FMML_Module4_Lab2_2024.ipynb

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      "name": "python"
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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/Harsha-070/FMML_IIITH/blob/main/FMML_Module4_Lab2_2024.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "QyMhDmOed0RJ"
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      "source": [
        "# FOUNDATIONS OF MODERN MACHINE LEARNING, IIIT Hyderabad\n",
        "# Module 4: Perceptron and Gradient Descent\n",
        "## Lab 2: Introduction to Gradient Descent\n",
        "\n",
        "Gradient descent is a very important algorithm to understand, as it underpins many of the more advanced algorithms used in Machine Learning and Deep Learning.\n",
        "\n",
        "A brief overview of the algorithm is\n",
        "\n",
        "\n",
        "*   start with a random initialization of the solution.\n",
        "*   incrementally change the solution by moving in the direction of negative gradient of the objective function.\n",
        "*   repeat the previous step until some convergence criteria is met.\n",
        "\n",
        "The key equation for change in weight is:\n",
        "$$w^{k+1} \\leftarrow w^k - \\eta \\Delta J$$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mx5OzL5jbnkO"
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      "source": [
        "# Importing the required libraries\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "\n",
        "random.seed(42)\n",
        "np.random.seed(42)"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hQpDHGOAh0It"
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      "source": [
        "We can start be choosing coefficients for a second degree polynomial equation $(a x^2 + bx + c)$ that will distribute the data we will try to model.\n",
        "\n",
        "Let's define some random x data (inputs) we hope to predict y (outputs) of."
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "def eval_2nd_degree(coeffs, x):\n",
        "    \"\"\"\n",
        "    Function to return the output of evaluating a second degree polynomial,\n",
        "    given a specific x value.\n",
        "\n",
        "    Args:\n",
        "        coeffs: List containing the coefficients a, b, and c for the polynomial.\n",
        "        x: The input x value to the polynomial.\n",
        "\n",
        "    Returns:\n",
        "        y: The corresponding output y value for the second degree polynomial.\n",
        "\n",
        "    \"\"\"\n",
        "\n",
        "    a = coeffs[0] * (x * x)\n",
        "    b = coeffs[1] * x\n",
        "    c = coeffs[2]\n",
        "    y = a + b + c\n",
        "    return y\n",
        "\n",
        "hundred_xs = np.random.uniform(-10, 10, 100)\n",
        "coeffs = [1, 0, 0]\n",
        "\n",
        "xs = []\n",
        "ys = []\n",
        "for x in hundred_xs:\n",
        "    y  = eval_2nd_degree(coeffs, x)\n",
        "    xs.append(x)\n",
        "    ys.append(y)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
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          "height": 452
        },
        "id": "8a-Tzv5fclE2",
        "outputId": "c734bb06-ee97-49fc-e491-749f39e9dc5c"
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      "source": [
        "plt.plot(xs, ys, 'g+')\n",
        "plt.title('Original data')\n",
        "plt.show()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bQr81EuciKhB"
      },
      "source": [
        "This is good, but we could improve on this by making things more realistic. You can add noise or **jitter** to the values so they can resemble real-world data.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ggni_nKPdFZ5"
      },
      "source": [
        "def eval_2nd_degree_jitter(coeffs, x, j):\n",
        "    \"\"\"\n",
        "    Function to return the noisy output of evaluating a second degree polynomial,\n",
        "    given a specific x value. Output values can be within [y − j, y + j].\n",
        "\n",
        "    Args:\n",
        "        coeffs: List containing the coefficients a, b, and c for the polynomial.\n",
        "        x: The input x value to the polynomial.\n",
        "        j: Jitter parameter, to introduce noise to output y.\n",
        "\n",
        "    Returns:\n",
        "        y: The corresponding jittered output y value for the second degree polynomial.\n",
        "\n",
        "    \"\"\"\n",
        "\n",
        "    a = coeffs[0] * (x * x)\n",
        "    b = coeffs[1] * x\n",
        "    c = coeffs[2]\n",
        "    y = a + b + c\n",
        "\n",
        "    interval = [y - j, y + j]\n",
        "    interval_min = interval[0]\n",
        "    interval_max = interval[1]\n",
        "    jit_val = random.random() * interval_max      # Generate a random number in range 0 to interval max\n",
        "\n",
        "    while interval_min > jit_val:                 # While the random jitter value is less than the interval min,\n",
        "        jit_val = random.random() * interval_max  # it is not in the right range. Re-roll the generator until it\n",
        "                                                  # give a number greater than the interval min.\n",
        "\n",
        "    return jit_val\n",
        "\n",
        "xs = []\n",
        "ys = []\n",
        "for x in hundred_xs:\n",
        "    y  = eval_2nd_degree_jitter(coeffs, x, 0.1)\n",
        "    xs.append(x)\n",
        "    ys.append(y)\n"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "LFYv43vpe5Y4",
        "outputId": "2ca18bc8-f8cf-4ec7-a877-dfcf1da41b67"
      },
      "source": [
        "plt.figure(figsize=(12, 6))\n",
        "plt.plot(xs, ys, 'g+')\n",
