MCMC_Example_2_Temp.ipynb

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      "source": [
        "**MCMC-Example**<br>\n",
        "Beta distribution<br>\n",
        "${f(x)} = {Cx^{\\alpha-1}}{(1-x)}^{\\beta-1}$"
      ]
    },
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        "id": "afTib6O4Ux15",
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      "source": [
        "import random\n",
        "import pylab as pl\n",
        "import scipy.special as ss\n",
        "from scipy.stats import beta\n",
        "import numpy as np\n",
        "\n",
        "%matplotlib inline\n",
        "pl.rcParams['figure.figsize'] = (17.0, 4.0)"
      ],
      "execution_count": 7,
      "outputs": []
    },
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      "source": [
        "# Lets define our Beta Function to generate s for any particular state. We don't care for the normalizing constant here.\n",
        "def beta_s(w, a, b):\n",
        "    return w**(a-1)*(1-w)**(b-1)\n",
        "\n",
        "# This Function returns True if the coin with probability P of heads comes heads when flipped.\n",
        "def random_coin(p):\n",
        "    unif = random.uniform(0,1)\n",
        "    if unif>=p:\n",
        "        return False \n",
        "    else:\n",
        "        return True\n",
        "\n",
        "# This Function runs the MCMC chain for Beta Distribution.\n",
        "def beta_mcmc(N_hops,a,b):\n",
        "    states = []\n",
        "    cur = random.uniform(0,1)\n",
        "    for i in range(0, N_hops):\n",
        "        states.append(cur)\n",
        "        next = random.uniform(0,1)\n",
        "        ap = min(beta_s(next,a,b)/beta_s(cur,a,b), 1) # Calculate the acceptance probability\n",
        "        if random_coin(ap):\n",
        "            cur = next\n",
        "    return states[-1000:] # Returns the last 100 states of the chain"
      ],
      "execution_count": 12,
      "outputs": []
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      "source": [
        "# Actual Beta PDF.\n",
        "def beta2(a, b, i):\n",
        "    e1 = ss.gamma(a + b)\n",
        "    e2 = ss.gamma(a)\n",
        "    e3 = ss.gamma(b)\n",
        "    e4 = i  (a - 1)\n",
