Differentiation_and_Richardson_Extrapolation.ipynb

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        "Make sure you remove `raise NotImplementedError()` and fill in any place that says `# YOUR CODE HERE`, as well as your `NAME`, `ID`, and `SECTION` below:"
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        "NAME = \"ARNOB MAJUMDER\"\n",
        "ID = \"20301089\"\n",
        "SECTION = \"07\""
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      "source": [
        "---"
      ]
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      "source": [
        "# Part 1: Differentiation: Forward, Backward, And Central\n",
        "---"
      ]
    },
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      "source": [
        "## Task 1: Differentiation\n",
        "\n",
        "We have already learnt about *forward differentiation*, *backward diferentiation* and *central differentiation*. In this part of the assignment we will write methods to calculate this values and check how they perform.\n",
        "\n",
        "The equations are as follows,\n",
        "\n",
        "\\begin{align}\n",
        "\\text{forward differentiation}, f^\\prime(x) \\simeq \\frac{f(x+h)-f(x)}{h} \\tag{4.6} \\\\\n",
        "\\text{backward differentiation}, f^\\prime(x) \\simeq \\frac{f(x)-f(x-h)}{h} \\tag{4.7} \\\\\n",
        "\\text{central differentiation}, f^\\prime(x) \\simeq \\frac{f(x+h)-f(x-h)}{2h} \\tag{4.8}\n",
        "\\end{align}"
      ]
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      "source": [
        "## Importing libraries"
      ]
    },
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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from numpy.polynomial import Polynomial"
      ],
      "execution_count": 48,
      "outputs": []
    },
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      "source": [
        "Here, `forward_diff(f, h, x)`, `backward_diff(f, h, x)`, and `central_diff(f, h, x)` calculates the *forward differentiation*, *backward differentiation* and *central differentiation* respectively. finally the `error(f, f_prime, h, x)` method calculates the different values for various $h$ and returns the errors.\n",
        "\n",
        "Later we will run some code to test out performance. The first one is done for you."
      ]
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      "source": [
        "def forward_diff(f, h, x):\n",
        "    return (f(x+h) - f(x)) / h"
      ],
      "execution_count": 49,
      "outputs": []
    },
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        "def backward_diff(f, h, x):\n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    return (f(x) - f(x-h)) / h\n",
        "    #raise NotImplementedError()\n",
        "    # --------------------------------------------"
      ],
      "execution_count": 50,
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        "def central_diff(f, h, x):\n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()\n",
        "    return (f(x+h) - f(x-h)) / (2*h)\n",
        "    # --------------------------------------------"
      ],
      "execution_count": 51,
      "outputs": []
    },
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      "source": [
        "def error(f, f_prime, h, x):\n",
        "    Y_correct = f_prime(x)\n",
        "    f_error = np.array([])\n",
        "    b_error = np.array([])\n",
        "    c_error = np.array([])\n",
        "    \n",
        "    for h_i in h:\n",
        "        # for different values of h (h_i)\n",
        "        # calculate the error at the point x for  (i) forward method \n",
        "        #                                         (ii) backward method\n",
        "        #                                         (ii) central method\n",
        "        # the first one is done for you\n",
        "        f_error_h_i = forward_diff(f, h_i, x) - Y_correct\n",
        "        f_error = np.append(f_error, f_error_h_i)\n",
        "\n",
        "        # --------------------------------------------\n",
        "        # YOUR CODE HERE\n",
        "        #raise NotImplementedError()\n",
        "        b_error_h_i = backward_diff(f, h_i, x) - Y_correct\n",
        "        b_error = np.append(b_error, b_error_h_i)\n",
        "        \n",
        "        c_error_h_i = central_diff(f, h_i, x) - Y_correct\n",
        "        c_error = np.append(c_error, c_error_h_i)\n",
        "        # --------------------------------------------\n",
        "        pass\n",
        "    \n",
        "    return f_error, b_error, c_error"
      ],
      "execution_count": 52,
      "outputs": []
    },
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      "source": [
        "## Plot1\n",
        "Polynomial and Actual Derivative Function"
      ]
    },
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      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "\n",
        "p = Polynomial([2.0, 1.0, -6.0, -2.0, 2.5, 1.0])\n",
        "data = p.linspace(domain=[-2.4, 1.5])\n",
        "ax.plot(data[0], data[1], label='Function')\n",
        "\n",
        "p_prime = p.deriv(1)\n",
        "data2 = p_prime.linspace(domain=[-2.4, 1.5])\n",
        "ax.plot(data2[0], data2[1], label='Derivative')\n",
        "\n",
        "ax.legend()"
      ],
      "execution_count": 53,
      "outputs": [
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K95tyb0CI20/t3Yk8rn3kitTJhRAWK892+9T8dt6dyKPHmMH3JbutjkQIMZDZ7aa04uap+e28O5H7+pmVEKXDUwhhpdoCaG2QRN5r8ZOgVEorQggLtffTxbp/6CH0h0QelwJ1RdBQaXUkQoiBqn1vBGmR95JM1RdCWK10D4TEQkiMJaeXRC6EEH1VutdUByzi/Yk8NB4GRZt3RCGEcDe7HUr3SSLvE6XMBZQWuRDCCtWHofWYmWluEe9P5OAYubLXvDMKIYQ7tY+akxZ5H8VPNGM4K3OtjkQIMdC0J3KLhh5Cf0nkCVPNfdFOa+MQQgw8JVkQMQoCwywLoX8k8thTzFR9SeRCCHezeMQK9JdE7hdgLqQkciGEO7W1mKW0LezohP6SyMGUV4p2gtZWRyKEGCgqDpiltKVF7iQJU6GpGqrzrY5ECDFQlFg/YgV6kMiVUs8ppUqVUrtPeO4epVShUirDcTvPNWF2Q0KquZfyihDCXUqzwMfPLKltoZ60yP8NLOng+Ye01qmO2wfOCasX4lNA+UoiF0K4T2mWWSjLL8DSMLqdyLXWGwDPXWLQP9iMXpFELoRwl9IsiJtgdRROqZGvUEplOkovkZ29SCl1s1IqXSmVXlZW5oTTdiBhKhRlSIenEML1mutMn5zF9XHoeyJ/EhgNpAJFwIOdvVBr/bTWOk1rnRYbG9vH03ZiaCocK4O6YtccXwgh2pXuM/fensi11iVaa5vW2g78E5jlnLB6SWZ4CiHcpX3FVW8vrSilEk748mLA2l2Q4ycBShK5EML1SvZAQKiZnm8xv+6+UCn1KrAAiFFKFQB3AwuUUqmABvKAW1wQY/cFhkLMWEnkQgjXK8o0jUcf66fjdDuRa62v7ODpZ50Yi3MkTIXDm62OQgjRn9ntULIbUpdbHQnQn2Z2tkuYCrUFcKzc6kiEEP1V5UFoqYchU6yOBOiXidwxw7Nwh7VxCCH6r+JMc58gidw1hk4D5QOF6VZHIoTor4ozzdT82FOsjgToj4k8MNSM6yyQRC6EcJGiTIidAH6BVkcC9MdEDjBsBhRulxmeQgjn09q0yD2krAL9NZEPTzNL2lbIHp5CCCerKzYzyD2koxP6ayIflmbupU4uhHA2D+vohP6ayGPHmxlXBdusjkQI0d+0J/L4SdbGcYL+mch9fM3oFenwFEI4W1EmRCVD0GCrIzmufyZyMHXykt3Q2mh1JEKI/qQ406Pq49CvE/lMsylqUabVkQgh+oumGqjK86j6OPTnRC4dnkIIZyveZe6lRe4mYfEQPkLq5EII52n/hC+J3I2GzZAWuRDCeYp2Qmi8aSh6kP6dyIenmT316l20R6gQYmA5usM0ED1MP0/kjp3njmy1Ng4hhPdrqoHybBg23epIvqd/J/KhqeAbCPmy0YQQoo+Ofm3upUXuZn6BprxyeJPVkQghvF3hdnM/dJq1cXSgfydygJFzTAdFc73VkQghvFnhDogeA8GRVkfyPf0/kY+aA9oGBV9ZHYkQwpsVbvfIsgr0IJErpZ5TSpUqpXaf8FyUUmqNUuqA497z3qqGzzI7BsmGzEKI3qo9CnVF3p/IgX8DS77z3J3AOq31WGCd42vPEjQYhkyWDk8hRO+118e9PZFrrTcAld95+iLgecfj54EfOCku5xo51yxp29ZidSRCCG9UuB18/D1q6doT9bVGHq+1LnI8LgY6ne6klLpZKZWulEovK3PzBJ1Rc6CtCYoy3HteIUT/ULgd4ieCf5DVkXTIaZ2dWmsNdLpJptb6aa11mtY6LTY21lmn7Z6Rc829DEMUQvSU3Q6FX3tsWQX6nshLlFIJAI770r6H5AKhsRA9VurkQoieqzgALXX9OpGvBq51PL4WeLePx3OdUXMgf4t5dxVCiO7y8I5O6Nnww1eBzcB4pVSBUupG4H7gHKXUAWCh42vPNHIuNFVD2V6rIxFCeJPC7RAQBjFjrY6kU37dfaHW+spOvnW2k2JxrcR55v7QRtNpIYQQ3XFkKwybZvYC9lD9f2Znu4iRZsPUg+utjkQI4S2aaqFkzzcDJjzUwEnkAMkLIO8LsLVaHYkQwhsUbANth5GnWh1JlwZeIm+pM4vfCCHEyeRvMUt8DJ9pdSRdGliJPHE+oKS8IoToniNbzBIfgWFWR9KlgZXIB0WZzSYkkQshTsbWajZvHzHb6khOamAlcjDllYKvZH1yIUTXijOhtQFGSiL3PMkLwN4m0/WFEF3L32LuJZF7oBGzwS9IyitCiK7lb4GIUTB4qNWRnNTAS+T+QTDiVEnkQojOaW0SuRe0xmEgJnIw5ZXSPVBXYnUkQghPVHkQjpVKIvdoyQvMvbTKhRAdOV4fn2NtHN00MBN5QiqExMKBj62ORAjhiY5sgaAIiBlvdSTdMjATuY8PjF0MOWtlur4Q4vvyvjBlFR/vSJHeEaUrjFsMTTVmZTMhhGhXfcTUyJPOsDqSbhu4iXz0mWYz1eyPrI5ECOFJDm0w90mnWxtHDwzcRB4YBomnQbbUyYUQJzi0AQbFQFyK1ZF028BN5ADjz4XybKjItToSIYQn0BoOfQ5J872mPg4DPZGPXWTupVUuhACoyIG6Iq+qj8NAT+RRSRB7itTJhRBG+9wSL6qPg5MSuVIqTym1SymVoZRKd8Yx3WbcYjj8pdnSSQgxsB3aAOEjzLaQXsSZLfIztdapWus0Jx7T9cYtMash5q6zOhIhhJXsdsjbaMoqSlkdTY8M7NIKwPBZpoc6a7XVkQghrFSyCxqrvK6sAs5L5Br4RCm1XSl1s5OO6R6+fpByoamTtzRYHY0QwioHPzf3AziRn6a1ng6cC/xUKfW9K6GUulkpla6USi8rK3PSaZ1k4sVmJ5ADn1gdiRDCKoc+h5