        "plt.title('Original data with jitter')\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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C34EDB/Tcc8/p97//vc444wydc845wS4JABBh6DoOAGi2Vq1apZycHH366acqKytT9+7ddeONN+p//ud/6pwJG+Fr586dSk1NVb9+/fTUU0/poosuCnZJAIAIQ9AGAAAAAMBBjNEGAAAAAMBBBG0AAAAAABwUlgPUysvL9e233yo+Pl5RUVHBLgcAAAAA0MxZliWfz6fk5GRFR9feZh2WQfvbb79ltlgAAAAAQMB99dVXOuOMM2o9JiyDdnx8vKSKHzAhISHI1QAAAAAAmrvS0lJ169bNzqO1CcugXdldPCEhgaANAAAAAAiY+gxfZjI0AAAAAAAcRNAGAAAAAMBBBG0AAAAAABxE0AYAAAAAwEENDtpr167V6NGjlZycrKioKL366qt++y3L0r333ivDMBQbG6vhw4frs88+8zvm+++/17hx45SQkKD27dtr0qRJKisrO6UfBAAAAACAUNDgoH3gwAGdf/75evLJJ6vdP2/ePD3++ONasGCBNmzYoHbt2mnkyJE6fPiwfcy4ceO0efNmrVq1Sn/729+0du1aZWdnN/6nAAAAAAAgRERZlmU1+sVRUVq2bJnGjBkjqaI1Ozk5WTNmzNCdd94pSSopKVFSUpIWLVqk6667Tlu2bNG5556rDz74QAMHDpQkrVixQj/5yU/09ddfKzk5uc73LS0tVWJiokpKSljeCwAAAADQ5BqSQx0do71jxw4VFxdr+PDh9rbExEQNGjRI69evlyStX79e7du3t0O2JA0fPlzR0dHasGFDtec9cuSISktL/R4AAAAAAIQiR4N2cXGxJCkpKclve1JSkr2vuLhYXbp08dvfsmVLdejQwT7mZHPnzlViYqL96Natm5NlAwAAAADgmLCYdXzWrFkqKSmxH1999VWwSwIAAAAAoFqOBu2uXbtKknbv3u23fffu3fa+rl27as+ePX77jx07pu+//94+5mQxMTFKSEjwewAAAAAAEIocDdopKSnq2rWrVq9ebW8rLS3Vhg0blJ6eLklKT0/X/v37VVhYaB/z1ltvqby8XIMGDXKyHAAAAAAAAq5lQ19QVlam7du329/v2LFDGzduVIcOHdS9e3dNmzZNc+bMUa9evZSSkqJ77rlHycnJ9szkffr00Y9//GNlZWVpwYIF+uGHH3Tbbbfpuuuuq9eM4wAAAAAAhLIGB+0PP/xQl112mf399OnTJUkTJkzQokWL9Otf/1oHDhxQdna29u/fryFDhmjFihVq06aN/ZrnnntOt912m6644gpFR0frmmuu0eOPP+7AjwMAAAAAQHCd0jrawRIu62ibPlO5hblyu9wy4o1glwMAAAAAaKSgraMNf2aZqZyCHJllZrBLAQAAAAAECEEbAAAAAAAHNXiMNmpn+ky7BbvILPJ7liQjzqAbOQAAAAA0YwRth+UW5iqnIMdvW9byLPtrT4ZH3mHeAFcFAAAAAAgUgrbD3C63MlMzJVW0ZGctz1L+6HylGWmSKlq0AQAAAADNF0HbYUZ81a7haUaaHbQBAAAAAM0bk6EBAAAAAOAggnYTMuIMeTI8dBcHAAAAgAgSZVmWFewiGqohC4UDAAAAAHCqGpJDadEGAAAAAMBBBG0AAAAAABxE0AYAAAAAwEEEbQAAAABA0Jg+U941Xpk+M9ilOIagDQAAAAAIGrPMVE5BjswygjYAAAAAAKhGy2AXAAAAAACILKbPtFuwi8wiv2dJMuIMGfFGUGpzAkEbAAAAABBQuYW5yinI8duWtTzL/tqT4ZF3mDfAVTmHoA0AAAAACCi3y63M1ExJFS3ZWcuzlD86X2lGmqSKFu1wRtAGAAAAAASUEV+1a3iakWYH7XDHZGgAAAAAADiIoA0AAAAACBojzpAnwxP23cVPFGVZlhXsIhqqtLRUiYmJKikpUUJCQrDLAQAAAAA0cw3JobRoAwAAAADgIII2AAAAAAAOImiHGNNnyrvGK9NnBrsUAAAAAEAjELRDjFlmKqcgR2YZQRsAAAAAwhFBGwAAAAAAB7UMdgGo6C5e2YJdZBb5PUsV092fvJg7AAAAACA0EbRDQG5hrnIKcvy2ZS3Psr/2ZHjkHeYNcFUAAAAAgMYgaIcAt8utzNRMSRUt2VnLs5Q/Ol9pRpokNauF2wEAAACguSNohwAjvmrX8DQjzQ7aAAAAAIDwwWRoAAAAAAA4iKAdYow4Q54Mj193cdbWBgAAAIDwQdAOMUa8Ie8wr19XctbWBgAAAIDwQdAGAAAAAMBBTIYWolhbGwAAAADCE0E7RLG2NgAAAACEJ4J2iGJtbQAAAAAITwTtEMXa2gAAAAAQnpgMDQAAAAAABxG0w0B1a2sDAAAAQKgwfaa8a7wyfSxJLBG0w0J1a2sDAAAAQKjYtGeTcgpytGnPpmCXEhII2gAAAACAU7Lv4D6/50jHZGgAAAAAgAYzfabMsoqu4lv3brWfi8wiSRVDYCO1V26UZVlWsItoqNLSUiUmJqqkpEQJCQnBLgcAAAAAIs6MlTP06PuP1rh/+sXT9cjIRwJYUdNqSA6l6zgAAAAAAA6i6zgAAAAAoMHuHHynxvUfJ0latnWZ5qydo9mXztbVva+WpIheNYkW7TDHNPoAAAAAguWv2/4qI85Q7069JUm9O/VWmpGmNCMtYsdnSwTtsGeWmcopyLEnIQAAAACAQDgxi3SK7SRJ9nOkI2gDAAAAAE5J/6T+8mR41D+pf7BLCQmM0Q5DJ06jXzl1fuWzFNnT6AMAAABoOjVlkTQjTZmpmcEsLaSwvFcY8q7xKqcgp8b9ngyPvMO8gSsIAAAAQESI5CzSkBxK0A5DJ3+KlLU8S/mj85VmpEmiRRsAAABA04jkLNKQHErX8TBkxFf9j7dyZj8AAAAAaCpkkfphMjQAAAAAABxE0A5zRpwhT4YnoheDBwAAABB4ZJGaMUYbAAAAAIA6NCSH0qINAAAAAICDCNoAAAAAADiIoA0AAAAAgIMI2gAAAAAAOIigDQAAAACAgwjaAAAAAAA4iKAdIUyfKe8ar0yfGexSAAAAAKBZI2hHCLPMVE5BjswygjYAAAAANCWCdoTJ/TCXVm0AAAAAaEItg10Amo7pM+0W7CKzSJKUV5SnS8+8VH069ZERZ8iIN4JZIgAAAAA0OwTtZiy3MFc5BTlVto9fOl6S5MnwyDvMG+CqAAAAAKB5I2g3Y26XW+lnpGvfoX3aum+r5qydI0maPXS2enfurU5tO8n0mbRqAwAAAICDCNrNmBFvVNuqPWfdHPtrWrUBAAAAwFkE7WbO7XIrMzVTW/ZtsbuM54/OV5qRJkky4mjNBgAAACKd6TOVW5grt8tNj1cHMOt4M2fEG0oz0nT5mZcrOy1bkpRmpNkPbiIAAAAALAfsLIJ2hDDiDbkHuoNdBgAAAAA0e3QdjyBGnCFPhofu4gAAAABk+kxt2rNJSz9dql4de0n677LAklgO+BREWZZlBbuIhiotLVViYqJKSkqUkJAQ7HIAAAAAIOx413irXQ64EhMn+2tIDnW86/jx48d1zz33KCUlRbGxserZs6fuv/9+nZjnLcvSvffeK8MwFBsbq+HDh+uzzz5zuhQAAAAAQA3cLreWjF0iqWIJYKli4uTC7EIVZhfK7WLoaWM53nX8d7/7nZ5++mk9++yz6tu3rz788EPdfPPNSkxM1NSpUyVJ8+bN0+OPP65nn31WKSkpuueeezRy5Eh9+umnatOmjdMlAQAAAAD+j+kz7UnPDv1wqGJjVMVTbKtYuow7wPGu41dddZWSkpL0zDPP2NuuueYaxcbGasmSJbIsS8nJyZoxY4buvPNOSVJJSYmSkpK0aNEiXXfddXW+B13HAQAAAKBx6DLeOEHtOj548GCtXr1a//73vyVJ//rXv/TOO+/oyiuvlCTt2LFDxcXFGj58uP2axMREDRo0SOvXr6/2nEeOHFFpaanfAwAAAADQcG6X2+4enj86X5L00I8eUnZatlaMW0GXcQc43nX87rvvVmlpqXr37q0WLVro+PHj+u1vf6tx48ZJkoqLiyVJSUlJfq9LSkqy951s7ty5ysmp+RMXAAAAAED9GPFVu4ZfnnK57hx8Z5Aqan4cb9F+6aWX9Nxzz+n5559XUVGRnn32WT388MN69tlnG33OWbNmqaSkxH589dVXDlYMAAAAAIBzHG/Rnjlzpu6++257rHW/fv20a9cuzZ07VxMmTFDXrl0lSbt375Zh/PdTlN27d2vAgAHVnjMmJkYxMTFOlwoAAAAAEc2IM+TJ8MiIY/IzJzneon3w4EFFR/uftkWLFiovL5ckpaSkqGvXrlq9erW9v7S0VBs2bFB6errT5QAAAAAAamDEG/IO8zLLuMMcb9EePXq0fvvb36p79+7q27evPvroIz366KP65S9/KUmKiorStGnTNGfOHPXq1cte3is5OVljxoxxuhw0gukzlVuYK7fLzQ0HAAAAAA3keNB+4okndM899+hXv/qV9uzZo+TkZLndbt177732Mb/+9a914MABZWdna//+/RoyZIhWrFjBGtohwiwzlVOQo8zUTII2AAAAADSQ4+toBwLraDetIrNIrjyXCrMLlWakBbscAAAAAAi6huRQx1u0EZ5MnymzzJRUEbRPfJYqJkmgdRsAAAAA6kbQhiQptzBXOQX+a5VnLc+yv/ZkeOQd5g1wVQAAAAAQfgjakCS5XW5lpmZKqmjJzlqepfzR+XbXcab7BwAAAMIPEx0HB0Ebkiqm9T/5xksz0hijDQAAAIQxJjoODsfX0QYAAAAAIJLRoo0qjDhDngwP3cUBAACAMMREx8HH8l6oE+M6AAAAgPDhXeOtMtHxiZjouHFY3guOYlwHAAAAED6Y6Dj4CNqot70H9sq7xkvLNgAAABDCmOg4+AjaqFZ14zre+eodzVk7R7069tLlZ15O2AYAAACAajDrOKqVW5grV55LrjyXspZnSZLmrJ0jSRq/dLxyC3ODWR4AAACAemCi4+BgMjRUq7JFe++BvXZL9k39b9LiTYs1e+hsDekxRJ3bdmbGQgAAAAARoSE5lKCNWjFjIQAAAAAw6zgc5Ha51atjL41fOl6zh87WnHVzmLEQAAAAAGpB0EatjHhDl595uTwZHqV3S5fWMWMhAAAAANSGydBQJyPekHeYV53bdg52KQAAAAAQ8gjaqDdmLAQAAACAujEZGgAAAAAAdWhIDqVFGwAAAAAABxG0AQAAAABwEEEbAAAAAAAHEbThCNNnyrvGK9NnBrsUAAAAAAgqgjYcYZaZyinIIWwDAAAAiHgEbTgqryhPZhlBGwAAAEDkahnsAhC+TJ9ph+ois8jevmXfFkkV624b8ay5DQAAACCyELTRaLmFucopyKmyffzS8ZKk7LRseYd5CdsAAAAAIgpdx9Fobpdb2WnZNe7PK8pTbmFuACsCAAAAgOCLsizLCnYRDVVaWqrExESVlJQoISEh2OVEtMru41v2bbFbsvNH5yvNSJNE93EAAAAAzUNDcihdx3FKjPiqQTrNSLODNgAAAIBTY/pM5Rbmyu1y04gVJug6DkcYcUat3cgBAAAANE7lUrqs7hM+aNGGI4x4w574zIjjUzYAAAAAkYugDcdUhm0AAAAAp6a6pXRPXFKXuZBCG0EbAAAAAEJMdUvpZi3Psr/2ZHho5AphBG0AAAAACDFul1uZqZmSKlqys5ZnVVndB6GLoA0AAAAAIYbVfcIbs44DAAAAAOAggjYAAAAAhDAjzpAnw0N38TASZVmWFewiGqq0tFSJiYkqKSlRQkJCsMsBAAAAADRzDcmhtGgDAAAAAOAggjYAAAAAAA4iaAMAAAAA4CCCNgAAAAAADiJoI2hMnynvGq9MnxnsUgAAAADAMQRtBI1ZZiqnIEdmGUEbAAAAQPNB0AYAAAAAwEEtg10AIovpM+0W7CKzyO9Zkow4Q0a8EZTaAAAAAMAJBG0EVG5hrnIKcvy2ZS3Psr/2ZHjkHeYNcFUAAABAYJk+U7mFuXK73DQ0NUMEbQSU2+VWZmqmpIqW7KzlWcofna80I01SRYs2AAAA0NxVzleUmZpJ0G6GCNoIKCO+atfwNCPNDtoAAAAAEO4I2gAAAAAQAMxXFDkI2ggaI86QJ8NDd3EAAABEBOYrihxRlmVZwS6ioUpLS5WYmKiSkhIlJCQEuxwAAAAAqNPJLdrVzVdEi3boakgOpUUbAAAAAAKA+YoiR3SwCwAAAAAAoDkhaAMAAABAgDFfUfNG0EbIMn2mvGu8Mn1msEsBAAAAHGXEG/IO8zImu5kiaCNkmWWmcgpy7AkjAAAAACAcELQBAAAAAHAQs44jpJy85MGJzxJLHgAAAAAIfQRthJTcwlzlFOT4bctanmV/7cnwyDvMG+CqAAAAAKD+CNoIKW6XW5mpmZIqWrKzlmcpf3S+vbYgszICAAAACHUEbYQUI75q1/A0I80O2gAAAAAQ6pgMDQAAAAAABxG0EbKMOEOeDA/dxQEAAACElSjLsqxgF9FQpaWlSkxMVElJiRISEoJdDgAAAACgmWtIDqVFGwAAAABOkekz5V3jlekzg10KQgBBGwAAAABOkVlmKqcgR2YZQRsEbQAAAAAAHMXyXgAAAADQCKbPtFuwi8wiv2epYnLfk5euRWQgaCOsmT5TuYW5crvc/E8MAAAAAZVbmKucghy/bVnLs+yvPRkeeYd5A1wVQgFBG2GtcixMZmomQRsAAAAB5Xa