        "    e5 = (1 - i)  (b - 1)\n",
        "    if (e2*e3)==0:\n",
        "        return 0\n",
        "    else:\n",
        "        return (e1/(e2*e3)) * e4 * e5\n",
        "\n",
        "# Create a function to plot Actual Beta PDF with the Beta Sampled from MCMC Chain.\n",
        "def plot_beta(a,b):\n",
        "    Ly = []\n",
        "    Lx = []\n",
        "    i_list = np.mgrid[0:1:100j]\n",
        "    for i in i_list:\n",
        "        Lx.append(i)\n",
        "        Ly.append(beta.pdf(i, a, b))\n",
        "        \n",
        "        \n",
        "    pl.plot(Lx, Ly, label=\"Real Distribution: a=\"+str(a)+\", b=\"+str(b))\n",
        "    pl.hist(beta_mcmc(1000,a,b), density=True,bins =25, histtype='step',label=\"Simulated_MCMC: a=\"+str(a)+\", b=\"+str(b))\n",
        "    pl.legend()\n",
        "    pl.show()\n",
        "    \n",
        "plot_beta(0.1,0.1)\n",
        "plot_beta(1,1)\n",
        "plot_beta(2,3)\n",
        "\n"
      ],
      "execution_count": 13,
      "outputs": [
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WWVq3bp1SUlL0y1/+Um+//bZeeeUV3X333R16z6efflqrVq1SQUGBHn30UZWVlWnevHlKSEhQYWGhFi1apA0bNuill17SRx99pMLCQrndbi1atEi7du3SPffco48++kgffvihoy7mffr0UXZ2ttauXavFixdr1qxZoXXr1q1TXl6e3G73Qbe/4oortHjxYtXV1emLL77QySefHFq3du1anXjiiW1ut3Tp0jZ/NvHx8XrllVf0+eefa/ny5brttttC3Z7POOMM5eXltfp65513JEm7d+/WwIEDJUnHHnusdu/uvCGxtm/frpUrV+r111/Xddddp7q6Om3atKnNevLy8lReXq6SkhJlZWWF9pGVlaWSkpJOq6k9HRlEDAAAAACOSHJyslatWqV//OMfWr58uWbNmqV58+bp6quvbtEuNjZW5513nqRAl+i4uDjFxMQoNzdX27dv79B7Pvroo3rllVckSUVFRdqyZYv69evXos27776rVatW6aSTTpIk1dbWqn///vrss880ZcoUNT1paNasWdq8eXO779kUgt966y29++67euaZZxzXO27cOG3fvl0vvviiLrjgAsfbzZgxQzNmzGi13Fqr//zP/9QHH3wgl8ulkpIS7d69W8cee6z+8Y9/ON6/MUbGGMft23P55ZfL5XJp+PDhOv7447Vx40bl5eWpsLCw096jsxGgAQAAAHQrt9utKVOmaMqUKcrNzdVzzz3XKkDHxMSEwprL5Qp1+Xa5XPJ6vZIkj8cjv98f2qaurq7Ve61YsULvvPOOPvnkEyUmJmrKlClttrPWavbs2frtb3/bYvnBuiy3Z/r06brjjjuUn5+vPn36hJaPGTNGa9askc/nO+RV6BkzZuj222/XihUrVFZW1mL7VatWafz48Y5rWbRokUpLS7Vq1SrFxMQoJycn9DM444wztH///lbb/O53v9PZZ5+tAQMGaNeuXRo4cKB27dql/v37O37f9hwYxo0x2rRpU4sr9uFWrFihzMxMFRcXh5YVFxe3uEe8qxGgAQAAgN4sdbA0N7Vz93cImzZtCl11lKTCwkIdd9xxh/VWOTk5evzxx+X3+1VSUqKVK1e2alNRUaG+ffsqMTFRGzdu1KeffhpaFxMTo8bGRsXExGjq1KmaOXOmbr31VvXv31979+7V/v37dfLJJ+tnP/uZysrK1KdPHy1ZssRReE1MTNR//dd/acSIES2WDx06VPn5+brnnnv061//WsYYbd++XevWrWtxH/RPfvITpaWlKTc3t8V93XfccYcuvvhinX766RoxYoT8fr8WLlyo66677qC1VFRUqH///oqJidHy5cv1zTffhNa1dwV6xowZeu6553TnnXfqueee08yZM9v93sP94he/0KRJk/SDk3NarVuyZIlmz56tbdu26euvv9bIkSMVHx9/yCvQaWlp6tOnjz799FOdfPLJev7553XzzTd3qKYjQYAGAAAAerNufmZzVVWVbr75ZpWXl8vj8WjYsGGhgb066rTTTtOQIUM0evRojRo1ShMnTmzV5rzzztOCBQs0atQojRw5Uqecckpo3Zw5czRu3DhNnDhRixYt0n333adzzjlHfr9fMTExmj9/vk455RTNnTtXkydPVlpamvLy8hzXd8UVV7S5/Mknn9Rtt92mYcOGKSEhQenp6XrwwQdbtMnKytItt9zSattx48bpkUce0ZVXXqmamhoZY0KPjlq6dKkKCgp07733ttjmhz/8oS688ELl5uYqPz8/NACZE3feeacuv/xyPfXUUzruuOP05z//WZJUUFCgBQsW6Mknn5QUuJK9ceNGVVVVKSsrS0899ZTOPfdcffnll212K5ekwYMHa9KkSaqsrNSCBQsUHx/vqKbHH39cV199tWpra3X++efr/PPPlyQtWLBAknTdddfp22+/VX5+viorK+VyufTII49o/fr1LXoDHA7T1jOzjlR+fr5tGj0v6s1NDTyvLtKipQ4AAAAc1TZs2KBRo0ZFugx0l52rpUETIvb25557rt56662I13Ewbf1/MMasstbmt9WeUbgBAAAAAF3irbfeinQJnYou3AAAAADQQb/5zW+0ZMmSFssuu+wy3XXXXRGqCN2BAA0AAAD0MtbaTn0cUW901113EZZ7uMO5nZku3AAAAEAvEh8fr7KyssMKD8DRwlqrsrIyxwOXNeEKNAAAANCLZGVlqbi4WKWlpZEuBd2h/DupYkOkq4ieOsLEx8crKyurQ9sQoAEAAIBeJCYmRkOGDIl0Geguc0+Jjqf9REsdR4gu3AAAAAAAOECABgAAAADAAQI0AAAAAAAOEKABAAAAAHCAAA0AAAAAgAMEaAAAAAAAHCBAAwAAAADggKMAbYxJM8a8bIzZaIzZYIyZ3NWFAQAAAAAQTTwO2/2PpDettZcaY2IlJXZhTQAAAAAARJ12A7QxJlXS9yRdLUnW2gZJDV1bFgAAAAAA0cVJF+4hkkolPWOMWW2MedIYk3RgI2PMHGNMgTGmoLS0tNMLBQAAAAAgkpwEaI+kiZJ+b62dIKla0p0HNrLWLrTW5ltr8zMyMjq5TAAAAAAAIstJgC6WVGyt/Sw4/7ICgRoAAAAAgF6j3QBtrf1WUpExZmRw0VRJ67u0KgAAAAAAoozTUbhvlrQoOAL315L+retKAgAAAAAg+jgK0NbaQkn5XVwLAAAAAABRy8k90AAAAAAA9HoEaAAAAAAAHCBAAwAAAADgAAEaAAAAAAAHCNAAAAAAADhAgAYAAAAAwAECNAAAAAAADhCgAQAAAABwgAANAAAAAIADBGgAAAAAABwgQAMAAAAA4AABGgAAAAAABwjQAAAAAAA4QIAGAAAAAMABAjQAAAAAAA4QoAEAAAAAcIAADQAAAACAAwRoAAAAAAAc8DhpZIzZLmm/JJ8kr7U2vyuLAgAAAAAg2jgK0EFnWmv3dFklAAAAAABEMbpwAwAAAADggNMAbSX93RizyhgzpysLAgAAAAAgGjntwn26tbbEGNNf0tvGmI3W2g/CGwSD9RxJGjx4cCeXCQAAAABAZDm6Am2tLQm+fifpFUmT2miz0Fqbb63Nz8jI6NwqAQAAAACIsHYDtDEmyRiT0jQt6RxJa7u6MAAAAAAAoomTLtwDJL1ijGlq/ydr7ZtdWhUAAAAAAFGm3QBtrf1a0vhuqAUAAAAAgKjFY6wAAAAAAHCAAA0AAAAAgAMEaAAAAAAAHCBAAwAAAADgAAEaAAAAAAAHCNAAAAAAADhAgAYAAAAAwAECNAAAAAAADhCgAQAAAABwgAANAAAAAIADBGgAAAAAABwgQAMAAAAA4AABGgAAAAAABwjQAAAAAAA4QIAGAAAAAMABAjQAAAAAAA4QoAEAAAAAcIAADQAAAACAAwRoAAAAAAAccBygjTFuY8xqY8yyriwIAAAAAIBo1JEr0D+TtKGrCgEAAAAAIJo5CtDGmCxJ35f0ZNeWAwAAAABAdHJ6BfoRSf8hyX+wBsaYOcaYAmNMQWlpaacUBwAAAABAtGg3QBtjpkv6zlq76lDtrLULrbX51tr8jIyMTisQAAAAAIBo4OQK9GmSZhhjtktaLOksY8wfu7QqAAAAAACiTLsB2lr7C2ttlrU2R9IVkt6z1l7V5ZUBAAAAABBFeA40AAAAAAAOeDrS2Fq7QtKKLqkEAAAAAIAoxhVoAAAAAAAcIEADAAAAAOAAARoAAAAAAAcI0AAAAAAAOECABgAAAADAAQI0AAAAAAAOEKABAAAAAHCAAA0AAAAAgAMEaAAAAAAAHCBAAwAAAADgAAEaAAAAAAAHCNAAAAAAADhAgAYAAAAAwAECNAAAAAAADhCgAQAAAABwgAB9CF6fX9v3VEe6DAAAAACIWnuq6rWvuiHSZXQLAvQh3P+3jTr/f/4hr88f6VIAAAAAICo99eE2nXz/u6r3+iJdSpcjQB/CuKxU1Tb6tOW7qkiXAgAAAABRaU1RuU4YmKI4jzvSpXQ5AvQhjM9OkyQVFpVHuBIAAAAAiD4+v9UXxRUan5UW6VK6RbsB2hgTb4xZaYxZY4xZZ4z5VXcUFg1y+iUqNSFGawjQAAAAANDK16VVqqr3Ki+7dwRoj4M29ZLOstZWGWNiJH1ojHnDWvtpF9cWccYYjc9O4wo0AAAAALRhdTArje8lAbrdK9A2oOkm4Jjgl+3SqqJIXnaaNu/er+p6b6RLAQAAAICosqaoXCnxHh2fnhTpUrqFo3ugjTFuY0yhpO8kvW2t/ayNNnOMMQXGmILS0tLOrjNi8rJT5bfSlyUVkS4FAAAAAKJKYVG5xmelyeUykS6lWzgK0NZan7U2T1KWpEnGmLFttFlorc231uZnZGR0dp0R03QzPPdBAwAAAECzukafNn67v9fc/yx1cBRua225pOWSzuuacqJPv+Q4ZR+TwH3QAAAAABBmbUmFfH7ba+5/lpyNwp1hjEkLTidImiZpY1cXFk3ysvsSoAEAAAAgTGFoALHUCFfSfZxcgR4oabkx5gtJ/1TgHuhlXVtWdMnLTtOuijrtrqyLdCkAAAAAEBUKi8qVmZag/inxkS6l27T7GCtr7ReSJnRDLVErL3hGpbCoXOeOOTbC1QAAAABA5BUWlfeq+5+lDt4D3VuNGZQqj8swkBgAAAAASNpTVa/ifbW9qvu2RIB2JD7GrRMGpnAfNAAAAACo+SlFedl9I1xJ9yJAO5SXnaYviivk99tIlwIAAAAAEbWmqFxul9HYzD6RLqVbEaAdGp+Vpqp6r7aWVkW6FAAAAACIqNVF5RoxIEWJse0Oq3VUIUA7NGFw4OZ4unEDAAAA6M2stVpTVB4abLk3IUA7dHx6slLiPARoAAAAAL3atj3Vqqzz9roRuCUCtGMul9G47FStKSZAAwAAAOi9mjLReAI0DmV8Vpo27tqvukZfpEsBAAAAgIgo3FGupFi3hvdPiXQp3Y4A3QF52Wny+q3W7ayIdCkAAAAAEBGFxRXKzUqV22UiXUq3I0B3QFMf/9U76MYNAAAAoPep9/q0YWdlr+y+LRGgO6R/n3gNSo1nIDEAAAAAvdL6nZVq8Pk1gQANJ/IGpzGQGAAAAIBeaU1R7x1ATCJAd9j4rDQV7a1VWVV9pEsBAAAAgG5VWFSuAX3iNDA1IdKlRAQBuoOa7oPmKjQAAACA3mZNcYXGZ/XOq88SAbrDxmamymUCQ7cDAAAAQG9RXtOgbXuqlTeYAA2HkuI8GjEgRYXFPMoKAAAAQO+xJpiB8rgCjY7Iy07TmqJyWWsjXQoAAAAAdIvCHeUyRsrNSo10KRFDgD4Medlpqqht1PaymkiXAgAAAADdYk1xuYZlJCslPibSpUQMAfowNA3ZXli0L8KVAAAAAEDXs9aqsKg8NKhyb9VugDbGZBtjlhtj1htj1hljftYdhUWzEQNSlBjr1poi7oMGAAAAcPQr3lervdUNvfb5z008Dtp4Jd1mrf3cGJMiaZUx5m1r7fouri1quV1GuZmpWl3ESNwAAAAAjn5N2Ycr0O2w1u6y1n4enN4vaYOkzK4uLNrlZadpw85K1Xt9kS4FAAAAALpU4Y5yxXlcGnlsSqRLiagO3QNtjMmRNEHSZ22sm2OMKTDGFJSWlnZOdVEsLztNDT6/NuzaH+lSAAAAAKBLrSkuV25mqmLcvXsYLcffvTEmWdJfJP27tbbywPXW2oXW2nxrbX5GRkZn