz7BrSUTYRrMYbO5Dta104c4Wm3X3EYNy9LO/bVyOp1R3QcAAIgfNptN2dnZ2rVrl5YuXarLLrsspPdHJF1YWVmpvLw8GS3BmGEYGjBggCorK5WdnR3SWo2NjVq3bp1Wrlxpub5+/Xpt3rxZubm5mjdvnr70pS/5vbe+vt5vtrVvJro7+Y5u9mRtw9j5wWYktNuH2GZPDNuzOmPU8Gy9suVzHTp6SoNy0zt+AwAAQDtqa2u1bt06rVmzRhUVFRo/frx+8pOfhLRGjxvM8eqrr2rgwIEqKSnxXPu3f/s3/cd//IcSExP15ptv6vbbb9eGDRuUlZVlee+qVau0fPlyy7WioiItWbIkEltvHZzRUirhPugWzs4PNrvRRh9id8lEdDPExcNc/00q9tUSEAMAgE5pamrSxo0b9de//lWbN2/W0KFDdc011+jQoUN6+OGHlZOTE9J6EQmICwoKVF1dLdM0ZRiGTNPU4cOHVVBQEPJazz//vG688UbLtdzcXM/3l1xyiQoKCvTpp5/qq1/9quW+WbNm6frrr7dca2xsVF1dZGpaW7tAtGSIwzypTpIruA7Yhzj6NcSSNGRAhtJSElSxv05XfmVoVPcCAAB6pksuuUQ2m0033HCD5s2bp9GjR0uS/vSnP3VqvYjUEOfk5KikpERlZWWSpLKyMpWUlIRcLlFVVaX33ntPU6ZMsVyvrq72fL9jxw4dPHhQI0aM8Ht/ZmamBg8ebPnyDqa7nd2nhtgMf+cHmz2hjbZr7o4W0c0Q2+02FQ111REDAAB0RnFxsU6cOKEPP/xQ27dv1/Hjx7u0XsTShUuWLNHChQu1YsUKZWZmetqqzZkzR3feeafGjBmjrVu36oc//KFOnjwpp9Op9evX6xe/+IWnm8Rf//pXXXHFFerbt69l7d/85jf65JNPZLfblZiYqGXLlkU20A1SmzXE4SyZMBLa6DIR/T7EbqOGZev/vbpTpxualJYS3ZpmAADQ8zz99NM6ePCg1qxZoyeffFI///nPdemll+r06dNqbg6QGOxAxKKjkSNH6rnnnvO7/oc//MHz/YQJE/T666+3ucZtt90W8Lpvz+JY5dcn2B24hvVQndFao+zF9UxbVPsQu40aniWHU/r0i2Mad27s/cMFAADEvkGDBukHP/iBfvCDH2jr1q1au3at7Ha7rr32Wt14441asGBB0GsxqS6Sunl0s/sZbQ3miIXssOQa0CExoAMAAITHhAkT9MADD+jNN9/UT3/6U+3atSuk98dGhNRLtHaZcPchDn/nB5s9oTXz7M1sjnoPYrf0tCQNHpCuCuqIAQBAGCUnJ6u0tNQz+yJYZIgjyGY3JJvdU8/rOegW7hriNtquxUqGWHLVEe/cX8eADgAAEHUExBFmsxuezHB3dJmQ3Qh8qM5hhnUASFcVD8tS/alGVdacivZWAABAL0dAHGleGVynaUo2e3jbrhkJbY9ujqUM8XBXy72KfdQRAwCA6CIgjjDvgNXpaA571wdXl4nAo5tjocOE25C8DKUmJ1BHDAAAoo6AOMIso5W7IWvb1mAOp9kUUzXEht2moqH96DQBAECcW758uYqLiz2dHz744ANde+21mjRpkm6++WbV1NREeYcExBHnPTijWw66tTOYI5YCYsl1sG5fZb0azobeQBsAAMS+Tz75RB988IEGDRokSXI4HLr33nu1aNEivfTSS5owYYJ+9atfRXmXBMSRZymZCH8ZQ7s1xDF0qE5yHaxzOJz69Itj0d4KAAAIUlVVlQ4cOGD5qq+v97uvsbFRP/vZz7RkyRLPtY8//ljJycmaMGGCJOnf/u3f9OKLL0Zq622KrQipF3BliFu7TIQ7a+u9voUj9jLExcNaDtbtr9WYc/pHeTcAACAYs2fP1tGjRy3X7rjjDs2bN89y7eGHH9a1116rwYMHe65VVlZq4MCBnp+zs7PlcDh07Ngx9evXr3s33o7YipB6AUsNscPshhriwIfqXMF37Byqk6TMPkkalNuHOmIAAHqQlStXKjU11XItMzPT8vO2bdv08ccf65577onk1jqNgDjCXIMz3DXE3XDQzQg8qc7paJY9MTm8zwqD4mHZeq+iWk6nUzabLdrbAQAAHcjPz1dGRka797z77rvas2ePrrzySkmuMotbbrlF3/ve93To0CHPfbW1tbLb7VHNDkvUEEeePUFytPYhDnsNcRtdJmQ2SzHUds1t1LAsHT/ZqKqa09HeCgAACJO5c+dq8+bN2rhxozZu3Kj8/Hw98cQTuvXWW9XQ0KCtW7dKkv785z9r8uTJUd4tGeKIs2aIu6mG2OwZXSak1gEdO/fXqqB/nyjvBgAAdCe73a5ly5Zp8eLFOnv2rAYNGqRf/vKX0d4WAXGk2QxDjsazrh8cZtg7P7Q1mMM1BCT2/nMPbRnQ8cneWl0+fki0twMAALrBxo0bPd9/+ctf1rp166K4G3+UTESapWSiG/oQt6zvdDotl7vlWWFgGHadPzJHH356JNpbAQAAvRQBcYR5Z3C7o/ODJ+j1PVhnNksx1mXCbdy5uao8ekqH66gjBgAAkUdAHGHek+rkCP+wDHdA7Fs24TRjs2RCcgXEkvQRWWIAABAFBMQR5t0Folt6A7d0kvAd3+yMwcEcbsPyM9QvPVkf7Dra8c0AAABhRkAcab6jm7uhy4Qkv/HNTrM57ENAwsVms2nsOf310e4jfrXPAAAA3Y2AOMK8J8l1RxmDu6+xX6cJR/h7HofTuKJc1Z04q8+rT0R7KwAAoJchII4wVw1xS7DaDVlbTw2xI0ANcYxmiKXWOmK6TQAAgEgjII4wv8Ec4c7aeg7VtdYQOx2m5HTE7KE6ScrLTlN+Tpo++pQ6YgAAEFkExJEWhRpizwG7GM4QS64s8fY9R2WajmhvBQAA9CIExBFms7e2XeuW0c32ACUTLdniWC6ZkKRx5+TqdEOzdh84Fu2tAACAXoSAOMJshiE5Ha6g2GF2Qw2x/6E69/dhb/EWZmPP7S9J+pCyCQAAEEEExBHWeujN7J5hGQEm1bmzxbFcQyxJfdOTNbwgk4N1AAAgogiII81d0tDc5DroFu7RzfYAk+rc38d4hlhy1RHv2Fers01mxzcDAACEAQFxhHkyxI0Nlp/Dvn6AQ3WxXkMsSRcU5aqp2aEde2uivRUAANBLEBBHmLvNmqPprOtCBAZzeGqIY7xkQpJGF+bIsNuoIwYAABFDQBxp7gxuU/dkiAPWEHsO1cV+QJyanKCioVnUEQMAgIghII4wTxeIlgxxuAdzBCqZ8NQQx/DoZm/j/v/27jy6rfrO//9Tu1fZlrwvceIkTpyNBAJhaWAIUDL9BgL0y4RfCqWl0G83OgOHQqbTkwCFtqE9mZYSSqcbpcOhLYVCEyAspUCAsoQEsjir4yyO5X1fZV3d3x+yRZx9saRYej3OycG6kq8+V7IuL7/9vp/PxByqatro6h2I9VBEREQkASgQR5nF5gAgONhDHLGlm4f1EI+eCjHAWROzCZqwaZfaJkRERCTyFIijLNzjO1QhHvFZJgb3Hzy4h3j0XFQHMKnUg8tpY6PaJkRERCQKFIijbTCUBsM9xI6I7J8jLswxOgKxw25l6jgv67c3YJpmrIcjIiIicU6BOMrCFVx/hHqIrZ8u/BEWHF09xABzZxZR29TN5ipNvyYiIiKRpUAcZZZwhXhw2rVo9BCPsgoxwNxZRaSnOFn9zu5YD0VERETinAJxlB22MMdIV22HZrEwDl66ebCHeBTMQzzE5bDx2TljeG9zHY2tvbEejoiIiMQxBeJosx7aQxyZhTmO1EM80tXoSPvXC8eBabLmvT2xHoqIiIjEMQXiKAtXiMOzTIzsRXUWqw0s1mGzTDAKWyYA8jwpnDsln5ff24N/wDj+N4iIiIicAgXiKBuaZm2oQhyJC90sNvtRlm4ePRfVDVnwmXG0d/l5+5PaWA9FRERE4pQCcZR92kPcP+z2iLLZh80yEe4hHmUVYgitWpfrSeHdjQrEIiIiEhkKxNF2WA9xBCrEVltc9BADWCwWzpqQzeaqJoyg5iQWERGRkadAHGWH9xCPfEg9tGWCUVwhBpgxIZvuvgDVB9pjPRQRERGJQwrEUTbUxxscbJkgAlOhWay2Q5ZuHr09xADTJ2QDsHFXU4xHIiIiIvFIgTjKPq0QR2baNSDUGnHwPMTG6Fup7mDejGSKclLZVKVALCIiIiNPgTjaDlmpLhJV28NbJgJgtWOxWEb8uaJlxoQctuxuxjCCsR6KiIiIxBkF4iiLRoXYYrUf0jJhjNr+4SHTJ2TT2x9gV01brIciIiIicUaBONosoZd8aNq1SMz8YLHZDpuHOBKzWUTT9PHqIxYREZHIUCCOMovFEpon2BgI3Y5YD/GhgXh0V4gz012MyU9nkwKxiIiIjDAF4hiwHDyzhGXk34JQy8RBSx0HA6P2grqDzRifTeWeFgYC6iMWERGRkaNAHAPhaq0tMhe6HWnp5tFeIYZQH3G/32Dn/tZYD0VERETiSNQCcXV1NYsWLeLKK69k0aJF7Nmz57DHvP3221x33XVMmzaN5cuXD7vv5z//ORdccAELFy5k4cKF3HfffeH7ent7+Y//+A+uuOIK5s+fzz/+8Y9IH85pGerntURgDmIArDZMY/jSzRF7riiaNj4biwW1TYiIiMiIilpKWrZsGYsXL2bhwoU8//zzLF26lCeeeGLYY0pKSnjwwQdZs2YNfr//sH1cc8013HPPPYdt/81vfkNaWhqvvvoqe/bs4Qtf+AKvvPIKqampETue0zIYTiNVtbXY7BAcCN82jcCoXLb5UO5UJ2ML3Gzc1cSiKybFejgiIiISJ6JSIW5ubqayspIFCxYAsGDBAiorK2lpaRn2uNLSUioqKrDbTy68vfTSSyxatAiAsWPHMm3aNN56662RGXwEhCvEEZr5ITTLxEE9xEZg1K5Sd6jpE7LZuqcF/4Bx/AeLiIiInICoBGKfz0deXh62wQBos9nIzc3F5/Od1H5eeOEFrrrqKm655RY2bNgQ3l5bW0tRUVH4dkFBAXV1dYd9f0dHBzU1NcP+NTY2nuJRnbpwZThCbQwWm2N4D3EwPnqIIXRh3UAgyPa9I9dH3NU7QEf34X+REBERkcQwalLSDTfcwNe+9jUcDgfvvPMO3/jGN3jxxRfJyso64X38/ve/55FHHhm2rby8nHvvvXeER3tsQ+E0YiH1kFkm4mFhjiFTx2djtYTmI54+IXtE9vnwnzbQ3TvAg1+/aET2JyIiIqNLVFJSQUEB9fX1GIaBzWbDMAwaGhooKCg44X3k5OSEv77ooosoKChg586dnHfeeRQWFnLgwAE8Hg8QqkjPmTPnsH3cfPPNXHvttcO2+f1+WlujPGtBuIc4ci0Th81DbHdE5LmiLS3ZQVlRBpuqRu7Cuj21HfT6A8O2dfX4efHdPXx+3kRs1tG75LWIiIgcX1RaJrxeLxUVFaxevRqA1atXU1FREQ6wJ6K+vj789datWzlw4ADjxo0DYP78+fzpT38CYM+ePWzatIm5c+cetg+3201xcfGwfwcH7WiJdIXYYhu+dDNxMsvEkBkTcti+t4W+Q0LsqTCMIA2tPbR19tN/UF/yOxtr+cNLW6k+0H7azyEiIiJntqilpHvvvZclS5bw6KOP4na7w9Oq3XbbbXz7299m+vTprFu3jjvvvJOuri5M0+SFF17gwQcfZO7cuaxYsYItW7ZgtVpxOBw89NBD4TD7la98hSVLlnDFFVdgtVq5//77SUtLi9ahnbTwBW6R6iG2xt/SzQebPiGbZ9/YxbY9Lcwszz2tfTW192EETQAaWnooyUsHwNfUDUBLZ9/pDVZERETOeFELxOPHj+fpp58+bPuvfvWr8NezZ88+6uwQh85LfLCUlBQefvjh0x9klES8h9hmh2HzEMfPRXUAU8Z5sFotbNzVdNqBuK65O/x1Q+ungbiupQeA1g4FYhERkXinlepiYaiHOEJToVmsw1eqw4iPpZuHpCQ5mFiSOSILdNQ194S/bmjpOWj7YIW4o/+0n0NERETObArEMRCNHmIwwzNNhGaZiI+L6obMmJDNzv1t9PafXh9xfUs3NqsFu81CQ2tvePtQUFaFWEREJP4pEMdAuJ83YvMQh/Y/VCU242hhjiHTx2djBE0qq5tPaz91zT3kZqWQk5USrhB39fjp7g2t9NeiQCwiIhL3FIhjIRo9xABDFeI46yEGqBjnwW6znHbbRF1zN3neFHKzkqlvDQVi32C7hNUCrbqoTkREJO4pEMeAJdLzEA/uP9xHbAQgjmaZAEhy2ikfk8XG0w7EPeR7U8k9qEI81C4xtjBDPcQiIiIJQIE4BsLV2oj2EB/SMhFnFWIITb9WVdMWbm84HtM0+dvaqnDVt7t3gM4eP/meFPI8KbR29uMfMMIX1E0Z66Gtsw/TNCN2DCIiIhJ7CsQxMNTPG7HFMgb3P7Q4hxlnC3MMmTEhm6AJW06wj3hvXSe/em4zq9buBqB+sCKc700l15MCQGNbL3XNPWSmuSjITiVgmHR0+yNzACIiInJGUCCOhajMMgEYgVB1M2hErBodS5NLPTjsVjbuPLG2iaqaNgDWb28APp1aLdRDHArE9S091DV3k+9NIcudBEBrp9omRERE4pkCcQwM9Q5HbB7icMuEAYNV4nibZQLA6bAxudRzwhfWVQ0uw1xV005bZ//wCvFgIG4IB+JUPIOBWDNNiIiIxDcF4hgIty9EqkJ80EV1Q33E8dhDDDBjYjbVvnY6e47f1rD7QDvpKaH5mDfsaKCuuZu0ZAdpyQ48GUnYrBYONHbR1NZLnjeFLLcL0FzEIiIi8U6BOAaGFsmI1CwTQzNKmEEjVCUmfgPx9PHZmCZsrjp2lTgYNNl9oI3PzCwiI83J+m0N1LX0kO8NVYZtVgs5Wcls3t1M0IQCbyqedFWIRUREEoECcSzYIntR3bAe4qGp1+LwojqA8jFZuJy24/YR+5q76e03mFicyazyXDbsaMDX1E2eNzX8mNysFHYP9hnne1NJctlJSbIP6yHuHzAIBjXrhIiISDxRII6BT5dujsxyyuEe4mAgvDhHvFaIHXYrMyfm8O6mWoxjBNXdNaH+4bKiDM6enEt7lx9fUzf5g7NLQCgQD+1iqHKclZ5ES3uoQmwETb72w9d47s2qCB2NiIiIxIICcQyEL3CLwsIcphGaozdi7RlngEvOLqalo/+YbRNVB9qw2yyMyXczqzw3vD3/4ArxYDh22q1kDbZLeNxJ4ZaJfXUdNLX3scfXHonDEBERkRhRII4BS7SWbjYMzDivEAOcNzWfZJeNN9fXHPUxVQfaKS1w47BbyUx3Mb44A/i0EgyQ50kO/debgtVqASDL7Qov5LFtTwugnmIREZF4o0AcC0NLN0dq2rWhhTmMQGjZ5oOeMx65HDYumF7Iuxtr8Q8Y4e39g1+bpklVTTtlhRnh+86eFKoS5x/SQ3zotlCFuB/TNNm2txVQIBYREYk3CsQxEOkK8cE9xPE+y8SQS2YV090X4KNt9QSDJv/91Hq+eO8a9vg6aGzrpbPHz/jizPDjF148nm9dP5O8Q3qIYXggzkpPwj9g0NMXYOtQhbhdgVhERCSexHdKOkOF+3kjNsvEpxViM44X5jjYWROzyUxz8cb6GjbubOL1dftxOmz84PEPWHR5OUC4TQIgI83FleeXDtuHNzOZmeU5zJ6cF97mGZyLeI+vA19TN+kpTjp7/PT1B0hy6eMjIiISD1QhjoVo9RAHjbhfmGOIzWblMzMLeXejj9XvVHPNJeO5/6sX0NDSw6PPbMRqgbEF7mPvw2rh+//vQs6e/OlFd0PLN7+32QfA+dPyAWjpVJVYREQkXigQx8DQLBCRmvnh4Fkmwj3EcTzLxJB5s0uwWOCK88Zwy1VTmVrm5Zarp+IfMCjKTSfJefK/FAwt3/zuJh82q4U5UwcDsdomRERE4kZ8lw3PUOFqbaR7iIct3RyZOY/PJBNLsvjNf30Wb0YSFktoloirPlNGS3sfOZnJp7TPoQpxQ0sPE0oyKcgO9RfrwjoREZH4oUAcA0P9vBFbqW5ololg4NNp1+K8h3hITtbw4GuxWPjSgqmnvL/UJDtOuxV/IMjk0iw8GaH9KxCLiIjEDwXiWIhSD3H7P5/79MK9BAnEI81isZDlTqK+pYeKsZ5QQHbYaFbLhIiISNxQII4BV+EEMs6/mqSSyRHZv9XhIvPC6xhoCV0IZk1Ow5ldFJHnSgSewUA8udSDxWLBe9DqdQBtnf20dvYx7qB5jkVERGT0UCCOAavdifeymyP6HJ5LvxDR/SeSnKxkGluTwu0YnozhgfgPL23l/S0+/ve+f43VEEVEROQ0KBCLHMctV02lq3cgfKGex51EVU1b+P5dNW20d/np7Q+QrLmJRURERh1NuyZyHN6MZErzP53D2DPYMmGaJgEjyL66TgCa2npjNUQRERE5DQrEIifJ406iz2/Q2x/gQGMXASMIQHO7ArGIiMhopEAscpI8GaG5iZvb+6iu7Qhvb2rTzBMiIiKjkQKxyEnyDi7W0dLRx57aduy2UG9xkyrEIiIio5ICschJGqoQt3SEKsRj8txkpDnVQywiIjJK6ZJ4kZOUle4CoKW9j+radmZNysViRYt1iIiIjFIKxCInKSXJQbLLzu7adlo7+xlX6Ka7d4D6lp5YD01EREROgVomRE6Bx53Ehu2NAIwryMCbkaSWCRERkVFKgVjkFHgzkujs8QMwttBNdmYyXb0D9PUHYjwyEREROVkKxCKnwDM404THnURGmgtvRmhZ5+YO9RGLiIiMNgrEIqcgazAQjysMrWCXkxkKxGqbEBERGX0UiEVOgScciDMA8GYOLdahQCwiIjLaKBCLnALvIRXioZaJRlWIRURERh0FYpFTMKXMw9mTczlrYg4ALoeN9BQnzVq+WUREZNRRIBY5Bd6MZO677QIy0lzhbTmZyeHlm5vaernjv9/gQGNXrIYoIiIiJ0iBWGSEeDOTwhXi19ftZ1dNOxt3NsZ4VCIiInI8CsQiIyQ7IzncQ7z24wMA7G9QhVhERORMp0AsMkK8maHFOqpq2tjj6wCgpr4zxqMSERGR47HHegAi8WJoLuLn3qzCYoHp47NVIRYRkYTU2trK3Xffzb59+3A6nZSWlnL//ffj8Xj4+OOPWbp0Kf39/RQVFfHjH/8Yr9cb0/GqQiwyQoamXlv78QGmlnmZMTGbprZeerWcs4iIJBiLxcKtt97Kyy+/zKpVqygpKeEnP/kJwWCQ73znOyxdupSXX36Z2bNn85Of/CTWw1UgFhkp2YMVYiNocvHMIopz0wE004SIiCSczMxM5syZE749c+ZMamtr2bx5My6Xi9mzZwNwww03sGbNmlgNM0wtEyIjxJsRWqzDarVw4YxC2rv6gVAf8YTiTAAe+O37FOem8aUFU2M2ThERkdNRV1dHe3v7sG1utxu3233ExweDQZ566inmzZuHz+ejsLAwfJ/H4yEYDNLW1kZmZmZEx30sCsQiIyTJaced6qSsKIOMNBcpSQ6sVgs1g33EnT1+Pqiso77FrUAsIiKj1pe+9CWampqGbfvWt77F7bfffsTHf//73yclJYUbb7yRV199NRpDPGkKxCIj6O6bZpOTFWqdcNitFHhT2N8Qmmli464mTBNqGrowjCA2W6hjyTRNBgJBnA5bzMYtIiJyoh5//HGSk5OHbTtadXj58uXs3buXxx57DKvVSkFBAbW1teH7W1pasFqtMa0Og3qIRUbUWRNzKMxOC98uzk0PV4g/GVykI2AEqW3qDj/m9XX7ufm+l+nTxXciIjIK5OfnU1xcPOzfkQLxihUr2Lx5MytXrsTpdAIwbdo0+vr6WLduHQB//OMfmT9/flTHfySqEItEUHFuGh9tq8cwgnyyo5HszGSa2nrZV99JSV7oorsN2xvp6h2gpqGLCSWx/Q1ZRERkJOzcuZNf/vKXjB07lhtuuAGA4uJiVq5cyUMPPcSyZcuGTbsWa1ELxNXV1SxZsiTcNL18+XLGjh077DFvv/02K1asYMeOHdx0003cc8894ftWrlzJiy++iNVqxeFwcMcddzB37lwAlixZwrvvvktWVhYA8+fP5+tf/3q0Dk3kqIpz0wkYJpuqmqht6uaLn6vgDy9tZZ+vg4tmhC4q2LG/FYD9DZ0KxCIiEhcmTpzI9u3bj3jf2WefzapVq6I8omOLWiBetmwZixcvZuHChTz//PMsXbqUJ554YthjSkpKePDBB1mzZg1+v3/YfTNmzOCWW24hOTmZbdu2ceONN/L222+TlBS6sv+rX/0qN954Y7QOR+SElOSF2idWv10NwHlT8nn1g33srQv1FXf2+PENtk/s16p2IiIiMRGVHuLm5mYqKytZsGABAAsWLKCyspKWlpZhjystLaWiogK7/fCcPnfu3HAD96RJkzBNk7a2tsgPXuQ0FA3ORfxhZR2Z6S7G5KdTmp/OvvrQ0s4794d+hi0Wwr3GQzbtatKiHiIiIlEQlUDs8/nIy8vDZgtdRW+z2cjNzcXn853S/p577jnGjBlDfn5+eNvvfvc7rrrqKr7xjW9QVVV1xO/r6OigpqZm2L/GxsZTGoPIiUhLdpCV7iJowsyJOVgsFsbkuznQ2M1AwGDnYLvE9PHZwyrEDS09fPcX7/Dye3tiNHIREZHEMeouqvvggw/42c9+xm9/sbKI5gAAIABJREFU+9vwtjvuuIOcnBysVivPPfcct956K6+99lo4gA/5/e9/zyOPPDJsW3l5Offee280hi4JqiQvndbOfs6amANAaX46waDJgcZudu5roygnjUmlWTz7j10EjCB2m5Vte0N/PTm0aiwiIiIjLyqBuKCggPr6egzDwGazYRgGDQ0NFBQUnNR+NmzYwHe+8x0effRRysrKwtvz8vLCX19zzTX88Ic/pK6ujqKiomHff/PNN3PttdcO2+b3+2ltbT2FoxI5MUW5aWzc1RQOxGPyQ1PT7PF1sGNfKzPLcyjOTcMImviauinJS2fb3tDPZG1j91H3KyIiIiMjKoHY6/VSUVHB6tWrWbhwIatXr6aiogKPx3PC+9i4cSN33HEHDz/8MFOnDl/lq76+PhyK165di9VqHRaShxxpWcHOzk4FYomo/3PROIpz08ILdhTlpGGzWtiwvYHWzn4mlmRRPNhrXNMQmo5t+2CF2NekCrGIiEikRa1l4t5772XJkiU8+uijuN1uli9fDsBtt93Gt7/9baZPn866deu488476erqwjRNXnjhBR588EHmzp3LfffdR19fH0uXLg3v86GHHmLSpEncc889NDc3Y7FYSEtL4xe/+MURL8wTiYXSfDel+Z/+IuawWynMSeOdjaGVesrHZFKcG5qNYn99F+dMNth9oB2n3UpTex/9AwYurWInIiISMVFLjePHj+fpp58+bPuvfvWr8NezZ8/mrbfeOuL3P/PMM0fd9+OPP37a4xOJpjH56eyv78RmtTCuMAOnw0Z2RhL7GzrZVdNGwDCZO7OQtR8foK6pm9KCIy+JKSIiIqdPSzeLxMBQxXhsoRvnYPW3OC+dmvpOtg/2D196TjHAsGWeRUREZOQpEIvEQGl+qGe4vCQrvK0kL52ahi627mkhz5NCxdhQj71PgVhERCSiFIhFYqCsKAOrBaaUecPbSnLT6PMbrN/ewORSD2kpTtJTnNTqwjoREZGI0pVnIjGQ703l0Xsuo8CbGt5WnBeqGvf7DSaVhirHhTmpqhCLiIhEmCrEIjFSlJOG1WoJ3x6aaQJg8thQIC7ITlUPsYiISIQpEIucITLTXKQlO3DarYwtyACgMDuNprZe+geMGI9OREQkfqllQuQMYbFYmFCcCYTmKoZQhRigvrmbMfluBgIGpkl4ZgoRERE5fQrEImeQu784e9jtwsFAXNsUCsQ/+v06uvsG+NE3PxOL4YmIiMQlBWKRM0h6inPY7aFA7GvqZtf+Nj6orMNmteAfMFQlFhERGSEKxCJnsNDUaw58Td1s29sCgBE0qa5tZ1KpJ8ajExERiQ+6qE7kDFeYncaGHQ38c5OPebNLANi5vy3GoxIREYkfCsQiZ7iC7FTqmntw2G3cctVUMtNdCsQiIiIjSIFY5Aw3NNPEleeXkpHmYkJx5gkF4uferGJrdUukhyciIjLqKRCLnOGmlnnJzkji2ksmAFBekklNQyc9fQNH/Z7OHj+/XbWZp17ZFq1hioiIjFoKxCJnuLMm5vC7pVeSk5UMwMQxWZgm7D7QDkB7Vz9/eGkr/oMW79iyuxnThE1VzfT2B2IybhERkdFCgVhklBlavGOobeKPr2znz6/t4P3NdeHHbKpqAiBgBPl4R2P0BykiIjKKKBCLjDKZ6S5yspLZtb+N1o4+Xn5/LwDvbfGFH7N5VzNTy7ykJNn5sLLuaLsSERERFIhFRqWhC+v++mYVhhFk+vhsPtpaT8AI0tnjp9rXzqzyHM6elMu6rfUEgyYAr6/bx4//d12MRy8iInJmUSAWGYUmlmTia+7mxXeruXhWMVdfXEZ3X4DNVU3h/uFp47M5d0o+rZ39VB1oo6G1h188s5G3Nhygrrk71ocgIiJyxtBKdSKjUHlJFgD9foPrL5tIricFp8PG+5vrsNosOB02ysdkUpybhsUCH1bWs6umjYARBODjHY3MvyD1mM9hGEGwWLBZLRE/HhERkVhShVhkFBpfkonVAhfOKGBMvpskp51Z5Tm8t6WOTbuaqBibhcNuIyPNxaQxWfztrSo+rKzn5v8zBW9GEh/vPP6Fdvf++j1++tT6KByNiIhIbCkQi4xCackOlt16AV+/7qzwtjlT82lq66W6toPp47PD28+dkk93X4DxxRlc9ZkyzpqYw8adjeG+4iPp6h1g485G3t1YS5+mbRMRkTinQCwySp09OZfMdFf49rlT8rEMdjdMOygQXzyriNL8dG6/fiY2m5WZ5Tl09gywu7b9qPveUtVE0AR/IMgGTdsmIiJxToFYJE5kpruoGOsJ9w8Pyfem8sh35jF+cP7isybmAPDJYNDtHzBYtXY33b2frnz3ya4mnA4bqUl2PtiiadtERCS+6aI6kThyy1VTqWvuwWG3HfUxHncSY/LT+XhHI5+fN5Hfv1DJqrW7ae/u58b5FQB8srORKeM8ZKS6+HBrHUbQ1MV1IiISt1QhFokjk0o9XHJ28XEfN3NiDluqm3lvs49Va3fjsFt59f19GEaQ1o4+9tV1ctbEHOZMzae9y8+2PS0AmKZJe1d/pA9DREQkqhSIRRLQzPIcBgJBHvrDOkry0vn3RbNo6ejjo20NfLIrtOzzWROzOaciF7vNwvtbQlXiH//vR3z5+69Q29gV4yMQEREZOQrEIgloapkXm9WCaZrc9YVzuOisQrLSXax5bw8bdzaSmuygrCiTlCQH08dn8/5mHyuf/pi1Hx8gYARZtXZ3eF99/gDf/8374Z5kERGR0UY9xCIJKCXJwb9dXk6eJ4WyogwALj9vDM+8vpP0VCfTx3vDPcNzphXw2LMbqW3qZtEV5TS29vLah/v4wr9WkJbs4Pk3q/igsg5/wOCs8pxYHpaIiMgpUYVYJEEtvnIyl507Jnz7s3NKCZrQ3uUPz0QBcP60fFKT7FxzyXi+cOVkrp5bRp/f4NX399Lc3stfXt+Jy2njk52NNLf3xuJQRERETosCsYgAoenZZg4G4YMDsTcjmT/cN5+vXD0Ni8XC+OJMpo33surt3Tzx4lYCRpDvfuk8TBP+8VFNrIYvIiJyyhSIRSTsps9VcM0l4ynOTRu2/dBp3K6eO57G1l5eX7efBZ8p4+xJuVSM9fD6uv2Y5tFXwBsJLR19EX8OERFJLArEIhJWPiYrXAk+lvOm5pPvTcGd6mTRFZMAuOzcEvbXd7Krpg2AYNAkYARHdHy1jV18+fuv8Pq6/SO6XxERSWy6qE5ETprNauF7t8zBMEzSkh0AXHRWEb/86yZe/3A/rR39/Ppvm0l22llxxyUjtqjHB5X1BIMmq9+pHtb/LCIicjpUIRaRU1Ka7w7PUAGQluxgztR8Xny3mu//9n16+wPsrm3nvU2+EXvODdsbANi1v41d+9tGbL8iIpLYFIhFZMRcPXc8+d5Ubls4jd9+7wqKclL58993jEjPb/+AweaqJi47twSnw8aa9/ac/oBFRERQIBaREVQxzsMv//Nyrr54PA67jf87byK7D7Tz0baG0973lqpm/IEgc2cWcfHMIt5cX0NP38AIjFpERBKdArGIRMy/nFNCTlYyTw9WiT/Z2cgfXtpKd+/JB9mPttfjsFuZWuZl/gWl9PkN3lyvad5EROT06aI6EYkYu83Kdf8ygV/+dRO3/eA16lt6gNBsEXffNPu4s1kcbMP2BqaWeUly2ikfk8W4Qjer3q5m4pgsxhdlnNS+REREDqYKsYhE1BVzSinKSSMjzckd/98sFl85mbc/qeWV9/cC0Ncf4Lk3d/GPj/ZjBEO9xkbQ5JX39/Lr5zfT0zdAQ2sP++u7OGdyLgAWi4V/u7ycmoZO7vjvN/nS/S+z+u3dMTtGEREZ3VQhFpGIcjlsPLbksvDtYNCkcncz//PXTQQCQZ59YxcNraEln5/++06uPL+UV97fy766TgDWb6/nvCn5AMyalBvez2fOKmL6+Gw+2lbPqx/s43+e20RpvpvpE7KjeHQiIhIPVCEWkaiyWi3cufhsUpIcPPbXTbicdn7wjYtY8sVzCQZNfv38ZgYGgiy5+Vwe+NqFtHf5eeYfu/BmJDEmL33YvjLSXMybPYZlXzmfwuxUVjy1nq4ef4yOTERERiuLmeBroHZ2drJjxw7Ky8tJT08//jeIyIjYVdPGzn2tXH5eKQ576Hdzwwiyu7adsQUZ4W0NrT38/E8fM31CNv92eflR97dzfyvfeXgtF84o5Ds3ngOAaYYCuIiInL54zkwKxHH85ookmj+/toM/vLQVp8PGQMAgNcnBXTeewzmT82I9NBGRUS+eM5N6iEUkbnx+3kScDistHf04HVY+3FLP/b95n9uvn8nl52mpZxEROTIFYhGJGzarhWsumRC+fd2/TOCHj3/Iz/60gTfW76eze4CWzj7OmZzLFz83BY87KYajPb7Wjj7cqU5sNl3uISISSQrEIhK3UpIcLL31fH79/Ca27G4mJyuF4rw03lx/gHc31vK5C8fR3uVnV00bQdPkgmkFXHRWIRlpLtq7+untDzC+OBOXwwbAtr0t/Pm1HXjcSXzhyslkRTBQt3b08f9+9BrlY7JYdusF4Z5qEREZeeohjuN+GBE5stqmLn77ty28v6WOjDQnE4ozGQgE2VzVRPCQM2KS08bsijyMoMk/N/lwpzrp6RvAYbdx/WUTGVvgxmKxhPczUguE/G7VFv765i5ME+bNLuE/bpilxUdEJKbiOTOpQiwiCacwO43v3TKH7t4BUpLs4aDZ1tnPB5V1BIwgGWkubFYL67bW895mH/1+g8VXTuaaS8bT2tHHr/+2mSde3Dpsv+MK3Sz4TBnnTsnDnRr6/lPR0e3nxXeruWRWMUW5aTy5ZhsedxL/dnk5yS6dtkVERpoqxHH8246IjAwjaBIMmoe1Leyv76S3P0DQNNnr62D129Xs8XUAYLFARqqLsqIMppR5KM13097VT1NbHxlpTi6cUXjUHub/fWkrf3ptByu/cykleek88vQn4ZX9MtNcTC3z8vXPzyAjzRXZAxcROUg8ZyYF4jh+c0UkukzTpLK6heradtq6+mlp72P7vtbwqnsQCsqmGfrv1DIvE4ozyc5MJjcrhcmlWTgcNr7ywCvMLM/hP28+DwjNz/xBZT01DZ34mrp5Y30NmekuvnvzeUwoyYzV4YpIgonnzKS/vYmIjBCLxcLUMi9Ty7zDtnf2+PE1dZOVnkSW24WvqZu3Pz7Au5t8vPjuHvwDRvixoR7lAP922aeLkNhsVi6YXgAUAPCvF47lB49/yN2PrOX/zpvIZ+eUkp2ZHJVjFBGJR1GrEFdXV7NkyRLa2trIzMxk+fLljB07dthj3n77bVasWMGOHTu46aabuOeee8L3GYbBAw88wNq1a7FYLHz1q1/l+uuvP+59xxPPv+2IyJnPNE26egc40NhF5e4WtuxupjAnla9cPe2Y39fe1c/P//wx72+pw2qBcyryuH5eORXjPFEauYgkmnjOTFGrEC9btozFixezcOFCnn/+eZYuXcoTTzwx7DElJSU8+OCDrFmzBr/fP+y+VatWsW/fPl555RXa2tq45ppruOCCCyguLj7mfSIiZzKLxUJ6ipPJpR4ml3q47tIJx/8mICPNxfdumUNdczevvL+XV9/fx92PrGV2RR43XFHOxJIsLVstInKCojKxZXNzM5WVlSxYsACABQsWUFlZSUtLy7DHlZaWUlFRgd1+eE5/8cUXuf7667FarXg8Hi6//HLWrFlz3PtEROJZvjeVL35uCr/67uV88XMVbN3Twl0Pr+XGZS/xg8c/4NX399LdOxDrYYqInNGiUiH2+Xzk5eVhs4Umt7fZbOTm5uLz+fB4TuzPez6fj8LCwvDtgoIC6urqjnvfwTo6Oujo6Bi27dBKtIjIaJTksnP9ZeX864Xj+GCLj027mtm4q5F/bvLx2LMbOW9qPpeeU8LZk3Oxn+TKd6ZpEjCCOOy2CI1eRCS2Euqiut///vc88sgjw7aVl5dz7733xmZAIiIjLC3ZwbzZY5g3ewymabJzfxv/WLeftz4+wNuf1JKe4uTcKXlkpLlISbJjmtDTN0Bvf4CevgA9fQP09AUGb4e+7ukPEAyalBVmcMWcMcydWURKkj08HV0waGIETbr7Bujo8tPU3sv2va1s39tKc3sv7jQXmWkuzpqYw/zzS0nSXMoicoaJylmpoKCA+vp6DMPAZrNhGAYNDQ0UFBSc1D5qa2uZMWMGMLwqfKz7DnbzzTdz7bXXDtvm9/tpbW091UMTETljWSwWysdkUT4mi68snMb67Q38Y91+1m9voKcvEJ7dwuW0keKyk5JkJznJQYrLTkZaCimDXycn2bHbrLy/pY5f/nUTv/zrpuM+t8NuZUJxJlPGeeno8dPQ2sNv/raZp/++g6vmljGuwE1aipOczGRyPSmRfinOKE+9sp2PttZz2bklXHJ2MSlJjlgPSSThRSUQe71eKioqWL16NQsXLmT16tVUVFSccLsEwPz583n66af57Gc/S1tbG6+99hpPPvnkce87mNvtxu12D9vW2dmpQCwicc9us3LelHzOm5If3hYwglgITet2IhZfOZmqmjbWb2/ANMFqtWC1WLDZQv9NTbbjTnWRme6iND/9sBaLrdUt/PnvO3hyzbZh2yeWZPIvZxczttBNv9+gf8DADIJJaBKkobmQvBlJTCr1HLZAyqH6BwwcNusZeVHhrpo2/vjKNlKTHTz6zEZ+u2oLl587hoWXjCffmxrr4YkkrKhNu1ZVVcWSJUvo6OjA7XazfPlyysrKuO222/j2t7/N9OnTWbduHXfeeSddXV2Ypkl6ejoPPvggc+fOxTAM7r//ft555x0AbrvtNhYtWgRwzPuOJ56nEBERORM1tfXS2tlHV88A1bUdvLm+ht217Sf0vUlOG1PKvLgcNnr6BujzG1gIhfO+foPGth46ewZIctoozkunMDsVh92KhVBwT3bZSXLaSXLaSHLZSUt2MLM8Jyqr/hlBk7t//hYNLb38YsllHGjo5MV39/DWhhqCJlw0o5CZ5TlMLMlkTF76Cf+iIhIt8ZyZtFJdHL+5IiKjxf76Ttq6+nE5bLgctiNWdw80dvHxjka27G4maJqkJjlwOW1gQtA0cTps5GQl481IoqPLz776TuqauzGCJmbQJGCY9PkD9PmNYfu1WS3Mrshj+oRsOrr9tHb0YQRNUlx2XE4bRtBkIBDE5bBxVnkO08d7T+kCw5f+uYdH//IJdy4+m0vPKQlvb27v5fm3dvPq+3vpGpwRJD3FwcWzipk3u4SJJZlYLGdetVsSTzxnJgXiOH5zRUTkcMGgiX/AoNcfoKmtl7Uf1/Lm+v20dPRjtUBmugur1Upffyg822wWHDYrfX6DgBHE5bThdSfR1Ru6GHFcoZuzJ+UxqTSLzh4/ze19mKaJx51EVnoSvf4ALe19PPnyNsoKM3jw6xceMeAGgya+5m527mvlw8p63tvswx8Ikp7ipLQgnXGFGVw2u4TxxVquW2IjnjOTAnEcv7kiInJijKBJZ7ef9FQntqP0Hvf5A2yuambd1no6uv2kpThwOWxs29PCjn2tBI/zf9OMNCc//MZnKMk7sf/XdPUO8O7GWnbsa2Wvr4NqXwf9foOzJ+dy5ZxSUpMdOOxWinLSotLycabbsruZtzbUYLdZcditJCfZcac4SU91UuBNpSg3jSSnZjg5HfGcmRSI4/jNFRGR6Ojs8bOvrpPMdBcedxIWC7R29NPS0Ueyy47HnYQ71XlaF/p19Q7w0rvVPP9WFe1dn86hb7VamD7ey0UzChlXlEFOZjJZ6UkjelGhaZp09wWwWiDJacdqtRAwgrR39WOxWPC4k0bsuU7FJzsbuf/X72GxWrBZLQwEggwEgoc9rjA7ldkVeZw3JZ+JYzJJdtnVjnIS4jkzKRDH8ZsrIiLxp3/AoLq2nYFAEP+AQWV1C29/fIDapu7wY5wOGxNLMpk0JouUZDv1zT00tfXiyUiiNN9NQXZoRgsjaOJy2CjITiU3K4W2zn6qfe3sq+ukoaWHxrZeGlp7aGztobc/1HtttYDLaae3PxB+vtysZKaM8+Jy2mjp6KOj209RThqTx3oYV+gm2WnH4bDicthw2G3YbRZaO/upb+mhrbMfiwWsFgsDAYO2Lj9dPX4KstOYWuahKCftmKF1y+5mlv3qn+R5UvjB1y8KV8sHAgadPQO0d/VzoLGLmoYutu1pYeOupnBYdtqtZKa7GFuQweSxWYwrzMBht2KzWsj3ppKdmTzi799oFs+ZSYE4jt9cERFJDKZpcqCxC19TN41tvdQ0dLFjbytVB9oIGCaZaS6yM5Nobu+jtbP/hPaZnuIgJyslPFd0TmYyFgt09YR6p9NSnGSmOfEHgmzd08LW6haMYBCvO5m0FAd7fB10dJ/aarBWq4XgYA9KapKdZJcdu90a6qfOd1OSl05P3wD76jvZsL0Bb0YyP/zmRWSlH79S3dcfYOOuJg40dtHe1U9zex8797dxoLHrsMdOKM7g/GkFZKYnAaELNyeXesj3piRkZTmeM5MCcRy/uSIiktgGAgaGYQ5bHbC9K1SZtQ62F/T0Bahr7qahpYeMdBdjC9yU5rtJTT69BUNM06SuuYf9DZ34Bwz8A0EGAkP/DZKZ7iI3KzncbmEETRx2KxlpLpKcNg40drFldwvVte34BwwGjCCtHX3sreukrbMfq9VCgTeV8UUZ3HL1VLwZp1fN7ej2U9vYRcAIYhgmO2vaeG+Tj+37Dl+rICcrmbLCDNJSHKSnOMn3pFBaEKq89/QFwq0kxbkj199tmiadPQPYbZZw20q0xXNmUiCO4zdXREQkHnV0+0l22U5p+ruT1dnjp6/fwGKB7t4BNlc1sbGqidrGbrp6B+js8dN/yFR+B3OnOkkb/OXCYrHgzUgiJyuZJKedxtZeGtt6cNit5GSl4HUn0Tb4C0tHtx+7zYLDZqOnf4Cmtj4Cxqd90U6HjaEi9dVzy/ji56ZE9HWA+M5MutxSRERERhV3qjNqz5We4iR9cHXx7MxkSgvc/J/PlIXvN02T5vY+9vg6qG/uJnWwlcQImuyv72J/fSd9/lC/tWGYNLf3smF7I/3+ADlZKWRnJhMwglQfaOejrfVkpLnI86QwsSQTI2gSCARxOdO4aEaomm4ETXr7h8+nPWtSbtRej3ilQCwiIiJyiiwWC9mZyUe8AO+cyXkxGJGcCq0LKSIiIiIJTYFYRERERBKaArGIiIiIJDQFYhERERFJaArEIiIiIpLQFIhFREREJKEpEIuIiIhIQlMgFhEREZGEpkAsIiIiIglNgVhEREREEpoCsYiIiIgkNAViEREREUloCsQiIiIiktAUiEVERERkxFVXV7No0SKuvPJKFi1axJ49e2I9pKNSIBYRERGREbds2TIWL17Myy+/zOLFi1m6dGmsh3RUCsQiIiIicsLq6uqoqakZ9q+jo2PYY5qbm6msrGTBggUALFiwgMrKSlpaWmIx5OOyx3oAIiIiIjJ6fOlLX6KpqWnYtm9961vcfvvt4ds+n4+8vDxsNhsANpuN3NxcfD4fHo8nquM9EQrEIiIiInLCHn/8cZKTk4dtc7vdMRrNyFAgFhEREZETlp+fT3p6+jEfU1BQQH19PYZhYLPZMAyDhoYGCgoKojTKk6MeYhEREREZUV6vl4qKClavXg3A6tWrqaioOCPbJUAVYoLBIAA9PT0xHomIiIjImWsoKw1lp+O59957WbJkCY8++ihut5vly5dHcninxWKaphnrQcRSfX09NTU1sR6GiIiIyKhQXFxMXl5erIcxohK+Quz1egFISkrCalUHiYiIiMiRBINB+vr6wtkpniR8hVhEREREEptKoiIiIiKS0BSIRURERCShKRCLiIiISEJTIBYRERGRhKZALCIiIiIJTYFYRERERBKaArGIiIiIJLSEX5gjWqqrq1myZAltbW1kZmayfPlyxo4dG+thRUVrayt33303+/btw+l0Ulpayv3334/H42HSpEmUl5eHF0V56KGHmDRpUoxHHFnz5s3D6XTicrkAuOuuu5g7dy4ff/wxS5cupb+/n6KiIn784x/H5eTnQ2pqavjmN78Zvt3Z2UlXVxcffPDBUV+jeLJ8+XJefvllDhw4wKpVqygvLweOfa6I5/PIkV6PY507gLg9fxztZ+NYn4t4PX8c6bU41rkDjv06jWbH+jwc6/2P15+NEWdKVNx0003mc889Z5qmaT733HPmTTfdFOMRRU9ra6v53nvvhW//6Ec/Mv/zP//TNE3TLC8vN7u6umI1tJi49NJLze3btw/bZhiGefnll5sffvihaZqmuXLlSnPJkiWxGF7MPPDAA+Z9991nmuaRX6N48+GHH5q1tbWHHeuxzhXxfB450utxrHOHacbv+eNoPxtH+1zE8/njaK/FwQ4+d5hm/J4/jvZ5ONb7H88/GyNNLRNR0NzcTGVlJQsWLABgwYIFVFZW0tLSEuORRUdmZiZz5swJ3545cya1tbUxHNGZZ/PmzbhcLmbPng3ADTfcwJo1a2I8qujx+/2sWrWKz3/+87EeStTMnj2bgoKCYduOda6I9/PIkV6PRD13HOm1OJZ4Pn8c77VIpHPH0T4Px3r/4/lnY6SpZSIKfD4feXl52Gw2AGw2G7m5ufh8vvCf/hJFMBjkqaeeYt68eeFtN910E4ZhcPHFF3P77bfjdDpjOMLouOuuuzBNk3POOYc777wTn89HYWFh+H6Px0MwGAz/aTzevf766+Tl5TF16tTwtkNfI7fbHcMRRsexzhWmaSb0eeRI5w5IvPPHkT4XiXz+ONK5A+L//HHw5+FY738i/2ycLFWIJaq+//3vk5KSwo033gjAG2+8wbPPPsuTTz7Jrl27WLlyZYxHGHlPPvkkf/vb33jmmWcwTZP7778/1kOKuWeeeWZYhUevkRzq0HMHJN75Q58GD4joAAAFaklEQVSLwx167oDEeJ2O9HmQ06NAHAUFBQXU19djGAYAhmHQ0NBwUn8SiwfLly9n7969/PSnPw1fBDP0GqSlpXH99dezfv36WA4xKoaO2el0snjxYtavX09BQcGwPwW3tLRgtVoT4jf4+vp6PvzwQ6666qrwtiO9RongWOeKRD6PHOncAYl3/jja5yJRzx9HOndA/J8/Dv08HOv9T9SfjVOhQBwFXq+XiooKVq9eDcDq1aupqKhIiD9zDlmxYgWbN29m5cqV4T9ptre309fXB0AgEODll1+moqIilsOMuJ6eHjo7OwEwTZMXX3yRiooKpk2bRl9fH+vWrQPgj3/8I/Pnz4/lUKPmr3/9K5dccglZWVnA0V+jRHCsc0WinkeOdO6AxDt/HOtzkajnj0PPHRD/548jfR6O9f4n6s/GqbCYpmnGehCJoKqqiiVLltDR0YHb7Wb58uWUlZXFelhRsXPnThYsWMDYsWNJSkoCoLi4mFtvvZWlS5disVgIBALMmjWL7373u6SmpsZ4xJGzf/9+br/9dgzDIBgMMn78eL73ve+Rm5vL+vXrWbZs2bCpcbKzs2M95Ii78sor+a//+i8uvvhi4NivUTx54IEHeOWVV2hqaiIrK4vMzExeeOGFY54r4vk8cqTX46c//ekRzx0rV65kw4YNcXv+ONJr8dhjjx3zcxGv54+jfU7g8HMHxPf542j/L125cuUx3/94/dkYaQrEIiIiIpLQ1DIhIiIiIglNgVhEREREEpoCsYiIiIgkNAViEREREUloCsQiIiIiktAUiEVERrlJkyaxd+/eWA9DRGTUssd6ACIi8WbevHk0NTVhs9nC26699lqWLl0aw1GJiMjRKBCLiETAY489xoUXXhjrYYiIyAlQy4SISJQ8++yz3HDDDdx///2cc845zJ8/n3/+85/h++vr6/na177GeeedxxVXXMGf//zn8H2GYfDYY49x+eWXM2vWLK677jp8Pl/4/nfffZfPfvazzJ49m/vuuw+tuSQicuJUIRYRiaKNGzcyf/583nvvPV599VW+9a1v8fe//53MzEzuvPNOJk6cyNq1a9m9ezdf/vKXKSkp4YILLuB3v/sdL7zwAv/zP//DuHHj2L59e3j5VoA33niDv/zlL3R1dXHddddx6aWXDlvSVkREjk4VYhGRCPjmN7/J7Nmzw/+Gqr0ej4ebb74Zh8PB5z73OcaNG8cbb7yBz+dj/fr13HXXXbhcLioqKrj++ut5/vnnAXj66af593//d8rKyrBYLEyePJmsrKzw891222243W4KCwuZM2cO27Zti8lxi4iMRqoQi4hEwMqVKw/rIX722WfJy8vDYrGEtxUWFtLQ0EBDQwMZGRmkpaUNu2/z5s0A1NXVMWbMmKM+X05OTvjr5ORkuru7R+pQRETinirEIiJRVF9fP6y/1+fzkZubS25uLu3t7XR1dQ27Ly8vD4D8/Hz27dsX9fGKiCQCBWIRkShqaWnhiSeeYGBggJdeeomqqiouueQSCgoKmDVrFitWrKC/v59t27bxl7/8hauvvhqA66+/np/97Gfs2bMH0zTZtm0bra2tMT4aEZH4oJYJEZEI+NrXvjZsHuILL7yQyy67jBkzZrB3717OP/98srOzefjhh8O9wCtWrGDZsmXMnTsXt9vN7bffHm67+PKXv4zf7+eWW26htbWVsrIyVq5cGZNjExGJNxZTc/OIiETFs88+y9NPP81TTz0V66GIiMhB1DIhIiIiIglNgVhEREREEppaJkREREQkoalCLCIiIiIJTYFYRERERBKaArGIiIiIJDQFYhERERFJaArEIiIiIpLQFIhFREREJKH9/3odZaeP7XxrAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try a 2 hidden