5lZmaKamiJTtreZbyR+crzUiTJJapjWAEbQAAAABoBCO+atfwNCPNDtqIXARthB3GwgAAAAAIZQRthB3GwgAAACDUGHGGPBkeuotDkhRlWZYV7CIaqrS0VImJiSopKVFCQkKwy0GAndyiXd1YGFq0AQAAADipITm0SdbR/uabbzR+/Hh17NhRsbGx6tevnz788EN7v2VZuvfee2UYhmJjYzV8+HB99tlnTVEKmiEj3rDHvlSG6xO/J2QDAAAACCbHg/Z//vMfXXLJJWrVqpXefPNNffrpp3rkkUd02mmn2cfMmzdPjz/+uBYsWKANGzaoXbt2GjlypA4fPux0OQAAAADgCNNnyrvGK9NnBrsUhDjHx2j/7ne/U7du3bRw4UJ7W0pKiv21ZVmaP3++Zs+erZ/+9KeSpMWLFyspKUmvvvqqrrvuOqdLQjPGWBgAAAAECkvLor4cb9H+61//qoEDB+raa69Vly5ddMEFFyg/P9/ev2PHDhUXF2v48OH2tsTERA0aNEjr16+v9pxHjhxRaWmp3wOQKrqRe4d5+R8dAAAAgJDheND+4osv9PTTT6tXr15auXKlbr31Vk2dOlXPPvusJKm4uFiSlJSU5Pe6pKQke9/J5s6dq8TERPvRrVs3p8sGAAAAgCpMn6kis8h+SPL7nm7kqI7jXcfLy8s1cOBAPfDAA5KkCy64QJ988okWLFigCRMmNOqcs2bN0vTp0+3vS0tLCduolekzlVuYK7fLTWs3AAAAGo2lZdEYjgdtwzB07rnn+m3r06eP/vKXv0iSunbtKknavXu3DOO/AWj37t0aMGBAteeMiYlRTEyM06WiGWP8DAAAAJzgdrmVmZopqealZYGTOR60L7nkEm3bts1v27///W/16NFDUsXEaF27dtXq1avtYF1aWqoNGzbo1ltvdbocAAAAAGg0I96o0nBz4jKzQHUcD9p33HGHBg8erAceeEA///nP9c9//lN5eXnKy8uTJEVFRWnatGmaM2eOevXqpZSUFN1zzz1KTk7WmDFjnC4HEcT0mTLLKsbInDh+ppIRV/V/kgAAAADgNMeD9oUXXqhly5Zp1qxZuu+++5SSkqL58+dr3Lhx9jG//vWvdeDAAWVnZ2v//v0aMmSIVqxYoTZt2jhdDiII42cAAADQlFhaFvUVZVmWFewiGqq0tFSJiYkqKSlRQkJCsMtBiDi5RfvE8TN7D+7V37f/XXcOvpNWbQAAAAAN1pAc6niLNhAstY2fKTKL9Oj7j2pc/3EEbQAAAABNyvF1tAEAAAAAiGQEbTRLRpyh6RdP194De1VkFtmTor214y25l7u1cvtKmT4zyFUCAAAAaI7oOo5myYg3FB8Trx8/92O/7TNXzZQk5RXlMTkaAAAAgCZBizaaLbfLrcLsQhVmFyp/dL4kafalsyVJS8YukdvlDmZ5AAAAAJopWrTRbFVOjmb6TMW2iq3Y+H9z7B/64ZDMsopZyllfGwAAAICTWN4LzZ53jbfK+tonogs5AAAAgLqwvBdwArfLrfRu6Vr66VL16thLM1fNtNfXliomTgMAAAAApxC00exVdiEf2XOkPft45fraAAAAAOA0JkMDAAAAAMBBBG1EFCPOkCfDQ3dxAAAAAE2GydAAAAAAAKhDQ3IoLdoAAAAAADiIoA0AAAAAgIMI2gAAAAAAOIigDQAAAACAgwjaAAAAAJo102fKu8Yr02cGuxRECII2AAAAgGbNLDOVU5Ajs4ygjcAgaAMAAAAA4KCWwS4AAAAAAJxm+ky7BbvILPJ7liQjzpARbwSlNjR/BG0AAAAAzU5uYa5yCnL8tmUtz7K/9mR45B3mDXBViBQEbQAAAADNzpjUMTJ9psaeO1ZflXylrOVZyh+drzQjTVJFizbQVAjaAAAAAJqdcpUrryhP7oFudW7bWZKUZqTZQRtoSkyGBgAAAACAgwjaQD2x/iIAAEBoM32miswi+yFVTIC298BeZadlK5r4gwCh6zhQT/b6iz5T3mFeZqkEAAAIMXVNgGbEGxpgDAhwVYhEBG2ggSrH+hC0AQAAQovb5VZmaqakipZsJkBDsBC0gVpUt/6iJG3Zt0US6y8CAACEEiO+6t9mTICGYCBoA7WorvuRJI1fOl6SlJ2WTTdyAAAAAH6YDQCohdvlVnZado3784rylFuYG8CKAAAAUB9GnCFPhofu4giKKMuyrGAX0VClpaVKTExUSUmJEhISgl0OmrnK7uNb9m2xW7JPHutDizYAAADQvDUkh9J1HKgDY30AAAAANARdx4F6MuKMWruRAwAAAIBEizZQb0a8YU98xlgfAAAAADVhjDYAAAAAAHVoSA6l6zgAAAAAAA4iaAMAAAAA4CCCNgAAAAAADiJoAwAAAADgIII2AAAAAAAOImgDAAAAAOAggjYAAAAAAA4iaAMAAAAA4CCCNgAAAAAADiJoA01so7lRwxYN00ZzY7BLAQAAABAABG2giW3et1kFuwq0ed/mYJcCAAAAIAAI2gAAAAAAOKhlsAsAmqON5ka7Bfvv2//u9yxJfTv11QBjQDBKAwAAANDEoizLsoJdREOVlpYqMTFRJSUlSkhICHY5QBXDFg1Twa6CGvdn9MjQmolrAlcQAAAAgFPSkBxKizbQBOaPnO/Xor1402Ld1P8mjTh7hKSKFm0AAAAAzRNBG2gCA4wBfl3DF29arBFnj9C4fuOCVxQAAACAgGAyNAAAAAAAHETQBppY3059ldEjg+7iAAAAQISg6zjQxAYYA5j4DAAAAIggtGgDAAAAAOAggjYAAAAAAA4iaAMAAAAA4CCCNgAAAAAADiJoAwAAAAgY02fKu8Yr02cGuxSgyRC0AQAAAASMWWYqpyBHZhlBG80XQRsAAAAAAAexjjYQgkyfqdzCXLldbhnxRrDLAQAAOCWmz7RbsIvMIr9nSTLiDP7mQbNC0AZCUGWXqszUTH7pAACAsPfwew/r0fcf9duWtTzL/tqT4ZF3mDfAVQFNh6ANAAAAoEmN6DlCj77/qJaMXaJDPxxS1vIs5Y/OV5qRJqmiRRtoTgjaQIigSxUAAGiuOrfrLEnq06mPvS3NSLODNtDcELSBEJFbmKucghy/bXSpAgAA4aqmRoTYVrGSpL0H9watNqCpEbSBEOF2uZWZmimp4pcQXaoAAEA4q6sR4e/b/66RPUcGuiwgIAjaQIgw4qt2DadLFQAACFc0IiCSEbQBAAAAOI5GBESy6GAXAKAqI86QJ8PDJ70AAABAGKJFGwhBRrzBxGcAAKDZoBEBkSbKsiwr2EU0VGlpqRITE1VSUqKEhIRglwMAAAAAaOYakkPpOg4AAAAAgIMI2kCYMn2mvGu8Mn1msEsBAAAAcAKCNhCmzDJTOQU5MssI2gAAAEAoafKg/eCDDyoqKkrTpk2ztx0+fFiTJ09Wx44dFRcXp2uuuUa7d+9u6lKAZmnvwb20bAMAAAAhpEmD9gcffKDc3Fz179/fb/sdd9yh5cuX6+WXX1ZBQYG+/fZbjR07tilLAZoF02eqyCyyH5L0zq53lFOQo8lvTNZGc2NwCwQAAADQdEG7rKxM48aNU35+vk477TR7e0lJiZ555hk9+uijuvzyy+VyubRw4UK99957ev/995uqHKBZyC3MlSvPJVeeS1nLsyRJc9bNkSQt27pMT3/4dDDLAwAAEYK5YoDaNVnQnjx5skaNGqXhw4f7bS8sLNQPP/zgt713797q3r271q9fX+25jhw5otLSUr8HEIncLrcKswu1YvwKzR46W5J0U/+b7P39kvqpyCzilx4AAGhSzBUD1K5JgvYLL7ygoqIizZ07t8q+4uJitW7dWu3bt/fbnpSUpOLi4mrPN3fuXCUmJtqPbt26NUXZQMgz4g2lGWla/9V6uyV78abF9v4pb06RK8/FJ8wAAABAEDketL/66ivdfvvteu6559SmTRtHzjlr1iyVlJTYj6+++sqR8wLhyu1y6+reV9e4P68oT7mFuQGsCAAANHfVzRVz4vd8yA/8V0unT1hYWKg9e/YoLS3N3nb8+HGtXbtWf/jDH7Ry5UodPXpU+/fv92vV3r17t7p27VrtOWNiYhQTE+N0qUDYMuIN3XvpverctrP6JfXTlDenSJLyR+crzai494w4I5glAgCAZia3MFc5BTl+2yrnjJEkT4ZH3mHeAFcFhCbHg/YVV1yhjz/+2G/bzTffrN69e+uuu+5St27d1KpVK61evVrXXHONJGnbtm368ssvlZ6e7nQ5QLM1wBig3NG59ifKkpRmpNlBGwAAwElul1uZqZmSKlqys5Zn8SE/UAPHg3Z8fLzOO+88v23t2rVTx44d7e2TJk3S9OnT1aFDByUkJGjKlClKT0/XxRdf7HQ5QLNnxBnKTstWXlFesEsBAADNmBFvyIj3D9N8yA9Uz/GgXR+PPfaYoqOjdc011+jIkSMaOXKknnrqqWCUAoQ9I96Qd5i34pcfnyQDAAAHmT5TuYW5crvcVUI2gJpFWZZlBbuIhiotLVViYqJKSkqUkJAQ7HIAAACAZqnILJIrz6XC7EK/lmsCOCJRQ3JoUFq0AQAAAISvyh51AKpH0AYAAABgM32mzLKKpbpOXMarkhFXdaw2AH8EbQAAAAA2lvECTh1BG4gQjKUCAAD1wTJewKkjaAMRwiwzlVOQo8zUTII2AACo4sQP5U9esotlvICGiQ52AQACz/SZ8q7xyvSZwS4FAACEiMoP5SvHZwNoPFq0gWaspslMYlvFKqcgR9u/366HfvQQLdwAAKBaRpwhT4aH7uJAAxG0gWasrslMnvv4OU1Pn07QBgAgQtVnhnEmPgMajqANNGMnTmby1o63NHPVTM0eOluKkuasnSNJ2rJviySW6gAAIBIxwzjQNKIsy7KCXURDlZaWKjExUSUlJUpISAh2OUBYcC93K68or8b92WnZ8g7zErYBAIggJ7doVzfDOH8bABUakkNp0QYixNhzx9YatPOK8mTE0z0MAIBIYsRXDdLMMA6cOoI2ECH6d+mv6RdP14izR2jfwX0av3S8JLEuJgAAAOAwgjYQIYx4Q4+MfESS/yQnfGoNAAAkZhgHnMQ62kAEMuIMZadlB7sMAAAQQiqHkDEmGzh1tGgDEejEX6R8ag0AAAA4i1nHAQAAAACoQ0NyKF3HAQAAAABwEEEbAAAAAAAHEbQBAAAAAHAQQRtAnUyfKe8ar0yfGexSAAAAgJBH0AZQJ7PMVE5BjswygjYAAABQF4I2AAAAAAAOYh1tANUyfabdgl1kFvk9S5IRZ8iIZw1uAABCiekzlVuYK7fLze9pIIgI2gCqlVuYq5yCHL9tWcuz7K89GR55h3kDXBUAAKhN5XCvzNRMgjYQRARtANVyu9zKTM2UVNGSnbU8S/mj85VmpEmqaNEGAAAAUBVBG0C1jPiqXcPTjDQ7aAMAgNDAcC8g9BC0AQAAgDDGcC8g9BC0AdTJiDPkyfDQXRwAgBDEcC8g9BC0AdTJiDf4JBwAgBDFcC8g9LCONgAAAAAADiJoAwAAAM0Ew72A0BBlWZYV7CIaqrS0VImJiSopKVFCQkKwywEAAAAANHMNyaG0aAMAAABhwPSZ8q7xyvSZwS4FQB0I2gAAAEAYMMtM5RTk2GtmAwhdBG0AAAAghFW2ZO89uDfYpQCoJ5b3AgAAAELURnOj7lt7n5ZtXabZQ2dLqlgru5IRV3VpLwDBx2RoAAAAQIi6cemNWvLxkhr3ezI88g7zBq4gIII1JIfSog0AAACEGNNnyiwzlRyfbG+7qf9NWrxpsWYPna0hPYaoc9vOLOMFhChatAEAAIAQUjkmO68or8ZjaMkGAo/lvQAAAIAw9fB7D9casq88+0q5Xe4AVgSgoQjaAAAAQBjpntCdCdCAEMcYbQAAACCE3Dn4To3rP06StGzrMs1ZO0eStGTsEvXp1Idx2UAYIGgDAAAAIcSI/++SXVv2bZEkje09VpefeTkt2UCYoOs4AAAAEKI6xXaSJGW7sgnZQBghaAMAAAAhqn9Sf3kyPOqf1D/YpQBoAII2AAAAEASVy3iZPrPGY4x4Q95hXlqzgTBD0AYAAACCwCwzlVOQI7Os5qANIDwRtAEAAAAAcBCzjgMAAAABYvpMuwW7yCzye5YkI86gmzjQDBC0AQAAgADJLcxVTkGO37as5Vn2154Mj7zDvAGuCoDTCNoAAABAgLhdbmWmZkqqaMnOWp6l/NH5SjPSJFW0aAMIfwRtAAAAIECM+Kpdw9OMNDtoA2gemAwNAAAAAAAHEbQBAACAIDDiDHkyPHQXB5qhKMuyrGAX0VClpaVKTExUSUmJEhISgl0OAAAAAKCZa0gOpUUbAAAAAAAHEbQBAAAAAHAQQRsAAAAAAAcRtAEAAAAAcBBBGwAAAAAABxG0AQAAAABwEEEbQNgzfaa8a7wyfWawSwEAAAAI2gDCn1lmKqcgR2YZQRsAAADBR9AGAAAAAMBBLYNdAAA0hukz7RbsIrPI71mSjDhDRrwRlNoAAAAQ2QjaAMJSbmGucgpy/LZlLc+yv/ZkeOQd5g1wVQAAAABBG0CYcrvcykzNlFTRkp21PEv5o/OVZqRJqmjRBgAAAIKBoA0gLBnxVbuGpxlpdtAGAAAAgoXJ0AAAAAAAcBBBG0DYM+IMeTI8dBcHADjG9JnyrvHK9LF0JICGI2gDCHtGvCHvMC+zjAMAHGOWmcopyLFXuACAhiBoA4gYtE4AAOpS+bti78G9wS4FQBgjaAOIGLROAABqY/pM/WXLX5RTkKM3P3tTUsXKFpUPPqgFUF/MOg4AAABIyi3MVU5BjiTp9xt+L0nKWp5l7/dkeOQd5g1GaQDCDEEbQLNm+ky7BbvILPJ7liomUmNsNwBEtsrfFelnpGvSBZP0zEfPaFSvUXr9s9c1e+hsDekxRJ3bdmbSTQD1FmVZluXkCefOnaulS5dq69atio2N1eDBg/W73/1Oqamp9jGHDx/WjBkz9MILL+jIkSMaOXKknnrqKSUlJdXrPUpLS5WYmKiSkhIlJCQ4WT6AZsa7xmu3TlSH1gkAwIyVM/To+4/WuH/6xdP1yMhHAlgRgFDUkBzqeIt2QUGBJk+erAsvvFDHjh3Tb37zG40YMUKffvqp2rVrJ0m644479Prrr+vll19WYmKibrvtNo0dO1bvvvuu0+UAiHBul1uZqZmSKlqys5ZnKX90vtKMNEmidQIAAACOc7xF+2R79+5Vly5dVFBQoEsvvVQlJSXq3Lmznn/+ef3sZz+TJG3dulV9+vTR+vXrdfHFF9d5Tlq0ATRGkVkkV55LhdmFdtAGAODEYUbLtizTnHVzdPug23Xoh0Ma22es+if1Z5gRgOC2aJ+spKREktShQwdJUmFhoX744QcNHz7cPqZ3797q3r17jUH7yJEjOnLkiP19aWlpE1cNAACASGHE/3e+ji37tkiSLjz9Qo3rNy6YZQEIY026vFd5ebmmTZumSy65ROedd54kqbi4WK1bt1b79u39jk1KSlJxcXG155k7d64SExPtR7du3ZqybADNlBFnyJPhqbW7OGttA0Bk69S2k98zADRGkwbtyZMn65NPPtELL7xwSueZNWuWSkpK7MdXX33lUIUAIokRb8g7zFtr9z/W2gaAyNa/S395Mjzq36V/sEsBEMaarOv4bbfdpr/97W9au3atzjjjDHt7165ddfToUe3fv9+vVXv37t3q2rVrteeKiYlRTExMU5UKAAAASPrvh7IAcCocD9qWZWnKlClatmyZ1qxZo5SUFL/9LpdLrVq10urVq3XNNddIkrZt26Yvv/xS6enpTpcDAHVirW0AAAA4yfGgPXnyZD3//PN67bXXFB8fb4+7TkxMVGxsrBITEzVp0iRNnz5dHTp0UEJCgqZMmaL09PR6zTgOAE7LLcytstZ21vIs+2vW2gYAAEBDOL68V1RUVLXbFy5cqIkTJ0qSDh8+rBkzZujPf/6zjhw5opEjR+qpp56qsev4yVjeC4CTTm7Rrm6tbVq0ASC8mD5TuYW5crvc/D8cgCMakkObfB3tpkDQBtBUWGsbAJoH/n8OwGkNyaFNOus4AAAAAACRhqANACeoz1rbG82NGrZomDaaGwNXGACgVqbP1IyVM7Ry+0oVmUV+k1tWPkwfSzcCCAy6jgNAAz338XMav3S8loxdonH9xgW7HACIeKbPlHeNV3lFebUex+SWAE5FQ3Jok62jDQAAAASCWWbaIXvJ2CXq06lPjZNbAkAgELQBoB42mhu1ed9mSdLft//d71mS+nbqqwHGgGCUBgARq3LViC37ttjbDv1wSJIU2ypWkpRmpDEZGoCAo+s4ANTDsEXDVLCroMb9GT0ytGbimsAVBAARrr7dxZl1HIBT6DoOAA6bP3K+X4v24k2LdVP/mzTi7BGSKlq0AQCBk1uYW2vIHt9vvLq060J3cQBBQdAGgHoYYAzw6xq+eNNijTh7BJOhAUCQuF1uZaZmSpI9Hlv67xhtI86QEU/IBhAcBG0AAACEHSO++iDdp1MfuooDCDrW0QaABurbqa8yemTUq7t45RhC1m4FgKaXnZZNV3EAIYEWbQBooAHGgHpPfLZp9yblFOQo/Yx0ujACQBMx4gx5Mjxyu9z8vxZASCBoA0AT2ndon98zAMB5Rrwh7zBvsMsAABtBGwAcVrmuqyRt3bfVfi4yiySJCXoAAACaOdbRBgCHzVg5Q4++/2iN+6dfPF2PjHwkgBUBAADgVDUkhzIZGgAEwUZzo4YtGqaN5sZglwIAAACH0XUcABx25+A7Na5/xfray7Ys05x1czR76Gxd3edqSRVdx9/a+ZYKdhVo877NfutzAwAAIPwRtAHAYSeu7bpl3xZJUu/OvVnXFQAAIEIQtAGgCXVq28l+3mhu1OZ9myVJf9/+d79nqWJ9blq3AUQC02cqtzCX5bgANFtMhgYATejEPyav/8v1KthVUOOxGT0y6r0+NwCEsyKzSK48lwqzC+ntAyBsNCSH0qINAE3oxLVd54+c79eivXjTYt3U/yaNOHuEpIoWbQAAAIQ/gjYABMgAY4Bf1/DFmxZrxNkjNK7fuOAVBQABYvpMmWWmpIoW7ROfpYqJIulGDqC5IGgDAACgyeUW5iqnIMdvW9byLPtrT4bH7gEEAOGOoA0AQdC3U19l9MiguziAiOF2uZWZmimpoiU7a3mW8kfn22O0jThaswE0HwRtAAiCAcaABk18ttHcqGkrp2n+yPnMTA4gLJ249GGlNCONydAANEvRwS4AAFC3zfs2q2BXgT2ZGgAAAEIXQRsAAAABZcQZ8mR46C4OoNmi6zgAhKiN5ka/5cBOfJakLm276N2v3pXb5WamXgBh5cSlDwGgOYqyLMsKdhEN1ZCFwgEgXA1bNEwFuwpq3J/WNU1FxUUqzC5kjCMAAEATa0gOpUUbAELU/JHz/Vq0F29arJv636QRZ4+QJEUpSuOWsgY3AABAqCFoA0CIGmAM8JthfPGmxbrw9AvVp1MfSRXL45z4LFWMe6QbOQAAQHARtAEgjLy9421NeXOK37as5Vn2154MD+MeATQJ02cqtzCXeSEAoB4I2gAQBvp26quMHhm6ZeAt+p9L/0dSRUt21vIs5Y/Ot8doM4MvgKZilpnKKchRZmomQRsA6kDQBoAwMMAYoDUT11S7L81IYzI0AACAEELQBgAAQLVMnymzzJTEvBAA0BAEbQAIU0acIU+Gh+7iAJpMbmGucgpy/LYxLwQA1I11tAEAAFCtk1u0q5sXghZtAJGCdbQBAABwyoz4qkGaeSEAoG7RwS4AAAAAAIDmhKANAACAOjEvBADUH2O0AQAAAACoQ0NyKC3aAAA/ps+Ud41Xps8MdikAAABhiaANAPBjlpnKKcghbAMAADQSQRsAUK28ojx7WR8AAADUH8t7AQCqrJVbacu+LZJYKxcIN6bPVG5hrtwuN/cuAAQBLdoAAOUW5sqV55Irz6Ws5Vn29vFLx8uV5/LrRs4YbiD0VQ4BoVcKAAQHQRsAILfLrey07Br35xXlKbcwVxJ/wAMAANSFruMAABnxhrzDvHIPdGvLvi0av3S8JCl/dL7SjLSKY1g7Fwhp1Q0BOXEoCENAACBwCNoAAEkVYfvkP8LTjDSlGWn2H/Bmmckf8ECIyi3MVU5Bjt+2E4eCeDI88g7zBrgqAIhMBG0AgB8jzlB2WrbyivLsbfwBD4Q+t8utzNRMSRUfhGUtz6JXCgAECUEbAOCnshu5EW/Yf5jX9w94ZjoGgqe2XikAgMAiaAMAqqgM2yd+X58/4CsnSstMzSRoAw7iQywACC/MOg4AABDiGjrbvxFnyJPhobs4AAQJLdoAgAY5+Q94ZjoGQs/JvVIAAIFF0AYANMjJf8AzURrQNPgQCwDCV5RlWVawi2io0tJSJSYmqqSkRAkJCcEuBwAi2slhoLqJ0moKA4w7RaSr7R7wrvFW+RDrRHyIBQCB1ZAcSos2AOCUnMpMx0yehkhX2z3Acl0AEL4I2gAAAAHSkF4cLNcFAOGLoA0AcEx9Zjpm3CkiWWULdq+OvdSnUx/uAQBophijDQAIKMadIhLU1HJdZBbJleeq9bXV3QPMZwAAwccYbQBAyGLcKZqzjeZGTVs5TdmubHvstaQqvThmXzpbvTv11ta9WzVn3Zw67wGW6wKA8ELQBgAEFONO0Zxt3rdZBbsKNPys4fa26pbAm7N2jt/33AMA0LxEB7sAAACAcGT6THnXeGX6TPv7Hf/ZIUnauX+npIoW7PRu6VoydolWjFuh/NH5kqT80fkqzC7UkrFLglI7AKBp0aINAAia+kyeBoSqyonNzul4jixZWvrpUi3dulSS9MxHz0iSspZn2cd7Mjx2V/LKFmzuAQBongjaAICgYdwpmoNH3ntERcVFNe5P65qm/Mx8GXGGPVa7EvcAADRPBG0AAIB6qm55ulHnjNLVfa6WJP2r+F96ZcsrGtVrlF7/7HXdf9n9uqrXVRpgDLDPQQs2ADR/BG0AAIB6qm5is/vX3m9/Pbb3WEnSxWdcrNc/e10/6fUTv5BNCzYARAYmQwMARLyTJ7UCauJ2uVWYXajC7MIqE5sVZhfqspTLJEnt27Sn5RoAIhgt2gCAiFc5qVVmamaVpceAE9W1PF20opXRI0NDug3xa8kGAEQWWrQBADgJLdxorAHGAK2ZuIaQDQARjqANAIhIps9UkVlkPyTZX7+18y3lFORUmSG68nWE8NAVyOvD0lwAgJrQdRwAEJGqm9TqxDWPa0I389AWyOvDxGYAgJoQtAEAEcntciszNVNSRUt21vIszb50tnp36q2te7dqzro5dku3VNF6SbAOPNNnKrcwV26Xm39/AEDYIGgDACJSdZNazVk7x+/7E1u4s9Oy5R7o9utmbp+rHiGcwNg49Wmhrm5taz4kAQAEE0EbAID/s2TsEvXp1Mdu4c4fna80I025H+YqryhPeUV59rEnhnBPhqfOLsR0Oa+fxnwgUdcwgPpcHwAAnETQBgBEvMpJrS4/83K/cFe5bJN3mFfugW5JqhLCK1/fFMKtFbyy3jGpY/TqtlcbVXflBxK9OvayP/SQam+hrm4YQCCuDwAANQlq0H7yySf10EMPqbi4WOeff76eeOIJXXTRRcEsCQAQgeqa1KqutZNrcqpdmp1sBTd9ph5+72FJ0p2D72z0+aoL/5Xb0s9It0PyqdY9ful4v+9ra6Fu7PUBAKCpBC1ov/jii5o+fboWLFigQYMGaf78+Ro5cqS2bdumLl26BKssAAAcW7YplLo0m2WmHn3/UUnSuP7jGh+0qwn/lduWjF3SuHNW84HEyRPT0UINAAgnQQvajz76qLKysnTzzTdLkhYsWKDXX39df/zjH3X33XcHqywAAGpt4W5ICG9Ml+Zwm9jL9Jnasm+LJOntHW9Lkv6+/e+SpGVblmnvwb3q3LZzrXVX94HEyRPT1beFmrWtAQChIMqyLCvQb3r06FG1bdtWr7zyisaMGWNvnzBhgvbv36/XXnvN7/gjR47oyJEj9velpaXq1q2bSkpKlJCQEKiyAQBotCKzSK48lwqzC2sNjN413iqh80QNaQU3faY27d6kfYf2aeu+rXZ4nT10tnp37q1ObTupf5f+9Zox/cTwn7U8Sw/96CEZ8Yb+8ulftGzrsjprqa3u6s5f+YHEln1bNH7p+Dr/3QAAaGqlpaVKTEysVw4NSov2vn37dPz4cSUlJfltT0pK0tatW6scP3fuXOXk1PxHBwAAzYWTE3tV11IsSXPW/be1uD7BvbrzzFw1s873nz10tob0GGK3aNektjHWtFADAMJRWMw6PmvWLE2fPt3+vrJFGwCAcFHfwOjkxF5ul1vpZ6TX2aJdn/OcHP4rW7SlihbpmatmavbQ2Zqzbo7uv+x+3fP2Pbq6z9Wn3Apd10R1AACEoqAE7U6dOqlFixbavXu33/bdu3era9euVY6PiYlRTExMoMoDAMBxwQiMJ4b2IrPIDtoNDcDVhf/LUy63z1E5hrx3596SpJTTUhpfMy3YAIBmIDoYb9q6dWu5XC6tXr3a3lZeXq7Vq1crPT09GCUBABBywi10dmrbSZ4Mj/p26tvouis/kAilCd8AAGiooHUdnz59uiZMmKCBAwfqoosu0vz583XgwAF7FnIAACKdk63gRpyh6RdPt78+lfOcHKIrt/Xv0l8je46UJA0wBpxSvQAAhLOgzDpe6Q9/+IMeeughFRcXa8CAAXr88cc1aNCgOl/XkNneAAAAAAA4VQ3JoUEN2o1F0AYAAAAABFJDcmhQxmgDAAAAANBcEbQBAAAAAHAQQRsAAAAAAAcRtAEAAAAAcBBBGwAAAAAABxG0AQAAAABwEEEbAAAAAAAHEbQBAAAAAHAQQRsAAAAAAAcRtAEAAAAAcBBBGwAAAAAABxG0AQAAAABwEEEbAAAAAAAHtQx2AY1hWZYkqbS0NMiVAAAAAAAiQWX+rMyjtQnLoO3z+SRJ3bp1C3IlAAAAAIBI4vP5lJiYWOsxUVZ94niIKS8v17fffqv4+HhFRUUFuxxbaWmpunXrpq+++koJCQnBLge14FqFF65XeOF6hQ+uVXjheoUXrlf44FqFl2BeL8uy5PP5lJycrOjo2kdhh2WLdnR0tM4444xgl1GjhIQEbtIwwbUKL1yv8ML1Ch9cq/DC9QovXK/wwbUKL8G6XnW1ZFdiMjQAAAAAABxE0AYAAAAAwEEEbQfFxMTI4/EoJiYm2KWgDlyr8ML1Ci9cr/DBtQovXK/wwvUKH1yr8BIu1yssJ0MDAAAAACBU0aINAAAAAICDCNoAAAAAADiIoA0AAAAAgIMI2gAAAAAAOIig3QC//e1vNXjwYLVt21bt27ev9pgvv/xSo0aNUtu2bdWlSxfNnDlTx44dq/W833//vcaNG6eEhAS1b99ekyZNUllZWRP8BJFrzZo1ioqKqvbxwQcf1Pi6YcOGVTn+lltuCWDlkevMM8+s8m//4IMP1vqaw4cPa/LkyerYsaPi4uJ0zTXXaPfu3QGqODLt3LlTkyZNUkpKimJjY9WzZ095PB4dPXq01tdxbwXOk08+qTPPPFNt2rTRoEGD9M9//rPW419++WX17t1bbdq0Ub9+/fTGG28EqNLINnfuXF144YWKj49Xly5dNGbMGG3btq3W1yxatKjKfdSmTZsAVRzZvF5vlX/73r171/oa7q3gqe5viqioKE2ePLna47m3Amft2rUaPXq0kpOTFRUVpVdffdVvv2VZuvfee2UYhmJjYzV8+HB99tlndZ63ob/7mgJBuwGOHj2qa6+9Vrfeemu1+48fP65Ro0bp6NGjeu+99/Tss89q0aJFuvfee2s977hx47R582atWrVKf/vb37R27VplZ2c3xY8QsQYPHizTNP0e/+///T+lpKRo4MCBtb42KyvL73Xz5s0LUNW47777/P7tp0yZUuvxd9xxh5YvX66XX35ZBQUF+vbbbzV27NgAVRuZtm7dqvLycuXm5mrz5s167LHHtGDBAv3mN7+p87XcW03vxRdf1PTp0+XxeFRUVKTzzz9fI0eO1J49e6o9/r333tP111+vSZMm6aOPPtKYMWM0ZswYffLJJwGuPPIUFBRo8uTJev/997Vq1Sr98MMPGjFihA4cOFDr6xISEvzuo127dgWoYvTt29fv3/6dd96p8VjureD64IMP/K7VqlWrJEnXXnttja/h3gqMAwcO6Pzzz9eTTz5Z7f558+bp8ccf14IFC7Rhwwa1a9dOI0eO1OHDh2s8Z0N/9zUZCw22cOFCKzExscr2N954w4qOjraKi4vtbU8//bSVkJBgHTlypNpzffrpp5Yk64MPPrC3vfnmm1ZUVJT1zTffOF47Khw9etTq3Lmzdd9999V6XEZGhnX77bcHpij46dGjh/XYY4/V+/j9+/dbrVq1sl5++WV725YtWyxJ1vr165ugQtRk3rx5VkpKSq3HcG8FxkUXXWRNnjzZ/v748eNWcnKyNXfu3GqP//nPf26NGjXKb9ugQYMst9vdpHWiqj179liSrIKCghqPqenvETQ9j8djnX/++fU+nnsrtNx+++1Wz549rfLy8mr3c28FhyRr2bJl9vfl5eVW165drYceesjetn//fismJsb685//XON5Gvq7r6nQou2g9evXq1+/fkpKSrK3jRw5UqWlpdq8eXONr2nfvr1fq+rw4cMVHR2tDRs2NHnNkeqvf/2rvvvuO9188811Hvvcc8+pU6dOOu+88zRr1iwdPHgwABVCkh588EF17NhRF1xwgR566KFah2EUFhbqhx9+0PDhw+1tvXv3Vvfu3bV+/fpAlIv/U1JSog4dOtR5HPdW0zp69KgKCwv97ono6GgNHz68xnti/fr1fsdLFb/HuIcCr6SkRJLqvJfKysrUo0cPdevWTT/96U9r/HsDzvvss8+UnJyss846S+PGjdOXX35Z47HcW6Hj6NGjWrJkiX75y18qKiqqxuO4t4Jvx44dKi4u9rt3EhMTNWjQoBrvncb87msqLQP6bs1ccXGxX8iWZH9fXFxc42u6dOnit61ly5bq0KFDja/BqXvmmWc0cuRInXHGGbUed8MNN6hHjx5KTk7Wpk2bdNddd2nbtm1aunRpgCqNXFOnTlVaWpo6dOig9957T7NmzZJpmnr00UerPb64uFitW7euMn9CUlIS91IAbd++XU888YQefvjhWo/j3mp6+/bt0/Hjx6v9vbR169ZqX1PT7zHuocAqLy/XtGnTdMkll+i8886r8bjU1FT98Y9/VP/+/VVSUqKHH35YgwcP1ubNm+v8/YZTM2jQIC1atEipqakyTVM5OTkaOnSoPvnkE8XHx1c5nnsrdLz66qvav3+/Jk6cWOMx3FuhofL+aMi905jffU0l4oP23Xffrd/97ne1HrNly5Y6J7hAcDTm+n399ddauXKlXnrppTrPf+JY+X79+skwDF1xxRX6/PPP1bNnz8YXHqEacr2mT59ub+vfv79at24tt9utuXPnKiYmpqlLjXiNube++eYb/fjHP9a1116rrKysWl/LvQXUbPLkyfrkk09qHfMrSenp6UpPT7e/Hzx4sPr06aPc3Fzdf//9TV1mRLvyyivtr/v3769BgwapR48eeumllzRp0qQgVoa6PPPMM7ryyiuVnJxc4zHcW3BCxAftGTNm1PqJliSdddZZ9TpX165dq8xoVznjcdeuXWt8zckD848dO6bvv/++xtfgvxpz/RYuXKiOHTsqMzOzwe83aNAgSRWtdoSBhjuV+23QoEE6duyYdu7cqdTU1Cr7u3btqqNHj2r//v1+rdq7d+/mXmqEhl6rb7/9VpdddpkGDx6svLy8Br8f95bzOnXqpBYtWlSZeb+2e6Jr164NOh7Ou+222+yJURvactaqVStdcMEF2r59exNVh5q0b99e55xzTo3/9txboWHXrl36xz/+0eDeU9xbwVF5f+zevVuGYdjbd+/erQEDBlT7msb87msqER+0O3furM6dOztyrvT0dP32t7/Vnj177O7gq1atUkJCgs4999waX7N//34VFhbK5XJJkt566y2Vl5fbf3iiZg29fpZlaeHChbrpppvUqlWrBr/fxo0bJcnvZkf9ncr9tnHjRkVHR1cZalHJ5XKpVatWWr16ta655hpJ0rZt2/Tll1/6fSqN+mnItfrmm2902WWXyeVyaeHChYqObvj0H9xbzmvdurVcLpdWr16tMWPGSKrokrx69Wrddttt1b4mPT1dq1ev1rRp0+xtq1at4h4KAMuyNGXKFC1btkxr1qxRSkpKg89x/Phxffzxx/rJT37SBBWiNmVlZfr888914403Vrufeys0LFy4UF26dNGoUaMa9DrureBISUlR165dtXr1ajtYl5aWasOGDTWuAtWY331NJqBTr4W5Xbt2WR999JGVk5NjxcXFWR999JH10UcfWT6fz7Isyzp27Jh13nnnWSNGjLA2btxorVixwurcubM1a9Ys+xwbNmywUlNTra+//tre9uMf/9i64IILrA0bNljvvPOO1atXL+v6668P+M8XCf7xj39YkqwtW7ZU2ff1119bqamp1oYNGyzLsqzt27db9913n/Xhhx9aO3bssF577TXrrLPOsi699NJAlx1x3nvvPeuxxx6zNm7caH3++efWkiVLrM6dO1s33XSTfczJ18uyLOuWW26xunfvbr311lvWhx9+aKWnp1vp6enB+BEixtdff22dffbZ1hVXXGF9/fXXlmma9uPEY7i3guOFF16wYmJirEWLFlmffvqplZ2dbbVv395eHePGG2+07r77bvv4d99912rZsqX18MMPW1u2bLE8Ho/VqlUr6+OPPw7WjxAxbr31VisxMdFas2aN33108OBB+5iTr1dOTo61cuVK6/PPP7cKCwut6667zmrTpo21efPmYPwIEWXGjBnWmjVrrB07dljvvvuuNXz4cKtTp07Wnj17LMvi3gpFx48ft7p3727dddddVfZxbwWPz+ezM5Uk69FHH7U++ugja9euXZZlWdaDDz5otW/f3nrttdesTZs2WT/96U+tlJQU69ChQ/Y5Lr/8cuuJJ56wv6/rd1+gELQbYMKECZakKo+3337bPmbnzp3WlVdeacXGxlqdOnWyZsyYYf3www/2/rffftuSZO3YscPe9t1331nXX3+9FRcXZyUkJFg333yzHd7hrOuvv94aPHhwtft27Njhdz2//PJL69JLL7U6dOhgxcTEWGeffbY1c+ZMq6SkJIAVR6bCwkJr0KBBVmJiotWmTRurT58+1gMPPGAdPnzYPubk62VZlnXo0CHrV7/6lXXaaadZbdu2ta6++mq/wAfnLVy4sNr/L574OS73VnA98cQTVvfu3a3WrVtbF110kfX+++/b+zIyMqwJEyb4Hf/SSy9Z55xzjtW6dWurb9++1uuvvx7giiNTTffRwoUL7WNOvl7Tpk2zr21SUpL1k5/8xCoqKgp88RHoF7/4hWUYhtW6dWvr9NNPt37xi19Y27dvt/dzb4WelStXWpKsbdu2VdnHvRU8ldno5Efl9SgvL7fuueceKykpyYqJibGuuOKKKtewR48elsfj8dtW2+++QImyLMsKSNM5AAAAAAARgHW0AQAAAABwEEEbAAAAAAAHEbQBAAAAAHAQQRsAAAAAAAcRtAEAAAAAcBBBGwAAAAAABxG0AQAAAABwEEEbAAAAAAAHEbQBAAAAAHAQQRsAAAAAAAcRtAEAAAAAcBBBGwAAAAAAB/1/EMtmwYiOEp0AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "umByA5Ghi_gt"
      },
      "source": [
        "We will now build our predictive model, and optimize it with gradient descent and we will try to get as close to these values as possible.\n",
        "\n",
        "To get a quantifiable measure of how incorrect it is, we calculate the Mean Squared Error loss for the model. This is the mean value of the sum of the squared differences between the actual and predicted outputs.\n",
        "\n",
        "$$ E = \\frac{1}{n} \\sum_{i=0}^n (y_i - \\bar{y_i})^2 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kGo9VtQDfG6F"
      },
      "source": [
        "def loss_mse(ys, y_bar):\n",
        "    \"\"\"\n",
        "    Calculates MSE loss.\n",
        "\n",
        "    Args:\n",
        "        ys: training data labels\n",
        "        y_bar: prediction labels\n",
        "\n",
        "    Returns: Calculated MSE loss.\n",
        "    \"\"\"\n",
        "\n",
        "    return sum((ys - y_bar) * (ys - y_bar)) / len(ys)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "yIRquRB3kcZA",
        "outputId": "0d14b1df-48f2-4551-9ad6-f5c817667cd2"
      },
      "source": [