hxMDjB6kh6zCmJXGtd6LgvBVYCszp4zdNa6zStdVpsbKwzTus8o+aZRbT2rLQ6EuEKbS1QXwblOVC43dyKMqEkC+qKwdZmdYTCaq2NkPclJJ9pdSS94tfXAyilQgAfrXWd4/Ei4L4+R+ZOPr6QchF8/TK0HIOAEKsjEr1ha4PSLChMh6MZZr2MyoNQexRT/euMgpAYM1IhLsXchs2AhKmm9Cb6v7wvoK0Rxi2yOpJeccZvaTywUpleXj/gFa219w3MnngxbHvGTA6adInV0YjuqsqDA2vMLW+jKZEBBEeZj8lJp0NkIgyKNsuSBoaZEQm2VrC1mM6t+hIzCaQ8B/a8A9v/ZY4REGZWwBtzNky4AMKHW/WvFK6W/TH4D4JRp1kdSa/0OZFrrQ8CU50Qi7VGzoHQeFNekUTu2epLYffbkPk6HP3aPBeZCKk/Mol32AzzdW+GkGltWvBHtppWWt5G+OhOcxs+EyZdClOWwaAoZ/6LhJW0NnsTJJ1htoL0QvK5sV17eWXHC9BcD4GhVkckTqS1Sapbn4L9H4K2mdLHOb+H8edB9GjnjP1VCsKHQfgl37yhl+fA3ndhzyqT0NfeAyk/gFk/huHeNW1CdKBsP1Tnw2m/tDqSXpNEfqKJF8NXT5uhiJMvszoaAaYEsutN2PSoqX8HR8Hcn8HUKyHuFPfEEDMG5v/K3IoyTekl803IfA0S55sEMPosr5tEIhzaR6uN9c76OMiEoG8bMRsGDzMf2YW12lrMp6PH0mDVT0D5wEWPwx1ZcM697kvi35UwBZY+BL/aB4v/aFbOfOkS+OdZ34xDFt7lwCcQN9EtfSAV9c0uOa4k8hP5+JiWXs5ax0gH4XZamxLG47Ng9c8gOBKufA1u/QKmXQX+wVZHaASGwpyfwu0ZcMEjcKwMXrgQXroUindbHZ3orqYayN/sltEquwtrmPOnT1mbVeL0Y0si/67U5aDtsPNVqyMZeI5sg2cXwZvXmoS9/A348Wdm3XhPLVv4BcKMa2FFuqnXF2yDp+bDh/9PFmLzBrmfmrWWxi52+akeXnuAIH8fZiY5v6NcEvl3RY82Q5C+fsm0DoXrHauAd1fAswuh+jBc+KhpgY9b7LkJ/Lv8g2Dez+HnGZB2g+mUfWwm7HpLfo882YE1Zljq8JkuPc3OI9Ws3VvCj+cnEx7s7/TjSyLvyLSrzESS/C1WR9K/aQ07XoTHZkDGK6YT82fbYfo1ZhSRNxoUBec/CD9eB2FD4O0b4bUfQZ3zP06LPrLbzPjxMWe7fOLXQ2uziRzkz/WnJbnk+JLIO5JyoZkM8vVLVkfSf1Udhhd/AKtXQOwE0wJf9AczYac/GDYDfvyp+TflrIUnTjWtc+E5Dm+ChnIz2cuFth+uYv3+Mm45YzShga55w5BE3pGAEJh0sZkc1FxndTT9i9aw7Vl4ci4UpJvW63XvQ7z3bHTbbT6+5lPGrV+Y6f9v3wjv3CK/U54i613wC3b5sMOH1mQTExrANXNGuewcksg7M+1qaD0mC2k5U10JvHw5vH+HmUhz22aYeZNXbXLbK7Hj4IZPYMFvYNcb8NQZ38xIFdaw22Dvahh7jkvXVtqUW84XOeXcesZoBgW4rnzTz/+C+mD4TLOf57ZnpLPKGfa9D0/OMbMzz/0rXL0KIkZaHZX7+PrBgjvh2vegrQmeOUd+t6x0ZKtZYyflIpedotVm597VWQyPDOaq2a5rjYPM7OycUnDqLfDeL80401FzrY7IO7U2wZr/NTNmh0yBS5+B2PFWR2WdxHmm1LLyFnj/V47y0t8gYBBaa6oaWimra6a83tzqmtqob26jvqmNFpudNpvGZrejlMLPR+Hn60Owvy9hQX6EBfkROSiAuMGBxIYFEhsaiJ+vtNU6lPUu+AWZkVEu8sLmw+wvqePpq2cQ5O/azntJ5F2ZcgWsuw+2PCGJvDfKc+Ct66E4E2b/FBbeA34BVkdluUodyr5THydE/40pO/9BftZWfhNwJ1/XhtPYauvwZ3wUBPj54O/jg4+PQmtNm13TZtO02Owd/oyvj2JoRBAjowaRGB3C+CFhjI0L45QhYUSGDOD/B7vdJPIxC13WuV5a18TDa7JZMD6Wc1LiXXKOE0ki70rAIJhxPXz5sFkuNTLR6oi8x55V8O5PwdffzMwcf67VEVmivL6ZzIJqMo7UkFlQzd6iWkpq26dpz2dxQDgPtj3KU7Zf83bKn7GPmE3c4EBiQgOJCQ1gcLA/oYF+BPv7ojoZU99qs1Pf1EZdUxtVDS2U1jVTWtdEUXUT+ZUN5Fc28J+dR3l56zcbaIyICmbq8AhSR0QwKymKlITBA6f1XrDNLFvswrLK/R/uo7nNzt0XTOz0/82ZJJGfzMybYNMjsPVpWPJHq6PxfLZWWPM78ylm+Ey4/N8Dah3vI5UNbM6tYFteJdvyKsmrMOuj+ygYGxfGvNExTEgYzCkJYYyJC2XI4PNQFZfDq8u47sDPYPxDMOXqHp3T39eHyJAAIkMCGBk9qMPXaK0pqW0mu6SOrKJaMguq+Tq/mvcyiwAICfBlRmIUp4+N4fRxsYyNC3VLArJE1rvgGwDjlrjk8F8dquSdHYXctmA0STHu2aRGaQs6W9LS0nR6errbz9trb91oJg7ckQVBg62OxnPVFsGb18GRLTDrFjOGup+XUqqOtbAxp5wvDpSxKbeCgqpGACIH+ZOWGEXaqEimjYxk0rDBXY9aaKyCN6+Hg5/BvNvh7HvcMpqntLaJrYcq+epQJZtyy8ktOwZAQngQZ50Sxzkp8cwZHU2gn5dO0Pouux0engxDJsPy15x++LqmVs79+0Z8lOKjX8x3+kgVpdR2rfX31k6WFnl3zL4Ndr8FGS/D7J9YHY1nyt8Cb1xjxkhf+my/XQbYbtfsPlrDur2lrM8uI7OgGq0hPNifOcnR3Hx6MnOSoxkdG4qPTw9atMGR8KO34MP/hi//DtVH4AdPunyjg7jBQVwwdSgXTB0KQGF1Ixuzy1i/v4yVXxfy8tZ8QgJ8WZgSz/mTEzh9XKzLO+5cKm8j1BaYFTRd4J7VWRytbuTNW+e6dLjhd0ki747hM8wOQpseNTVzL91FxCW0hvTnzCJR4cPh6pUQP9HqqJyqqdXGptxyPtlTwrp9pZTVNeOjIHVEBL84exynj4thyvAIfHuSuDvi62cmSEWOMuWp2qNw5atu3Y1oWEQwV8wayRWzRtLUamNzbgUf7ynmoz3FvJtxlEmPfE8AABkkSURBVLBAP5ZMGsLF04cxOym6Z29WniDjFQgMh1POd/qh388s4u0dBfz87LHMGBXp9ON3RUor3XVwPbxwEZz7FzMsUUBbM3zwX2bd8DHnwKX/NC3LfqCuqZVP95Xy8Z5i1u8vo6HFRmigH2eMi+XsCXEsGB9HlCtHfuxZaWaBRo6Cq96BiBGuO1c3tNrsbM6tYPXOo3y0u5j65jYSwoO4ZPowLp8xgkQ31YL7pKkWHhgHU6+ACx526qGLahpZ8vBGEmNCeOvWOfi7qOO4s9KKJPLu0hr+vRQqDpgV7gI67lQaMOpK4I2rzcSK0+6As+7y3oWuHGoaW1mTVcKHu4rYeKCcFpud2LBAFqXEs2jiEGYnR7m3Vpz3Jbx6pZl5eNXbHrOMQWOLjbV7S3h7RwEbssuwa5iVFMWVs0Zw7qQEzy297HjRrO1z41oY4bzVDhtbbCx7ejM5pfW8//P5Lu3gdGkiV0otAf4O+ALPaK3v7+r1XpnIwWzG++/zYdH/wdwVVkdjncIdZkW/pmqza48Xb1bdnrzfzzzKFznltNo0wyKCWTJpCOdOGsL0kZHWlg9K9sCLl0Bbo1mffeRs62LpQHFNE2/vKOCN9CMcrmggPNifS6cPZ/mpIxkT52H73j53rtkAZMU2py2PbLdrVry6gw93F/PPq9NY6OIx4y5L5EopXyAbOAcoALYBV2qtszr7Ga9N5ADPX2j+uG7fOTA3aM5807RqQmLhilfM1mdepq6plbV7S3hvZxEbDpQdT97nT0ngvMkJTB0e7llD76rz4cWLoaYQlr0EYxdaHdH32O2aLQcrePmrfD7ZU0yrTTN3dDRXzx7FwpR4l5Uauq0iFx6dDmffDfPvcNphH/h4P499lsNd50/gpvnJTjtuZ1w5amUWkKO1Pug40WvARUCnidyrnflbeG6RmXLuxF8Ij2e3mVmuXz4Mo+bBD1+AkBiro+q2+uY21u0t4f3MItZnl9HSZmdoeBDXzU3k/ClDPS95nyhiJFz/kdkb9NUr4JKnYNKlVkf1LT4+irljYpg7Joby+mbeSD/Cy1vy+cnLOxgyOIgfnWo6UGPDAq0JcOerZt/XqVc47ZCvfZXPY5/lcOWsEdzoonXGu8sZLfLLgCVa65scX18NnKq17rT2EBYWpmfMmNGn87pam38IzaFDaQ2OpC0wgrbAcOz+wdh9/Pln6D9I88vlnLp7KLeHomyt+LY2OG71+DXX4N9UjV9TFX7NNXhoeui2EF8bd6XkMSe6lncLY3g0Zxht2vNnAdp9/GmMTOZY1HgaI5PRPv74ttQxqGI/IRX7Caw/6lX/NyG+Nv40OZdJ4cd4MHsE7xd59hupRtEYkUztkGk0RSSB3UZI5X7Cir9267X3QfPK7D0cPhbE/9s1xinHrI1PpTLpHIKrDhKXvRKlO14mwdk+//xza8eRK6VuBm4GCAy06F25C1r50BieSEPUOJoGj6AtKOL493xaj+HXXINvcx3+9hYeaJjDqqFZ/Nb3Be6suRi7bwB2/0E0B0XQFhAKPt9cVmVrwb+xgoCGMgLqiwk8VkxAQ5nb/uP7anhwE3+cfJChQc38LXs4q4/GWh1Sl+w+/jREjqYhajyNEUloX398W+oJLd1FSMU+AusKvSp5n+iYzZdfZ47h3omH+PX4IwT72nmrIM7qsDql0AyqzmVQdS6tQZHUxqdSHzuZYzEpBNQXE1byNSHl+/DRbSc/WB/Mjq5lSFArT+YOc8rxaoakUZV4JsGVB4g78B+P+Ft2Rot8DnCP1nqx4+vfAGit/9TZz3hSjXxfcS3/+iKPD3YXUdfUxuAgP+aNiWGGY0beKUPCCOloV49198HGB+G6D8yKdg52u6a0rpn8ygYOltWzv6TOTIs+WktVQysAAb4+TBo2mBmjIpkxKpKZiVFEh3remxsH1phZrb5+ppSSeJrVEXWouqGFtXtL+Wh3MRsOmLJJbFgg504awvmTE0hLjOr7GG9P0tZiNqnYuxrOvAtO/y+v2dv0WHMbK78u5IXNeWSX1BMe7M8P04Zz1exRjIp20WiP5y8wNfLbM/u0pZvNrnnwk/08sT6X8ycn8PAVqW6v/buys9MP09l5NlCI6excrrXe09nPeEIi33qwgn98nstn+8sYFODLuZMSWDolgXljYgjw68Z/TssxePxUCBwMt2w46S+I1pqCqkZ2FdaQcaSaHYeryCysoaXNvJuPiQtlVlIUpyZFMTs5mvjBFk460hq+eMi8WcVPgiteNuOZPciRygbW7i1hTVYJWw9VYrNrEsKDWDJpCOdNTmD6yMj+lby/y9ZmOp13vmqm9C+812uSOZi/h62HKnlx82E+3lNMm11z2pgYfnTqSOd2jpbsMbtR9bGTs6K+mdtfy+CLnHKunDWC3180yZJFxlw9/PA84GHM8MPntNb/19XrrUzkBVUN/P69LD7eU0J0SADXz0vkqtmjiBjUi8kde/8Dr18Fi/8Ec27r8Y83t9nYXVjDV4eq+OpQBel5VdQ1m4+ZyTEhnJoczexkNyf25nqzamHWKtOhduFjHjFmvs1mZ0d+NZ/tL+WzfaXsKzbbpY2JC2XxxHgWTxzC5GEe3GHpCna7mZCV/qxZ22bJ/V6521JJbROvbzvCa1/lc7SmiZjQQC6dPozL04YzJq6Py8yu/jlkvmHWSerlDNmtByu4/bUMqhpa+P1Fk/jhTOsmZw34CUGtNjtPbzjIo58eQKFYcdYYbjwtqW+TF7Q2W5cd/tK0ymPG9ilGm12TdbSWLQcr2Hywgm2HKo8n9qSYEE5NiuLU5ChmJUUzLCK4T+fqUHmOeWMq329aeHN/ZmkrL7+igY05ZXxxwGyXVdfUhp+PIi0xkoUT4lk4Id47ZhS6ktbw8W9hy+Mw/RpY+rDXTsyy2TXr95fy2rYjfLqvFJtdM21kBD9IHcb5UxKI6Wn5saES/jYBpiyDCx/pcTwltU386YO9rMo4ysioQTzxo+lMGhbe4+M404BO5MU1Tfzs1R1sy6vi3ElDuGtpivMSYe1ReHKeWWfkprXg57xad3ti33ywnK0HK/kqr5K6JpPYh0UEMzMx8lu1/D591Nv7Hqz6iemovexZGH2Wk/4V3aO15khlI1/lVbLlYAVbDn6zkuDQ8CBOGxvDWafEMW9MDGFB/m6NzeNpDZ/+ATY+YJLWRU/0qRbsCUrrmlj1dSFvby9kf0kdvj6KeWNiWDJxCOekxHdvGOPGv8G6e+Enm3s0K7aivpmXtuTz9IZcWm2am09P5rYzXbvnZncN2ES+8UAZt7+WQVOrjT9dMpmLUp3Tc/0t+96H15bDnBWwuMuqUp/Y7Jq9RbWk51WyLa+Kr/IqKaszmxQMCvBl0rBwpgwLZ8qICCYNHcyo6JCT14ltrfDp782Ke0OnwQ9fdMu6HjWNrewprGFXYQ1f51ezPb/q+L8lcpA/pyZFM2d0NKeNjSE5JmRglUx6a8MD5v8y5SK45Jl+s4TwvuJaVmcc5b3MIvIrG1AKpo2I4PRxsZw2JoapIyK+X1O3tcLfp0L0aLj2Pyc9h92u2VlQzStb83l351Fa2uwsnBDHXeeneNSnvgGZyF/YnMfdq/cwNi6UJ340w7VTht//ldlM96q3zRZSbtDegbojv4qv86vJOFJNVlHt8Q7UYH9fxg8JY3y82cRgdFwIyTGhDI0INh26NQXw1g1mvZQZ18GSPzt9Zce6plbyyhs4VHGMAyV17CuuY39xHfmVDcdfMzJqkFm3e1QkaaMiGR8f5n2r6nmKzY/Dx/8D4841m3r0o5U6tdbsL6nj490lrNtXwq7CGrT+diNm8vBwkmNCGV2wkkEf3Q5Xvg7jv7+BxLHmNnLL6skuqWdTbjmf7y+j4lgLwf6+XDJ9GNfNTWRsvGu2geuLAZXItdY89mkOD67JZuGEeB65MtX1H4taG+HpM+FYKdy4xrQELNBqs7O/2OwCs9dxO1BST8WxluOv8VFwaehuftf2KP6qjY+SfkPZqAvMLjOD/AkP9ic4wJdBAX4E+fvgqxQ+PgqF+VTQYrPT0manocVGXVMbdU2tVB5roeJYC2V1zRTXNHG0ppGj1Y2U13/7vEkxIZwyZDApQwczeVg4k4eFD+z9I11h2zOmYZF8pllGwQM6q12huqHF9CflVpBZWMOeo6YR40cbnwb8ilo1mFuD/0pIoD+DAn2/9TtbXt98/DiRg/w5Y1wsZ55iVrUMD/bc0t2ASeRaa/7v/b0888UhLpk2jL9cNsV9w4TKc+DZcyA4wiRzD5rCXnWshdyyevJLyhm9409MLXmHPL9k/sfvV6TXRx9vxfdVaKAfQ8KDGBoRzNDwIEZGDyIpOoTEmBCSYkI8d2W8/ubrl2D1z8w6+stfd9kmw56k1WYnt6yetm3PM2n7XbyU/Fd2BM7iWEsbDS02Anx9GBToR2igL8MighkTZz6pJsV0owTpIQZMIv/jB3t5esNBrpubyO+Wprj/I/qRr8wEhPhJpjbnSa2hwh3wzs1mKd65P4Oz/hf8AtFaU9vURnVDC9UNrdQ0ttLQYqOp1UZjqw2bXaO1xq7Bz1fh7+ODv58iJMCPsCB/woL8iAoJICokQBK1J9n1lvn/HjoNrnqr36wV36W2Fnh0BoTGwk3rvGpsfXcMiK3envviEE9vOMjVs0dx9wUp1nSQjZhltjp7/Sqzf+UPX7C+TtnaCOvvNzschcbDNash+Yzj31ZKER5sSiqjoi2MUzjX5MvAP9j8Hj5/AVy10iS4/izjJajJh6UP9bsk3hXvmz3Qifczi/j9+1ksnhjPPRdOtHaUw4SlZsuuAx+bFesaq6yL5dBGMzzyy4dh2o/gts3fSuKinzvlfLjyNVP2+9e5poO7v2prhg0PwvCZMOZsq6Nxq36RyNPzKvnl6xnMGBnJ36+Y5hn1rpk3mpb5ka/guSXu/wOqPuJoiS0Fextc8y5c+Kip34uBZczZZi/V+hLzu1iRa3VErrH5cbOx8pn/M6Ba49APEnlFfTMrXvmaoRFBPHNtmmfVaCdfZoYj1h6Ff55tFqFytcZq+OyP8NhM2P8hLPgN3LYFkhe4/tzCc42aY/psWhtMMi/KtDoi56opgA1/hfHnu30ymyfw6kRut2vueGMnlQ0tPLZ8eu/WS3G15DPgho9MS/jly+DdFdBU4/zzNNXA+j/Dw1Pg8z/DuMVmS6sFd3pWh6uwztBUuP5D8PU3WxbmfWF1RM7zyV2g7bCk00VX+zWvTuRPbTjI59ll/O/SFMvXQOhS/ES4+XM47ZeQ8TI8Phu2PgUtDSf/2ZMp3g3v/RL+lgLr/whJ8826Lz983uwsI8SJYsfDjZ9AWILZC3TvyWc9eryD62HPSrMJuIet0ukuXjv8cPvhSn741BaWTBrCY1dO854p3AXpZubdka0QHAWzfmymVMeldK+upzWUZpmyyf4PoHA7+AXBxEtg9q2QMNX1/wbh/RoqzYJvR3fAuX8xv4feyNZqOvNtzXDbVutHiLlYvxpH3tRq47y/b6TFZufD2+d75yJKhzebkSTZH5mvw4bC6DMhKtkswBU2xOyT2doIzXVQnm3WVi7eBXVHzc8MnQaTLoPU5b1eolMMYC3HzMYh2R+aNc3Pvsf7lsFd93uzWFgnU/H7m341jvyxT3M4WH6MF2+c5Z1JHEzn06g5piM0Zx3krIXsj6GhvOPX+/hBzDgYNdeUT8YuhsEJ7o1Z9C8BIbDsJfjwv82iadVH4AdPmLHn3uDQRrNL17SrBkQS74rXJfJ9xbX84/NcLpk2jPlj+8HkhsFDYfrV5gamlVRbBPXF4ONv/qgCQiB8RL9ZzU54EF8/M+chYiSsvRuqD5v1WcKGWB1Z1xoqzazV6NGmNDTAeVUit9k1d769i8HB/ty1tPvrC3uVgBCIGWNuQriDUnDaL0xSfOcWs/jbFS/DsOlWR9Yxrc06MsfK4Mq15m9mgPOqgtiLm/PIOFLN75amECUr5gnhXBMuMCNafPzMLNCvX7Y6oo5tegT2vQcL7zZDKoV3JXJ/Px/OmzyEi1KHWh2KEP3TkEnw40/NNPd3bzP7t7Y2Wh3VNzLfgDW/g4kXw+yfWh2Nx/C6UStaa+8ZaiiEt7LbzAzhjQ9A/GSz/V/seGtjyv3UDJkcOcfMmHbitoreorNRK31qkSul7lFKFSqlMhy38/pyvG6e09WnEEL4+MLZ/wvL34TaQnjqdNjyJNids259jx3ZBq9fDTHjTf1+ACbxrjijtPKQ1jrVcfvACccTQniKcYu+WavnozvhxYug8pB7Y9j7H7MMb0iMWVc9yINncVvEq2rkQggLhMWbpXAveMRsTvL4qWZ9e3fUzjc/YVriQyaZjSIGS/9YR5yRyFcopTKVUs8ppQbAFiRCDEBKwYxrzUJsE5bC+j+ZhL7rLVNPd7Zj5fD2j+Hj35jzXfsfj9o60dOctLNTKbUW6Gh2wG+BLUA5oIHfAwla6xs6Oc7NwM0AI0eOnHH48OE+hC2EsNTBz02ppTTL1K3P+G8zksSnj8tIaw2Zr8NHvzFLU8z/lTl2X4/bT7h8rRWlVCLwntZ60sle68o9O4UQbmK3Q9Yqs2xy2T4YPMys+5P6I4hK6tmx2pph9zuw9R9QlGGGP174KMRNcE3sXsola60opRK01kWOLy8GdvfleEIIL+LjA5MugZQfmAk6O56HDQ+YDR4SpkLifEg63WxEHhpvlgNopzVU50P+FjiyBbJWm3WGYsabWvy0q6QV3gN9apErpV4EUjGllTzglhMSe6ekRS5EP1VTYEojOZ9CwVdgazHPKx8IHWI2tWipN2WT9u8FhJkNWGbeZEbHyBDjTvWrZWyFEF6gtREKtkFFjlkIrvaoSd5BgyEg1CzXPHK2WYtfWt/d0q+WsRVCeAH/YFNaSTrd6kj6PRlHLoQQXk4SuRBCeDlJ5EII4eUkkQshhJeTRC6EEF5OErkQQng5SeRCCOHlJJELIYSXs2Rmp1KqDOhs+cMYzIqKnkhi6x2JrXcktt7z5Pj6EtsorXXsd5+0JJF3RSmV3tEUVE8gsfWOxNY7ElvveXJ8rohNSitCCOHlJJELIYSX88RE/rTVAXRBYusdia13JLbe8+T4nB6bx9XIhRBC9IwntsiFEEL0gOWJXCn1V6XUPqVUplJqpVIqopPX5SmldimlMpRSbtmVogexLVFK7VdK5Sil7nRTbJcrpfYopexKqU57wC26bt2NzYrrFqWUWqOUOuC4j+zkdTbHNctQSq12cUxdXgelVKBS6nXH97c69sd1i27Edp1SquyEa3WTG2N7TilVqpTqcItJZTziiD1TKTXdg2JboJSqOeG6/a5PJ9RaW3oDFgF+jsd/Bv7cyevygBhPiw3wBXKBZCAA2AmkuCG2CcB4YD2Q1sXrrLhuJ43Nwuv2F+BOx+M7u/h9q3fTtTrpdQBuA/7heHwF8LoHxXYd8Jg7f79OOPfpwHRgdyffPw/4EFDAbGCrB8W2ALNZvVPOZ3mLXGv9ida6zfHlFmC4lfGcqJuxzQJytNYHtdYtwGvARW6Iba/Wer+rz9Mb3YzNkuvmOMfzjsfPAz9wwzm70p3rcGLMbwFnK+WWjS2t+j/qFq31BqCyi5dcBLygjS1AhFIqwUNicyrLE/l33IB5B+2IBj5RSm1XSt3sxpjadRbbMODICV8XOJ7zFFZft85Ydd3i9TcbhBcD8Z28Lkgpla6U2qKUcmWy7851OP4aR8OiBoh2YUw9iQ3gUkfp4i2l1Ag3xNVdnv63OUcptVMp9aFSamJfDuSWPTuVUmuBIR1867da63cdr/kt0Aa83MlhTtNaFyql4oA1Sql9jnc9T4jNJboTWzdYdt2s0lVsJ36htdZKqc6GbY1yXLdk4FOl1C6tda6zY+0H/gO8qrVuVkrdgvnkcJbFMXmDHZjfsXql1HnAKmBsbw/mlkSutV7Y1feVUtcBS4GztaOA1MExCh33pUqplZiPfX1OSE6IrRA4sRUy3PFcn50stm4ew5Lr1g2WXDelVIlSKkFrXeT4mF3ayTHar9tBpdR6YBqmXuxs3bkO7a8pUEr5AeFAhQti6XFsWusT43gG0wfhKVz2O9ZXWuvaEx5/oJR6QikVo7Xu1RoslpdWlFJLgP8GLtRaN3TymhClVFj7Y0wnZIe9we6ODdgGjFVKJSmlAjCdUS4d5dBdVl23brLquq0GrnU8vhb43qcHpVSkUirQ8TgGmAdkuSie7lyHE2O+DPi0swaPu2P7Ts35QmCvG+LqrtXANY7RK7OBmhPKapZSSg1p7+dQSs3C5OLevzm7qxe3i97dHEwdK8Nxa++dHwp84HicjOkx3wnswXx894jY9De949mYFpu7YrsYU/NrBkqAjz3oup00NguvWzSwDjgArAWiHM+nAc84Hs8Fdjmu2y7gRhfH9L3rANyHaUAABAFvOn4fvwKS3XGtuhnbnxy/WzuBz4BT3Bjbq0AR0Or4fbsRuBW41fF9BTzuiH0XXYzusiC2FSdcty3A3L6cT2Z2CiGEl7O8tCKEEKJvJJELIYSXk0QuhBBeThK5EEJ4OUnkQgjh5SSRCyGEl5NELoQQXk4SuRBCeLn/Dztt7mOzSzqZAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "04304098e81e9ec18e28518a5eb177d6",
          "grade": true,
          "grade_id": "plt2_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "lFKcFVDwniIv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "d272a8f2-aa83-441d-fdfc-e0a3dad37cc9"
      },
      "source": [
        "h = 1\n",
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "x = np.linspace(-2.0, 1.3, 50, endpoint=True)\n",
        "y = forward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Forward; h=1')\n",
        "y = backward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Backward; h=1')\n",
        "y = central_diff(p, h, x)\n",
        "bx.plot(x, y, label='Central; h=1')\n",
        "\n",
        "data2 = p_prime.linspace(domain=[-2.0, 1.3])\n",
        "bx.plot(data2[0], data2[1], label='actual')\n",
        "\n",
        "bx.legend()\n"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff27c885ed0>"
            ]
          },
          "metadata": {},
          "execution_count": 54
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "18a8931acbb2421ebd9752d28037c7ce",
          "grade": true,
          "grade_id": "plt3_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "z9sU1w9lniIv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "21e192cb-fd0b-4841-95ef-aa2f2529c869"
      },
      "source": [
        "h = 0.1\n",
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "x = np.linspace(-2.2, 1.3, 50, endpoint=True)\n",
        "y = forward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Forward; h=0.1')\n",
        "y = backward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Backward; h=0.1')\n",
        "y = central_diff(p, h, x)\n",
        "bx.plot(x, y, label='Central; h=0.1')\n",
        "\n",
        "data2 = p_prime.linspace(domain=[-2.2, 1.3])\n",
        "bx.plot(data2[0], data2[1], label='actual')\n",
        "\n",
        "bx.legend()\n"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff27c83f790>"
            ]
          },
          "metadata": {},
          "execution_count": 55
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HsrOzSUxMRAjBrFmz2Lp1K8HBwWRnZ7N69Wree+895s6dy1dffcVNN93EW2+9xcsvv8yoUUcb43x8fEhOTgagurr6lJa1XRz7n8qJpKSksG/fPhwcHIiIiODuu+8mKCiIefPmkZmZ+Zv1999/PwsWLDjOllan0+Hh4UF1dbXZwVFimxTWtODn5oCTveqQWVCbh32nYJD7oG5/lm0Juecg0DpAZfcKisT2+OGHH/jhhx+Ij48H1EET2dnZBAcHExoaah7mMHLkyFPmnAHmzZtn/vh0lrVnwvTp0/Hw8AAgKiqKgoICgoKC+Pzzz//gq5P0BU6sWKlP28/HLxvQDU6BqVO79Vm2JeRaHfgOgcrf7m4kluV0O2dLER0dfcpZk0IIli1bxh133HHc9fz8fLM1LKj2sK2trad8xrFWtKezrD0TTnxuly3t7+3Iu2xpAwMD0ev11NfX4+Pj84eeLel9FNW0Mib0aCqsNT8XALuB3W85bFs5clDTK3JHfl4wbdo02tvbzYMgAA4cOMC2bdu49NJL+eCDD2hqagKgpKSEioqK097Pzc3NbF97Ms7Esvatt97irbfe+kOv4/PPPz+pLe2CBQsAmDVrFqtWrQJgzZo1TJs2zeKdgBLL0qE3cqS+9fhmoKIyAOyDg07xr84e2xTyukJob7J2JBILoygK69at48cff2Tw4MFER0ezbNky+vfvzyWXXMINN9xgnpM5Z86c04o0HJ2z2XXYeSJnYlmbkZHR7bvlW2+9lerqasLDw3n11Vd5/nl1iEdpaSmXX365ed38+fMZP348mZmZBAYGsmLFim6NQ9J9lNa1YhQQ5KXWkLd0tuBa0Ui7tysap+6vK7c9G9tDG+CLm2HxZghI6N7AJMch7U1/y8yZM1m7di329pY1QepJ5Ne5+9maVcmCDxL5/PZxjA3zIbMmk0PXXU2ITzjxX3xz1vc9lY2tbe7IQebJJVZh48aNfUrEJZbB3AxkGiiR35DPgFpwHBRqkefZnpB7h4HGTubJJRJJr6WotgV7rYZ+bo4AFJdl4dECnuGW+c3H9oTcXLkihVwikfROimpaCPR2QqNRD63rctIBcAkdbJHn2Z6QA/hFSCGXSCS9lsKaluOmArUV5AFgPyjEIs+zUSEfBrUF0PHbFmqJRCKxNoXVxzcDaYpVfyBLlB6CLQs5Aqql54pEIuld1Ld00tCmNwt5bVstXpVtdHi7WaT0EGxayIEKmV6RHGXLli3s2LHjnO7h6uraTdFIzleKak0Dl01CXtBQQL9aAUEDLPbMMxZyRVE+UBSlQlGU1GOueSuK8j9FUbJN770sE+YJeIeBRifz5JLj6A4hl0jOla7Sw66BEl2lh84WOuiEP7YjXwnMOOHaw8BPQoghwE+mP1senT34hMta8vOEq6++mpEjRxIdHW1u19+0aRMJCQnExcUxffp08vPzeffdd3nttdcYMWIE27ZtY9GiRcd5tXTttpuampg+fToJCQnExMSwfv16q7wuSd8kv7oZOOpDXmIqPfQYfPJu4e7gjE2zhBBbFUUJOeHyVcAU08ergC1Az7gr+UVAWervr5N0C2XPPkt7evf+BuQQOYz+jzzyu+s++OADvL29aW1tZfTo0Vx11VUsXryYrVu3EhoaSk1NDd7e3tx55524urrywAMPAJyyhd3R0ZF169bh7u5OVVUV48aNY9asWdLfRNIt5FY008/dATdHOwDqc9UNp2OIZZqB4NzdD/sJIY6YPi4D+p1qoaIotwO3AwQHB5/jY1Hz5OnfQGcb2Dme+/0kvZZ//vOfrFu3DoCioiKWL1/OpEmTCA1VfzD+6LAFIQSPPPIIW7duRaPRUFJSQnl5Of379+/22CXnHzmVTYT7Hz1raS/IB8A+uPt9yLvoNhtbIYRQFOWUxi1CiOXAclC9Vs75gX4RIIxq5Ur/mHO+neT0nMnO2RJs2bKFH3/8kZ07d+Ls7MyUKVMYMWIEGRm//9uBTqfDaDQCYDQa6ejoAOCTTz6hsrKSpKQk7OzsCAkJoa2tzaKvQ3J+IITgcEUT1ySoVrVGYURXUglYrvQQzr1qpVxRlAEApven9xHtTvxMra4yT96nqa+vx8vLC2dnZzIyMti1axdtbW1s3bqVvDy1yaKmpgb4rU1tSEgISUlJAGzYsIHOzk7zPf39/bGzs2Pz5s0UFBT08KuS9FUqGttpbNebd+RlzWX4Vevp9HW3WOkhnLuQbwAWmj5eCPTcqZHPYFC0UJHeY4+U9DwzZsxAr9cTGRnJww8/zLhx4/Dz82P58uXMnj2buLg485SfK6+8knXr1pkPOxcvXswvv/xCXFwcO3fuNA+RuPHGG9m7dy8xMTF89NFHp7SslUj+KLkVqr32YD9VyPMb8ulfK1ACu3+YxLGccWpFUZTVqAebvoqiFANPAM8DXyiKcitQAMy1RJAnReegliHKEsQ+jYODA999991J/+6yyy477s9Dhw7lwIEDx13btWuX+eMXXngBAF9fX3bu3HnSe3YNqpBIzoacSvX7p2tHXtBQQFgNuIwJt+hz/0jVyvxT/NX0borlj+MXIVMrEomk15Bb0YSrgw5/N3XsX8mRbEa0gvvgoRZ9rk11dn6T+w3P7n726AX/SKg5DPp26wUlkUgkJnIqmxjs72ouZW04rG407QdZrmIFbEzIc+ty+TLrSzoN6qEVfsNAGKA6x7