1hiVQgOJ7WAgMQAAAABHr0afX2tLKnr9/c+SwwBtjIlRIDwvstb+tWtL6hkGpsarf0pc6GHiAAAAAHA02vTtftV7/b3+/mfJ2SjcRtJTkjZYax/q+pJ6BmOMxmenqZCBxAAAAAAcxRhArJmTK9CnSfqRpLOMMYXBrwu6uK4eIS87Tdv2VKu8piHSpQAAAABAl1hTVK5+SbHK6psQ6VIirt3HWFlrP5RkuqGWHqfpDMya4gr9y4ij/75vAAAAAL1PYVG5xmenKdA5uXfr3UOoHaHcrFQZEzgjAwAAAABHm8q6Rm0traL7dhAB+gj0iY/R8P7Jenv9bvn9NtLlAAAAAECnem/Dd7JWmjCYAC0RoI/YnO8N1ZclFVqyqijSpQAAAABAp6mq9+q3b2xQbmaqTh2aHulyogIB+ghdMhKxVfgAABhWSURBVDFTJ+X01bw3NmpfNYOJAQAAADg6PPL2Zn23v16/vmis3C7uf5YI0EfMGKN7Z45VZZ1XD/59U6TLAQAAAIAjtunb/Xrm4+264qRs7n8OQ4DuBKMG9tHsyTl6ceUOBhQDAAAA0KNZa/V/X1urPvEe/ce5J0S6nKhCgO4kt04brozkOP3y1bXyMaAYAAAAgB7qldUlWrltr/7PeSeob1JspMuJKgToTpISH6O7vj9KX5ZU6E8rd0S6HAAAAADosIraRt3/tw3Ky07T5fnZkS4n6hCgO9GM8YM0+fh+evDNjSqrqo90OQAAAADQIQ+/vVl7qxt030Vj5WLgsFYI0J0oMKDYGNU0+DTvjY2RLgcAAAAAHFtbUqHnP9muq045TmMzUyNdTlQiQHey4QNSdM0ZQ7RkVbEKtu+NdDkAAAAA0C6/PzBw2DFJsbrtnJGRLidqEaC7wC1nDdfA1Hj98tW18vr8kS4HAAAAAA5pyaoird5Rrl+cP0qpCTGRLidqeSJdwNEoKc6j/zt9tG5Y9Lle+PQb/dtpQyJdEgAAAIDu8nCuVBElAwunDm63SXlNg+a9sVEn5fTVxRMzu6GonosA3UXOH3uszhierof+vlnfzx2o/n3iI10SAAAAgO5QsUOaWxHpKhx74K1Nqqzz6tcXjZUxDBx2KHTh7iKBAcXGqt7r1/1/2xDpcgAAAACglTVF5Xpx5Q5dfWqOTji2T6TLiXoE6C40JD1JP/2X4/Vq4U69ufbbSJcDAAAAACEVtY36xV+/VEZynP797OGRLqdHIEB3sRumDFNuZqpuWLRKz3+yPdLlAAAAAICK9tbokt9/rC3f7df9P8hVSjwDhzlBgO5iCbFuLZ5zis46ob/ufm2d5i5dJ5/fRrosAAAAAL3Uqm/26aL5H6l0f72e/8nJOnv0gEiX1GMQoLtBUpxHT/woXz85bYie/Xi75jxfoOp6b6TLAgAAANDLLPtip678w6dKjvforzecqslD+0W6pB6l3VG4jTFPS5ou6Ttr7diuL+no5HYZ3X3haA1JT9Q9S9fp8ic+0VOzT9KxqcHRuVMHS3NTI1tkk9TB0q1fRroKAAAAAJ3EWqvHV2zVg29tUv5xfbXwx/k6Jik20mX1OE4eY/WspMckPd+1pfQOP5qco6xjEnXTos81c/6Hemr2SRqbmRpdgTVagjwAAACAI9bg9euuV77UklXFmpk3SA9cOk5xHneky+qR2u3Cba39QNLebqil1zhzZH8tue5UuYzR5U98onfW7450SQAAAACOQhU1jZr99EotWVWsn00drkdm5RGej0Cn3QNtjJljjCkwxhSUlpZ21m6PWqMH9dFrN56moRnJmvNCgZ76cJusZXAxAAAAAJ1j255q/eD3H2nVN/v08KzxunXaCBljIl1Wj9ZpAdpau9Bam2+tzc/IyOis3R7V+veJ10s/PUVnjxqgXy9brxmPfaT3N5cSpAEAAAActtL99Zq7dJ3Oefh97a1u0B+vPVk/mJAV6bKOCk7ugUYXSoz1aMFVJ+qvq0v08NubNfvplTp5yDH6j/NG6sTjjol0eQAAAAB6iIraRi38YKue/nC7Gnx+XZ6fpVumDtfA1IRIl3bUIEBHAZfL6NITs3Th+IFavLJI/++9r3TJ7z/R1BP66/ZzR2rUwD6RLhEAAABAlKpt8OmZj7dpwYqtqqzz6sLxg3Tr2cN1fEZypEs76jh5jNWLkqZISjfGFEu6x1r7VFcX1hvFedyafWqOLsvP0jMfbdeC97fqgkf/oQvHDdLPp41QTnpSpEsEAAAAECUavH4t/ucO/b/3vlLp/nqdOTJDt