        "rand_coeffs = (random.randrange(-10, 10), random.randrange(-10, 10), random.randrange(-10, 10))\n",
        "y_bar = eval_2nd_degree(rand_coeffs, hundred_xs)\n",
        "plt.figure(figsize=(12, 6))\n",
        "plt.plot(xs, ys, 'g+', label = 'original')\n",
        "plt.plot(xs, y_bar, 'ro', label = 'prediction')\n",
        "plt.title('Original data vs first prediction')\n",
        "plt.legend(loc=\"lower right\")\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bYbwBb4Ckomw",
        "outputId": "294cf39c-c868-4741-daf4-02ec586be1ae"
      },
      "source": [
        "initial_model_loss = loss_mse(ys, y_bar)\n",
        "initial_model_loss"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "146807.86204726336"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IEcvjxbJa8cq"
      },
      "source": [
        "We can see that the loss is quite a large number. Let’s now see if we can improve on this fairly high loss metric by optimizing the model with gradient descent.\n",
        "\n",
        "We wish to improve our model. Therefore we want to alter its coefficients $a$, $b$ and $c$ to decrease the error. Therefore we require knowledge about how each coefficient affects the error. This is achieved by calculating the partial derivative of the loss function with respect to **each** of the individual coefficients."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YhiloANqkSFc"
      },
      "source": [
        "def calc_gradient_2nd_poly(rand_coeffs, hundred_xs, ys):\n",
        "    \"\"\"\n",
        "    calculates the gradient for a second degree polynomial.\n",
        "\n",
        "    Args:\n",
        "        coeffs: a,b and c, for a 2nd degree polynomial [ y = ax^2 + bx + c ]\n",
        "        inputs_x: x input datapoints\n",
        "        outputs_y: actual y output points\n",
        "\n",
        "    Returns: Calculated gradients for the 2nd degree polynomial, as a tuple of its parts for a,b,c respectively.\n",
        "\n",
        "    \"\"\"\n",
        "\n",
        "    a_s = []\n",
        "    b_s = []\n",
        "    c_s = []\n",
        "\n",
        "    y_bars = eval_2nd_degree(rand_coeffs, hundred_xs)\n",
        "\n",
        "    for x, y, y_bar in list(zip(hundred_xs, ys, y_bars)):    # take tuple of (x datapoint, actual y label, predicted y label)\n",
        "        x_squared = x ** 2\n",
        "        partial_a = x_squared * (y - y_bar)\n",
        "        a_s.append(partial_a)\n",
        "        partial_b = x * (y - y_bar)\n",
        "        b_s.append(partial_b)\n",
        "        partial_c = (y - y_bar)\n",
        "        c_s.append(partial_c)\n",
        "\n",
        "    num = [i for i in y_bars]\n",
        "    n = len(num)\n",
        "\n",
        "    gradient_a = (-2 / n) * sum(a_s)\n",
        "    gradient_b = (-2 / n) * sum(b_s)\n",
        "    gradient_c = (-2 / n) * sum(c_s)\n",
        "\n",
        "    return (gradient_a, gradient_b, gradient_c)   # return calculated gradients as a a tuple of its 3 parts"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rN0jR2Dhkpjn",
        "outputId": "e294fa45-c71e-4fe4-a3f0-279cdf76bb1d"
      },
      "source": [
        "calc_grad = calc_gradient_2nd_poly(rand_coeffs, hundred_xs, ys)\n",
        "\n",
        "lr = 0.0001\n",
        "a_new = rand_coeffs[0] - lr * calc_grad[0]\n",
        "b_new = rand_coeffs[1] - lr * calc_grad[1]\n",
        "c_new = rand_coeffs[2] - lr * calc_grad[2]\n",
        "\n",
        "new_model_coeffs = (a_new, b_new, c_new)\n",
        "print(f\"New model coeffs: {new_model_coeffs}\")\n",
        "\n",
        "# update with these new coeffs:\n",
        "new_y_bar = eval_2nd_degree(new_model_coeffs, hundred_xs)\n",
        "updated_model_loss = loss_mse(ys, new_y_bar)\n",
        "\n",
        "print(f\"Now have smaller model loss: {updated_model_loss} vs {initial_model_loss}\")"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "New model coeffs: (-3.4872074852403587, 7.879149056895183, -4.941405407033594)\n",
            "Now have smaller model loss: 49608.172144854274 vs 146807.86204726336\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "5rjqrqclk4BI",
        "outputId": "4f9d86d7-d37f-4bc5-e140-98bf98ecdf74"
      },
      "source": [
        "plt.figure(figsize=(12, 6))\n",
        "plt.plot(xs, ys, 'g+', label = 'original model')\n",
        "plt.plot(xs, y_bar, 'ro', label = 'first prediction')\n",
        "plt.plot(xs, new_y_bar, 'b.', label = 'updated prediction')\n",
        "plt.title('Original model vs 1st prediction vs updated prediction with lower loss')\n",
        "plt.legend(loc=\"lower right\")\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lOzSlzJIfvid"
      },
      "source": [
        "We’re almost ready. The last step will be to perform gradient descent iteratively over a number of epochs (cycles or iterations.) With every epoch we hope to see an improvement in the form of lowered loss, and better model-fitting to the original data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bBkU4dRnlHKy"
      },
      "source": [
        "def calc_gradient_2nd_poly_for_GD(coeffs, inputs_x, outputs_y, lr):\n",
        "    \"\"\"\n",
        "    calculates the gradient for a second degree polynomial.\n",
        "\n",
        "    Args:\n",
        "        coeffs: a,b and c, for a 2nd degree polynomial [ y = ax^2 + bx + c ]\n",
        "        inputs_x: x input datapoints\n",
        "        outputs_y: actual y output points\n",
        "        lr: learning rate\n",
        "\n",
        "    Returns: Calculated gradients for the 2nd degree polynomial, as a tuple of its parts for a,b,c respectively.\n",
        "\n",
        "    \"\"\"\n",
        "    a_s = []\n",
        "    b_s = []\n",
        "    c_s = []\n",
        "\n",
        "    y_bars = eval_2nd_degree(coeffs, inputs_x)\n",
        "\n",
        "    for x,y,y_bar in list(zip(inputs_x, outputs_y, y_bars)):    # take tuple of (x datapoint, actual y label, predicted y label)\n",
        "        x_squared = x ** 2\n",
        "        partial_a = x_squared * (y - y_bar)\n",
        "        a_s.append(partial_a)\n",
        "        partial_b = x * (y - y_bar)\n",
        "        b_s.append(partial_b)\n",
        "        partial_c = (y - y_bar)\n",