qB9WGsMUFK0nPIr2/3klPRxGC/owO9DQWFgBTy4xje5EVsZge59eo0avwi1PcyT24RHB0dqa6ulj/sfRQhBNXV1Tg6yj6M7qCxrZPyhnZzfrzD0IFTSQ1CUbAPCbHos7utjrwnCP7hIHdvNJK+4BDDvIeBzxBQNDJPbiECAwMpLi6msrLS2qFILISjoyOBgYHWDqNPkFuptuZ3VawUNRYxsFqgH+CDxsLjAW1KyH2iEzB89V8Kc5Jh6Gy1o9MrVO7ILYSdnZ25e1IikZyertLDrh15fkM+A6sFuiGWTauAjaVWnEyTvhsOHTx60W+YtLOVSCRWJ6eyCTutYjbLKqjNY0ANuA+xzJzOY7EpIXcYopbwaHILMQq19Rq/CKjJBX2HFSOTSCTnO7kVTQzyccFOq8pqdV469gZwHRJh8WfblJBrXV3o6O/FgCPtlDSVqBf9hoFRr5YhSiQSiZXIqWwi3O+oWVZrjlpNZx9mOR/yLmxKyAHshoQTXCHIrDEdcPqb2qtlnlwikViJToORwuoWBvsfLT1UCksBsA8NUS9UZsFboyFvW7c/3+aE3Cs6ngG1kHnE1IrtMwRQpJBLJBKrUVDdjN4ozAedjR2NeJU30+nujM7LNDitIg2qssDBrdufb3NC7hIVjUZA1aEU9YK9M3gNkkIukUisRk7F8aWHBQ0FDKwWGIOPmdNZkQEoR/tfuhGbE3LHCPWT0JmVffSiX6SsJZdIJFYjt/K3rocB1eA0+BizrIpDqtGfXffb2dqckNsFBWFwsMOruJ7atlr1ol8EVGWDQW/d4CQSyXlJbkUTAzwccXFQW3NKizNwbwWvocOPLqpIV/2hLIDNCbmi0SDCggiugIwaUzrFPxKMneq0IIlEIulhThzv1pCtzklwNpVM09mmlkn7R1nk+TYn5ABukcMZVCHIrDYJ+YA49X1pivWCkkgk5yVCCHIrmsxpFQB9njp1yj4sTL1QlaWOpvS3zBATmxRy9+hY3Nqg8LBJuH2Hgp0zHJFCLpFIepayhjaaOwwMNu3IhRDYF1disNNiN8B02Nk1yUzuyI/SdeDZnJ6mXtBo1V156T4rRiWRSM5Hcszj3dQa8srWSvwrO+kI8EXRatVFlemgsQNvyzQH2aSQOwxV8072+WW06U3TzwfGw5ED8sBTIpH0KCeaZRU0FBBQLdCGBB9dVJEOvkNAZxkXRJsUcq27O3p/L4IrjOTUmYZKDBgB+laokmWIEomk58ipbMLdUYefqzreLb8yC/96cDvWLKvikMUqVsBGhRzAYWgEgyoE6TWm3NPAePW9PPCUSCQ9SG5F83Hj3cozU9AI8I4wlR62N0JdoRTyk+EZHcfAasguM+XJfcLB3lXmySUSSY9yollWY45aTefYZZbV1azoJ4X8NzhGR6EVUJe2X72g0cgDT4lE0qPUt3ZS2dh+XMWKcrgYoRxTelhxSH0vd+S/xSk6GgBNVh4Go0G9ODAeylOhazizRCKRWJCu1vyuHXlZcxn9y9vpGOCDpmsWakUG6JzAK8RicdiskOsGDkTv7kJwSQeFjeqkagbGg75NGmhJJJIeoatipWtHnlmbSVClQBd+TJlhxSHVRkSjtVgcNivkiqKgixxKaNkx3uTmA0+ZXpFIJJYnp7IJe62GIC/VCCun/BD9a8ErKu7ooop0izUCdWFTQl5U08L27Crzn73iRhJUCVllqaYLoeDgLoVcIpH0CLkVzYT4OqMzjXerTN+HRoDbMJNwt9RAU5lF8+NgY0L+zpYc/vxJEkajAMB5eAxaAdWpyeoC84GnLEGUSCSWJ/cEs6y2rCzgaNPi0dZ8KeRm4oO9aGjTc7hKNXHvOvAUGTlHF3UdeMphzBKJxIK06w0U1rSYzbJa9a04F1Vh1GmwDzZ1dfZAxQrYmJAnBHsCkFyo+pDrBg6k092Z/kVNVLWaUi4DR4Ch4+gnUCKRSCxAQXULhmPGux2uO0xghUAfPABFp/qSU5GupnvdAywai00JeZivK+6OOvYV1gHqgacSMZjQMkF69QkdntIJUSKRWJCjZllHK1aCKwXOQ48Z5VaZoe7GTV2flsKmhFyjURgR7MU+044cjh54Zh974OnoIQ88JRKJRekqPQwzuR4eLk7FtxE8uypWhLC4x0oXNiXkAPFBnmSWN9LUrrocusfGoxVQmbpXXaAoqoGWFHKJRGJBsiuaCPB0wtleTaPUZxwAwLHroLOpHFprLV56CDYo5AmDvBACDhSp6ZWuA0/9oayjiwbGQ/kh0LdbI0SJRHIekFZaT9RAd0BtzTfk5AHgOGSIuqDrnM7PMlOBjsXmhHxE4G8PPDvcnPDKr6a5U61mYWC8OsOzPM1aYUokkj5MS4daPRdtEvLylnL8jrRicLJHN3CgusjCU4GOxeaE3MPZjnB/1+MOPIkII7RMkFZlEm7Z4SmRSCxI+pEGhIDhAz0AyKrNIqhKQNggs50tFYfA2Rdc/Swej80JOah58n1FdQihNgZ5jxhNUCWkFCeqCzyDwclLCrlEIrEIqSUNAEQHqDvyrJpMgirBfVj00UUVGT1y0Am2KuTBXtQ0d1BQ3QKAZ/wotAKOJG1XFyiKafSbLEGUSCTdT1ppPT4u9vR3Vx0Oi/IP4t4KrhGmNIrRaCo9tHxaBWxUyBMGHZ8ndxoxAgBxMAO90TSzc2C8mqPqbLVKjBKJpO+SWtJAdICHOY3SnKnmw82t+fVF0NFkWztyRVHyFUU5qChKiqIoe7vjnqdjiL8brg5HG4N0Pj509vchpKiD7NpsddGAEWDUywNPiUTSrbTrDWRXNJoPOtsN7djnHwHAYWhXxUrPeKx00Z078qlCiBFCiFHdeM+TotUoxAV5sK/oaGOQS3w8Q0sEyeVJ6gV54CmRSCxAdnkTnQZhPujMrctlUJkRvY8HOm9vdVEPlh6CjaZWAOKDvEg/0khLh5pK8Ro1Dq9myE7foS7wCFRPjKUTokQi6UZSS+oBzDvyrNosQsoF9sOOac2vSFf9VZw8eySm7hJyAfygKEqSoii3n2yBoii3K4qyV1GUvZWVlef8wPhgTwxGwcFi9ZPalSdv2bdPrWbpOvCUO3KJRNKNpJU24OagI9jbGVAHwAdUg2dM/NFFlek9llaB7hPyiUKIBOAyYKmiKJNOXCCEWC6EGCWEGOXnd+51lfHBXgAkm/LkjhERGB3s6J9XT0lTibpo4Aj1E9rRcs7Pk0gkEoBUU0enRqMedNYfOoBWgFOUqULFoIfKLNsTciFEiel9BbAOGNMd9z0d3i72hPg4mw20FJ0OTVQEQ0oE+ypMu/CB8SCMUHbQ0uFIJJLzAINRkH6kgWhTflwIgcjKBcCxS8hr88DQ3mOlhwC6c72BoigugEYI0Wj6+BLg6XOO7AxICPZiW04VQggURcF71DhCVqSyvm/rY5sAACAASURBVDiRKwdfCQEj1YVFuyF4bE+EJLEyeoOR1k4DeoNAbxTom1voKCzAUF+Pc2cbTvp2FHt7NE5OaDQd2Lkq6DydUDwGgvtA0DlY+yVIejGHK5to6zQy3NQIVNlaSb+SFvQujtgFmDzHe/igE7pByIF+wDpTPaUO+FQIsakb7vu7xAd7snZfCcW1rQR5O+McH4/OCFXJu2Ey4NYffIZA/jaY8JeeCEnSw5Q3tJFcUEtyYS0p+dW0pqYRXZ5OdG02gxoq8G9uNq9tB2pPcg+9TiDcDXh4deAZaI/LUH90A4LUDuHw6RA6Gewce+w1SXovqaVdB51HW/NDygTKkNCjrfllB0HR2paQCyEOA3G/u9ACdOXJ9xXVEeTtjFOcGoZLVgl1bXV4OnpCyEQ4uEbNW2m74/8tiTURQrAzt5ov9haxJ7+WI7XNxFbmcNGR3Txcegjn9k4ACv0gM0Rhs7dCm6cRNzsjiqMDNfZ2NBs06DtA6QDPRgP96joZWK1hSLGOllzglxo6/evwC96NX8B76DycYcglEDlTfe/gZt1PgsRqpJU04KDTMNjkQZ5VlcHISnCffowEliSpaRV75x6Ly6aVbVh/NxztNCQX1DIrbiA6Hx+MAf4MLakkpTKFKUFTIPRCSPoQjuyHwJHWDllyljS161mXXMyqnQXkVDQRpGnn1urdxO77CZeGZlocYHeEQv1gJ3w86wjStDJZ2DMoZDKOw2ZC+EXg7G2+X3O7noyyBlJLGvgps4R3ivZh55hDvCGbIQWFjM3QY7fXkZqk/miHeRFcvR3ntLWgdYCwKTD2dhg83eKTXyS9i9TSeiIHuKPTqseL5elJ2OvBI0atmkMIVcijru7RuGxayHVaDbGBqoFWF+4Joxn683/ZWZ6kCnnIhepf5G+VQm6D5FQ08fGuAtYkFdPUrudCdz0P1X9P/+2/oOs0khymkHaZNyGhDlxZnEKQzhVi5kHE5TBoAujsT3pfFwcdIwd5M3KQNwsvCKGoJp4v9hbx+Z4idno18e3MI4xx2k9I0g4m76ulIF2HYegoBk0KxvXILpSPr1XvP+0xGDS+hz8rEmsghCCttIFZcQPN1zrSMwFwiDRVqNQchrb6o+dzPYRNCzmoB54rth+mrdOAo50W14SReH7zX/LSd8MowNUffCMgbxtMvM/a4UrOkKqmdp7/LoM1ScXYaRVmD/FgTtZ/cfp0PUZhZGeMPZ1XjmWyKOeGnC0oZR5w4cMw9g511N8fJMjbmb9eEsE904fwU0YFqxML+S4rGO/wGZTNSsX1l/VM21mK9v1S2mLDibj2BpwLP4IPZ0D4xTDtUbXcVdJnKapppbFNz/AA9furw9CBS14FBjstDmFh6qISU2e5FPI/RnywJ50GQVppPSMHeeM8SnUI0O5Pp21+G446RzW9krIaDJ2gtbNyxJLTYTAKVicW8uKmDFo6DNwxMYTrynbR8tYjaJva2R6jof3Gy1jQUoRn1ufg6AlTH1VTHWch4Cei02q4NLo/l0b350BxHY+tT2PtrnhGRUzE97rDNK77gIt+zCH/yRx0V1zK4IsD0e77FyyfDFFXwfQnwGdwN3wmJL2NowedasXK4frDDCo3og8NQtGZpLR4L9g59+hBJ/QRIQfYV1jHyEHe2IeHY/RwZVh+M2nVaYzsN1JNr+x5X+3yDLJ4ibvkLDlYXM+jXx9kf3E948K8eSLWkeYX7qczvZDMQQo5917ITYOjCdr8ovoPpj0KY+4AR3eLxBMb6Mm6JRfwxd4iXtiUwb6N/Vlw4bsUzEuh5O1XuPi/P5G63YVBj7+Bp2Ma7HoHsv8Hl70I8TfJ/HkfI620Hp1GYWg/9bA7qyaTkHKB04xj6sVLklTDvh4urLBZr5Uu/N0cCfRyMlvaKoqC8+jRRBUe0xgUMlF9n7fVSlFKTkdDWyePr09l1tvbKalr4425MTzbth3DrTdizCvkv/NDiXj3TZZRQ9D3j6uNXkt2wKQHLSbiXWg0CtePCebnv05h3uggVu4s4MVN/Qm7bzVfPzyeUvtmjty/jIx1hRgWbVZ/pd5wF3y5UB28K+kzpJY0MKSfG452WgAKs5JwbQOf2NHqAn0HlB2AgIQej83mhRzUMsQuS1sAj3ET8GuA7EO/qhdcfNVyoPztVopQcirSSuuZ+c/tfLyrgIXjQ/jfzREEP7+U9nc+IGmolsr3H+WvVy8k9vNb1K/fZS/Bgg3gNahH4/RysefZa2JYv3QCvq723Ls6F7eAh1Hef5kNU13Q/7iV/fMX0JTwD7joScj4L/xrgvye6yOoB5315rQKQH2qasjnYhoAT3kqGDog0OIGsL+hTwh5QrAnR+rbKKlTh0g4j1H/hzQmHcAojOqikAvVDk99h7XClJzAl3uLmP3ODjr0Rr688wLudiqiYPZMSM9h/bwgprz7MVfkfoey7nbwHQpLflVz4RrrfdvGBnqy7s8TuHpEAK/9mM2anf7Mf/5bvn9gAi0t9eTNv4Giw26IW74HnSOsnAk/Pa2ez0hslorGdqqaOhhuEvJOYyearHyEohwdJmGlg07oI0I+frAPANuzVVdFh/BwDO4uhOW1klOXoy4KvRA6W45+siVWo11vYNnagzy45gAjB3nxzV0X4Pz5G1TcfR8lbh0kPjeXvy59nUGfL4Ks7+Gip+CWTb3mENHJXsurc+N4alY0WzIrWfjeIWZe8Rqt7/+DtBANTc++QsbbnyBu+Rnib4Rtr6iC3lJj7dAlZ4nZutZUsZJVk0VIiZ7OkAFonJzURSXJ4OIHHkE9Hl+fEPKIfm70c3dga1YVAIpGg8OoBDVPXm7Kkw+aAChqu77EahTXtnDduztZnVjIkimD+XBuFHl33QAffM6uEU74rFrOHZFTsPtgBrQ1wMKNMPFe0GitHfpxKIrCwgtCWH37OJra9Vzzzq+0K+OJXfkZP1zoCus2sf/2P2GY8ixcu0I9aF9xCdQWWDt0yVmQVtqAokDkAHVHnlKxj/AjAtcRx1jXliSpu3ErHHL3CSFXFIVJQ/zYll2J3qCmUnwumIR/PWQdMuUonb2h33Ap5FZke3YVM9/cTl5lM/++eST3xbhx4NoZOO/JYPOcwcz68H+Mq8iCj69VTfkX/9zrzc5Gh3iz8e6JRA5w565P97Fpnx3zXv+Gr+cFok3JYP81l9PhNQ4WfA3NFaqYSzdOmyO1pJ5QXxdcHdRqlLzUHbi2gXeC6fuzrR6qsqySVoE+IuQAk4b60dCmZ79p0ITzGLXMsH1v8tFFoRdCUSLo260R4nnN+pQSFn2YSD83RzbcPZEJopKDs2eiVNay9YEp3P7EGny2vAj/vV9tp7/l+x4/0Dxb+rk7snrxOOaOCuSfP+fw3uYa7nl0Pd/dNxZDTQ0Hr5tFc7uP+po0WvjwcllBZWOklR61rgVoObAfAKdYk8dKaQogrFKxAn1IyCeG+6JRYGvW0Tx5p7szAdm1HGlSB6MSciHo26B4jxUjPf/4z8587v08hZGDvFizZDwuB38l98braRFtZP7fApbc8By6z2+E3e/CuKUwf7XFywq7G3udhheujWXRBSGs2J7Hs//N5f5bVnDwybl0dLSSOX8OdSVNcOsPql3ux9dC6lfWDltyBtQ2d1BS12o+6CxvLsc3rxaDox0O4aZzm66zt4FSyM8JLxd7YgM9+cUk5IpGg11CLFGFgr3le9VFgy5AzZPLkrCeQAjBGz9m89j6NKYP68eqW8ZQu+krKpbeQ6mHoPGtv3PjtDtQPpoFh7fAlW/AjGd7XT78TFEUhSeujOLOyYP5eFchD69NZeGsJ6l9/UEa7PQULFpEbWahenAbMArW3AK7/mXtsCW/Q1ppA3DUunZ/5X7CSwWaYUNQtKbv1ZIk8A47zpitJ+kzQg4weagfB4rrqGtRSwz9J07Dvx6SU0z26E6eMCBW9V2RWBSjUfDUN4d47ccsZicE8O5NCeSvfpfGZU9xOECL94q3uTx6Bqy6Eioy4PrVMHKRtcM+ZxRF4aEZEdx30VDWJBVzz2f7uPiCRbT88+9UuhgpXLyY2oMZcPM6iLwSNj0MO9+xdtiS05B2Qmv+gdIkQirAK+GY85uSZKvlx6GPCfmkoX4YBWzPUatXXMdfAEDrjl10Gk11vCEXQnEidLZaK8w+T6fByF+/3M/KHfncMiGUl+fEkfneK4hn3yJzsAPDVq1mbP8oWHkFVOfCDZ/B0EusHXa3oSgK91w0hGWXDWPjgSMs/SSZ6Qnz6XjjUapMYl6XkgJzVqpi/v0ySP7I2mFLTkFqaQMBnk54uahOmuX7d2NnAJc4k0laQyk0lkoh7y7iAj1wd9TxS6aaXrEPC0Pv78Ww7NajZYihk9Tuq6JEK0bad2nXG1jycRLr9pXwwCVDeWxmJOn/fgnN6x9wINKJsR99zVBXX1XE64rgxi9h8DRrh20R7pg8mKdmRfPDoXKWfJzMxQnzaXv971Q5G8i/7TbqD+xXSxMHT4cNf5E5815KasnRjs52QzuadHVGp1NcrLqgxFRQIYW8e9BpNVw4xI+t2ZXmOZ6ek6YSmy/Ymr9ZXRQ8HhSNzJNbAL3ByD2rU/gxvYJnrormrmlDSP/3K2je+JD9UU5M+HAdAVodrLwcGo/ATV+plUR9mIUXhPCPq4fzc0YFD391kMtH30jba8uoczKQe9siGg8fhnkfq9+Xa29XG6AkvYaKxjbyqpoZFaJOI0uvTiesxIDB2wNdv37qopIk0Oigf4zV4uxTQg4waagv5Q3tZJY3AuAxeQpOHVCw8wd1gaO76k4m68m7FYNR8MCX+9mUVsYTV0Zx8/gQ0pe/ivL6CvZHOTHxg3UECtTSu+ZquPnr82Ygw03jBnHfRUP5KrmYl77P5IpxC2h+8a+0oyd9wXxayqvU9FK/4fD5zbI0sRexJ081PhsTqnaPp1SkEH5E4BQXe3RGZ8le9Wtn52StMPuikPsBR8sQXcaNQ2g1DDh4hPz6fHVR6IWqb3BHi5Wi7FsIIXj064N8nVLKg5dG8KcJoaR/9Ba8+h4Hhzky4f2vCNTYw6qZauPEgq8haLS1w+5R/jI9nPljgnlnSy6rduRzxaTbqHnuLjSt7Ry86Vo6m/Vw01rwDoXV89XvT4nVScyrxtlea06tpOfvZWANeIwwGWMZjVCyz6ppFeiDQj7Aw4mh/VzN7fpaNzd0ccOJOyz4pfgXdVHIJDB2qiZaknNCCMHTGw+xOrGIpVMHs3RqOOlrVmB87m3Swx0Yt2INQY4e8PFs1Wvk5nVWa5qwJoqi8MxV0Vwc1Y8nv0nj24NHuOKSpWQ9MgfH6iaSFs3BqHWBBetVv46PZ6vVPBKrsjuvhpGDvLDTahBC0HhAzYeb8+PV2dDRKIXcEkwa4kdiXg0tHXoAvCdPJ6wc9qSZ0ivB49Sc1uEt1guyj/DKD1l8+Gs+f5oQwgOXRJD93RfoH3+ZvCB7Rq34gmC3/vDpPKjOges/PS9FvAudVsOb8+NJCPbi3s9S2HW4mvlzn2b34nG4ZZexd+kChIu/KuZaB1g9T01DSaxCXUsHmeWNjAlRa8NLm0vxz6tHKOA4fLi6yIqOh8fSJ4V8coQfHQYjuw+rbnOuF6qDJZQ9B6hvrwcHV9VEK2OjOvVacla8vTmHtzbnMH9MEI/PjKJk58+0/O1JSvvpGL5yNcE+IfDFAjWHeO0KCJts7ZCtjqOdlhULRxHs48zij/aSWd7In+5ezrarQ3D79SD7n3pAtSaYvxoajsAXN0vrZSuxN78WIWBMqCrkKRUpRBQLlNBgtK6u6qKSJLB3A98hVoy0jwr56BBvHO005i5Ph2HDEN4exOYa+LXENGwi6ip1l1iRbsVIbZdPdxfy0veZXD1iIP+4Oobq9P2UL/0LNW4KQe8tJ6T/MPh6CeT8qHZsRs2ydsi9Bk9ne1bdMgZney0LP0ikpsnADU99zq7xXjh8/h2ZK99ShxNc/Q4U/Aob75MbDiuwO68ae62GuCB1nOT+8n1ElAg8xhxzSF+SpA7dtnI3cp8Uckc7LWNDfcwHnopGg8eFkxmRD1sLt6iLhs0EFEjfYK0wbZafM8p59OuDTInw46Xr4mgtLSTnloV0aIw4v/kcUYPHwaaHIHWNOi0nYYG1Q+51BHg6sfJPY2hs07Pk4yQctC7MeP1L0sId6HzxbUq2/Q9i5sDkhyDlY9j5lrVDPu9IzKthRJCnebRbecpunDrAZZTpoL6zDcpSrZ5WgT4q5KC26x+uaqaoRq1McZ00CdcWQcmeX9Ab9eDWT/VeObTeypHaFgeK61j6yT6iBrrz9g0JGBvrSLn5WuxaOmh54a+MHTkLfnkBEpfDBXfDhHutHXKvJXKAOy9fF0dyYR1PrE+jv/tAot96nwovDUfuvY+G/ByY/DBEXQ0/PAaZm6wd8nlDU7ue1NIGc1qlpbMFp7Q8AJxHmYS7PFUtmpBCbjm6yhC70iuuEycitBoiDzWSUqHO2iPqKqg4BFXZ1grTpiisbuGWlXvwcbXng0WjccLAzkXX4FHeTMnfb2L6RbdB8n9gy3Mw4ka4+Bk5Sf53uDxmAEunDuazPUV8vLuQyJBROLzyFMJg4OCtN2BoaYGr/6X++v7VreoOUGJxkgtqMRiFWcjTqtOIKDJi6O+DXf/+6qJectAJfVjIB/u5EODpZE6vaD08cBozmnGZ8EvRFnVR5JXqe7kr/11qmztY9GEinQbByj+Nwc/Vgc1L59Ivo4KMO6cza97fIXczbLxXbbm/8g0p4mfI/RdHMDXCj6c2pJGYV8OEcXMofGAOnqWN7LrrJoSdk2oq5uAGq6+Hpgprh9znScyrQatRGDlI7ehMKd/HsCKB66gxRxcVJYJrf9WW2Mr0WSFXFIVJQ/3YkVtNp2lqkOelMxhQI8hI+p+6yH0gBI6RQv47tHUauO2jvRTXtfL+wlGE+7vyyxNLGLg9i4PXDGfO3W+qh8ZfLFCHJF+3ErR21g7bZtBqFF6/Pp5gb2f+/EkSpXWtzL7xaRKvicB7VyYprz8J7gPUSpbmKtX+1qC3dth9msS8GoYHeOBimghUkLYTzxbwGDNOXSCE2oEbMrFXbFj6rJADTB7qS1O7nqQCtc3Wddo0hAIBScUUNhSqi6JmQdkBqMmzYqS9F4NRcO9nKSQX1vL6vBGMDvFmz4oX6ffFL6SN7881//gUpakCPpmrtijf8AU4evz+jSXH4eFkx/IFI2nrNHLHf5Jo1xu57smPORDjiv3yLyja/C0MjIcrX1ftJTb/w9oh91naOg2kFNUx1pRWEUJg2KemtJxHmTo6Kw6po/sGT7VWmMfRp4V84hA/HO00bDxQCoCdvz+62GjGZhqPdnlGmsriZPXKSXn+u3Q2pZXx6BVRXB4zgKyf1uH4yofkhrsw4+2vsTN0qr/ut1TBDZ+DZ89PEO8rhPu78dq8ERwsqeeRdQdxsXNh9BsrOeKjofyBv9FclA9x16u+7dtfg8zvrB1yn2R/UR0dBqO5EaigoYBBec3oPVywDw1VF+WaTPjCplglxhPp00Lu6qDjkqj+fLP/CO16AwA+l80kpAJS9pkqALwGqSZah6SQn8hniYW8ty2PheMHcevEUMoykml44FGqvLUkvP8Zro6usHaxOiH+2hXqjlFyTlwc1Y/7LhrK2uQSPt5VQNjAaOxeeBSl00DyHTdibG+HGS/AgDhYd4f8TdICJObVoChqPwpASmUKw4oFdvFxR42yDm8BnyHgEWi9QI+hTws5wOyEAOpbO9mcoR56ul10MQBOvx6gsUN1SCTqKrX7sK7IWmH2OnbkVvHo16lMGurHYzOjaKouI+e2WzAogn7v/JOB/cPhf4+r3bEznoNhl1s75D7D3dPCmRLhxzMb00ktqWfyhPnk/PlSfA/X8OvjS8DOEeaaBlF8uVCtZ5Z0G7vzaojo54aHs3rOk5W1k3514DvOZLmsb1cbtXpJWgXOAyGfGO6Ln5sDa5OLAbAPDMA4NIRRmXp+LT2myxMg/RsrRdm7OFzZxJKPkwn1deGtG+JRDJ3s+tO1uNe20/l/9xMVOw32fqg2qYy5A8YtsXbIfQqNRuHVuSPwdrHnrk+TaWzrZM7tr7BvSgC+63dy8Kv3wSsErvk3HNmvNl9JuoVOg5GkglpzfhygaY86rN3cCFS8Bzpbek1aBc4DIddpNVwVN5DNmRXUNqueFX4zriSiBLbtM1Wr+AxW/YRlnpy6lg5uW7UXrUZhxcLRuDno+PGe6wnIqqFo6ZVMvOw29bT+2wcg/GK49Flrh9wn8Xax580b4imqbWXZ2oNoFA2Xv/wZBYH2dD7zKtU5aRBxGUy8D5JWQspqa4fcJ0gtqae102D2Hy9rLsM7swyDoz2OwyLURbmbQdGqFSu9hD4v5ACzEwLpNAjzoafHjBkAGH/aTlWrandL1FVQuAsay6wVptXpNBhZ8nEyxbWt/PvmkQT7OLP51QcI3pxB5sxoLl/ygjpj8/ObwScc5qwArc7aYfdZRod4c//FQ9l44AifJhbi6erLwNdexYAg7c+3qPnyqY+qc2g33gfladYO2eZJzFON9kaHqvXj20u2MzxfoIuPQdGZvtcPb1GbgHpRddZ5IeRRA90Z1t+Nr5JLAHAIC0OJCGdiqp6vc75WF0XOAsR5m14RQvD4+lR2Hq7mudkxjA7xJmn9+/R7/1tyYn244vlPUdrqVUtaRQPzP+tV38h9lSWTBzNpqB9PfXOIQ6UNxMZMp/Qvs/ErbGDbY3eo/5Feu0KdfPXFQuhotnbINk1iXg1hvi74uzkCsO/ADwTUgN+ki9QFrbVQmtyr8uNwngg5qIeeKUV1HK5sAsD/2rmElcGObZ9hFEbwHwa+Eedtc9CK7Xnm4RDXjgzkcMpWePxVyvo7MGn5V9gpGljzJ6jNV2dMeodaO+TzAo1G4bW5cXg527H002Sa2vVc+adn2D85AP8Nu0nf8B/VN2j2ctXNc9PD1g7ZZjEYBYn5Nea2/E5DJx27TPnxCReoi/K3gzD2qvw4nEdCftWIADQKrNun7srdZ16B0GoYuruUxLJEdVHULPU0urnKipH2PJszKnj223RmRPfnrxdHUFteSMmfl6LXwZDlH+Dh2Q++fwRyf4aZr0LIBGuHfF7h4+rAP6+Pp6C6mUfWHkRB4ZIXP6aov47mJ5+nvuiwKiwT74PkjyBtnbVDtkkyyxppbNObhTy5IpmI3HYM3h44DDH5jeduBntXCOxdowq7RcgVRZmhKEqmoig5iqL0yi1BP3dHJoT7sja5BKNRoPP2xmXSJCanwdqMNeqiqKvU/20zNlo32B4kq7yRu1fvI3KAO6/Oi0Pf2cru2+biUa/H4cUnCB6SAHtWQOK/Yfxd0pLWSowN8+H+i4eyYX8pn+8pwtujP94v/h/aTiPJSxdg1Oth6iMQMAo23AN1hdYO2eZIzFOnMXUJ+faibcQUCNwnTDy+fnzQhF5nQXHOQq4oihZ4G7gMiALmK4oSda73tQTXJgRSUtfKnnz1QMPr6mvwbBKU//IDNW01auWKdxikfmXlSHuGmuYObl21Byd7Le8tGIWTnZbv753HoOx6qu+Zy4jp89Rv3G8fhCGXwsVPWzvk85o/TwlnQrgPT31ziNzKJkaNmUX+bRfRP6ua7S/8VRWXa99XNyNf3Sb9WP4gifk1BHg6EejlDEDunh9xbwGPiab68bpCqMntdflxAEWc4+QRRVHGA08KIS41/XkZgBDiuVP9Gzc3NzFyZM9bPxo1dhSN/DMu1Rn4Hv4enRA8X1lJ8jBYMcANpzQnbgwuY3HYERYlDiO/xanHY+wphKKhLHIu7a4DGHDoMxyajnCBez03Z7WxMcyO/7Z4E+TUxjsJWVR12LE0eSgtButOQZGA3s6V0thF6NrrGZD2CQg9C5yqGZtv5MUgdwo7nJjmX8PjUQWszO/PyvwB1g7ZJhBAUcKfcarPxy/3WwwuBiYH1XDjFiMP+fnSoNVyef9q/jas0Kra8MsvvyQJIUadeL07UisBwLEtkcWma8ehKMrtiqLsVRRlb2dnZzc89o+jMXbiXJNFs3cERkWHXlHY6+DImEyBEtKKQPBNqS9tBoU5gZVWibEnEEB16MW0uwfhm7sJh6YjDHZv5obsNpIDtPy32RM3nZ5nYw6jFwrLDoZJEe8l6Dqb8Dm8iQ7X/tQGTURBwxcGL6pd4ZbaBhwUAz9XePPdEW9uHlRGnEejtUO2CTqc/THau+BoMtPrDOwkJl9QYq+lQat+74/ybqCy3Y78FkdrhnpyhBDn9AbMAd4/5s83A2+d7t+MHDlSWItfsyvFoIc2ig0pJUIIIVpSUsShiGHinnujxJ4je9RFG+4R4mk/IZoqrRanJXlva64Y9NBG8fL3GUIIIdL3/ST2xA0TmyfHicbaCiH0HUKsnCnE075CFOy0crSSk/HwVwdEyMMbxa/Z6vfor9+tEKnDhonv/3S5uqCtUYg34oV4JVKI5morRmobvPpDpgh5eKOobGwTQghxz3dLxP7oYeLIs8+pCwwGIV4IFWLtHVaMUghgrziJpnbHjrwEONbyLtB0rVcyLsyHgR6O5pZ9x9hY7IaEc1mywpqsL02LloChHfZ+YMVILUNXhcplw/tz30VDKSvLpWzpPRg1GoYuX4mrh6/atZm3FWa9CcHjrB2y5CQ8NjOSUF8X7vsihdrmDi6YcQuZV8URtOMwuz96BRxc1YatpgrYcLcc3vw7fJ9WxqhBXvi6OtBh6KAhcRd2enDtKjssPwgt1b2u7LCL7hDyPcAQRVFCFUWxB64Hem2vu0ajcFV8AFuzq6hsbEdRFHwWLCC43EDhtu+pb68HvwgIvwj2vK8a5PQR0o80cNenyUQOcOeVuXG0tjWQdNs8vOv0uL3yDAOHjoBd/1Jbvifer1qmSnolzvY6/nl9PDXNHTy89gBCCC5/agUFwU7oxj16oAAAIABJREFUXl1BeW6q6kZ50RNqFVbyR9YOuddSWN1CRlkjl0SpI9ySypOIyG1D2OmO+o/3MtvaEzlnIRdC6IG7gO+BdOALIUSv7hWeHR+AwSj42lRT7jFzJri7cXFiBxsPm0oPx/0Zmsohda0VI+0+yhvauGXlHlwddby/cBT2WvjuL9cSltNM6/0LiZw6G7J+gB/+DsNmwrTHrB2y5HcYHuDBg5dG8H1aOZ/tKcLRwYWwV99AMQoO3nObWpI4bimETlYbhapzrR1yr+SHQ6otxyXR/QDYVrKN+MPgGD8CjbNawcLhLeAXCW79rRTl6emWOnIhxLdCiKFCiMFCiP/rjntakiH93BgT6s372w/T1mlA4+SEz7x5jMkS/G/3ajXXP3ga+A2DXW/b/K+lLR16bl21h/rWTlYsHM0ADye+fvY2oreXUHbNBYy99WF1VNuaW9QSzNnLQXPe9IrZNLdNDGNiuC9Pm0oShw6/kIo7ZxGQU8/m5/+ifh3/v707j4uq+v84/jozrLIjiIgIuIviivsuarlvqVnm8tXKrNS0xdJs0bJcstQ0NTV3zX1JzdxyF1FABBMFN5BNFJB9mLm/P+70/fXNjQwZBs/z8ZiHI3Nk3nMZP9w59yy9F4LWSl07Xm+agQYl2b6oJGqWd8CnrB0AUecP4p2i4BxknJavy4UbJ0vksMM/PbP/W8d1rEZSRh7rgtWr1C6DBiGEoMbhWMJTwtV9+Jq9AYkR6rRcM6U3KIxdH0bUrQzmDWpAHS8n9qz8nFprTnOrkTftvlgCGQmwpj9YlVHXULGyM3VsqZA0GsHsAfWwsdQwdn0o+QUGOo+azuWG5Si39hDRJ/eAk5e6GXb8Wfh9hqkjlyipmXmEXLtDZ3/1bDzuXhzlz6mD8Ow7dFAb3TwFBbkltlsFnuFC3qKKG039XFlwOIZcnR7LChWwC+pAx3DYfH6t2qjuQChTVu03NlNf7r7Ib1FJTOnuT1AtD04dWkv5metIqeRA68WbEbosWNsfsu+o+2063TdyVCrhPBxtmN63LhfiM/h2fzQajYbmc34iw15D4vsTyclMg9q9od5LcHSWusqnBMCBi8kYFOhcW+0yORZ/jMDLBkQVX6y8jWM4Yg6BxkKd0VlCPbOFHOCdTtVJuZfHmtPqWbn7kKHY5yhk/bKbmLQYdTPhwP/Apd1m2b+46uQ1lh67yrAWvgxr6Udk1O8Y3ptGrp0lDVdsxMrGRl0xLykKBqyACvVNHVl6Qs/XKc/AQG8W/h7D6dhU3D380E4Zh3tKPoc+GKY26vI1OHmrXSy5GSbNW1Lsi0rEy9mW2hUcAThz6SA148C143P/3yjmIFRsoo4EKqGe6ULerHJZmlcuy8LDMeTk67ENDMSydi16n1SYc2qm2qjxSPW38elFpg37Dx26lMwnOyIJqlmOj7v7c+1WFLfeeBNbHfgsXoxj+UrqGtYxB6D7HKjWydSRpX9pSg9/KrmWYfzP4WTk6mjW/VWudKmN34FLnNq8QF3qtu8SSI+DPe+bOq7JZeUVcOTybTr5eyCEIE+fR8HxYLQGcAgydqukxkDieXUTjxLsmS7koJ6V387MY83p6wghKD92HO5pBiz2HuXkrZPqVeo6/SB0NeSkmTpuoZyPS+OtNeeoWd6RuYMakHovgfCRL+OZosdx5jQq1G0GR2ZC6Cpo8x40GmrqyFIRsLO24NuB9UnMyGXKtgsAdPpyOYnlrWH696TEX4FKTaH1uxC+rtSMyHpSR6JT1GsKxtEqIYkh1IvOR1/WCZs6ddRGEZsAodaAEuyZL+RN/FxpVdWNhYdjyM4vwK51a6zr12XAScG3p2aiN+ih+WjQZZnFWNwryZkMW34G5zJWLBvWmAIlkwOj+lI9Nhfx0VtU6dwXwtbCoS+g3iBoP8nUkaUi1KCSC2M6VGNb2C22h8VjY+uA16xZ2OYYCB43HIPBAG3fV3e42TVOPTt/Ru2LSsK5jCVNfNXVDk9c+536sQrOHToiNBp1tFrERnVLtxJ+7eiZL+QA73SqRmpWPqtOqmflHmPG4pKux/vwJXbE7ADPeuDTSu1e0eWYOu5DxaflMGTpaTQCVo9siou9YMv4vtQPTSdnZF9qD35TvXCz4231CnyPueroHKlUebN9FRpWcmbytgvEp+VQPbAjyUM6UTniNvvnf6Cukth3ibo64tZRYNCbOnKx0+kNHLiYRFBNDyy0ahlMPPobtvng3NHYzZgQDqmXIeAFEyYtHFnIgUY+rrSu5saiI7Fk5RVQpnlzbBs1ov8pLYuC55Gty4Z2EyEjDn7/2tRxHyg1M49Xlp7mXm4BPw1vQiVXG9ZOHkCzgwlkdGtBgwnT4GYwbBis7oQ0YCVYWJk6tvQUWGg1zBlYH4NBYcLPYegNCkHvzuFGDWfKLdnF5fNH1A3Hu3wN147CiXmmjlzsgq/eISO34L/dKtF3o6kUnoTexpIyzYzLUkRsBI2lcRvIkk0WcqN3OlXnTlY+K41n5e5jxuCYoaP+iSRWRK0Av9ZQfzAcn6uOLS9BMvMKGP7TGeLv5rB0WGNqV3Bk9YzhNNsazZ1W/jSZsRhxKxRW9wP7cvDKFrnfZinnU9aOT3rW5lTsHZYcjUWj1VL/u6UUWAiuThhLXm4WNBgMtXrAwWlwK8zUkYvVr5GJ2FhqaFPNHYBt0VtoHK1QplVLNNbW6qeUC5vVQQBlXE2c9vFkITdqWMmFdjXcWXwkhsy8AuyaNsGudWsGHdew5eRSUrJToPNUsHWBHWNKzMfRXJ2eV1eEEHkrgwUvNyTQ15ll818ncMUZbtfzpsWCdYiUKFjVB2ydYejOEjvNWCpa/RtVpEud8szed4kL8el4+PpTMGEk3jdz2fvpSLVbrcdcsHNTN6LIzzZ15GKhKAr7IpNoU80dWystOr2OmP3bcMkCtx591EbXT8C9BLPoVgFZyP/HuI7VuZutY8WJawCUnzwJK4PgxX05fB/2vfqbucvX6i7awYtNGxYo0BsYuz6Uk7GpzOpfl3Y13Fi84DWaLDxKelUPWizbikiLhZW91dmaQ3eCU0VTx5aKiRCCL/sEUNbOmjHrQsnOL6DZ4PFca1mZqtvDOL1vhfqe7vOD2he8b7KpIxeLiPh0EjNy/zsJ6EjcEeqFZWAoY4N9u7bGRhvB0g6ql+xhh3+Shfwv6ns708nfg7kHLnMxIQMrHx/cXnudFlEGrvy2mei70eowpKqd4MBUSLv5+G/6lOQV6HlrbSi/RqqzNnvW82ThD6/SYsFxsv3K0WTNDrS5ibCyF2i0ahF38TVZXsk0XOys+GZgPa6mZjF1VxQAbWev4K6LJflTZnL79k31wnfztyBkKVzaY9K8xWFfZBIaAUE1ywGwI2oTzaLB+bnn1W6VgjyI2g61uqvLVpgBWcj/ZnrfAJxsLRm95hz3cnWUfXUk2koVGfGrgTknZmBAgW6zAQV+mWCSBbWy8wsYuSKEvZGJTOnuzystKjJv0Qhaf3+S3ErlCFy7Awv9HVjRAww6GLJDvbglPZNaVHFjVNsqrAu+yZ6IBMo4u+E2fSou6XqOjn9FXSQuaAp4BMD2t+BekqkjP1W/RibSxM8VFzsrUrJTyDlyDNs8BeeexouaVw5AbhrUMY9uFZCF/D5u9tbMG9SA66lZfLglAmFlRYVPPqX8HQNem0+oXSwuPtBhMlz+FSKLd1JFRq6OIUuDOX7lNjP61eWV5hVZMHcY7eefRuftTqN129HqUtQinp8FQ7ZDuZrFmlEqed7pWJ26FZ2YuCWCW2k51Gzbi+QBbagZnMQviyaChbW6cXN+JmwfbfYrfj5MbEoml5Mzec7YrbIzdictI/Xg5kqZJk3URhEbwda1RK92+HeykD9A08plefe5Guw6n8DqU9exb9kSx9696XtS4cSOH9h2ZRs0HaUu3L/nA8i5Wyy5UjPzGLT4FOFxacwb1JBeDcuxcOYgghadI79yBRqs34E2/SIs7aheuBqyDcoHFEs2qWSzstDw3YsN0OkNjDcOSWw3eT4JlZ3wXLiDyAuH1F/4nafBlf1w+gdTR34qNoTcRKsRPF+nPIqisPf8JhrGgGu3HgitFvLuqd1Ltfuo4+3NhCzkDzGqTRXa13Bn6q6LRMSl4/nxZKz8KjNhl5bvfv2U00kh6hX/7Duw7+lvwpCYnsuARSe5kpzJ4iGBNKwM8yZ3JeinSLLr+NJw3Q60cQfUPvEybjByv/qLRpKM/Nzs+NQ4JPGH32PQWFpSd95yBIIb498hMyddXVuoehf1PX0r1NSRi1SuTs+GMzfp7O+Bp5Mt4SnheJ65joVewbF7d7XRH7uhIAcC+ps27D8kC/lDaDSCbwbUx83eitFrz3JPY4X33O+w12l5b6eGCQfGEWtrDy3eUtcsObviqWWJTcnkhR9OkJSRx8r/NMHOLpaf3+5Gt623yG8WQOCqrWjDFqsbQ3g1hBH7wNXvqeWRzFf/RhXpVteTOb9FE3YzDbcqtdB8MBrfG3ns+nioOiSx9wJ1vsGm/6hnqKXE9rB40rJ1DG3hC8C2K9toGyWw8K2ETZ3aaqOIjeoKkd5NTRf0CchC/ggudlbMf7khCWm5vLcxHKsqVfCc+jl+13J4cX8+o/e/we2mr6v7e+4cA8FLijzD9rB4esw7RlZeAWtGNiH6zhYuvTGCzidz0PbvQf1FK9Hs/xD2fwq1+8Ir28xiAoNkGkIIvuwdQDkHa8auD+Vero76L71FYttaBPxyid+2fau+f/r9CHevqStkloL+ckVRWHHiOjU8HGjq50q2LptzIbuodV2PS6/eCCEg67a6ZG2dfma3Q5Z5pTWBhpVcmNilJvuiklh67CpOPXrgMngwQaeyabs3gbFH3yf3hWVQo6u6+3wRTXfOydfzwabzjF0fRi1PRzaPDmTnyUm4jf+GhlcMuHz4HtU/nIjY9AqELIOW46DfUrC0KZLnl0ovpzKWfPtiA+Lu5jBxcwSKotBq1grS3Gyw+2IxV6+Hg08LaPeReoYautrUkf+1kOt3iUrIYGgLX4QQ/Hb9N1qfyUbRanF+wTg6JXIrKHqz61YBWcgLZUQrP56r7cG0Xy4yY+8flP3gA5z69aX3MR3VtoXx0anP0PVbCv691UkVR2b+q+e7nHSPXt8f4+ezN3mzfRW+GODG6vkD6DrtEF7ZNlT64QfKB7rC903VoVLd50Cnz8zuLEIynSZ+rkzoXJ1fIhJYdeo6lg4O+Hw3D/tshfBxr5JXkAetx4NfG9j9HqRcMnXkf2XFiWs42ljQu0EFAHZFbabDBYFjp05YuKvT9InYpG6w7FHbhEmfjPyfXwhCCL57sQGDmlRiweEYXloajHh3Ek69ejHwqAGn1b8yYNcgQlqNVreHOzhNvf3Dj6SKorAx5CY95x8nNTOf716uTL52JQff6EP/9fFYVK9KrXU/4ZCwGDYOBUdPeO2wuouRJP1D/39BP4rzcWlUbNiKnFEDqXHxHlumDVcnkvVdos4K3jisRK/8+ShJGbnsvZDIgEBvylhZcCPjBja/n6VMjgGXlwapjZL/UPfmDHjBLFcElYW8kGwstUzvG8C3A+sTeSuDbvOPEz10LE69ejHgmIGXV9zg7e0jmFzOnTv1Bqpn5b9NKXQxPx+XxqsrQ3hv03kCvG0Y0PECB1a/RNAHW2kboWA3cigB7/fFclMPdXhYx89g5EHwrPuUX7lUWv15Qd/d3prRa86Rnq2jyVufkBToS52fQ9nzy1x1XZ4+iyA5CvZ+aOrIT2TN6RvoFYVXmvsA6kXOzucUNJV9KNO4sdro6Cx1Sn6j4SZM+uRkIf+HejfwYufbrSjnYM2wledY034o7h99RO1YPd+vsiHm8C565kaxOeB5DCfmwuJ26kc2ve6+76UoCqdiU3ll6Wl6zj/O6aspdG15Fbv0j6j86RJGbcvFxbcGfvOnUMntGGL3OHVc+BsnoNU40FoU/wGQSpU/L+gnpufy7qZwAJrPW02WszX2n/1AVOxpqNYRWoyBs8vVFQHNSH6BgbWnb9C+Rjl8ytqhN+gJPbKJqgkK7i+9ol7kTI1RX1fjEWBX1tSRn4hQTHBFOjAwUAkJCSn25y1KuTo9n+2MZF3wTRr5uDDMLYfqi77CEBfHlVpOLG2SiUNVL567k4RvWgK+1m54Nn4NbaNhKNaOHI5OYd7BKMJTzuPgHEdF9wTKR0fR5Vg2/jdBcSiDZ1d/nB1DEfdugrUjdPocGg6VfeFSkVt67CpTd0UxuVstRrauTNLZ4yQPGcmlKjYErT+Ai7UDLO8KSZHqHAUPf1NHLpTtYfGMXR/Giv80oW11dw7cOMAf775Nu2hLah49htbBAbaNVgv5uAh12GUJJoQ4qyhK4H1fl4X839kWGs8Xuy+Sci8PW10uQ5OCeT7yINY5mVzytSK4cgERPoLrHmCpQMUCPZYFZbmFBsuCu/gkG2gSrdD0isA+y4De2QbPugKXcrFoLDXqNOGAAVCzK1g7mPrlSqWUoiiMWn2WAxeT2fB6cxr5uBD54zdoZi3heHdfhs/YhTYzGRa3Bcsy8NohdUnnEq7PguOkZes4ML4tCgaGrunF+1/HUrZPP7ymToW712FuA2jyqrqyaQknC/lTpCgKl5LucfxKKieu3CbsUjwdLh2l480QKt1LBiDXQkuOtQa9lR690OOaAZYF6kUVYWHAoUIeDhVzcPDKRfg0Vot37T5g727KlyY9Q9JzdPSYdwyd3sAvY1rjUsaSU6NexPHIeUIn9mDw0Blw4zT81A0qt4WXflYviJZQ5+PS6Dn/OJ/08Gd4Sz+2Xt7KpWmT6HkGqu7ejZWvL+wcB2FrYGw4OFYwdeTHkoW8GOn0Bs7HpRFy7S5ueRn4XY/C5dZVrPNzMWRnQW4Wlm6OWFXwwMrbA1v/amgstaAYwMFTXZRLkkzgQnw6fReeoL63M6tHNMUiL4fTPYPQpqaTs+gz2jYdoM5b2PUOtJ6grppYQk34OZw9FxI49VEQVhZ6Bq7uwuffJOPWuQtes2ZBejzMra/ulNR9jqnjFsrDCrm8WvYUWGo1NPJxpZHPnzMs5Zonknmo4+XEzBfqMnZ9GJO3RfB1v7oE/Lia6L69yXv/M65uqItf4H/UreGOzlY3JvfvZerY90nNzGPn+VsMDPTG0caS5RdW0+RIEpY6cBs1Sm10Yq568tRynGnDFgF51UySpP/Rq74XYzpU5eeQOJYcjcXeryplZ3yBV7KBU28PJjUnFbrOhIqNYesbkBRl6sj3WX78GvkFBoa28CE9L501wYvofk6D43PPYV21qrrm+tmfoO6LpeITsCzkkiTdZ1zH6nQL8GT6nj/YH5WET6deGF4bRP2ILH7+sD85GGDAKrC2h/UvFdtSzoURm5LJ4iOx9KxXgarlHFh2YRltTtzDKleP2xvGs/GT80Cfr85eLQVkIZck6T4ajWBW/3oEeDkxdn0oFxMyqDPuY7KDGtNubwKLvxlCgb27WszT42DjcCjIN3VsFEXh4+0XsLbUMLl7LRKzEtl2bjU9z2mxDwrCpkYNyEqFM8vUxbFKyc5ZspBLkvRAtlZalgwJxN7GgpErQridmU+DOT+S6V+JdisusGj1OyjeTaDHdxB7CLaNAoPBpJl3hN/i+JVU3n+uBuUcbFgYvpB+h/KwztPjPmaM2ujUAtBlQ+t3TZq1KMlCLknSQ3k42vDjkMakZuXx+qoQ8oWWBkvXo3NzJHDOflbtnwUNXlYnq13YDHveN9myt+k5Oqbuukjdik681NSHmLQYwo5toWOoAZeXXsamRnW1Cyh4Mfj3LFVbIMpCLknSIwVUdGLOgPqcu5HGmHWhKI5OBCxfj7XGEu+Pl/HLmTXQcqw6jf/MEjj8lUlyzt53iTtZeXzROwCtRjD37HeM2KegdXbC/e231F8wu8are9m2ec8kGZ8WWcglSXqsLgGefNazNvuiknhr7Tk0Pj5U+XE5rtkatBO+4MSl39Sz8vqD4fev4PTiYs0XfjONVaeuM6S5LwEVnTiXdA7dngNUi9Pj8e67aB0d4dxKdbP09h+Wur1sZSGXJKlQhrbw5ZMe/vwamcSYdaHY1G2A17y5eKVC8pvjOHj5V7W/vEY3tYslYlOx5NIbFCZti8Dd3prxnauTnJ3MJ3snMOQwWAXUxqlPH0i+qG6U7tcWWpWOkSp/JQu5JEmFNrylHx9392fPhUTGrg/FqVV73L6aRrV4A6lvj2f7xS3wwlLwaQlbX4fL+596plUnr3EhPoMpPfyxtChgzIG3GbjlNk65Gip8+hmiIFcdVWNtr66vXoKXFXhSspBLkvSPjGjlx+Rutdgdkci49WG4d+2N+xdT8b+hUPDOJ6wKXwWD1kK5WrDhZYjc9tSyJGXkMmtfNK2rudGljgeTjk2i0r4LNLpUQLkJE7CtXRv2ToSUi+q66g4eTy2LKf2rQi6E+FQIES+ECDPeuhZVMEmSSq6RrSszqWstfolIYOyGMFx79cVz5tfUjBc4fDCH+Wd+QBm8TZ3Cv3EoHP+uyEez5Or0vLsxnHy9gam96rAgfAFXTu9j6CGBfdu2uA4bqo6kObdCnYZfNahIn78kKYq1VuYoijKrCL6PJElm5NU2lVFQ+HL3H+QXGJg9oAtec6xg/HisJ/3EjPdTeXfwVrQ73lR3y7pzFbrOKpINUXJ1el5bdZajl28zo19dItIPsjp4EfN222JV1g7Pr6Yj7l5TVzes2AQ6TP73L7gEk10rkiQ9sdfaVOHTHv4c/COZHvOOEVenOT6LFuN1z4pWn+7ki3WjudttNrR6R91haN1AyM34V8+Zk69n5IoQjl5OYUa/ulTzuc30Q1P4cqstDqm5eM2aiYWDHWwaru6/2e9H0FoW0SsumYqikL8lhDgvhFgmhHjoSvNCiNeEECFCiJCUlJQieFpJkkqCYS392PBaM/J0BvouOME2C2+qr9+Ina0TPWYH89n0ruyp0hSl+7cQcwiWd1GXkH0CWXkFDP8pmBMxt5n1Qj1a1BS8t28sH26BCjdz8JrzDWVqV4ENg+FWKPScXyoWxXqcx65HLoTYD5R/wEOTgFPAbUABpgKeiqI8dkv30r4euSQ9i+5k5fPOhjB+j06hR70KTGvjya2xo+DCJQ7UE8QMa8fESkF4bB8LVnbQ5Svw713oXesz8woYvjyYs9fvMntAXbAPYf6pb3h9QzoBMQVUmDEDp/oe6pn4vUR4frq6808p8tQ3lhBC+AK7FEWp87i2spBLUulkMCgs/D2G2fsu4VvWjvn9A3DduJw7S5eS6CL4sY8dfdu/Qr8z6xFJkVCphVpwK9R/5Pe9l6tj6LJgwuPSmdjTgSN3FpP0Rygf7bLC41YOnlOn4uyVAPs/BUcv6L8cvBoVz4suRk+lkAshPBVFSTDefwdoqijKi4/7d7KQS1Lpdio2lTHrQrmdmUcnfw9etb+L/Tefo6Tc5vc6gsgX6vGcmzetQzfjlJWqrtfSYcp9wwPzCvT8cj6BhYdjuHonlU4twjhxeztBl20YsSsXS+syVJg6GfuUVRC9B2p2h17fg62ziV750/W0CvkqoD5q18o14PU/C/ujyEIuSaVfamYeS49dZW3wDdKydTR0tWBc8gnK7t1MgdCzp6HgcAMLvDzK0j4xhvb5Cl7Nx0LdASThxrLTf7AxLIL0/FTcXdPRuhzGKzaV0aHueEQmYlu3Dl5vdsXy3Gy1K6XzNGj6eqG7asyR3LNTkiSTyMnXsy0snuXHrxKdlElN7jH++gG8wk+gMRi47GvDoZr5XPEUWDoVoNNCooUFuRqBUBQqpkCtmwodL1vjezUHrb0lZQMUXL1vIDSAs0+p7Ur5O1nIJUkyKUVROH4lleXHr3LwUjIu2el0vBnCc9eDqZCVCoBOA3cdLbAWClaKAetsA5p89QzbokwBZWtm4VzHBo1fU/BuCpWaQ4UGYGFlypdWbOTmy5IkmZQQglbV3GhVzY1cnZ7sfD3Z+b3Jzisg59p1dBcvIqIv4pt1BwsLLWi0aGytsK3kRBn3fCy9KyF8mkPZqqW6++RJyEIuSVKxs7HUYmOpxdXOeCZdPgCala6lZYuTnNkpSZJk5mQhlyRJMnOykEuSJJk5WcglSZLMnCzkkiRJZk4WckmSJDMnC7kkSZKZk4VckiTJzJlkir4QIgW4XuxP/L/cUNdSNwfmlBXMK6/M+vSYU15zyeqjKIr7379okkJeEgghQh60ZkFJZE5ZwbzyyqxPjznlNaesDyK7ViRJksycLOSSJElm7lku5ItNHeAfMKesYF55Zdanx5zymlPW+zyzfeSSJEmlxbN8Ri5JklQqyEIuSZJk5p6ZQi6EmCmE+EMIcV4IsVUI8cBttoUQzwshLgkhrgghJhZ3TmOG/kKISCGEQQjx0CFRQohrQogIIUSYEMJke+f9g7wl4di6CiF+E0JcNv7p8pB2euNxDRNC7CjmjI88TkIIayHEBuPjp4UQvsWZ7wF5Hpd3mBAi5S/Hc6QpchqzLBNCJAshLjzkcSGEmGt8LeeFEA2LO+MTURTlmbgBnQEL4/2vga8f0EYLxACVASsgHPA3QdZaQA3gMBD4iHbXALcScGwfm7cEHdsZwETj/YkPeh8YH8s00bF87HECRgM/GO+/CGww4c++MHmHAfNNlfFvWdoADYELD3m8K7AHEEAz4LSpMxfm9syckSuKsk9RlALjX08BFR/QrAlwRVGUWEVR8oH1QK/iyvgnRVEuKopyqbif90kVMm+JOLbG51xhvL8C6G2CDI9SmOP019ewCQgSwmSbWJaUn2uhKIpyBLjziCa9gJWK6hTgLITwLJ50T+6ZKeR/8x/U37p/5wXc/Mvf44xfK6kUYJ8Q4qwQ4jVTh3mMknJsPRRFSTDeTwQ8HtLORggRIoQ4JYQozmJfmOP03zbGk5N0oGyxpLtfYX+u/YxdFZuEEN7FE+2m+Oq5AAACLUlEQVSJlJT36T9SqjZfFkLsB8o/4KFJiqJsN7aZBBQAa4oz298VJmshtFIUJV4IUQ74TQjxh/GMo8gVUd5i8aisf/2LoiiKEOJh4299jMe2MnBQCBGhKEpMUWd9RuwE1imKkieEeB3100QHE2cqVUpVIVcUpeOjHhdCDAO6A0GKsUPsb+KBv54tVDR+rcg9Lmshv0e88c9kIcRW1I+5T6WQF0HeEnFshRBJQghPRVESjB+Zkx/yPf48trFCiMNAA9S+4KetMMfpzzZxQggLwAlILYZsD/LYvIqi/DXbj6jXKUqqYnufFqVnpmtFCPE88D7QU1GU7Ic0OwNUE0L4CSGsUC8kFeuIhcISQtgJIRz+vI96MfeBV+JLiJJybHcAQ433hwL3fZoQQrgIIayN992AlkBUMeUrzHH662t4ATj4kBOT4vDYvH/rY+4JXCzGfP/UDmCIcfRKMyD9L11xJZepr7YW1w24gtr3FWa8/XnVvwKw+y/tugLRqGdfk0yUtQ9q31wekAT8+vesqKMEwo23SFNlLWzeEnRsywIHgMvAfsDV+PVA4Efj/RZAhPHYRgAjijnjfccJ+Bz1JATABthofE8HA5VN9bMvZN7pxvdoOHAIqGnCrOuABEBnfM+OAEYBo4yPC+B742uJ4BGjxkrSTU7RlyRJMnPPTNeKJElSaSULuSRJkpmThVySJMnMyUIuSZJk5mQhlyRJMnOykEuSJJk5WcglSZLM3P8B2ZQqfLTEWiMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "a68d54e8ab1303582d48ca0a484c013d",