587UmMG8VSdrtJugLbWXtkdhaBZYqxHN545TFedfJwWfLBVz3y0Ta9/uUsX5WXqkhMzdcqQfnK5uPkfAAAA6I2+rajT0jUleuHTb1S0t1aTco7R4z+cqJNyuAW0q9GFO4qlJsbo/5x3gv7t1Bw9tvwr/WVVsf7yebEGpsZrxvhBumhCJt27AQAAgF6gsq5Rb375rV4tLNEnX5fJWmnC4DTdO3OspozIYHTtbkKA7gH694nXvTPH6hfnj9LbG3br1dUleurDbXrig681ckCKZk4YpJl5mcpMY3AAAAAA4GjR4PVrxabv9Gphid7Z8J0avH7l9EvULWcN18y8QdzjHAEE6B4kIdatGeMHacb4Qdpb3aDXv9ipVwt36oE3N+mBNzdp0pBjdO6YY3Xq0H4aOSCFbt4AAADoXR7OlSp2RLoKKXXwYW+6r7pBn35dpg+2lOpvX36ritpG9UuK1b9OGqyZeYOUl53G1eYIIkD3UMckxepHk3P0o8k52lFWo9cKS/Tamp369bL1ofWTj++nU4f106lD05XTL5H/aAAAADi6VeyQ5lZEuooOqar36p/b9urjrXv00Vdl2vBtpayVkmLdmjZ6gGZOyNTpw9IV43ZFulSIAH1UGNwvUTdPHa6bpw7XzvJafbK1TB9vLdPHW/fo9S93SZIGpsZr8tB+mnx8P00YnKYh6clyH+wKdepgaS4j97WQOli69ctIVwEAAIAebl91g9burNDKbXv10Vd7tKa4Qj6/VazHpRMH99Vt00Zo8tB0jctKJTRHIQL0UWZQWoIuOTFLl5yYJWuttpfV6OOte/Tx1jKt2FSqv35eIklKjHVr9MA+GpuZqjGDAq/D+yfL43YRFNvCCQUAAAB00Hf767SupFJrSyq0dmeF1pZUqqS8VpLkdhmNz0rV9f8yVKcO7aeJx/VVfIw7whWjPQToo5gxRkPSkzQkPUk/PPk4+f1WX5VW6cvipv/AFfpzQZFqGnySpDiPSycM7KPRA/toaEaShvZP1tD0ZGX2TTj41WoAAACgl6uoadTWPVX6urRaW0urtPnb/Vq7s0K7K+tDbY5PT9LE4/rqx5OPU25mqnKzUpUSHxPBqnE4CNC9iMtlNGJAikYMSNElJ2ZJknx+q+1l1YGzYiWBs2JvrN2l8prG0HaxHpeG9EvS0P5JOj49WcdnJCknPUlZfROUkRzHvdUAAKD3iJZBqiRuMetmNQ1eleyr1Y69Nfq6tFpf76nS1u8Cr3uqGkLtYtyBi1inDU3XmMxU5WamatTAFMLyUYIA3cu5XUZDM5I1NCNZM/MyQ8v3Vjfo69IqbS1tPpO2cdd+vbVut3x+G2oX63EpKy1BmX0TlNU3QVl9E5XVN0GZaQkamBYI2LEe7t0AAABHiWgapIpbzDqNtVblNY36trJOO8trVbyvViXltSreV6PifYH5vdUNLbY5JilWQzOSNPWEAaELTUP7Jyu7b0LgtkgclQjQaNMxSbE6JukY5ecc02J5g9evHXtrtGNvdeAXS/AXSvG+Gv19Z6XKDvjFIkn9kmLVv0+8BvSJ04CUeA1IDUz3T4lXenKs0pPj1C85VomxHI4AAACORcvAr1F8Jdzr82tfTaPKqutVVtWg7/bXaXdlvXZX1um74Ou3lXX6bn+9Grz+FtvGelyhC0RjM1OVmdZ8wWhoRpLSEmMj9F0hkkgs6JBYj0vD+idrWP+2H9pe0+DVzvJaFe2r1e6K4C+o/XX6rjIwvW5npfZU1cva1tsmxLjVLzlW/ZLjlJ4Uq37JseqbFKu+ibFKS4hRWmKs+iY2v6YmxijOw0ALAAD0CtHSdfoInu/b6aIltD6c2y1B3m+N9itR5TZJ+5SifTZZFUrWPpuscpusfUpRmedO7XniE5VVN2hvdYP21TS0+bkzOc6j/sGLO/nH9dWAPvGhCz6Zwd6V6UlxcjEOEA5AgEanSoz1aFj/FA3rn3LQNl6fX3uqGrS7sk57qxu0p6peZdUNKqsKnBncU92gbyvrtG5npcqq69Xoa+O3Xuj93EpNiFGf+Bj1SfAEX2PUJ94TfA0sT46LUXK8R8lxHqUEX5PjPUqK9TBAWk8XLR+opKg+Aw8AhyXafsdGS9dptOTgb5+1VvVev/bXeVVV71VVnVf76xtVFZzfX+dVZW2jKusaVVnrDbyGT9c2qqK2Uf6DfyxUn3iP0lPilG6l4f2TAxdmkuKUHrxA0y8pVukpcRrQJ17JccQgHB6OHHQ7j9ulY1PjdWxqfLttrbWqafCpvLZR+6obVFHbqH01DSqvaVR5TYP21TS2+GX7bWWdNn+3P/TLtq0zjgdKjHUrOc6jpDiPEmPdSor1KCnOrcQ4j5Ji3UqM9Sip8XIlLv9KCTFuJca6lRDrDk57wqYDy+M9bsXHuhTrdjHAWnfgXjQA6DrR9DsW3cLnt6pr9Km20Rd4bfCppiEw33Laq5qw+ap6r2rqvapu8Kmmwavq+ubXqnqvquu98h4q/QYlxLhbXBRJT47V8RlJSon3qG9irFITYtQ3MVZ9k2KUmtDcOzE1IYaLIugWBGhENWOMkoLhNjMtoUPb+v1W1Q1eVdQ2hn5xh5/1rDpgvqbRp5r6wPyeqgZV761RTb1P1Q1eVftmyP/Wpo7VLr8S1KB4NShB9Yo3gel4NSjONAZe1ag4NSreBKZDy0yjYoPr4tSoWBN8lVdxalCs8So2OB/4ajxgWeC1V+T3aOpKx71o0SvarqLx74P2RMsxG02/Y3sBa618fqsGn18N3sBXvdevBp9fjWHLGrx+1fv8qm/0q97ra27X4tWnusa2X+vD5kNBuTGwvMHnb7/QA8THuJQc51FibPBiRLDH37F94oOf49yh3n8pwdfkuBglxbmVEnxt6jnI4LOIdgRoHLVcLqOU+JhOeWRAU7ej2uBZ1poGX9i0N3RGti74x6gu7Kxtnden2obmZfXewPT+4Gt9G6+dJcZtFON2hb5i3Uaxnub5GI9LMa5AG4/bKDa4vGna4zbyuANtPMH5GFfw1e2SJ7g8xm3kcTXNB9u6jDzBfbublruC023MN7UJzB+wPPga9Vf0oyUURUOIjzbRdBUtWv59oiWgSZxUaEs0HbNRzForv5W8fr98fhv68oa/+mxofaOvaXnrea8v0L5putEXbOO38vqa2zf6/PL6/KHljb7wbQLTgbDbPN20XWBbGwjBvrB1wUDc6PM76j3nhMdlFB/jVpzHFXqNC827lJYYq/gYlxJi3IoP+wrMu0K96g7saZcQ61ZijCc0nRDj5sovehUCNOCAMSb0h6VvF7+Xtc1nnts6m1zvbeOsdPA1dGY6ON0Y9se5vsV803ob+mNe2+gLTTf6/Gr0+9UY+uNvW3xYcNADq0sYE/hA4DKBUO0KC9fhy9xNXyZsOtimabnLpTaWNW/jchm5jFosd7kUau8yTV8Ktg22Dwb98G1N07QJTDfvQ8G2Rm5X87Qr2KapbdMy02JZcxtz4LxvlFxflwXeW83rQ69q3k/LV0lqu23T+xiFvU+geWBezetN03YuycyfLFNZJCMbWCcro8AB1DRt2pru7M9iXEVrLZoCWhecVLDWylrJNk1LwXkbCihN834bbDN/smxliRQ8Sq2M/GFHrQ07UpuW+eUK7q+5rf+Adm0tb3uZK7hPI3/SFOmrPfJbyW+t/KHvwcrvb1omKVh/07wNtm1u03q9z9+yrS/Y1h443bStv3k/Pn/rdT5/YN4G1/usDS3326b1Lds27dNnJZ/fH3jfYHhteh9fWPsW8wcsj5TQyeOwk8oxTSeVw05cN51oTo7zhNrFegK3erU8qd18Ijt8fej1gOm40GswHIfNx3pchFqgixjbWae5wuTn59uCgoJO32+XmJsaPR8ggB7C77dqbDpb7wubDn/12xZn8MOvBnh9/lbzbV41CNtPiw9iYW38tvkKQ+hD2wHtQm3C9uH3K9QufL9N09aGrQ9+2GzxoS/Yxn+QD5noHE1B/cBwHlippqkWy8O3CTZT2CbNy1tsH9Y2uK55TqFAb1rNt/6AemD4P7CFqSiS0joW6Ns7oXA4f8pteZGUmtVyWTv7tcEW4cttq7bNbZrX2VZtWyyrr5Ksv0VIbVrXPG3C6msr1Da9O90/O0PoZN8BJ/6MUauTiOEnI5tOKoZORoadlHSHnWQMP1kZfmL0wGVul+R2ueR2SR6XK9DOfcA6E96DKfzVFZpv7gkVXO4ObxsIm+GB+MAeVDEul9xhvbA8PaFXFBBtelDuMsasstbmt7WOK9AAOszlMopzucUAlgcXHqZbXQUKhnWrpvmwK0xhV4oCV1bCtwu8Krhd0z5saLvm/Shsvul9wts1dXsMvar5vRVq37wPhbWxYesDF8DCruCpOTg1XwEMvxJ44BXAttc17bfN5WHLAjMtg9rB2rUIfda2aBPYTevg13K7lvtpK7RatVzYOoBKKnxLGjrhoG3a2+fBtBXmW7UJb1L4psywvEO3aWO/oZMHpmWrFuvC2pqDrmt5gqL1CZDmdqGWB2