        "        c_s.append(partial_c)\n",
        "\n",
        "    num = [i for i in y_bars]\n",
        "    n = len(num)\n",
        "\n",
        "    gradient_a = (-2 / n) * sum(a_s)\n",
        "    gradient_b = (-2 / n) * sum(b_s)\n",
        "    gradient_c = (-2 / n) * sum(c_s)\n",
        "\n",
        "\n",
        "    a_new = coeffs[0] - lr * gradient_a\n",
        "    b_new = coeffs[1] - lr * gradient_b\n",
        "    c_new = coeffs[2] - lr * gradient_c\n",
        "\n",
        "    new_model_coeffs = (a_new, b_new, c_new)\n",
        "\n",
        "    # update with these new coeffs:\n",
        "    new_y_bar = eval_2nd_degree(new_model_coeffs, inputs_x)\n",
        "\n",
        "    updated_model_loss = loss_mse(outputs_y, new_y_bar)\n",
        "    return updated_model_loss, new_model_coeffs, new_y_bar"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nj6K6SXol_bi"
      },
      "source": [
        "def gradient_descent(epochs, lr):\n",
        "    \"\"\"\n",
        "    Perform gradient descent for a second degree polynomial.\n",
        "\n",
        "    Args:\n",
        "        epochs: number of iterations to perform of finding new coefficients and updatingt loss.\n",
        "        lr: specified learning rate\n",
        "\n",
        "    Returns: Tuple containing (updated_model_loss, new_model_coeffs, new_y_bar predictions, saved loss updates)\n",
        "\n",
        "    \"\"\"\n",
        "    losses = []\n",
        "    rand_coeffs_to_test = rand_coeffs\n",
        "    for i in range(epochs):\n",
        "        loss = calc_gradient_2nd_poly_for_GD(rand_coeffs_to_test, hundred_xs, ys, lr)\n",
        "        rand_coeffs_to_test = loss[1]\n",
        "        losses.append(loss[0])\n",
        "    print(losses)\n",
        "    return loss[0], loss[1], loss[2], losses  # (updated_model_loss, new_model_coeffs, new_y_bar, saved loss updates)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "GD = gradient_descent(30000, 0.0003)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z3lunb-DH0HM",
        "outputId": "24128d52-9f18-45cc-9848-975a8bc2c7f8"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "Brk2qRFlmAQM",
        "outputId": "af4e226a-ae06-4577-e630-3d3f86eb2ebd"
      },
      "source": [
        "plt.figure(figsize=(12,6))\n",
        "plt.plot(xs, ys, 'g+', label = 'original')\n",
        "plt.plot(xs, GD[2], 'b.', label = 'final_prediction')\n",
        "plt.title('Original vs Final prediction after Gradient Descent')\n",
        "plt.legend(loc = \"lower right\")\n",
        "plt.show()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gS2KZ6SxfnAI"
      },
      "source": [
        "This trained model is showing vast improvements after it’s full training cycle. We can examine further by inspecting its final predicted coefficients $a$, $b$ and $c$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "efY8ehhvmCRz",
        "outputId": "32280395-85fe-4470-a637-08be33df9a7c"
      },
      "source": [
        "print(f\"Final Coefficients predicted: {GD[1]}\")\n",
        "print(f\"Original Coefficients: {coeffs}\")"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final Coefficients predicted: (0.9999579417260247, -0.002867610798230069, -0.012778521556486263)\n",
            "Original Coefficients: [1, 0, 0]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s8PuwB87fjP5"
      },
      "source": [
        "Not too far off! A big improvement over the initial random model. Looking at the plot of the loss reduction over training offers further insights.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "HnswAURtmFBG",
        "outputId": "199b6faf-f1fd-47b7-9991-d07654933a6c"
      },
      "source": [
        "plt.figure(figsize=(12, 6))\n",
        "plt.plot(GD[3], 'b-', label = 'loss')\n",
        "# plt.xlim(0,50)\n",
        "plt.title('Loss over 500 iterations')\n",
        "plt.legend(loc=\"lower right\")\n",
        "plt.xlabel('Iterations')\n",
        "plt.ylabel('MSE')\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lu7fnsphdJpo"
      },
      "source": [
        "We observe that the model loss reached close to zero, to give us our more accurate coefficients. We can also see there was no major improvement in loss after about 100 epochs. An alternative strategy would be to add some kind of condition to the training step that stops training when a certain minimum loss threshold has been reached. This would prevent excessive training and potential over-fitting for the model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V3oxAVdtePYa"
      },
      "source": [
        "# Things to try\n",
        "\n",
        "\n",
        "\n",
        "1.   Change the coefficients array and try a different polynomial instead of our $x^2$.\n",
        "2.   Increase/decrease the learning rate to see how many iterations will be take to coverge. Does it even converge on a huge learning rate?\n",
        "3. Take a degree 5 polynomial with 5 roots and try different initializations, instead of random ones. Does it converge on different values for different initializations? Why does initialization not matter in our case of $x^2$?\n",
        "4. Can you modify the algorithm to find a maxima of a function, instead of a minima?\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#1. Changing Coefficients Array:\n",
        "#//If you want to change the coefficients array for a polynomial, you can modify the values in the coefficients array accordingly. Here's an example using a degree 3 polynomial://\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Generate some data points\n",
        "x = np.linspace(-5, 5, 100)\n",
        "y_true = 0.5 * x*3 - 2 * x*2 + 3 * x + 2  # Original cubic polynomial\n",
        "\n",
        "# Add some random noise to the data\n",
        "np.random.seed(42)\n",
        "noise = np.random.normal(0, 10, size=len(x))\n",
        "y_noisy = y_true + noise\n",
        "\n",
        "# Fit a cubic polynomial to the data\n",
        "degree = 3\n",
        "coefficients = np.polyfit(x, y_noisy, degree)\n",
        "\n",
        "# Generate the fitted curve\n",
        "y_fit = np.polyval(coefficients, x)\n",
        "\n",
        "# Plot the data and the fitted curve\n",
        "plt.scatter(x, y_noisy, label='Noisy Data')\n",