          "grade": true,
          "grade_id": "plt4_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "QAiVfHxCniIw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "cff38555-48e6-4955-cd92-510740b2c9aa"
      },
      "source": [
        "h = 0.01\n",
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "x = np.linspace(-2.2, 1.3, 50, endpoint=True)\n",
        "y = forward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Forward; h=0.01')\n",
        "y = backward_diff(p, h, x)\n",
        "bx.plot(x, y, label='Backward; h=0.01')\n",
        "y = central_diff(p, h, x)\n",
        "bx.plot(x, y, label='Central; h=0.01')\n",
        "\n",
        "data2 = p_prime.linspace(domain=[-2.2, 1.3])\n",
        "bx.plot(data2[0], data2[1], label='actual')\n",
        "\n",
        "bx.legend()\n"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff27cd30b90>"
            ]
          },
          "metadata": {},
          "execution_count": 56
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "4d802ba0cb9f6582992226c4898ab0af",
          "grade": true,
          "grade_id": "plt5_test",
          "locked": true,
          "points": 2,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "-ZUdiK_sniIw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "8f0ee14c-38c1-482b-8d77-dae6fea91d63"
      },
      "source": [
        "fig, bx = plt.subplots()\n",
        "bx.axhline(y=0, color='k')\n",
        "\n",
        "h = np.array([1., 0.55, 0.3, .17, 0.1, 0.055, 0.03, 0.017, 0.01])\n",
        "err = error(p, p_prime, h, 2.0)\n",
        "\n",
        "bx.plot(h, err[0], label='Forward')\n",
        "bx.plot(h, err[1], label='Backward')\n",
        "bx.plot(h, err[2], label='Central')\n",
        "bx.legend()"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff27cacbd90>"
            ]
          },
          "metadata": {},
          "execution_count": 57
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
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          }
        }
      ]
    },
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      "metadata": {
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        "id": "Gs3FQ6gGniIw"
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      "source": [
        "## Part 2: Richardson Extrapolation\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
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          "cell_type": "markdown",
          "checksum": "446cd2f0472413299f074ff754675ef8",
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        "id": "VCFJEL7RniIw"
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      "source": [
        "## Instructions\n",
        "\n",
        "\n",
        "Today's assignment is to:\n",
        "1. Implement Richardson Extrapolation method using Python\n",
        "\n",
        "## Richardson Extrapolation:\n",
        "We used central difference method to calculate derivatives of functions last task. In this task we will use Richardson extrapolation to get a more accurate result.\n",
        "Let,\n",
        "$$ D_h = \\frac{f(x_1+h) -f(x_1-h)}{2h}\\tag{5.1}$$ \n",
        "\n",
        "\n",
        "General Taylor Series formula:\n",
        "$$ f(x) = f(x_1) + f'(x_1)(x - x_1) + \\frac{f''(x_1)}{2}(x - x_1)^2+... $$\n",
        "Using Taylor's theorem to expand we get,\n",
        "\n",
        "\\begin{align}\n",
        "f(x_1+h) &= f(x_1) + f^{\\prime}(x_1)h + \\frac{f^{\\prime \\prime}(x_1)}{2}h^2 + \\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + \\frac{f^{(4)}(x_1)}{4!}h^4 + \\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^6)\\tag{5.2} \\\\\n",
        "f(x_1-h) &= f(x_1) - f^{\\prime}(x_1)h + \\frac{f^{\\prime \\prime}(x_1)}{2}h^2 - \\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + \\frac{f^{(4)}(x_1)}{4!}h^4 - \\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^6)\\tag{5.3}\n",
        "\\end{align}\n",
        "Subtracting $5.3$ from $5.2$ we get,\n",
        "$$ f(x_1+h) - f(x_1-h) = 2f^{\\prime}(x_1)h + 2\\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + 2\\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^7)\\tag{5.4}$$\n",
        "So,\n",
        "\\begin{align}\n",
        "D_h &= \\frac{f(x_1+h) - f(x_1-h)}{2h} \\\\\n",
        "&= \\frac{1}{2h} \\left( 2f^{\\prime}(x_1)h + 2\\frac{f^{\\prime \\prime \\prime}(x_1)}{3!}h^3 + 2\\frac{f^{(5)}(x_1)}{5!}h^5 + O(h^7) \\right) \\\\\n",
        "&= f^{\\prime}(x_1) + \\frac{f^{\\prime \\prime \\prime}(x_1)}{6}h^2 + \\frac{f^{(5)}(x_1)}{120}h^4 + O(h^6) \\tag{5.5}\n",
        "\\end{align}\n",
        "We get our derivative $f'(x)$ plus some error terms of order $>= 2$ Now, we want to bring our error order down to 4.\n",
        "\n",
        "If we use $h, \\text{and} \\frac{h}{2}$ as step size in $5.5$, we get,\n",
        "\\begin{align}\n",
        "D_h &= f^{\\prime}(x_1) + f^{\\prime \\prime \\prime}(x_1)\\frac{h^2}{6} + f^{(5)}(x_1) \\frac{h^4}{120} + O(h^6) \\tag{5.6} \\\\\n",
        "D_{h/2} &= f^{\\prime}(x_1) + f^{\\prime \\prime \\prime}(x_1)\\frac{h^2}{2^2 . 6} + f^{(5)}(x_1) \\frac{h^4}{2^4 . 120} + O(h^6) \\tag{5.7}\n",
        "\\end{align}\n",
        "Multiplying $5.7$ by $4$ and subtracting from $5.6$ we get,\n",
        "\\begin{align}\n",
        "D_h - 4D_{h/2} &= -3f^{\\prime}(x) + f^{(5)}(x_1) \\frac{h^4}{160} + O(h^6)\\\\ \n",
        "\\Longrightarrow D^{(1)}_h = \\frac{4D_{h/2} - D_h}{3} &= f^{\\prime}(x) - f^{(5)}(x_1) \\frac{h^4}{480} + O(h^6) \\tag{5.8}\n",
        "\\end{align}\n",
        "Let's calculate the derivative using $5.8$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
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          "cell_type": "markdown",
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        "id": "EwMxR-plniIx"
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      "source": [
        "## 1. Let's create a function named `dh(f, h, x)`\n",
        "function `dh(f, h, x)` takes three parameters as input: a function `f`, a value `h`, and a set of values `x`. It returns the derivatives of the function at each elements of array `x` using the Central Difference method. This calculates equation $(5.1)$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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        "nbgrader": {
          "cell_type": "code",
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        "id": "F6BRYPykniIx"
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      "source": [
        "def dh(f, h, x):\n",
        "    '''\n",
        "    Input:\n",
        "        f: np.polynomial.Polynonimial type data. \n",
        "        h: floating point data.\n",
        "        x: np.array type data.\n",
        "    Output:\n",
        "        return np.array type data of slope at each point x.\n",
        "    '''\n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()\n",
        "    return (f(x+h) - f(x-h)) / (2*h)\n",
        "    # --------------------------------------------"
      ],
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
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        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "36b3dddc8be0efb9a97fb5768d9d8ced",