layers, with 10 neurons each\n", "epochs = 200\n", "\n", "network = []\n", "network.append(Dense(x_dim,10))\n", "network.append(ReLU())\n", "network.append(Dense(10,10))\n", "network.append(ReLU())\n", "network.append(Dense(10,1))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 399, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try ONE hidden layer, with 10 neurons each\n", "epochs = 200\n", "\n", "network = []\n", "network.append(Dense(x_dim,10))\n", "network.append(ReLU())\n", "network.append(Dense(10,1))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 333, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try a 3 hidden layers, with 5 neurons each\n", "epochs = 200\n", "\n", "network = []\n", "network.append(Dense(x_dim,5))\n", "network.append(ReLU())\n", "network.append(Dense(5,5))\n", "network.append(ReLU())\n", "network.append(Dense(5,5))\n", "network.append(ReLU())\n", "network.append(Dense(5,1))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's try with a bigger dataset... LFSR order 12" ] }, { "cell_type": "code", "execution_count": 361, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training:\n", "(3686, 12)\n", "(3686, 1)\n", "Testing:\n", "(409, 12)\n", "(409, 1)\n" ] } ], "source": [ "lfsr_order = 12\n", "\n", "lag = np.array([1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1])\n", "state = np.ones(lfsr_order)\n", "\n", "x_dim = lfsr_order # how many bits are in each x\n", "training_size = int(2**lfsr_order * 0.9) # size of training dataset\n", "testing_size = int(2 ** lfsr_order * 0.1) # size of testing dataset\n", "\n", "X = []\n", "Y = []\n", "\n", "x = []\n", "for i in range(x_dim):\n", " x.append(lfsr())\n", "\n", "for i in range(training_size):\n", " y = lfsr()\n", " \n", " X.append(x.copy())\n", " Y.append(y)\n", " \n", " x.append(y)\n", " x.pop(0)\n", " \n", "X = np.array(X)\n", "Y = np.expand_dims(np.array(Y), axis=1)\n", "\n", "print(\"Training:\")\n", "print(X.shape)\n", "print(Y.shape)\n", "\n", "X_test = []\n", "Y_test = []\n", "\n", "for i in range(testing_size):\n", " y = lfsr()\n", " \n", " X_test.append(x.copy())\n", " Y_test.append(y)\n", " \n", " x.append(y)\n", " x.pop(0)\n", "\n", "X_test = np.array(X_test)\n", "Y_test = np.expand_dims(np.array(Y_test), axis=1)\n", "\n", "print(\"Testing:\")\n", "print(X_test.shape)\n", "print(Y_test.shape)" ] }, { "cell_type": "code", "execution_count": 362, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try 2 hidden layers, with 12 neurons each\n", "epochs = 200\n", "learning_rate = 0.1\n", "\n", "network = []\n", "network.append(Dense(x_dim, 12, learning_rate=learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 12, learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 1, learning_rate))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Not learning anything... Need to REDUCE the learning rate...**" ] }, { "cell_type": "code", "execution_count": 367, "metadata": {}, "outputs": [ { "data": { "image/png": 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oIwYAAGhfBOIg5Y5tDMR5tE0AAAC0KwJxkDq8Wx0P1gEAALQvAnGQckSEyB5mpWUCAACgnRGIg5RhGHLHRrLSBAAAQDsjEAcxd2yE8ovYvhkAAKA9EYiDWGJs4251fr/f7FIAAAC6LAJxEHPHRqi61quyyjqzSwEAAOiyCMRB7PDSa6w0AQAA0H4IxEHscCBmpQkAAID2QyAOYk0zxKw0AQAA0G4IxEEsIjxEjogQWiYAAADaka2jPmjXrl2aNWuWSkpK5HK5lJmZqT59+jQ756mnntKKFStksVgUEhKimTNnatSoUZKkWbNm6eOPP1ZMTIwkaezYsbrjjjvk8/k0Y8YMbdu2TWFhYYqLi9MjjzyiXr16ddSttavE2AgCMQAAQDvqsED88MMPa+LEiRo/fryWLVum2bNna/Hixc3OGTp0qG655RbZ7Xbl5OToxhtv1Jo1axQeHi5Jmjp1qm688cajxp4wYYIuuugiWSwW/e1vf9NDDz2kRYsWdch9tbekuEjtPFBqdhkAAABdVoe0THg8HmVnZysjI0OSlJGRoezsbBUVFTU7b9SoUbLb7ZKkgQMHyu/3q6Sk5IRjWywWjRkzRhZL460MHz5cBw8ebIe7MEdKfKTyi6rU4PWZXQoAAECX1CEzxLm5uXK73bJarZIkq9WqxMRE5ebmKjY29pjXLF26VL169VJSUlLTsRdffFFLlixRz549dc8996h///5HXffyyy/r4osvPuaYZWVlKisra3asri641/hNiY+Uz+dXQXGVUuKjzC4HAACgy+mwlomWWLdunebNm6cXXnih6djMmTOVkJAgi8WipUuXavLkyXrvvfeaQrYk/eUvf9GOHTuO2y6xaNEizZ8/v9mxtLQ0zZkzp13uoy0kfxuCDx6qJBADAAC0gw4JxMnJycrPz5fX65XVapXX61VBQYGSk5OPOnfDhg2677779PTTT6tfv35Nx91ud9OvJ0yYoN///vfKy8tTjx49JEkvvfSSsrKytGjRoqa2i/91880366qrrmp2rK6uTsXFxW1xm+0iJSFSknSwsEKS+8QnAwAAoMU6pIc4Li5O6enpysrKkiRlZWUpPT39qHaJL7/8UjNnztSTTz6pwYMHN3svPz+/6derV6+WxWJpCsmvvvqqXnvtNb344otyuVzHrcPpdCo1NbXZV0JCQlvdZrtwRYXJHmZTbmGl2aUAAAB0SYbf7/d3xAft2LFDs2bNUllZmZxOpzIzM9WvXz9NmTJFd911l4YMGaKrr75aBw4caDYbPHfuXA0cOFCTJk2Sx+ORYRiKiorS/fffr+HDh6uiokIjR45USkqKHA6HJCk0NFSvv/56QHWVl5dr27ZtSktLa7o+2Mz443/kcoTpkSnnml0KAADopjpDZmqtDgvEwaozfHMzF3+mHftLteDXPzS7FAAA0E11hszUWuxU1wmkJEQpv5il1wAAANoDgbgTSI77duk1dqwDAABocwTiTuC7lSZ4sA4AAKCtEYg7gZSmtYgrTK4EAACg6yEQdwLRUaGKCGfpNQAAgPZAIO4EDMNQcnwkLRMAAADtgEDcSaTER327Wx0AAADaEoG4k0iJj1RBUZXqG1h6DQAAoC0RiDuJ5PhI+fxSQTFLrwEAALQlAnEnwUoTAAAA7YNA3EmwFjEAAED7IBB3Es7IUEXZQ3SggBliAACAtkQg7iQMw1BqYpT2E4gBAADaFIG4E0lNdGh/QbnZZQAAAHQpBOJOJDUxSsXltaqorje7FAAAgC6DQNyJpCY2rjRxgFliAACANkMg7kRS3Q5Joo8YAACgDRGIOxF3bIRsVoNADAAA0IYIxJ2IzWpRcnwkD9YBAAC0IQJxJ5Oa6NC+fAIxAABAWyEQdzK9k5zKLaxUbb3X7FIAAAC6BAJxJ9M72SGfX8wSAwAAtBECcSfTO8kpSdqbV2ZyJQAAAF0DgbiTSYmPVIjNot25zBADAAC0BQJxJ2O1WtQz0aE9ucwQAwAAtAUCcSfUO9mhPbRMAAAAtAkCcSfUO8kpT2mNKqrqzC4FAACg0yMQd0K9kxsfrNuTRx8xAADAqSIQd0J9vg3Eu+kjBgAAOGUE4k4oLjpckeE2HqwDAABoAwTiTsgwDPVOdvJgHQAAQBsgEHdSvZOc2pNbJr/fb3YpAAAAnRqBuJPqnexUZU2DPKU1ZpcCAADQqRGIOykerAMAAGgbBOJOqneSQ5J4sA4AAOAUEYg7qaiIUMW77Np1kEAMAABwKgjEnVjfFKd25ZaaXQYAAECnRiDuxPqlRGt/QYXq6r1mlwIAANBpEYg7sb4p0fL5/NrLFs4AAACtRiDuxPr2aFxpYudB2iYAAABai0DciSXFRsoeZtUuAjEAAECrEYg7MYvFUO8kJytNAAAAnAICcSfXt0e0dh8sZQtnAACAViIQd3J9U6JVWdOgguJqs0sBAADolAjEnVy/lG8frDtAHzEAAEBrEIg7ud5JThmGtJsH6wAAAFqFQNzJhYfZlBIfxdJrAAAArUQg7gL6prDSBAAAQGsRiLuAvinRyi+qUmV1vdmlAAAAdDoE4i6gX49oSexYBwAA0BoE4i5gQKpLkrRjf4nJlQAAAHQ+NrMLwKlzOcIU77Lrm30EYgAAEBxqa2v12GOPae3atQoLC9Pw4cP16KOPateuXZo1a5ZKSkrkcrmUmZmpPn36mForgbiLGJAazQwxAAAIGn/4wx8UFhamd955R4ZhqLCwUJL08MMPa+LEiRo/fryWLVum2bNna/HixabWSstEFzGgp0sHDlXyYB0AADBdZWWlli5dqhkzZsgwDElSfHy8PB6PsrOzlZGRIUnKyMhQdna2ioqKzCyXGeKu4nAf8c4DpRoyIN7kagAAQFeVl5en0tLmD/I7nU45nc6m1/v27ZPL5dL8+fP16aefKjIyUjNmzFB4eLjcbresVqskyWq1KjExUbm5uYqNje3Q+zgSgbiLOByIv9lXQiAGAADtZtKkSU3tD4dNmzZN06dPb3rt9Xq1b98+nX766XrggQe0adMm3X777Zo3b15HlxsQAnEXER0VpoQYO33EAACgXS1cuFB2u73ZsSNnhyUpOTlZNputqTVi2LBhiomJUXh4uPLz8+X1emW1WuX1elVQUKDk5OQOq/9Y6CHuQgakuvQNgRgAALSjpKQkpaamNvv630AcGxurs88+Wx999JEkadeuXfJ4POrTp4/S09OVlZUlScrKylJ6erqp7RISM8RdyoBUl9ZuzlVFdb2i7CFmlwMAALqxRx55RL/+9a+VmZkpm82muXPnyul0as6cOZo1a5aefvppOZ1OZWZmml0qgbgrOXKDjmGnJZhcDQAA6M569uypl1566ajj/fv31+uvv25CRcdHy0QX0j+1cQtn+ogBAAACRyDuQqKjwpQYw451AAAALUEg7mIG9HRpx/7Sk58IAAAASQTiLmdAqku5nkpVVNWZXQoAAECnQCDuYr57sI5ZYgAAgEAQiLuY/t8G4u08WAcAABAQAnEX44wMVWJsBBt0AAAABIh1iLug01JdLL0GAAC6tPr6em3atEk5OTkqKyuT0+nUoEGDNGzYMIWEtGyDMgJxF9Q/NVoffXlQ5VV1ckSEml0OAABAmykuLtaCBQv0r3/9S9HR0erXr58iIyNVWVmpl156SaWlpbrqqqs0ZcqUgLeEJhB3QWk9YyRJ3+wt0RmDEk2uBgAAoO1MnDhR11xzjZYtWya3233U+/n5+Vq+fLluvPFGrVixIqAxCcRd0Gm9XDIMaeueIgIxAADoUpYtW6bQ0OP/BNztdmvy5Mm66aabAh6Th+q6oIjwEPVyO5Szt9jsUgAAANrU8cJwWVmZNm/eLI/Hc8LzjoVA3EUN6hOrbXuK5fP5zS4FAACgXb399tsaN26cfve73ykjI0OLFi1q0fUE4i5qYK8YVVTX62BhhdmlAAAAtKn8/Pxmr19++WVlZWXp1Vdf1fLly/Xss8+2aDwCcRc1sHfjg3Vb99A2AQAAupbp06fr+eefl9frlSQ5HA59+OGH2rNnj95///2AV5c4jEDcRaUmOhQRbiMQAwCALueVV16Rz+fT9ddfr/Xr1+uhhx7SypUrdccdd2jVqlV64oknWjQeq0x0URaLobReMcrZU2R2KQAAAG3KZrNpypQpuvzyy/XYY48pKipKs2fPbvHM8GHMEHdhg3rHak9umaprG8wuBQAAoE15PB4VFRXpscce06WXXqpbbrlFr7zyivz+li8oQCDuwgb2jpHPL23fxzbOAACg61i4cKEuv/xy/fa3v9UVV1yhmpoavfrqq8rNzdX111+vzZs3t2g8Wia6sLRejQ/W5ewp0pAB8SZXAwAA0Daee+45LV++XImJicrLy9Odd96pyy+/XPfcc4+2b9+u3/zmN1q8eHHA4zFD3IU5I0PVIyGSB+sAAECXEhcXp23btqm+vl45OTmKj/9u4m/AgAEtCsMSgbjLG9g7Vlv3FreqnwYAACAYPf7441q8eLHGjx+vpUuXas6cOac0Hi0TXdyg3jFatX6fCoqr5Y6NMLscAACAUzZo0CAtWLCgzcZjhriLG9i7cfmRnN0svwYAADq/999/v03PkwjEXV7vJIfCQq3aupc+YgAA0PmtWLFCGRkZeu655/TFF1+ouLhYdXV1Ki4u1oYNG7RgwQJlZGTorbfeCnhMWia6OKvVotN6urSVDToAAEAX8MQTT2jr1q1asmSJ7r//fu3fv1+GYUiSevXqpdGjR+tPf/qTTjvttIDHJBB3A4N6x2rpf7errt6r0BCr2eUAAACckoEDB2r27NmSpOrqapWVlcnpdMput7dqPFomuoGBvWPU4PXrGzboAAAAXYzdbpfb7W51GJYIxN3C4H5xMgzpqx2FZpcCAAAQdAjE3YAjIlR9k6P15XYCMQAAwP8iEHcTQwbEa8vuItXVe80uBQAAIKgQiLuJoQPiVd/gYxtnAADQZSxatEhFRae+khaBuJsY3C9OFkO0TQAAgC7jk08+0ZgxY3TbbbdpxYoVqqura9U4BOJuItIeon6pLm3mwToAANBFPPPMM1q1apVGjx6tRYsW6bzzztODDz6ozz77rEXjEIi7kaH947V1T5Fq6hrMLgUAAKBNxMTE6IYbbtCSJUv00ksvafPmzbrpppt08cUX65lnnlFlZeVJxwg4EL/44ovasmWLJGnjxo268MILdfHFF2vDhg2tvwN0qCED4tXg9StnN7vWAQCArmPt2rX61a9+pZtuuknx8fHKzMzU3LlztWXLFk2ZMuWk1we8U93ChQt1zTXXSGrcMm/SpEmKjIzUY489ptdff731d4AOc3rfWFkthr7cXqjhaYlmlwMAAHBKMjMz9eabb8rhcGj8+PFavny53G530/vDhg3TWWedddJxAg7E5eXlcjgcqqio0NatW7Vw4UJZrVZlZma27g7Q4SLCQ3RaTxcP1gEAgC6htrZW8+fP19ChQ4/5fkhIiN54442TjhNwIE5OTtYXX3yh7du3a+TIkbJaraqoqJDVag28aphuyIB4/eOD7aqqqVdEeIjZ5QAAALTabbfdpvDw8GbHSktLVVNT0zRT3L9//5OOE3AP8f3336+77rpLzz77rO68805J0gcffKAhQ4a0pG60s9r83arauem47w8dEC+fz6/sXfQRAwCAzu3OO+9UXl5es2N5eXmaNm1ai8YJeIb4ggsu0Jo1a5odGzt2rMaOHduiD0T78rzzV9Ue3K7UO55USPTRfcKD+sTKZjW0eXuhRqa7jzHC8dWX5Kvec1AhsckKiUlqq5IBAABaZdeuXRo4cGCzYwMHDtTOnTtbNE7AM8Tbt29XYWFj72llZaWefPJJPffcc2poYAmvtuJrqJO3ukLe6gr5Glq+sLSvtko1B7bJ761X8X/+fsxzwkNtGtg7Vl+2cD1iv8+rg4v/n/Je/a32PTdD9UUHW1wfAABAW4qLi9OePXuaHduzZ49cLleLxgk4EN99990qKyuT1PhE32effaaNGzdq9uzZLfpAHJu3qlx7/nSL9vzxZu35483a++db5a0ub9EY1bu/knxehfc6XRVffajyL/9zzPOG9I/Xzv0lqqiuD3zsXV/KW16kmAsnyrDYVPS8jSfgAAAgAElEQVTByy2qDQAAoK1dffXVmj59uj744ANt375dq1at0l133aVrr722ReME3DJx4MAB9evXT36/X++++67efPNNhYeHa8yYMQFdv2vXLs2aNUslJSVyuVzKzMxUnz59mp3z1FNPacWKFbJYLAoJCdHMmTM1atQoSdKsWbP08ccfKyYmRlJju8Ydd9whSXr++ef12muvac+ePXrmmWd00UUXBXpbQaNmf478ddWKPmecDItVJR//S9W7Nysq/QeSGtsVDmU9JW95sSIHnaPYi244aozqnRtlhIbLfc0DKvjn4zq0/P9U8tEbCnX3VcIVd8gSFiGpsY/41Xe36qsdhTrne8kB1Vex+b+yhEfJdfY4yetV8eolqtmfo/DUQW33mwAAANACU6dOlc1mU2ZmpvLy8pSUlKRrr71WP//5z1s0TsCBOCwsTBUVFdqxY4eSk5MVGxurhoYG1dbWBnT9ww8/rIkTJ2r8+PFatmyZZs+ercWLFzc7Z+jQobrllltkt9uVk5OjG2+8UWvWrGl6enDq1Km68cYbjxr7zDPP1I9+9CM9+OCDgd5O0Kk9sE2yWBUz+qcyrDaVff6OqndsVFT6D1RfdFAHFz8kv7dBoQk9VfLxPxUxYITCe34XRv1+v6p2bpS99/dktUcp6boHVbz6NdUX5apy66eqO7RXYckD5Bh6oQb1OV2hIVZt+ubQcQOx3+9T6boshcQkKyzlNFVu/VSOoRfJsIUo+pxxKtuwUp73Fivl5t/JMIyO+m0CAABoYrFYNHnyZE2ePPmUxgk4EGdkZOjmm29WZWVlUyjNzs5WamrqSa/1eDzKzs7Wiy++2DTWo48+qqKiIsXGxjadd3g2WGpsiPb7/SopKVFS0okf4Dre2nOdSc2BrQpz95ElJEySFN5niKp2bZLf71fhOy/I761Xyk2/lS06UfuemSbP+4uUcvPvVF94QL66annLi9RQkq+Y8xs3TzFsIU2zyFXbv5Bn1WJVbV+viq9XKyHjF/pevzht+ubQUXU0lBWq6pv1qt79lSpz1koyZI1qnJV3nHGJJMkSGq6Y0T9V4YpnVLTqJYX3TFfEaSMJxgAAoMPV1dVp165dKi4ult/vbzp+7rnnBjxGwIH417/+tdasWSObzaZzzjlHkmQYhn71q1+d9Nrc3Fy53e6mNYutVqsSExOVm5vbLBAfaenSperVq1ezMPziiy9qyZIl6tmzp+65556A1pU7UllZWVMf9GF1dS1/eK2t+X1e1R7cIcew71o9IvoNV9XWTxtbJ3ZuUOyYmxWa0EuSFHvRDTq0fL7y/v7bxlaLhnpZIxwKiU9V1JALjho/YsAZihhwhny1Vcp7Y64O/ftJ/ajXWL283aqCb7IVHdUYwr2VJSpYPl++qjLJsChm9E9Vm79LNXuzlXzDwwpz92ka0zHsIpVvWqXST5ap9JNlcp55heJ+NEmGEXBbOgAAwClZv369fvnLX6qurk4VFRWKiopSZWWlkpKS9P777wc8TsCBWJLOP/98HTx4UBs2bJDb7W63NYjXrVunefPm6YUXXmg6NnPmTCUkJMhisWjp0qWaPHmy3nvvvRZtDLJo0SLNnz+/2bG0tDTNmTOnrUpvlbpD++Svr1F4j++WDbH3Hy7JUPF/XpbNlajokZc1vecYepG8VWUqen+xQt19ZY1wqnrXJiVc8QsZluP/fljCIpR83YMq+Pc8pWx5W/dFSxWvvamKI86xRSco+dY/KMTlliU8UpLk9zbIsDb/o2JYrEq56VF5q8pVsvZfKluXJW9VqRKvnCbDyoYfAACg/f3+97/X5MmTNWnSJJ155plat26d5s+fL7vd3qJxAg7EBQUFuvvuu7Vx40a5XC6VlJRo+PDheuKJJ5rtGX0sycnJys/Pl9frldVqldfrVUFBgZKTj+5f3bBhg+677z49/fTT6tevX9PxIz9jwoQJ+v3vf6+8vDz16NEj0FvQzTffrKuuuqrZsbq6OhUXFwc8RlvyVpUp/x+Pq2bfFklSWI/Tmt4LiU5UyqTfy1tZovAeaTJszUOm65zxsvcdppCYJBlWm+o9BxSa2Pukn2nYQpQ4Yaaqhl+iJxZ/rAGpLo0f/e1Mu2EoPHWgrHZH82usx/5jYlisskW5FPfDSbJFxaho1Us6ZFiUOH7G0fdaU6mCfz0h+XxK/PG9stqjTlorAADAiezevVs33XRTs2NTp07VmDFjdOuttwY8TsCBeM6cORo0aJAWLFigiIgIVVVV6Y9//KMefvhhPfvssye8Ni4uTunp6crKytL48eOVlZWl9PT0o9olvvzyS82cOVNPPvmkBg8e3Oy9/Pz8plC8evVqWSyWkwbx/+V0OuV0OpsdKy8v75BA7PfWq2DpPDVUFCvytBGKPP185b36qBpKCxV91hUKiU05arOL8CMC8rEc2cIQSBg+zLBYFdlvqML71+mdnR5df4r9v4ZhyHXuBPlqq1Ty0T/kHHmZwnukNb3fUF6kvFcfVV3hQcmQ9v/lboXEJCn67CsVmXZmqz+3rVVs+Vhl699qfLjx/Gtl7z345BcBAADTOBwOVVRUyOl0KiEhQdu3b5fL5VJVVVWLxjH8R3Yfn8DZZ5+tNWvWKCTku5nKuro6jRo1Sp9++ulJr9+xY4dmzZqlsrIyOZ1OZWZmql+/fpoyZYruuusuDRkyRFdffbUOHDjQLOjOnTtXAwcO1KRJk+TxeGQYhqKionT//fdr+PDhkqS//vWvWrx4sYqKihQZGamwsDCtWLFCUVEnn4UsLy/Xtm3blJaWJofDcdLzW8vvrdehN59RfeEB1eZul2ELlWELkfvaWbL3Or3dPvdE3vlkt+a/vklP33+xerpP/d59ddXa9/Q0WSIciuj3/abjlTlr5a0ul/ua+xuXlFu7VPVFuWooKZBj+BhZQu0yrDY5R4yVzRnX4s/1+/0q3/i+Qt19FJ4yoHlNDXUq+/xtOb9/iSyh3+11XvnNetXs+Vqhib3kGHqRyj5/W4Vv/0UhcSny19epobJE7h/fe8qB3e/3q3zT+6ovPKCwlAGKOv08SVL1nq9V9c36ZueGJvZW1JALTviPE7/fr4qvPlRoQi+FJfU9pdoAAGiJjspMLfG73/1OQ4cO1ZVXXqnnn39ezz//vGw2m84//3w99thjAY8TcCC+5JJL9OSTT2rQoO+W+srJydH06dP17rvvtvwOgkRHf3P9fr9KVr+uipyP5Z4ws0Uzu20tz1OpKY+9p6kThujKUf1OfkEAKrasVeGKZ+X3freDoTXKJfdVdyss+buHIH11NSr495Oq3rlJkuRvqJO992AlTXz4JIHQp9qD2xWWMkCGYZHf59WhN59VxZerZNhClXjV3c1CbNnG91X45tOK+9HPFX1WhiSpznNQ+xf88ttCvIq/4g4Vvv0X2fsMlfua++Svr1XuK79RQ1mhet35VNP6za1Rtf1z5S15TLLaJG+DnGdlNLaXfPCyZLHIsHz7Qxq/T/6GOjnPvFxxP/q5fFXlqt6bLckvyZC91+my2KPkWfmCyj5/W7aYJKVO/ZNq9nwtX121wnumyxrpUu3+nMbfG/q4AaBbaCjzSFKrJpRaKhgD8f9av369KisrNWrUKFksgT/oH3DLxOGG5WuuuUYpKSk6ePCg/vnPf2rGjKP7RXF8hmEoZvRPFDP6J2aXoqS4SCXFRWjTN4faLBBHpZ+rqPSTL3NiCQ1X0jX3N70u/exNeVa+oOodGxQx4Ixm53orS+X3NsjqiFXpp8tV9P5iRX1vtGIu+Kk87zyvqu2fK/rcCarZ/ZXy35ir+LFTFDFghKyOWFVs/q8kqfzL/zQF4qIP/ibDFqLUqX9S7uKHVPjmMzJCwho3L7GFSrZQJVx+uw68cL9KPv7XMTdBOZK/of6oHm+/zytveZE8q15SSGyyekx+Qp53X1TZuixJkr3PELmveUCWsMamf7/fJ897i1S2LksNpYdUm7tD3vKipvGsjjiFJfVT1TefKWLACFVt/1wH/nqv6j0HGt+PdCm85yBV5nwie9+hir/stma939aomBM+cAkACD7emkr566qP+35d/h7lL/2TIgedrcQrp3dgZcHB6/Xq0ksv1YoVKxQaGipJGjlyZKvGCjgQ/+QnP1HPnj2VlZWlrVu3KjExUU888YTWrVvXqg9GcBh2WoI+3HBA9Q0+hdjMWzLNecYlKv1shTyrFsveb5gMi1V+v09Fq/6m0k+WSZLs/c9Q7f4c2ZzxqvjqQ1V89aEkQ/Fjp8g5Yqx8ddXK/8cfVPjWc5KksJTTVHvwG9liklSXv0t1BXsaWxW2fqqYC65XSHSiYi66QYeWzVP02VfK5viupz0sub+iBo9S6bqsE7Zy1Bfnaf/z9yky7SwlXHGHDKvt257p36quoHFvdffV98kSEqb4y26T69wJ8nsbFBKX0myJOsOwND6cGOlS0Qd/kzUqRsk3zJE1MlreihIVLJunqm8+U+yYmxV99pXK+/ujqt61STEXXK/wXukqWPakKnM+UWT6uarM+VT7nv5FszpD3X2VdN2Dsjli2vLbBgBoJ+WbVunQimcln/eE54Uk9FLsBRM7qKrgYrVaZbVaVVtb2xSIWyvgloljqaur07Bhw7Rly5ZTKsJMnWH6vz19+lWufvviOj1627kanpZoai0VOWtV8I/HFX/5HXIMvVCH3nxGFZv/o6ihF8vmiFXJR/+QDEOpk5+Qt7pc9cW5Ck3o1ewBPr+3XpVb16m+OE/FH74m+RrU4+eZOrDo1zJCwuSvrVJE2llyX3W3DFuI/H5/Y5tBj7SjZlDrSwq079npiho8SolXTpMk1ebv1qF//5+8VaWy9xkiX31tYy+wzyuLPUqGNUS+2mrJkGJG/1Sh8amy9xveoocWa/Ztkc3lbhbQG8o8aig91LQ7obeqXPVFB5q2zm6oKFG954DsvQer9uB21RbsbrrWV1ul4v8ukSRZI5yKueA6OYZc2KLvDQDgxKq2f6HClc/LXx/YDr4n5PfLW1kie58hihx8/nFPMyw2Raad2bRMansLxsz08ssva9WqVbrtttuUlJTU7P+3PXv2DHicUw7EQ4cOVU5OTmuHMF0wfnM7Uk1dg2546C2NPbePpkxon3WlA+X3+3Vw8YOq9xyULTpBdXk7FXPB9XKdd7UMw1DVjg3yVpXJcYzNR46lZt8W1RflyjHsYpVteE+1B79RSGyyos++MuD2Ac/7i1T6yXJFpI2UDItqdm+WERoue+/vqeKr1ZL8cp1/jUITezf1QxsWqxzf/1FQPfRWm7tTZRvfVV3eLtUe/Eb2/t+XYWvZv6atdodiL5woa2R0O1UJAG2nZt8WlX72pvw+X6uuD08ZoOhzJ5xwwyl/Q72KPnxV9YUHVLX9c4XEpzabpDkVNme8XD+YEFTPhARjZjry2bYjGYbRoglbZoiD8Jvb0R756yfaX1CuBb/6oenbL9fm71bhWwsaHzAbeZmcw8eYWo+3ukKH/v2kGsoat7m2RsUo4fI7ZItOUEXOWlV8tVqJV05v6gUOdv6GennefVE1+1v+d7bekytbdLwcwy6WdPSfE0t4pBxDL1J90UFVbf/ihGOFxKcG1ZJ7ADq/hrJCVWR/JPl88tVVq/STf8sSHtGqf8T7vQ2q9xxURNpZJwy4VTu+UM3ebIUk9FJoYi8lXHbbKT2IHey6cmY6aQ/x2rVrj/tefX19mxYDc5x1ulvrt+RrX365eiU5T35BOwpz91GPSYEvk9LerPYoJV3362O+FzXoXEUNCnyf9GBg2EIUf9nUVl1bsz9H+W/MbVwh4zjKN61S3aG9Af3IMPqc8YoYMKJVtRyLYbU1rrDBw4OAafw+r2pzd8jf8D/5wDAUltxflpAwSY0taQ2lh046ni06XiGuo/ccaCgvUn1RbtNrX22VCt96Tt6K7/YVCO+ZLvc1D8ga0fLg5vf7VfLxv1T84auq2nb8Z6UMW6gSxk2nDa0LOGkgfvDBB0/4/rF2m0PnMjI9SdKX+iw73/RAjOAVnjpIve76S7Ml9Y5UuWWtDr35tEITeinpJ7NksR/nf0J+vzzvLVTpJ8uaHphsK/Z+31fihF/KEmYnGOOU+Bvq5Verf4B6UobF2u5/Rv1+33H/vgbKsIYE9JNDv88rf32tDmU9pcqcT455Tqi7r5J+Mks1+7eq4N9PSoHUZrEp8cppihh0dtOhmn1blP/GH45afcHqiFWPyU8oJLYxlxi20Fb/1NMwDMWc92O5zrnyhC0XhsV63N1c0TEmTpx43O/zyy8ffwLnf51Sy0RX0JWn/1tixhP/UXiYVZnTRpldCjqx+pJ8WSNdTbNAx+P3+xtnkU6wnFBL1ebvUtH7L0l+nyz2KLl/fK/sfczti0fn4/d5VfjWApVvfK9dP8cIDVfiuLsUOfDsk5/cCvUl+cpb8pjqC/ef0jhhPQYq6doHTth2UHNgm/Jfz5S3skSSGle/SR3Y7JyGskIVvv1X+etrJDXO3saM+ol0ksBavPo11ezNPup4SEJPxf1wUrN/VIS6+8pqP/mGXGi9YMxM//rXv5q9PnTokP7xj3/oyiuv1LRp0wIeh0AchN9cM/zt7S16/b1teumRy+SMPLWlSwCzVO/NVu3+HJV/9aHqPbkKje8hSbJGRiv+stuO2h492JR/9aFKP13ebJmlxr7122WLTmi3z/X7/Sr9ZFnTg6Idwd5niGLH3NQUaCq3rlPJR2/I7/fLdc44WUIjVLz6Nfm9jT96D0s5TXGX3tq4VvhxeKvLVfjWcwrvebrCkvupePVrihl9vcJ7nHbUubW5O+V59wX5aptv7+qrrVZDaYEcw3+okJijf1TfVipzPlVt3k6FJqTqWD35p6qhrFCSoeizMmRYWzcT7auvVekn/5bNGaek6x9qal1oKPPo0IpnmtZKry/KldURK8ewMQpL6a+IvsOOOV5dwV5VbV8vIzRCjmEXnfQfzlLjbqPlG1fJX/fd98mwhSpqyIWEXxN0lsy0Z88e/epXv9Irr7wS8DUE4k7yzW1v2/YW6555H+ruiWfoohGBL1MCBCNvdYWKPni5acaqZm+2DKtNEcd5kM9qj5Lr3Ks6bOmiw2pzd6h84/vy+33y1VapMvsjhSb2kc313RKINXu+khEa3mb91tbIaLl+8GNZQsLUUOZRyaf/VkNRrqq2f66w1IGyRrT/KiL++lpV79qk8J7pColPlb+hThVfrW5cn9tibVzD27AoJDZJIXGp8nsbVL3jC4Ul91do0vE3EarZ+7XqPQcbX1isks8rIyRcUYPPbz4T6ferIvsjWcLsCksecNQ4kQPPlmPohW1818356mpU9J+X1VBa2C7jGyGhijnvGoUmnNp/z2v25yhvye+b/f2p2rFBvprKpp/AWO1RirnwBtmiXKdcN4JbZ8lMNTU1Ou+88/T5558HfA2BuJN8c9ubz+fXzb95R0P6x+v+n7VulxcgWNUV7lfBsnnNdv87kreqTKEJveQ88zIFMltnCbMrMu2sE/YO1hzYprpD+477vq+2UsX/fVWSIUtouCQpYsAIxY+d0mznw8a1r5+Ut7L0pHUFwltZopjR1yky/QfK+/ujaqgskdXukGPYxYq54PoOW2mm7IuVKv7oH019pOG9ByvhijtlWKw69NYC+euqlHDlNFlCG1dwqfh6tYo+eEX+hrrjjmkJi1D82Cmq2rFBdQV7FDvmJnneffGYbQMhcSlKHP/LDtnutrOrO7Sv8e/Ptw+sWSOdSrhyusJO8I8TdE3BmJneeOONZq9ramq0cuVKhYSE6Pnnnw94HAJxEH5zzfLkkg36+MuD+ttvLpPNat6udUBHq9qxQfn/fFz+upqAr4kYMEKxF914zB7I6t1fyrPyRZ2s/SA0qV/jDoIdOLOW98ZcVe/cJMMWIsNiVdJPHyTYAAhIMGamn/3sZ81eR0REaNCgQZo0aZJiYgLfnZVHI9HkzNOT9O66vfp6p0fDTmu/fkUg2ET0/7563/VX+WoqAjq/8pv18qx8QVXbj//juIgBIxR36a0nXNTf6ojt8NUw4i6+Ufu++VzWKJeSr38o6PuqAeBEXnrppTYZh0CMJsPTEmSzWvRZdj6BGN2OJcwe8AYr0SMvU3iPgaovzj3m+5aQcNn7Dw/Kpd9CYlOUOvkPskbF8lASgE5v6dKlGjRoULMd63JycpSTk6MJEyYEPA6BGE3sYTYNPS1e67LzdOu4wabvWgcEs7DkfgpL7pytBqEJvcwuAQDaxLx587R06dJmx5KSknTHHXe0KBDTKIpmzjo9SbmFlTpwKLAfHQMAAJiloqJCUVHNf9rlcDhUVlbWonEIxGjmzPTGdSbXfZ1vciUAAAAn1r9/f73zzjvNjr377rvq379/i8ahZQLNJMZGqE+yU59tydOPLzp6fU4AAIBgce+992rq1Kl666231LNnT+3du1dr167VggULWjQOM8Q4ypmnu5W9q0gVVcdf7xMAAMBsI0eOVFZWloYMGaLq6moNHTpUWVlZGjGiZZsZMUOMo5w9OEmvv/+N1mXn6eKRPHwDAACCU11dnRISEjR16tSmY/X19aqrq1No6PG3ev9fzBDjKGm9YpQQY9fqjQfNLgUAAOC4fv7zn+vrr79uduzrr7/Wrbfe2qJxCMQ4imEYOn9YD23YWqBy2iYAAECQ2rZtm4YNG9bs2NChQ5WTk9OicQjEOKbRw3vI6/Nr7eZjbzwAAABgNofDocLCwmbHCgsLZbcHttHSYQRiHFP/1Gglx0Vq9YYDZpcCAABwTJdcconuuecebdu2TdXV1dq6daseeOABXXbZZS0ah0CMYzIMQ6O+30Nfbj+kkvJas8sBAAA4ysyZM9W/f39de+21OuOMM3Tdddepb9++uvvuu1s0juH3+/3tVGOnUF5erm3btiktLU0Oh8PscoLK7twyTX/8A93+46G64ry+ZpcDAABMFMyZye/3q7i4WDExMTIMQz6fTxZL4PO+zBDjuHonOdTTHaXVG2mbAAAAwcswDMXGxmrbtm3KzMzU6NGjW3Q96xDjuAzD0Kjhqfr7yhx5SqsVF92yBnUAAID2VlRUpOXLl2vp0qXKycnRiBEj9OCDD7ZoDGaIcUKjhqfI75fWbGJNYgAAEBzq6+v1zjvv6Pbbb9fo0aO1ZMkS/fCHP5TT6dS8efNa/FAdM8Q4odREh/qlRGv1xgMaP7q/2eUAAADovPPOk2EY+vGPf6zp06dr8ODBkqS///3vrRqPGWKc1PnDU7R1T7Hyi6rMLgUAAEADBw5UeXm5Nm3apM2bN6u0tPSUxiMQ46RGDe8hSVrDw3UAACAIvPTSS3r33Xd13nnn6YUXXtB5552n22+/XVVVVWpoaGjxeARinFRSXKTSern0IYEYAAAEiR49eugXv/iFVq5cqYULFyohIUEWi0Xjxo3T3LlzWzQWgRgBGTW8h3YeKNXBQxVmlwIAANDMyJEj9eijj+qjjz7SQw89pG3btrXoegIxAnL+sMa2CWaJAQBAsAoLC1NGRob++te/tug6AjECEu+ya3C/OP3n833q5psbAgCALoZAjIBdPLKnDhyq1Na9xWaXAgAA0GYIxAjY+cNSFBpi1arP9pldCgAAQJshECNgEeEhOvd7yfpw4wHV1nvNLgcAAKBNEIjRIpec00uV1fVavYGH6wAAwMnNnz9fAwcObFr5YePGjRo3bpwuvfRS3XLLLfJ4PCZXSCBGCw3pH6+e7ii9+fEus0sBAABB7uuvv9bGjRvVo0fjalU+n0/33XefZs+erXfeeUcjR47U448/bnKVBGK0kGEYuvwHfbV9X4m28XAdAADdTl5envbv39/sq6ys7Kjz6urq9Jvf/EZz5sxpOvbVV18pLCxMI0eOlCT99Kc/1dtvv91RpR+XzewC0PlcPLKnFq/I1psf7VJarxizywEAAB1o0qRJKiwsbHZs2rRpmj59erNj8+bN07hx45Samtp0LDc3VykpKU2vY2Nj5fP5VFJSIpfL1b6FnwCBGC0WER6iC0f01Hvr9urWcd+TMzLU7JIAAEAHWbhwoex2e7NjTqez2esNGzboq6++0r333tuRpbUagRitcsUP+uqtj3frvXV79OOLTjO7HAAA0EGSkpLkcDhOeM5nn32mHTt2aMyYMZIa2yxuvfVW/exnP9PBgwebzisqKpLFYjF1dliihxit1DvZqcH94rTi493y+di5DgAAfGfq1Klas2aNVq1apVWrVikpKUnPP/+8Jk+erJqaGq1fv16S9Oqrr2rs2LEmV0sgxim44gd9lV9UpS+2FphdCgAA6AQsFovmzp2rRx55RJdccok+++wz3XPPPWaXRcsEWu+cIcmKcYTpzY92aWS62+xyAABAkFq1alXTr8844wwtX77cxGqOxgwxWi3EZtGl5/TR5zn5yvNUml0OAABAqxCIcUrGnttbhmHo7bW7zS4FAACgVQjEOCVx0Xad870krfx0r+rqvWaXAwAA0GIEYpyyy3/QV+VVdVqz6YDZpQAAALQYgRinbOiAeKUmRunNj3aZXQoAAECLEYhxygzD0OU/6Ktte0v0zb5is8sBAABoEQIx2sTFI3sqPNSqrDXMEgMAgM6FQIw2EWkP0Y/O7q3/frFf+UVVZpcDAAAQMAIx2szVFw2QYRh6Y9U3ZpcCAAAQMAIx2kxctF2XnN1L763bo0PF1WaXAwAAEBACMdrU1RefJun/t3fn8VGW9/7/XzOTnWQymayTjZCVkLAHcEMrYEEbAbUefHhw1357rLTHntqi7Q+X9hxFv/VbPeLx5++0WvvtEWv1oMUqBRFZBCGyE0ggZN/3ECAsM/P7Y8JgDotYk9zJzPv5eOQhXDOJn/vOzc07F5/7uuCdTzRLLCIiIsODArH0q7ioMGZOSWXVlkpaOzVLLCIiIkOfArH0u+/OyMLldvPuJ4eMLkVERETkK7ZqLG0AACAASURBVCkQS79LiB7BjMkpfLS5gvauHqPLEREREbkoBWIZELfOyuK008W76zRLLCIiIkObArEMiMSYcGYUpLJyYzl1Ld1GlyMiIiJyQQrEMmDuuCGXwAATv31vn9GliIiIiFyQArEMGLs1hNuuy2FrcQNF+xuNLkdERETkvBSIZUDdOD2DxJgR/Od7ezh12mV0OSIiIiLnUCCWARUYYOb+efnUNh/l/fVlRpcjIiIicg4FYhlwU8YkMHVMAm+uLqGp7ZjR5YiIiIj0oUAsg+J/3TQWgFdX7DG4EhEREZG+FIhlUMTZw7jtuhw+39fA1n0NRpcjIiIi4qVALINm3tUZpMRH8P/+9256Tpw2uhwRERERQIFYBlFggJkffHc8Te3HeePD/UaXIyIiIgIoEMsgy0uPpvDKUazceJh9h1uNLkdEREREgVgG353fGUNcVBgvvrWDnpNqnRARERFjKRDLoAsNDmDRP0ygruUof/zogNHliIiIiJ9TIBZDjM+KZc7laby/vowDlW1GlyMiIiJ+TIFYDHNP4RjskaG8sHwHJ085jS5HRERE/JQCsRgmLCSQRbdOoKapmzf/VmJ0OSIiIuKnFIjFUJNGx3Hd1FTe/eQgpVXtRpcjIiIifkiBWAx379x8oqwhPP9f27XqhIiIiAw6BWIxXHhoIA/fNona5m5+95d9RpcjIiIifkaBWIaE8dmxzL8mgw8/q2BrcYPR5YiIiIgfUSCWIePOG3JJc1h58a0dtB/pMbocERER8RMKxDJkBAZY+MnCyRzrOc2Lb+3E7XYbXZKIiIj4AQViGVJGJli5u3AMRfsb+cvGw0aXIyIiIn5AgViGnBuvSmfqmAR++/4+9hxqMbocERER8XEKxDLkmEwm/uUfJ5EUO4Jn3thGY9sxo0sSERERH6ZALENSWEggv7hnGk6Xm3997XOOn9D6xCIiIjIwFIhlyEqMDeenCwuorO9i6RvbcDpdRpckIiIiPkiBWIa0SaPj+KdbxvPFgSZefme3Vp4QERGRfhdgdAEiX2XO5Wk0dxznT2tKiY0K5bbrcowuSURERHyIArEMCwvnjKal4zh//OgAMZGhzJqaanRJIiIi4iMUiGVYMJlMPHTrBNo6e3jp7Z2EhQRwxbhEo8sSERERH6AeYhk2AgPMPHr3FLJSbCz9QxEbd9UaXZKIiIj4AAViGVbCQgJ58nuXM3pkFM/9oYh122uMLklERESGOQViGXbCQgJ54oHLyUuP4f/81xesLao2uiQREREZxhSIZVgKDQ5gyf3TGJsZw2+Wb2fN1iqjSxIREZFhSoFYhq2QoAD+n/suY0JWLC/+aQertlQaXZKIiIgMQwrEMqwFB1r4xb3TmJgTx0tv7+TDz8qNLklERESGGQViGfaCAi384p6pTBkTz8vv7ObdTw4aXZKIiIgMIwrE4hMCAyw8etdUpk9I4rWVxbzx12Jt8ywiIiKXRBtziM8IDDDzL/84mbCQAN7++CBtXT380y3jCQ60GF2aiIiIDGEKxOJTLGYTP/jueKIiQli+uoSymk4evWsKibHhRpcmIiIiQ9SgtUyUl5ezYMECZs+ezYIFC6ioqDjnPcuWLeM73/kON954IzfffDMbNmzwvrZ48WKuvvpq5s2bx7x58/iP//gP72stLS3ce++9zJ49m7lz57Jr167BOCQZokwmE/84ZzSP338ZrZ3H+ef/8ymbdtcZXZaIiIgMUSb3IDVa3nnnndxyyy3MmzeP9957j3feeYc33nijz3s2bNhAQUEBoaGhHDhwgIULF7Jx40ZCQkJYvHgx+fn5LFy48Jyv/eijj5KSksKDDz5IUVERjz32GKtWrcJkMn1lXUeOHKG0tJTs7GwiIiL67XhlaGhqP8azbxRRUtXO3Onp3F2YR2CAWudFRES+Ll/OTIOSDFpbWykuLqawsBCAwsJCiouLaWtr6/O+6dOnExoaCkBOTg5ut5uOjo6v/PofffQRt912GwAFBQUEBQWxZ8+ec97X1dVFTU1Nn4/m5uZvengyhMVFhfH0D67ixunpvL/hMI++vJGm9mNGlyUiIiJDyKAE4vr6euLj47FYPA83WSwW4uLiqK+vv+DnrFixgtTUVBISErxjr732GjfeeCMPPvggZWVlALS3t+N2u7Hb7d73ORwOGhoazvmav//975k5c2afjx/96Ef9dZgyRAUGmPne/LH87M4CqhqO8KNfr2Nr8bnXh4iIiPinIflQ3datW3nhhRf43e9+5x17+OGHiY2NxWw2s2LFCu6//37WrFnztb7uXXfdxU033dRn7OTJk7S3t/dL3TK0XTU+ifSkSJb+vohf/vZzbv5WJnfckEuARS0UIiIi/mxQkoDD4aCxsRGn0wmA0+mkqakJh8Nxznt37NjBI488wrJly0hPT/eOx8fHYzZ7yp0/fz7Hjh2joaGBqKgogD7tF/X19X1mls+wWq0kJyf3+YiNje3XY5WhLTEmnOd+OJ3rr0jj3XWHeOzlTTS3Hze6LBERETHQoATi6OhocnNzWblyJQArV64kNze3T5sDwO7du3n44Yd58cUXycvL6/NaY2Oj99cbNmzAbDYTHx8PwJw5c1i+fDkARUVF9PT0kJ+fP5CHJMNYUKCFB28ZzyMLJ1NR38mPnl/Hlr0Xbt8RERER3zZoq0yUlZWxePFiurq6sFqtLF26lPT0dB544AF++MMfMnbsWG655RZqa2u9QRfg2WefJScnh7vvvpvW1lZMJhPh4eH89Kc/ZcKECQA0NzfzyCOPUFdXR3BwME8++SSTJk26pLp8+YlJ+Wq1zd08+4ciDtd2MmtKKg/MzycsJNDoskRERIYcX85MgxaIhypf/ubKpTl12sXy1SX8+eNSom2h/K/5Y5mWf247j4iIiD/z5cykp4nE7wUGmLnj+lye+cF0QoIC+NVrW3nqt1toaD1qdGkiIiIyCBSIRXrljrLz4r98i3sK89hzqIUfPLuWt9aUcOq00+jSREREZAApEIt8SYDFzM3XZvLyT2dSMCae//vhARb970/YvKceP+8uEhER8VkKxCLnERsVyqN3TeXJBy4H4N9e38q/vLCe7SVNCsYiIiI+RoFY5CImjY5j2SMz+OE/TKCj+wSPv7qZx/5jE8XlrUaXJiIiIv1kSO5UJzKUWCxmrps2km9NTmbVlkreWlPKz17ayITsWG76ViYTs2MxmUxGlykiIiJ/JwVikUsUGGCh8Kp0Zk1N5a+bynlvfRmPv7qZNIeVeVdncM2kJAIDLEaXKSIiIl+T1iH24TX1ZGCdOu3k0+21rPj0EJUNR7Bbg7nhylF8e+pIoqwhRpcnIiLSr3w5M2mGWOTvFBhgYdbUVGZOSWFHaTMr1h3i/354gDdXlTA1L4FvTxvJxJw4LGa1U4iIiAxlCsQi35DJZGJSThyTcuKoaTrC6s+r+Liois176omJDGHm1FRmTUklIXqE0aWKiIjIeahlwoen/8U4p0672