        "plt.plot(x, y_fit, label='Fitted Curve', color='red')\n",
        "plt.plot(x, y_true, label='True Curve', linestyle='--', color='green')\n",
        "plt.legend()\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Fitting a Cubic Polynomial')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "8qJkikQXTAPH",
        "outputId": "9b033529-7920-4cd9-a2ec-0686e0fc799b"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#2.*Increase/decrease the learning rate to see how many iterations will be take to coverge. Does it even converge on a huge learning rate?*\n",
        "\n",
        "#If the learning rate is too large, it may result in divergence rather than convergence. You can modify the learning rate in the optimization algorithm you are using (e.g., gradient descent). Be cautious with very large learning rates as they might cause the algorithm to oscillate or diverge.\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Quadratic function: f(x) = x^2\n",
        "def objective_function(x):\n",
        "    return x**2\n",
        "\n",
        "# Gradient of the quadratic function: f'(x) = 2x\n",
        "def gradient(x):\n",
        "    return 2 * x\n",
        "\n",
        "# Gradient Descent Algorithm\n",
        "def gradient_descent(initial_x, learning_rate, num_iterations):\n",
        "    x = initial_x\n",
        "    history = [x]\n",
        "\n",
        "    for _ in range(num_iterations):\n",
        "        x = x - learning_rate * gradient(x)\n",
        "        history.append(x)\n",
        "\n",
        "    return history\n",
        "\n",
        "# Visualize the impact of different learning rates\n",
        "learning_rates = [0.01, 0.1, 0.5, 1.0, 2.0]\n",
        "num_iterations = 50\n",
        "initial_x = 4.0\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "for lr in learning_rates:\n",
        "    history = gradient_descent(initial_x, lr, num_iterations)\n",
        "    plt.plot(range(len(history)), history, label=f'LR={lr}')\n",
        "\n",
        "plt.axhline(0, color='black', linestyle='--', linewidth=0.8, label='Optimal Value')\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Parameter Value')\n",
        "plt.title('Effect of Learning Rate on Convergence')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "l2lHZf-mTCSo",
        "outputId": "960421ff-442d-46fa-d2af-e84d2f53d60d"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#3.For a degree 5 polynomial with 5 distinct roots, different initializations can indeed lead to convergence to different local minima. This behavior arises because higher-degree polynomials can have multiple local minima, and the convergence depends on the starting point.\n",
        "#Let's illustrate this with an example. Consider the following degree 5 polynomial:\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "The convergence behavior of optimization algorithms, such as those used in solving polynomial equations, can indeed be influenced by the choice of initial values. However, for polynomials with real coefficients, like the case of a degree 5 polynomial, the roots are determined by the coefficients, and the choice of initial values may not have a significant impact on the convergence.\n",
        "\n",
        "If you have a polynomial of the form:\n",
        "\n",
        "\\[ P(x) = a_n x^n + a_{n-1} x^{n-1} + \\ldots + a_1 x + a_0 \\]\n",
        "\n",
        "where \\(a_n, a_{n-1}, \\ldots, a_0\\) are real coefficients and \\(n\\) is the degree of the polynomial, the roots are the values of \\(x\\) for which \\(P(x) = 0\\). The roots depend only on the coefficients of the polynomial.\n",
        "\n",
        "In the case of a quadratic polynomial (\\(n = 2\\)), such as \\(ax^2 + bx + c\\), the roots can be found using the quadratic formula:\n",
        "\n",
        "\\[ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\]\n",
        "\n",
        "In this case, the roots are determined solely by the coefficients \\(a\\), \\(b\\), and \\(c\\), and the choice of initial values for an optimization algorithm (like for iterative methods such as Newton's method) doesn't matter because there's a closed-form solution.\n",
        "\n",
        "For higher-degree polynomials, such as a degree 5 polynomial, finding the roots may involve numerical methods since there isn't a general formula for polynomial roots of degree 5 or higher. However, these numerical methods are designed to converge to the correct roots regardless of the initial values, especially when the coefficients are real.\n",
        "\n",
        "The roots are determined by the coefficients, and the choice of initial values in numerical methods generally doesn't affect the convergence to the correct roots. This contrasts with certain situations in neural network training, where initialization can play a crucial role due to the non-convex nature of the optimization landscape."
      ],
      "metadata": {
        "id": "hZksBJ8fU_Wn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#4.Can you modify the algorithm to find a maxima of a function, instead of a minima?\n",
        "\n",
        "\n",
        "\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Define the original objective function\n",
        "def original_objective(x):\n",
        "    return x**2 - 2*x\n",
        "\n",
        "# Define the modified objective function for maximization\n",
        "def modified_objective(x):\n",
        "    return -original_objective(x)\n",
        "\n",
        "# Initial guess\n",
        "initial_guess = 0.0\n",
        "\n",
        "# Minimize the negation of the original objective function (maximize the original function)\n",
        "result = minimize(modified_objective, initial_guess)\n",
        "\n",
        "# Extract the maximizer\n",
        "maximizer = result.x[0]\n",
        "\n",
        "print(\"Maximizer:\", maximizer)\n",
        "print(\"Maximum value:\", -result.fun)  # Negate the result to get the maximum value\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7Dy3-uthWDNV",
        "outputId": "9dd7211c-1c75-4b07-9dcb-b6a9af55ac8f"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Maximizer: -1034.24\n",
            "Maximum value: 1071720.8576\n"
          ]
        }
      ]
    }
  ]
}