          "grade": false,
          "grade_id": "cell-0c13cf39da895e01",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "QNCZ1QxyniIy"
      },
      "source": [
        "## 2. Let's create another funtion `dh1(f, h, x)`.\n",
        "`dh1(f, h, x)` takes the same type of values as `dh(f, h, x)` as input. It calculates the derivative using previously defined `dh(f, h, x)` function and using equation $5.8$ and returns the values."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "6ae95f8d4c68cb8306001ca5f9752220",
          "grade": false,
          "grade_id": "cell-ed364c63e8c23e35",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "tM6YOR3hniIy"
      },
      "source": [
        "def dh1(f, h, x):\n",
        "    '''\n",
        "    Input:\n",
        "        f: np.polynomial.Polynonimial type data. \n",
        "        h: floating point data.\n",
        "        x: np.array type data.\n",
        "    Output:\n",
        "        return np.array type data of slope at each point x.\n",
        "    '''\n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()\n",
        "    return (4 * dh(f, h/2, x) - dh(f, h, x)) / 3\n",
        "    # --------------------------------------------"
      ],
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "7d794eaafc49abd1e798a85026114d67",
          "grade": false,
          "grade_id": "cell-4eb597d5a4be4420",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "Zt4qjdMVniIy"
      },
      "source": [
        "## 3. Now let's create the `error(f, hs, x_i)` function\n",
        "The `error(f, hs, x_i)` function takes a function `f` as input. It also takes a list of different values of h as `hs` and a specific value as `x_i` as input. It calculates the derivatives as point `x_i` using both functions described in **B** and **C**, i.e. `dh` and `dh1`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "57af2549c86921869eab0881ae72fd42",
          "grade": false,
          "grade_id": "cell-4aef4fe1b49d44da",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "0JyAd9TcniIy"
      },
      "source": [
        "def error(f, hs, x_i):  #Using the functions we wrote dh() my c_diff  and dh1() which is my first order c diff, we find the error through appending their diffrences with Y_actual ny f(x)\n",
        "    '''\n",
        "    Input:\n",
        "        f  : np.polynomial.Polynonimial type data. \n",
        "        hs : np.array type data. list of h.\n",
        "        x_i: floating point data. single value of x.\n",
        "    Output:\n",
        "        return two np.array type data of errors by two methods..\n",
        "    '''\n",
        "    f_prime = f.deriv(1)   #first order derivitive f^1(x)\n",
        "    Y_actual = f_prime(x_i)  \n",
        "\n",
        "    diff_error = []\n",
        "    diff2_error = []\n",
        "\n",
        "    for h in hs: #where h is my loop counter iterating through hs\n",
        "        # for each values of hs calculate the error using both methods\n",
        "        # and append those values into diff_error and diff2_error list.\n",
        "\n",
        "        # --------------------------------------------\n",
        "        # YOUR CODE HERE\n",
        "        #raise NotImplementedError()\n",
        "        e1 = Y_actual - dh(f, h, x_i)\n",
        "        e2 = Y_actual - dh1(f, h, x_i)\n",
        "        diff_error.append(e1)\n",
        "        diff2_error.append(e2)\n",
        "        # --------------------------------------------\n",
        "        \n",
        "    print(pd.DataFrame({\"h\": hs, \"Diff\": diff_error, \"Diff2\": diff2_error}))\n",
        "\n",
        "    return diff_error, diff2_error"
      ],
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "e1e6e88bb67c3769e422424e3b101ce3",
          "grade": false,
          "grade_id": "cell-ed3e46dc9c1804fd",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "4mkvTZcqniIz"
      },
      "source": [
        "## 4. Finally let's run some tests\n",
        "function to draw the actual function.\n",
        "\n",
        "### Draw the polynomial and it's actual derivative function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "98c555e4aede6188c8531178d3013480",
          "grade": false,
          "grade_id": "cell-0da2679376673916",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "AGdx3IhxniIz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "outputId": "2f40c0f0-20d0-4ddd-af25-9380be397bcd"
      },
      "source": [
        "def draw_graph(f, ax, domain=[-10,10], label=None):\n",
        "    data = f.linspace(domain=domain)\n",
        "    ax.plot(data[0], data[1], label=label)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "\n",
        "p = Polynomial([6.0, 2.0, -7.0, -7.0, 1.5, 1.0])\n",
        "p_prime = p.deriv(1)\n",
        "draw_graph(p, ax, [-2.4, 1.5], 'Function')\n",
        "draw_graph(p_prime, ax, [-2.4, 1.5], 'Derivative')\n",
        "\n",
        "ax.legend()"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff27befab10>"
            ]
          },
          "metadata": {},
          "execution_count": 78
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "ebcddecf0623331e7f7147da731c67a8",
          "grade": false,
          "grade_id": "cell-d291e8def1fd93fe",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "EgK7NagOniIz"
      },
      "source": [
        "### Draw the actual derivative and richardson derivative using `h=1` and `h=0.1` as step size."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "fae4bb70108b896682a6950fc66b0f1a",
          "grade": true,
          "grade_id": "cell-a55ea4a66a38f4e1",
          "locked": true,
          "points": 6,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "qlx3Y_e3niIz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "101f1739-55b9-4cd9-d03e-317539d9c441"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "\n",
        "draw_graph(p_prime, ax, [-2.4, 1.5], 'actual')\n",
        "\n",
        "h = 1\n",
        "x = np.linspace(-2.4, 1.5, 50, endpoint=True)\n",
        "y = dh1(p, h, x)\n",
        "ax.plot(x, y, label='Richardson; h=1')\n",
        "\n",
        "h = 0.1\n",
        "x = np.linspace(-2.4, 1.5, 50, endpoint=True)\n",
        "y = dh1(p, h, x)\n",
        "ax.plot(x, y, label='Richardson; h=0.1')\n",
        "\n",
        "ax.legend()\n"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff27c2cd1d0>"
            ]
          },
          "metadata": {},
          "execution_count": 71
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "efabbb55aa021747d9bbdd2c0bfda2be",
          "grade": false,
          "grade_id": "cell-aa732ac513c32594",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "KShe_FjPniIz"
      },
      "source": [
        "### Draw error-vs-h cuve"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "c3e2d5ef6eb54fa473d58d8ec6af67f3",
          "grade": true,
          "grade_id": "cell-47f9daf2fe2b2d07",
          "locked": true,
          "points": 6,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "tjnPCoD5niI0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "452fce77-d2ca-47f5-e1da-6affac00333c"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.axhline(y=0, color='k')\n",
        "hs = np.array([1., 0.55, 0.3, .17, 0.1, 0.055, 0.03, 0.017, 0.01])\n",
        "e1, e2 = error(p, hs, 2.0)\n",
        "ax.plot(hs, e1, label='e1')\n",
        "ax.plot(hs, e2, label='e2')\n",
        "\n",
        "ax.legend()\n"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       h       Diff         Diff2\n",
            "0  1.000 -46.000000  2.500000e-01\n",
            "1  0.550 -13.704006  2.287656e-02\n",
            "2  0.300  -4.058100  2.025000e-03\n",
            "3  0.170  -1.301335  2.088025e-04\n",
            "4  0.100  -0.450100  2.500000e-05\n",
            "5  0.055  -0.136134  2.287656e-06\n",
            "6  0.030  -0.040501  2.025000e-07\n",
            "7  0.017  -0.013005  2.088040e-08\n",
            "8  0.010  -0.004500  2.500489e-09\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff283e98fd0>"
            ]
          },
          "metadata": {},
          "execution_count": 72
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yhkbcuteniI0"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}