kX6ikRtsO21jX1pNAB68J7W4S/Z3jPj9CJnDa2C++J4XKF99w4sNdHc0+Tg7V1hb1Hcw+X4L+Eadmb5WC9VFr0eAnrTRPeGyW8V43rwOmwnxMAoCU+/gJAF3C5jFwOAg16oeKrpHVPRLoKKX2wdNkDka4CAIAexVGANsacJ+l/JLklPWmtndelVQEAcLRisCwAAHqsdm8UMsa4Jc2XdL6k0ZKuNMaM7urCAAAAAACIJk5G2pgk6Str7dfW2gZJiyXN7NqyAAAAAACILk66cGdKKgqbL5Z08oGNjDFzJM0JzlYZYzYdeXndIl2/MnsiXQTgULokjlf0JByz6Gk4ZtGTcLyiZ/mV6SnH7HEHW9Fpg4hZaxdKWthZ++suxpiCgw1RDkQbjlf0NByz6Gk4ZtGTcLyipzkajlknXbhLJGWHzWcFlwEAAAAA0Gs4CdD/lDTcGDPEGBMr6QpJS7u2LAAAAAAAoku7XbittV5jzE2S3lLgMVZPW2vXdXll3afHdTtHr8bxip6GYxY9DccsehKOV/Q0Pf6YNdbaSNcAAAAAAEDUc9KFGwAAAACAXo8ADQAAAACAA70iQBtjzjPGbDLGfGWMubON9XHGmJeC6z8zxuR0f5VAMwfH7M+NMeuNMV8YY941xhz0WXVAd2jvmA1rd4kxxhpjevQjLNCzOTlejTGXB3/PrjPG/Km7awTCOfhcMNgYs9wYszr42eCCSNQJSJIx5mljzHfGmLUHWW+MMY8Gj+cvjDETu7vGI3HUB2hjjFvSfEnnSxot6UpjzOgDml0jaZ+1dpikhyX9V/dWCTRzeMyulpRvrR0n6WVJD3RvlUAzh8esjDEpkn4m6bPurRBo5uR4NcYMl/QLSadZa8dI+vduLxQIcvg79peS/mytnaDAE3Me794qgRaelXTeIdafL2l48GuOpN93Q02d5qgP0JImSfrKWvu1tbZB0mJJMw9oM1PSc8HplyVNNcaYbqwRCNfuMWutXW6trQnOfqrA89mBSHHye1aSfq3ACcq67iwOOICT4/X/kzTfWrtPkqy133VzjUA4J8esldQnOJ0qaWc31ge0YK39QNLeQzSZKel5G/CppDRjzMDuqe7I9YYAnSmpKGy+OLiszTbWWq+kCkn9uqU6oDUnx2y4ayS90aUVAYfW7jEb7J6Vba19vTsLA9rg5HfsCEkjjDEfGWM+NcYc6koK0NWcHLNzJV1ljCmW9DdJN3dPacBh6ehn3ajS7nOgAUQvY8xVkvIl/UukawEOxhjjkvSQpKsjXArglEeBroVTFOjh84ExJtdaWx7RqoCDu1LSs9ba/zbGTJb0gjFmrLXWH+nCgKNNb7gCXSIpO2w+K7iszTbGGI8CXV/KuqU6oDUnx6yMMWdLukvSDGttfTfVBrSlvWM2RdJYSSuMMdslnSJpKQOJIUKc/I4tlrTUWttord0mabMCgRqIBCfH7DWS/ixJ1tpPJMVLSu+W6oCOc/RZN1r1hgD9T0nDjTFDjDGxCgyssPSANkslzQ5OXyrpPWut7cYagXDtHrPGmAmSnlAgPHNvHiLtkMestbbCWpturc2x1uYocN/+DGttQWTKRS/n5HPBqwpcfZYxJl2BLt1fd2eRQBgnx+wOSVMlyRgzSoEAXdqtVQLOLZX04+Bo3KdIqrDW7op0UU4d9V24rbVeY8xNkt6S5Jb0tLV2nTHmXkkF1tqlkp5SoKvLVwrc8H5F5CpGb+fwmH1QUrKkJcHx7nZYa2dErGj0ag6PWSAqODxe35J0jjFmvSSfpDustfRMQ0Q4PGZvk/QHY8ytCgwodjUXgxApxpgXFTgJmR68L/8eSTGSZK1doMB9+hdI+kpSjaR/i0ylh8fwfwsAAAAAgPb1hi7cAAAAAAAcMQI0AAAAAAAOEKABAAAAAHCAAA0AAAAAgAMEaAAAAAAAHCBAAwAAAADgAAEaAAAAAAAH/n9qIhnb+mxPTAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1224x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1224x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1224x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yy2PXNI3Y3Lc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}