FrcwN8+r2RHSRNuN+SlR3Pt5BSuGp/IiNBAo0sUERH5Wnw5MykQ+/A3V4aGpvZjfLq9ho+3VVPb3E1QgJnL8h1cW5DCxOxYLBatfigiIkOfL2cmtUyIDLC4qDBunZnNd2dkcbC6g7VF1azfUcP6nbVERQRzzaRkZhSkMCox0uhSRURE/JICscggMZlMZKdGkZ0axX1z8yna38DaompWbjzMik/LSE+M5NqCFK6ZlERUhFapEBERGSxqmfDh6X8ZHjq7T7BhZy1ri6o5WN2B2ex5SG/mlBSm5TkIDFBLhYiIGM+XM5NmiEUMFhkeTOFV6RRelU514xE++aKaT4qqWfpGI5HhQcwoSGX2ZSNJig03ulQRERGfpBliH/5pR4Yvp8vNrtJmPtpSwdZ9DThdbvIzopk9bSRT8xIIC9EqFSIiMrh8OTNphlhkCLKYTUwaHcek0XG0d/WwZlsVf/u8kl//13YCLCby02OYMiaeKWMScMRofWMREZFvQjPEPvzTjvgWl8vN/oo2thU3sLW4gerGbgASosMYnxXLuMwYxmXGYosINrhSERHxRb6cmTRDLDJMmM0m8tKjyUuP5u7CPOpbjlK0v5FdB5vZuLOWVVsqAUhzWBmXFcP4rFjGjIomXJuAiIiIXJRmiH34px3xH06ni7LaTnYdbGbXwWb2l7dx8rQLkwlGJUaSnxFNfnoMeenRWEcEGV2uiIgMQ76cmTRDLOIDLBazd43jW2dmc/KUk5LKdvaWtbD3cCsffVbB++sPAzAyIYL8jBjyMzyzzVrzWERE/J0CsYgPCgq0MDYzhrGZMQCcOu2ktKqDvYdb2FvWypptVXywqRyA5LhwT0BOjyZ3lJ24qDAjSxcRERl0CsQifiAwwOLtP14wC047XRyq6WBvWSt7y1r4dHsNH22uACAmMoTcUdHkptnJHWVnlMOKxaLNQURExHcpEIv4oQCLmdEj7Yweaee7M7JwOl2U13exv7yN/RVtFJe3smFnLQChwRayU6MYMyqa8Vmx5IyMIkABWUREfIgeqvPhBnGRv5fb7aa5/TjFFW3sL29lf0UbFfVduN0QGhzAuMwYJmbHMnF0HIkx2kFPRMQffJ3M1N7ezk9/+lOqqqoICgpi5MiRPPXUU9jtdnbu3MmSJUs4ceIESUlJPPfcc0RHRw/SUZyfArECscgl6T52kl2HWthZ2syOkiYa244BZ9dBHjPKzug0O47oEZhMJoOrFRGR/vZ1MlNHRwclJSVMmzYNgKVLl9LZ2cmvfvUrZs+ezdNPP01BQQEvv/wy1dXVPP3004NxCBeklgkRuSThYUFcOS6RK8clAlDX0s2OA01sL+m7DrItPJjRaVHkpnkCcmayjaBAi5Gli4jIILPZbN4wDDBhwgTefPNN9u7dS3BwMAUFBQDcdtttzJw5U4FYRIanxJhwEq8K5ztXpeNyualuOuLtQd5f0caWvQ2Ap185MzmS0Wl2z4N6aXairFrqTURkuGpoaKCzs7PPmNVqxWq1nvf9LpeLN998kxkzZlBfX09iYqL3NbvdjsvloqOjA5vNNqB1X4wCsYh8Y2aziZEJVkYmWJlzeRoAHUdOcKCyjQMVbRSXt/HBpnJWfFoGQJw9jIykSDKTbWQkR5KRZNOW0yIiw8Tdd99NS0tLn7GHHnqIRYsWnff9v/zlLwkLC2PhwoWsXr16MEr82hSIRWRA2CKCuSzfwWX5DsCzFnJZbSf7y9soqWrncG0nm/fUe98fHRlCRtKZgBxJZooNuzVE/cgiIkPM66+/TmhoaJ+xC80OL126lMrKSl555RXMZjMOh4O6ujrv621tbZjNZkNnh0GBWEQGSWCAxbvU2xlHj5/icF0nZTUdlNV0Ulbbwbb9DZx51NcWHkx6b0DOSLaRkRRJvD1MIVlExEAJCQmXtBDB888/z969e3n11VcJCgoCID8/n56eHoqKiigoKGD58uXMmTNnoEv+SlplQqtMiAwpx0+cpqKui7JaT0g+VNNBVeMRXC7PrSo8NNDbZpGR7AnKjugRmM0KySIiA+nrZKaDBw9SWFhIWloaISGe50aSk5NZtmwZ27dv5/HHH++z7FpMTMxgHMIFKRArEIsMeSdPOamo76Kstnc2ubaTirouTjtdgGdt5PSkyD5BOTk2XDvsiYj0I1/OTGqZEJEhLyjQs1tedmqUd+zUaRfVjUe8AbmspoOPNldy8tRh7+eMcljPtlwk2RjpiCAwQEvAiYhIXwrEIjIsBQaYSU+KJD0pkut6x5wuN7VNRyir9bRaHK7t5NPtNXz4WQUAFrOJ1IQIz2xyko30pEhGJVoJCwk07DhERMR4CsQi4jM8gddKaoKVayenAOByuWlsO8bhWs9De2W1nXyxv4mPt1UDYDJBYswI0pM8D+2dCdmR4VoGTkTEXygQi4hPM5tNOGJG4IgZwZXjPYvBu91u2rp6KKvt9ATlmg5KKtvYsLPW+3kxttDeVgvPg3vpSZFER2oZOBERX6RALCJ+x2QyER0ZSnRkKFPHJHjHjxw7yeGaTk9Pcq2n5WJr8dll4CLDg0hPjOx9gM8zo5ygFS5ERIY9BWIRkV4RYUGMz45lfHasd+zMMnCHe9stymo7eW99GaednpTsXeEi6WxQTonTChciIsOJArGIyEWEBgeQO8pO7qizG4qcOu2iqqGrty/Z03ax6vNKTpx0AhAcZCE9MZKsVBtZyTayUqO0VrKIyBCmQCwi8jUFBpg9LRPJtj4rXNQ1d1NW08HBas/HR5sreb93GbgRIQFkJNvISrGRlRJFZoqNuKhQ9SSLiAwBCsQiIv3AYjaREh9BSnwE3+pd4cLpdFHd1M3BqnYO9gblL7dbWEcEkZnSG5J7Z5Lt1hAjD0NExC8pEIuIDBCLxUyaw0qaw8p100YCcOq0Z9e9Q9VnZ5LfLj3o3Zrabg3pnUU+O5NsHRFk5GGIiPg8BWIRkUEUGGAhKyWKrJQoru8d6zl5mvLaLg5W984kV3Xw+b4G7+fE28M8M8nJnm2pM5JtRIQpJIuI9BcFYhERg4UEnfvg3tHjpyir7eBQdQelvTPJm3bVeV+Ps4eRmezZcS+zNyhrMxERkb+PArGIyBA0IjSQcZmxjMs8uwTckWMnKavpoKzGszV1WW0nn+2u974eExnifdgvs3cmWT3JIiJfTYFYRGSYiAgLYkJ2HBOy47xj3cdPUV7bG5B7g/KXNxOxW4NJ/9IsckaSjRibdtwTEfkyBWIRkWEsPDSQsZkxjM2M8Y4d6zlFeV0XZTUd3pnk7QcacX1px72MJFvvRiKekJwQHaaQLCJ+S4FYRMTHhIUEkpceTV56tHes56Rnxz1PSPZsJvLf6w7h7E3JYSGeHfc8u+55ZpOTY7Xjnoj4BwViERE/EBIUwOg0O6PTvrzjnpPK+iO9W1J3cLi2k482V3KydzORoAAzoxIjSU/2bE2dkWRjpCOCwACLUYchIjIgFIhFRPxUYICFzBQbmSk2wLNOstPpoqa527MtdY0nKH+6vYYPP6sAPBuQpCZE9Gm5GJUYSWiw/joRkeFLdzAREfGyWMyMTLAyMsHKtb077rlcbhrbjnlnkctqOtm2v4E126oAMJkgMSa8tx/ZM5OcnhyptZJFZNhQIBYRkYsym004YkbgiBnBVeOTAHC73bR19fTOIndSVtPB/oo21u+o9X5eXFQoGcm9M8lJWgZORIYuBWIREfnaTCYT0ZGhREeGMjUvwTve2X2Cw7Weh/bOBOXNe86ulWyLCCbjzMN7yTYykiKJt2uFCxExlgKxiIj0m8jwYCbmxDEx5+xayV9eBq6sNyzvKG3G1bvCxYjQwLMhuTcoJ8aGYzErJIvI4FAgFhGRAXW+ZeBOnHJSWd/lDchlNR18sKmcU6ddAAQHWRjlsPZpuUhNsBIYoGXgRKT/KRCLiMigCw60kJ0aRXZqlHfstNNFTVM3ZTUd3paLtUXVfLCpHIAAi4nUBGvvg3uemeQ0h5UQrXAhIt+Q7iIiIjIkBFjMpDmspDmszJziGXO53DS0HvUuAVdW28mWvQ2s3upZ4cJsgqS48HN23hsRGmjgkYjIcKNALCIiQ5bZbCIxNpzE2HCmTzy7wkVLR48nIPfuurenrIV122u8n5cUG052qo3s1CiyUmyMSowkKFAbiojI+SkQi4jIsGIymYiNCiU2KpTL8h3e8Y4jJyir7eBQdQelVR3sKG3mky88ITnAYiItMZKsFBvZKVFkp9pIiovQg3siAigQi4iIj7BFBDN5dDyTR8cDZ2eSS6vbOVjVzsHqDtZ9cXbXvdBgC5nJnnCc1TuTHGsL1RJwIn5IgVhERHzSl2eSrxyXCHh6kmubuymtaqe0NyS/t76M007PEnC2iGCyU6LISrV5/6sd90R8nwKxiIj4DbPZREp8BCnxEcyckgrAqdNOyuu6OFjVTml1Bwer29m2vwG3JyPjiB5BVqqNrN5Wi/SkSEKC9NeniC/Rn2gREfFrgQFnl4D7Tu/Y0eOnOFTTwcHqDkqr2ik+3OrdltpsNjEyIaL3gT1PSE6Nj8Bi0RrJIsOVArGIiMj/MCI0kPFZsYzPivWOtXX1nJ1Frmpn4646Vm2pBCAo0EJmcqQ3IGenRmlLapFhRIFYRETkEtitIUzLdzCtd2ULt9tNfctRb0A+WN3Bh5+V8956z257EWFBfXqRs1OisEUEG3kIInIBCsQiIiJ/B5Pp7BrJ35qUDHh226us7/K2Whys7uBPJSW4evuR46JCvbPIWalRZCbbCNVOeyKG059CERGRfhJgMZORbCMj2cacy9MA6DlxmrLaTm9ALq1qZ9PuOsDTj5zmsJKbZmf0yChGp9nVaiFiAAViERGRARQSHEBeejR56dHesc7uExys7uBAZRsHKtpYW1TFB5vKAc/Sb18OyJnJNu2yJzLAFIhFREQGWWR4MAW58RTkejYRcbrcVDV0sb/CE5APVLSzeU894NllLyPJRk5aVG9QthNjCzWyfBGfo0AsIiJiMIvZxKjESEYlRnLDFaMAz1bUZ2aQD1S289FnFby//jAAMbZQRo/0BOTcUXbSEyO17JvIN6BALCIiMgTZIoK5LN/BZb2rWpw67aK8rtMbkPdXtLFxl6cXOSzE05YxLjOG/IwYRiVGYjGrD1nkUikQi4iIDAOBAWbvBiJze8daOo5TXN7K7kMt7DnUwrbiRgDCQwO9AXlsZgwjE6yYFZBFLkiBWEREZJiKsYVy9cRkrp7oWfattfM4ew61eAJyWQuf72sAPGsij8uKYWJ2LBOy44i3hxlZtsiQo0AsIiLiI6IjQ/nW5BS+NTkFgKb2Y+wta2HXwRZ2ljazqbfFwhEzgglZsUzIjmVcVizhoYFGli1iOAViERERHxUXFcaMglRmFKTidrupaepmR2kTO0ubWbe9mg83V2A2QVZKFBOyY5mYE0fOyCgC9ICe+BkFYhERET9gMplIiY8gJT6CudMzOO10UVLZzs7SZnaUNvH2x6W8taaU0GALYzNimZjjmUFOig3XRiHi8xSIRURE/FCAxezdMOQf54ym+/gp9hxqZkdJMztLm9la7Ok/jo0KPdtekRmLLSLY4MpF+p8CsYiIiBAeGsjlYxO5fGwiAA2tR9lR2syOkiY+213H6q1VAKQ5rIzLjGF8Viz5GdGEhaj/WIY/BWIRERE5R0L0CK6/fATXX56G0+mirLaTXQeb2X2whY82V/D+hsOYzSaykm2My/IE5Nw0u7aZlmHJ5Ha73UYXYaQjR45QWlpKdnY2ERERRpcjIiIy5J067eRARbsnIB9qoaSqHZfLTWCAmdw0O+OzYhmfFUNmsk076PkQX85MmiEWERGRryUwwMLY3k0/AI71nGLf4VZ2HWxh96Fm/vDhfv7woWcHvfz0GMb3ziCnJkToAT0ZkhSIRURE5BsJCwlkypgEpoxJAKCz+wS7D7V4Z5DPPKBnCw9mXGYM43pnkBOiRxhZtoiXArGIiIj0q8jwYKZPSGL6hCQAmtqOsftQs3cGef3OWgDi7GGM731Ab1xmDFHWECPLFj+mQCwiIiIDKs4exqypI5k1daR3g5BdB5vZdbCZz/bUe1ewSE2I8PQfZ8aQnxHDCO2gJ4NEgVhEREQGzZc3CCm8Kh2ny83h2g7P7PHBZlZtqeQvGw5jNkFmiq03IMeSO0orWMjA0SoTPvzEpIiIyHBz6rSTA5Xt3iXeSqvacbrchARZmJgTx7S8BApy44kM1wYhg82XM5NmiEVERGTICAywMDYjhrEZMTDn7AoW2/Y3snVfA5v31GM2Qe6oaKblJTAtL4HE2HCjy5ZhTjPEPvzTjoiIiC9xu92U1XSyZV89W/c1UF7XBUBKfDhTxyRwWb6DrNQoLGYt7TYQfDkzKRD78DdXRETElzW2HWPrvgY+31fP3rJWnC43tvBgpoyJZ1peAuOzYwkJ0j+G9xdfzky6SkRERGRYireHceP0dG6cnk738VN80dtWsWl3Hau3VhEUaGF8VoxnjeTceGJsoUaXLEOUArGIiIgMe+GhgVwzKZlrJiVz6rSLfYdb+HxvA1v3N7KtuBGA9KRIpoyJZ+qYBDKTbZjVWiG91DLhw9P/IiIi/s7tdlPdeIStxY1sK27gQEUbLjfYIoKZkhvPlDHxTMiOIzRYc4RfxZczk777IiIi4rNMJhOpCVZSE6x8d0YWXUdPsv1AI1uLG/mst7UiwGJmXGYMU8bEM2VMAvH2MKPLlkGmGWIf/mlHRERELuy008X+8ja2FjewrbiB2uajAIxMiPD0HY+JJ2ekXatW9PLlzKRA7MPfXBEREbl0dc3d3taKfYc9q1ZEhAVRkBvH1LwEJmbH+fV20r6cmdQyISIiIgIkxoYz/5pw5l+TQffxU+woaWJrcQNF+xv55IsaLGYTeenRTM3zzB4nxmhDEF+hGWIf/mlHREREvjmny01JZRtb9zWwbX8jVQ1HAEiKDfeG4zFpdiwWs8GVDixfzkwKxD78zRUREZH+19B6lG29rRV7ylo57XQxIjSQyaPjmDImgcmj44gICzK6zH7ny5lJLRMiIiIiX0NC9AjvhiDHek6xs7SZbcWNFO1vZP2OWsxmE7lpdqaOiefysYk4YkYYXbJ8Bc0Q+/BPOyIiIjJ4XC43B6vb2VbcyNbiBsrrugDPhiBXjkvkyvGJJMUO375jX85MCsQ+/M0VERER4zS1HeOzPXVs2lXHgcp2ANIcVq4cn8iV4xJJiR9eucOXM9OgBeLy8nIWL15MR0cHNpuNpUuXkpaW1uc9y5Yt469//Stms5nAwEAefvhhpk+f3uc9n3/+OXfffTc///nPWbhwIQA7d+7k6aef5tixYwQFBfHUU0+Rl5d3SXX58jdXREREhoaWjuN8truOTbvr2F/RhtsN6YmRXD0xiekTk4iLGvqbgfhyZhq0QHznnXdyyy23MG/ePN577z3eDQH6PgAADwhJREFUeecd3njjjT7v2bBhAwUFBYSGhnLgwAEWLlzIxo0bCQkJAaC7u5t77rkHu93O9OnTWbhwIW63m6uvvprnn3+eKVOmUFRUxJIlS/jggw8wmb56IW1f/uaKiIjI0NPaeZxNu+tYv72WkirPzHFump1rJiZx5fgkbBHBBld4fr6cmQZlfZDW1laKi4spLCwEoLCwkOLiYtra2vq8b/r06YSGhgKQk5OD2+2mo6PD+/ozzzzDfffdR1RUlHesvb2dI0eOMGXKFAAKCgpoaGhg3759A31YIiIiIl9bdGQoc6dn8L9/dDX/32OzuOP6XI72nOKV/97DXU+t4vFXN/PxtiqO9ZwyulS/MSirTNTX1xMfH4/FYgHAYrEQFxdHfX09drv9vJ+zYsUKUlNTSUhIAODTTz/lyJEjzJkzh3Xr1nnfZ7fbiYqKYs2aNcyaNYu1a9dy9OhR6urqyM/P7/M1u7q66Orq6jN28uTJfjxSERERkUuXED2Cf5iVzT/Myqaivov1O2r4dEctv1m+g2V/3kVBbjzXTEymYEw8wYEWo8v1WUNy2bWtW7fywgsv8Lvf/Q7wBNlf//rXvPbaa+d9/0svvcRzzz3HsmXLGD9+PFlZWd7w/WW///3veemll/qMZWdn88QTT/T7MYiIiIh8HWkOK2mOMdxxfS4lVe18ur2Gjbvq2LynntDgAK4an8iMghTGjIrGbP7qtlC5dIMSiB0OB42NjTidTiwWC06nk6amJhwOxznv3bFjB4888ggvv/wy6enpAJSWltLc3Mytt94KeNokPvnkEzo6OnjooYfIy8vj9ddfBzwzvldeeSWZmZnnfO277rqLm266qc/YyZMnaW9v7+cjFhEREfn7mEwmRo+0M3qknfvn5rOnrIVPvqhhw85aVm+tIt4exrWTU5hRkKI1jvvJoATi6OhocnNzWblyJfPmzWPlypXk5uae0y6xe/duHn74YV588cU+q0QUFBSwefNm7+8XL15Mfn6+d5WJ5uZmYmNjAXj11VeZMmUKI0eOPKcOq9WK1WrtM3bkyBEFYhERERmSLBYzE7LjmJAdxz/dPI7P9tTzSVE1b60pYfnqEsaMsnPnDWPIS482utRhbdBaJp544gkWL17Myy+/jNVqZenSpQA88MAD/PCHP2Ts2LE8+eST9PT0sGTJEu/nPfvss+Tk5Fz0a7/11lv85S9/weVykZ+fz7/9278N6LGIiIiIDLaQ4ABmFHhmhpvbj7NuezWfbq+haH+jAvE3pI05fHgJEREREZH+4suZaVCWXRMRERERGaoUiEVERETErykQi4iIiIhfUyAWEREREb+mQCwiIiIifk2BWERERET8mgKxiIiIiPg1BWIRERER8WsKxCIiIiLi1xSIRURERMSvKRCLiIiIiF9TIBYRERERv6ZALCIiIiJ+TYFYRERERPpdeXk5CxYsYPbs2SxYsICKigqjS7ogBWIRERER6XePP/44t99+O6tWreL2229nyZIlRpd0QQrEIiIiInLJGhoaqKmp6fPR1dXV5z2tra0UFxdTWFgIQGFhIcXFxbS1tRlR8lcKMLoAERERERk+7r77blpaWvqMPfTQQyxatMj7+/r6euLj47FYLABYLBbi4uKor6/HbrcPar2XQoFYRERERC7Z66+/TmhoaJ8xq9VqUDX9Q4FYRERERC5ZQkICERERF32Pw+GgsbERp9OJxWLB6XTS1NSEw+EYpCq/HvUQi4iIiEi/io6OJjc3l5UrVwKwcuVKcnNzh2S7BGiGGJfLBcCxY8cMrkRERERk6DqTlc5kp6/yxBNPsHjxYl5++WWsVitLly4dyPK+EZPb7XYbXYSRGhsbqampMboMERERkWEhOTmZ+Ph4o8voV34/QxwdHQ1ASEgIZrM6SERERETOx+Vy0dPT481OvsTvZ4hFRERExL9pSlRERERE/JoCsYiIiIj4NQViEREREfFrCsQiIiIi4tcUiEVERETErykQi4iIiIhfUyAWEREREb+mQDxIysvLWbBgAbNnz2bBggVUVFQYXdKgmjFjBnPmzGHevHnMmzePDRs2ALBz507mzp3L7Nmzuffee2ltbTW40v61dOlSZsyYQU5ODqWlpd7xi10PvnytXOh8XOj6AN+8Rtrb23nggQeYPXs2N954Iw899BBtbW3AxY/XF88FXPx85OTkcOONN3qvjZKSEu/nrV27ljlz5nDdddfxz//8zxw/ftyoQ+hXDz74IHPnzmX+/Pncfvvt7N+/H/DP+8aFzoW/3TPOeOmll/rcP/3xfjFg3DIo7rjjDveKFSvcbrfbvWLFCvcdd9xhcEWD69prr3WXlJT0GXM6ne5Zs2a5t23b5na73e5ly5a5Fy9ebER5A2bbtm3uurq6c47/YteDL18rFzof57s+3G7fvUba29vdW7Zs8f7+mWeecT/66KMXPV5fPRdu94XPh9vtdmdnZ7u7u7vP+Zzu7m73FVdc4S4vL3e73W73Y4895v73f//3Qal3oHV1dXl/vXr1avf8+fPdbrd/3jcudC787Z7hdrvde/fudd93333eY/fX+8VA0QzxIGhtbaW4uJjCwkIACgsLKS4u9s6A+Ku9e/cSHBxMQUEBALfddhsfffSRwVX1r4KCAhwOR5+xi10Pvn6tnO98XIyvXiM2m41p06Z5fz9hwgTq6uouery+ei7gwufjYtavX09+fj5paWmA53x8+OGHA1nmoImIiPD+uru7G5PJ5Lf3jfOdi4vx1T8nJ0+e5KmnnuKJJ57wjvnr/WKgBBhdgD+or68nPj4ei8UCgMViIS4ujvr6eux2u8HVDZ6f/OQnuN1uJk+ezI9//GPq6+tJTEz0vm6323G5XHR0dGCz2QysdGBd7Hpwu91+e638z+vDarX6xTXicrl48803mTFjxkWP1x/OBfQ9H2fccccdOJ1Orr76ahYtWkRQUNA55yMxMZH6+nojSh4QP//5z9m0aRNut5v//M//9Ov7xv88F2f40z3jhRdeYO7cuSQnJ3vHdL/oX5ohlkHxxz/+kffff5933nkHt9vNU089ZXRJMoT48/Xxy1/+krCwMBYuXGh0KUPC/zwf69at49133+WPf/wjhw4dYtmyZQZXODj+9V//lXXr1vHwww/z7LPPGl2Ooc53LvzpnrFjxw727t3L7bffbnQpPk2BeBA4HA4aGxtxOp0AOJ1OmpqavtY/HQ93Z441KCiI22+/ne3bt+NwOPr8s2hbWxtms9nnf3q92PXgr9fK+a6PM+O+fI0sXbqUyspKfvOb32A2my96vL5+LuDc8wFnr43w8HBuvfXWC14bdXV1PvnnZP78+Xz++eckJCT4/X3jzLlob2/3q3vGtm3bKCsrY+bMmcyYMYOGhgbuu+8+Kisr/fp+0d8UiAdBdHQ0ubm5rFy5EoCVK1eSm5vrE/+UdSmOHTvGkSNHAHC73fz1r38lNzeX/Px8enp6KCoqAmD58uXMmTPHyFIHxcWuB3+8Vi50fQA+fY08//zz7N27l2XLlhEUFARc/Hh9+VzA+c9HZ2cnPT09AJw+fZpVq1Z5r43p06ezZ88e72oKy5cv5/rrrzek9v509OjRPq0fa9euJTIy0i/vGxc6F8HBwX51z/je977Hxo0bWbt2LWvXriUhIYHf/va33H///X57vxgIJrfb7Ta6CH9QVlbG4sWL6erqwmq1snTpUtLT040ua1BUV1ezaNEinE4nLpeLjIwMfvGLXxAXF8f27dt5/PHHOXHiBElJSTz33HPExMQYXXK/+dWvfsXf/vY3WlpaiIqKwmaz8cEHH1z0evDla+V85+OVV1654PUB+OQ1cvDgQQoLC0lLSyMkJASA5ORkli1bdtHj9cVzARc+H/fffz9LlizBZDJx+vRpJk6cyGOPPcaIESMAWLNmDc899xwul4vc3FyeeeYZwsLCjDyUb6ylpYUHH3yQ48ePYzabiYyM5Gc/+xl5eXl+d9+40LmwWq1+d8/4shkzZvDKK6+QnZ3tl/eLgaJALCIiIiJ+TS0TIiIiIuLXFIhFRERExK8pEIuIiIiIX1MgFhERERG/pkAsIiIiIn5NgVhEZJjLycmhsrLS6DJERIatAKMLEBHxNTNmzKClpQWLxeIdu+mmm1iyZImBVYmIyIUoEIuIDIBXXnmFK664wugyRETkEqhlQkRkkLz77rvcdtttPPXUU0yePJk5c+awefNm7+uNjY18//vfZ+rUqVx33XX86U9/8r7mdDp55ZVXmDVrFhMnTuTmm2/us63tZ599xre//W0KCgp48skn0Z5LIiKXTjPEIiKDaPfu3cyZM4ctW7awevVqHnroIT7++GNsNhs//vGPycrKYsOGDRw+fJh77rmHlJQULr/8cl577TU++OADXn31VUaNGkVJSYl3m2OAdevW8ec//5nu7m5uvvlmrr32Wq6++moDj1REZPjQDLGIyAD4wQ9+QEFBgffjzGyv3W7nrrvuIjAwkBtuuIFRo0axbt066uvr2b59Oz/5yU8IDg4mNzeXW2+9lffeew+At99+mx/96Eekp6djMpkYPXo0UVFR3v/fAw88gNVqJTExkWnTpnHgwAFDjltEZDjSDLGIyABYtmzZOT3E7777LvHx8ZhMJu9YYmIiTU1NNDU1ERkZSXh4eJ/X9u7dC0BDQwOpqakX/P/FxsZ6fx0aGsrRo0f761BERHyeZohFRAZRY2Njn/7e+vp64uLiiIuLo7Ozk+7u7j6vxcfHA5CQkEBVVdWg1ysi4g8UiEVEBlFbWxtvvPEGp06d4sMPP6SsrIxrrrkGh8PBxIkTef755zlx4gQHDhzgz3/+M3PnzgXg1ltv5YUXXqCiogK3282BAwdob283+GhERHyDWiZERAbA97///T7rEF9xxRXMnDmTcePGUVlZyWWXXUZMTAwvvviitxf4+eef5/HHH2f69OlYrVYWLVrkbbu45557OHnyJPfeey/t7e2kp6ezbNkyQ45NRMTXmNxam0dEZFC8++67vP3227z55ptGlyIiIl+ilgkRERER8WsKxCIiIiLi19QyISIiIiJ+TTPEIiIiIuLXFIhFRERExK8pEIuIiIiIX1MgFhERERG/pkAsIiIiIn5NgVhERERE/Nr/D5mxuXJxyuT3AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try 2 hidden layers, with 12 neurons each\n", "epochs = 400\n", "learning_rate = 0.0001\n", "\n", "network = []\n", "network.append(Dense(x_dim, 12, learning_rate=learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 12, learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 1, learning_rate))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 369, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try a single hidden layers, with 24 neurons\n", "epochs = 1000\n", "learning_rate = 0.0001\n", "\n", "network = []\n", "network.append(Dense(x_dim, 24, learning_rate=learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(24, 1, learning_rate))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 371, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try 2 hidden layers, with 24 neurons each\n", "epochs = 1000\n", "learning_rate = 0.0001\n", "\n", "network = []\n", "network.append(Dense(x_dim, 24, learning_rate=learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(24, 24, learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(24, 1, learning_rate))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 372, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's try 3 hidden layers, with 12 neurons each\n", "epochs = 1000\n", "learning_rate = 0.0001\n", "\n", "network = []\n", "network.append(Dense(x_dim, 12, learning_rate=learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 12, learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 12, learning_rate))\n", "network.append(ReLU())\n", "network.append(Dense(12, 1, learning_rate))\n", "network.append(Sigmoid())\n", "\n", "colors = sns.color_palette()\n", "\n", "losses = []\n", "accuracies = []\n", "for i in range(epochs):\n", " layer_activations = forward(network, X)\n", " layer_inputs = [X] + layer_activations #layer_input[i] is an input for network[i]\n", " output = layer_activations[-1]\n", "\n", " # calc mean loss\n", " mean_loss = np.mean(squared_error_loss(Y, output))\n", " losses.append(mean_loss)\n", " \n", " # calc test accuracy\n", " predict = np.round(forward(network, X_test)[-1])\n", " accuracy = 1 - (np.sum(np.abs(predict - Y_test)) / Y_test.shape[0])\n", " accuracies.append(accuracy * 100)\n", " \n", " # gradient loss\n", " loss_grad = grad_squared_error_loss(Y, output)\n", " \n", " for layer_index in range(len(network))[::-1]:\n", " layer = network[layer_index]\n", " \n", " loss_grad = layer.backward(layer_inputs[layer_index],loss_grad) #grad w.r.t. input, also weight updates\n", " \n", "e = np.arange(epochs)\n", "\n", "fig, ax1 = plt.subplots()\n", "\n", "ax1.set_xlabel('Epoch')\n", "ax1.set_ylabel('Loss')\n", "ax1.plot(e, losses, color=colors[0])\n", "\n", "ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis\n", "\n", "ax2.set_ylabel('Accuracy (%)') # we already handled the x-label with ax1\n", "ax2.set_ylim(-1, 101)\n", "ax2.plot(e, accuracies, color=colors[1])\n", "\n", "ax1.grid()\n", "ax2.grid()\n", "\n", "fig.tight_layout() # otherwise the right y-label is slightly clipped\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }