Kmeans_Class.ipynb

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        "<a href=\"https://colab.research.google.com/github/OptimizationExpert/Pyomo/blob/main/Kmeans_Class.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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          "text": [
            "Requirement already satisfied: pyomo in /usr/local/lib/python3.11/dist-packages (6.8.2)\n",
            "Requirement already satisfied: ply in /usr/local/lib/python3.11/dist-packages (from pyomo) (3.11)\n"
          ]
        }
      ],
      "source": [
        "!pip install pyomo\n",
        "from pyomo.environ import *\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random\n",
        "import pandas as pd"
      ]
    },
    {
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      "source": [
        "random.seed(100)\n",
        "N = 30\n",
        "df = pd.DataFrame()\n",
        "df['x1'] = [random.randint(1,50) for i in range(N)]\n",
        "df['x2'] = [random.randint(1,50) for i in range(N)]\n",
        "df"
      ],
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              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 30,\n  \"fields\": [\n    {\n      \"column\": \"x1\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 14,\n        \"min\": 4,\n        \"max\": 50,\n        \"num_unique_values\": 23,\n        \"samples\": [\n          4,\n          33,\n          10\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"x2\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 13,\n        \"min\": 1,\n        \"max\": 50,\n        \"num_unique_values\": 24,\n        \"samples\": [\n          18,\n          10,\n          23\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(df['x1'],df['x2'])\n",
        "plt.xlabel('X1')\n",
        "plt.ylabel('X2')\n",
        "plt.grid()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "hCss9gEhNCUV",
        "outputId": "50cdb674-efe6-4ddf-c486-a9916c8b763e"
      },
      "execution_count": null,
      "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": [
        "clusters = {k:[random.randint(1,50) , random.randint(1,50)] for k in range(2)}\n",
        "clusters"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-dx5mbryBobS",
        "outputId": "a7503418-3ab4-436c-e13b-225c861daa3c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: [9, 40], 1: [36, 49]}"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "plt.scatter(df['x1'],df['x2'])\n",
        "plt.xlabel('X1')\n",
        "plt.ylabel('X2')\n",
        "plt.grid()\n",
        "for i in range(len(df)):\n",
        "  plt.text(df['x1'][i],df['x2'][i],s= str(i), c='blue')\n",
        "for k , [x0,y0] in clusters.items():\n",
        "  plt.scatter(x0,y0,c='red')\n",
        "  plt.text(x0,y0,s= str(k), c='red')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "HG-h79MaBoZN",
        "outputId": "1ce0936c-2552-47c8-b731-00e385abbdaa"
      },
      "execution_count": null,
      "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": [
        "for counter in range(5):\n",
        "\n",
        "  assign = {}\n",
        "  for i in range(len(df)):\n",
        "    x1,y1 = df['x1'][i],df['x2'][i]\n",
        "    d={}\n",
        "    for k,[x0,y0] in clusters.items():\n",
        "      d[k] = ((x1-x0)**2 + (y1-y0)**2)**0.5\n",
        "    assign[i]= min(d,key=d.get)\n",
        "\n",
        "  assign\n",
        "\n",
        "  belong = {}\n",
        "  for k in clusters.keys():\n",
        "    belong[k] = [i for i in range(len(df)) if assign[i]==k]\n",
        "    xavg = sum([df['x1'][i] for i in belong[k]])/len(belong[k])\n",
        "    yavg = sum([df['x2'][i] for i in belong[k]])/len(belong[k])\n",
        "    clusters[k] = [xavg, yavg]\n",
        "\n",
        "  clusters\n",
        "  plt.figure()\n",
        "  plt.scatter(df['x1'],df['x2'])\n",
        "  plt.xlabel('X1')\n",
        "  plt.ylabel('X2')\n",
        "  plt.grid()\n",
        "  for i in range(len(df)):\n",
        "    plt.text(df['x1'][i],df['x2'][i],s= str(i), c='blue')\n",
        "  for k , [x0,y0] in clusters.items():\n",
        "    plt.scatter(x0,y0,c='red')\n",
        "    plt.text(x0,y0,s= str(k), c='red')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "_L9evG0WBoW2",
        "outputId": "73479c5e-beef-4bbe-ce9d-8551c2b75f84"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Gi5W+/NLoTRQebjReHDCguteZN+k9Lf7K9DkyZ8+e5cEHH+TNN9/k+eefr9peWFjI0qVLWb16NcOGDQNg+fLl9OrVi4yMDAYNGlTn45WVlVFWVlZ1v6ioCAC73Y7dbvfgM/E/d17XgTuuuY3dX/+Hgq/28OeHbmTAVR0JDLDpd2mCyt+5fvfmqOv9UHAgkoz0APolnWfChCDOnz+P3V49qeTQIRg8OIhHHnHw7LMOwsJg3z4bgYFOzBjGyueQ+e0pTpwto0ObEPp3vcKS72m9H3yDJ8ehoY9peiKTlJTE3XffzfDhw10SmczMTOx2O8OHD6/a1rNnT2JjY0lPT3ebyMyfP5958+bV2v7xxx/TqlWrpn8CzUjBV3vY+JXZUUhqzS5+YoqCr/YAUP1RdC+ZmZkEB1e3jn/ppf5cf72TIUP2kpsLubnGukp79ng/3rqcADZ+aXYUjaP3g2/wxDiUVC5OdhGmJjJvvfUWe/fuZffu3bX25eXl0aJFC9rV6EzWqVMn8vLyah1fadasWcysrB/EOCPTpUsXRo4cSZiWo7wsdrud1NRURowYQXBwsNnhNFsaB99Q3zj079+fu+6q7r/00ENB/PznDpKTryQry0a3bk5++UsH996rUqDG0vvBN3hyHCqvqFyMaYnMkSNHePLJJ0lNTSU01H1p4KUKCQkhJCSk1vbg4GC92BtJv0PfoHEwT4XDyWffN4387LszDOoR6TJBNigoiMqhycsz1lL6/e8Def55ePFFSEmxMWFCAFu2wO23m/EM/I/eD77BE+PQ0MczbbJvZmYmx48fp1+/fgQFBREUFERaWhqLFy8mKCiITp06UV5ezunTp12+Lz8/n6ioKHOCFpFmKyU7l8ELNzN5pXEGefLK3QxeuJmU7Nw6j69sy3HvvTBjhrGg3DPPwP/7f+o7JtKUTEtk7rzzTr744guysrKqbjfddBMPPvhg1b+Dg4PZtGlT1ffs37+fw4cPk5CQUM8ji4g0rcqGizWX+a9suFhXMtOhAwQFQVyc6/ZevcypWhLxV6ZdWmrbti3x8fEu21q3bk379u2rtj/66KPMnDmTiIgIwsLCmDZtGgkJCW4n+oqINLXLbbjYooVRar1/v+v3fPUVdO3qoWBFmiHTq5bqs2jRIgICAhg/fjxlZWWMGjWK1157zeywRKQZudyGi7Gx8ItfwH33wZAhMHQopKTAhg2wdavXwhfxez6VyGyt8e4ODQ0lOTmZ5ORkcwISkWbvchsurlgBP/iBMR9m/nx44gm47jqjF9ngwR4OWqQZ8alERkTE1zSm4SLA5MnGTUQ8wydaFIiI+Co1XBTxbUpkRETqoYaLIr5NiYyIyEWo4aKI71IiIyLSAKPjo9nx9DCWTRwAwLKJA9jx9DAlMX5m/nyjbL5tW4iMhLFja5fQl5ZCUhK0bw9t2sD48ZCfb0q4ghIZEZEGCwywVc2FGdg9QpeT/FBampGkZGRAairY7TByJBQXVx8zY4ZRRr92rXH8sWMwbpx5MTd3qloSERH5XkqK6/0VK4wzM5mZxnpAhYWwdCmsXg3DhhnHLF9urNickXFhN3TxFp2RERERcaOw0Pga8X1RWmamcZZm+PDqY3r2NBZATE/3fnyiMzIiItLMVTic7Mop4PiZUiLbhlZdNnQ4YPp0uPVWqOyok5dntJ9o1871MTp1MvaJ9ymRERGRZislO5d5G/a5tKGIDg9lTmIc7yVHk50NO3aYGKBclBIZERFpliq7mtdsCJpXWMqEiWWEHK1gV3ognTtX74uKgvJyOH3a9axMfr6xT7xPc2RERKTZcdfV3OmEk6m9Kfkqiisf3ElsV9cj+veH4GDYtKl62/79cPgwJCTgE7p1A5ut9i0pyezIPENnZEREpNlx19W8IDWe4n0xRI7bw8myEj7adYqbukUQHg4tW0J4ODz6qNEgNCICwsJg2jQjifGViqXdu6Giovp+djaMGAE//KF5MXmSEhkREWl23HU1P/tZV4CqruaJycb25cvhkUeMfy9aBAEBxkJ4ZWUwahS89pqnI264jh1d7y9YAFdfDbffbk48nqZERkREmh13Xc0ru5lXqqureWgoJCcbN19XXg6rVhlnkGx+un6jEhkREWl2Krua5xWW1ponA0ZD0CgLdTV3V0L+7rvGxOTKs0n+SImMiIg0O5Vdzaes2osNXJIZq3U1r6+EfOnSaMaMgZgYEwP0MFUtiYhIs+QPXc0rS8hrTlzOKyzlseQv+eQTJz/5iUnBeYnOyIiISLM1Oj6aEXFRdV6W8XXuSsjBOMN05ovOBLYuZ/SYFlSfZ/I/SmRERKRZCwyw1ZrQawXuSsjBWA/n7BedaR13hL1HrrDk82soXVoSERGxIHcl5ACl33SgoqgVbfp8V+9x/kBnZERERCzIXQk5QMvuJ6pKyes7zh/ojIyIiIgFVZaQu5v9YsOoXrJKCfnlUiIjIiJiQZUl5FB7Kq/VSsgbQ4mMiIiIRflDCXljaY6MiIiIhVm5hLwpKJERERGxOKuWkDcFXVoSERERy1IiIyIiIpalREZEREQsS4mMiIg0D9u2QWKi0QraZoN33zU7ImkCSmRERKR5KC6Gvn0hOdnsSKQJqWpJRESahzFjjJv4FZ2REREREcvSGRkREfFPFRWwfTvk5kJ0NNx2GwQGmh2VNDElMiIi4n/eeQeefBK++656W+fO8OqrMG6ceXFJk1MiIyIi/uWdd+C//gucTtftR48a29etMycu8QjNkREREf9RUWGciamZxED1tunTvRqSeJYSGRER8R/bt7teTqrJ6YQjR4x/5+RAVhYcPuyV0MQzlMiIiIj/yM1t+LEzZ8KNN8Ls2Z6LRzxOc2RERMR/REc37LgtW+COOzwainiHzsiIiIj/uO02ozrJZqt7v80GXboYx4lfUCIjIiL+IzDQKLGG2slM5f1XXtF6Mn5EiYyIiPiXceOMEusrr3Td3rmzsV3ryPgVzZERERH/M24c3HuvVvZtBpTIiIiIfwoM1ITeZkCXlkRERMSylMiIiIiIZSmREREREctSIiMiIiKWpURGRERELEuJjIiIiFiWEhkR8WlHj8JDD0H79tCyJVx/PezZY3ZUIuIrtI6MiPisU6fg1lth6FD46CPo2BEOHIArrjA7MhHxFUpkRMRnLVxo9Pdbvrx6W/fu5sUjIr5Hl5ZExGe9/z7cdBP88IcQGQk33ghvvml2VCLiS5TIiIhPqXA4ST90kveyjnLokJMlS5xccw1s3AhTpsATT8DKlWZHKSK+wtREZsmSJfTp04ewsDDCwsJISEjgo48+qtpfWlpKUlIS7du3p02bNowfP578/HwTIxYRT0rJzmXwws3c/2YGT76VRfl5J8GdChnyQC433giPPw6PPQavv252pCLiK0xNZDp37syCBQvIzMxkz549DBs2jHvvvZd//etfAMyYMYMNGzawdu1a0tLSOHbsGOPUfl3EL6Vk5zJl1V5yC0urtgW2KYV2RUxZtZeU7FwAevWCw4fNilJEfI2piUxiYiJ33XUX11xzDddeey0vvPACbdq0ISMjg8LCQpYuXcrLL7/MsGHD6N+/P8uXL+fTTz8lIyPDzLClicyfDwMGQNu2xvyHsWNh//7q/d98AzZb3be1a82KWjyhwuFk3oZ9OGtsD7nyFPaCNgDM27CPCoeTr76Crl29H6OI+CafqVqqqKhg7dq1FBcXk5CQQGZmJna7neHDh1cd07NnT2JjY0lPT2fQoEF1Pk5ZWRllZWVV94uKigCw2+3Y7XbPPgk/Vfl7a+rf39atgfz3fzvo39/J+fMwe3YgI0fa+Oc/z9O6NURF1f7L+89/DuDllwMYPvw8zW04PTUOvmBXTgEFZ88REui6vcPNX3P4L7dyJuNq6HWM3ywq4k9/CuO11yqw22umPd7hz+NgJRoH3+DJcWjoY9qcTqc5nwbf++KLL0hISKC0tJQ2bdqwevVq7rrrLlavXs2kSZNckhKAgQMHMnToUBYuXFjn482dO5d58+bV2r569WpatWrlkecgTaOwsAUTJ47hhRd20Lv3yTqPmTHjdq66qpBp07K8G5yYZvfuTvz1r3Hk5ramU6cS7rnnECNHfmt2WCLiYSUlJTzwwAMUFhYSFhbm9jjTz8hcd911ZGVlUVhYyLp165g4cSJpaWmX/XizZs1i5syZVfeLioro0qULI0eOrPcXIe7Z7XZSU1MZMWIEwcHBHvs5Bw8aX8eMuZn4+Nr79+6FnJxgVqxoQ0JCjMfi8FXeGgcz7MopYPLK3W72niD0oW10B5ZNHMDA7r2B3l6MzpU/j4OVaBx8gyfHofKKysWYnsi0aNGCHj16ANC/f392797Nq6++yn333Ud5eTmnT5+mXbt2Vcfn5+cTFRXl9vFCQkIICQmptT04OFgv9kZqit9hhcPJrpwCjp8pJbJtKAO7RxAYYMPhgF/8wljF9cYb6/4ZK1caEz2HDDH9ZWsqf3wtD+oRSUSbluQVltaaJwNgA6LCQxnUI5LAAJu3w6uTP46DFWkcfIMnxqGhj+dz/yM4HA7Kysro378/wcHBbNq0ifHjxwOwf/9+Dh8+TEJCgslRyuVIyc5l3oZ9LlUp0eGhzEmM473kaLKzYceOur/33DlYvRqee85LwYpXBQbYmJMYx5RVe7GBSzJTmbbMSYzzmSRGRHyHqYnMrFmzGDNmDLGxsZw5c4bVq1ezdetWNm7cSHh4OI8++igzZ84kIiKCsLAwpk2bRkJCgtuJvuK7Kktra/61nVdYyoSJZYQcrWBXeiCdO9f9/evWQUkJ/PjHHg9VTDI6PpolD/WrlexGfZ/sjo6PNjE6EfFVpiYyx48f58c//jG5ubmEh4fTp08fNm7cyIgRIwBYtGgRAQEBjB8/nrKyMkaNGsVrr71mZshyGdyV1jqdUPBJb0q+iuKqx3cS2zWB6r+/XS1dCvfcYzQNFP81Oj6aEXFRdV5+FBGpi6mJzNKlS+vdHxoaSnJyMsnJyV6KSDxhV06By1/YlQpS4yneF0PkuD2cLCvho12nuKlbBOHh0LJl9XEHD8K2bfD3v3sxaDFNYICNhKvbmx2GiFiEz82REf9z/EztJAbg7GfGqmb5a4w5T4nf56vLl8Mjj1Qft2wZdO4MI0d6MkoREbEiJTLicZFtQ+vc3vXpD13ur3lsUJ1/if/ud8ZNRESkJnW/Fo8b2D2C6PBQN7NfjFkx0eHGXAgREZFLoURGPK6ytBZqT+VVaa2IiDSGEhnxisrS2qhw18tMUeGhLHmon0prRUTksmiOjHiNSmtFRPzTG28E8Kc/wTffGPd794bZs2HMGM//bCUy4lUqrRUR8T9XXulkwQK45hpjjbCVK+Hee+Gzz4ykxpOUyIiIiEij/L//5+TC1kgvvABLlkBGhhIZERERsZCKCli7FoqLwRutEZXIiIiIyCWrcDjZlVMAGCu4tz4XyeBbbZSWQps2sH49xMV5Pg4lMiIiInJJUrJzmbdhHwVnz/HiQJi8cjftQlux+G/x9O0Uybp1MHEipKV5PplR+bVII2zbBomJEBMDNhu8+67rfput7tvvf29KuCJiYXPn1v4s6dnT+3GkZOcyZdXeWj30jhef47fbdvOfkFzmz4e+feHVVz0fjxIZkUYoLjberO76mubmut6WLTM+fMaP926cIuIfevd2/UzZscO7P7/C4WTehn0469hXuW3ehn1UOJw4HFBW5vmYdGlJpBHGjKl/nYSoKNf7770HQ4fCVVd5Ni4R8U9BQbU/V7xpV05BrTMxAP/Z0pMW3f9DUNg5vv1PEJN+VsrWrS3ZuNHzMSmREfGS/Hz48ENjfQURkctx4IBxKTs01KgImj8fYmO99/OPn6mdxABUlLTgxAd9qSgOISDkPP+Md7JxI4wY4fmYlMiIXKLKmfqXujrxypXQti2MG+eFIEXEL1z4eRMW25Zly9rSq5eN3FyYNw9uuw2ys43PFm+IbBta5/aouz+nrKL6c/D1xwaRcHXdxzY1JTIil6Bypv6Fp1ajw0O/b4pZf7+oZcvgwQeNv6RERC7G7edN7zhGj4rm5puha1f429/g0Ue9E9PA7hFEh4eSV1ha5zwZG0YPvYHdI7wTEJrsK9Jg7mbq5xWWMmXV3nq/d/t22L8ffvITT0YoIv7iYp83Kdm5tGsH114LBw96L67AANv3f7gZScuFKu/PSYzzag89JTLi8+bPhwEDjFOnkZEwdqyRFFzo0CH4wQ+gY0cIC4MJE4w5KU2lITP1ARyOuo6ApUuhf3+jwknMdeYMTJ9u/CXbsiXccgvs3m12VCLVGloZVFjk5NAhiK7/ZHCTGx0fzZKH+hEV7np6OSo8lCUP9WN0vHcDuqRE5rXXXmP48OFMmDCBTZs2uew7ceIEV6kUQzwgLQ2SkoyeHampYLfDyJFG6TMYX0eONMqaN2+Gf/wDysuN9V0cjqaJwd1MfUd5IOX5YZTlhxmxZpaQlQWHD1cfU1RkLNetszG+4Sc/MV5Hf/0rfPGF8doZPhyOHjU7MhGDu8+bU5t7UXo4AnthS3L+1ZIRd9kJDIT77/d+jKPjo9nx9DCWTRwAwLKJA9jx9DCvJzFwCYnM4sWL+cUvfkHPnj0JCQnhrrvuYv78+VX7Kyoq+Pbbbz0SpDRvKSnwyCPG+gl9+8KKFUaikJlp7P/HP4zW8StWwPXXG7eVK2HPHiOxaQruZuqX54WTu+I2clfcBsDi37XmxhuN9vWV3nrL6AZrxoeNuDp3Dv7v/+DFF2HIEOjRw1hkrEcPo8GdiC9w93lz/kwoJzbcyNE3b+fEezcS0vo8GRnGmWgzBAbYqubCNLTowRMaPNn3jTfe4M033+SBBx4AYMqUKYwdO5Zz587xm9/8xmMBitRUWGh8jfh+LllZmXE2JiSk+pjQUAgIMBaLGj688T/T3Uz90NgCuj79YdX9NY8NIuHq9i7HPP64cRPznT9vNLSrOeG6ZUvvLywm4o67z5uO937mcv/FxwZx9dWtvBGST2vwGZmcnBxuueWWqvu33HILmzdv5k9/+hOzZs3ySHDSfFU4nKQfOsl7WUdJP3SSiu/nnjgcxvyGW2+F+Hjj2EGDoHVrePppKCkxLjU99ZTxH1ZubtPEUzlT393fGzaMagJvztSXhrnwtZR9/CSDEpz89rdw7JjxGlm1CtLTm+61ItJY+ry5NA0+I9OhQweOHDlCt27dqrbFx8ezefNmhg0bxrFjxzwRnzRD9ZU4v5ccTXa261/PHTsac1CmTIHFi40zMfffD/36Gf9uCpUz9aes2osN1wm+Zs3Ul4ur67V0xS1XcHZrf668MoTAQON1cv/91ZcqRcymz5tL0+CP+cGDB/POO+/U2h4XF8emTZv46KOPmjQwaZ7qKzmcMLGMdesr2LIFOnd2/b6RI43KpePH4cQJYyLn0aNN2wrA12bqS/3cvZZOB53i7PBPWL8zjyNHYNcuYwK5ahXEl+jzpuEafEbmmWeeIdPNnyy9e/dm8+bNrFu3rskCk+bHXcmh0wkFn/Sm5Ksornp8J7FdE6i9goGhQwfj6+bNRlJzzz1NG+Po+GhGxEVd1sq+4j0XK1+1AQs3/YsdT3fi1CkbGzcaE4Av1bZtRifzzEzj0tT69cbyACJNQZ83DdPgRGbt2rXMmTPH7f6wsDD+8Y9/NElQ0jy5KzksSI2neF8MkeP2cLKshI92neKmbhGEhxuTNAGWL4devYzLTOnp8OSTMGMGXHdd08cZGGCrNaFXfIu71xLAua87ADYOR5zlj389w/JFYfTsCZMmXfrPqex+PnmyWk+IZ+jz5uIafGlp5cqVDBw4kOzs7Fr73njjDeLj4wkKUscDuXzuSg7PftYVZ1kw+WsS+C55OIkJEURHw9tvVx+zf7/xl3CvXvCb38Cvfw0vveSduMX3uHstATjKgilI7c2xP9/OvKdaM3gwbNwIwcGX/nPGjIHnnzcWYxQRczQ488jOzmbq1KncdNNNzJkzh6effprvvvuOyZMns3v3bl566SUeV42pNIK7ksMLy5uh7hLnBQuMmwi4fy0BtO6VS+teRolSXa8lEbGWBp+RCQsL4y9/+Qtvv/02r776Kv369eP666/HZrPx+eefK4mRRlPJoTQVT72WKjsRg3H5qsJNSwoR8Z5LLk4dNGgQ119/PZ9//jkOh4Nnn32Wrl27eiI2aWZ8sRmZWJMnXksp2bkMXriZySuNxkyTV+5m8MLNpGRrARoRM11SIrNmzRri4uJwOBx8+eWXTJkyhZEjRzJjxgxKS91fkxZpKJUcSlNpytdSQzoRi4g5GjxHZvz48WzcuJH58+czbdo0AF588UXGjh3LpEmT+Pvf/86KFStISEjwWLDiG5KTjZLTvDyjYuMPf4CBA5vu8VVyKE2lKV5LDSnlnrdhH6AkW8QMDU5k8vLy+Oyzz7jmmmtctt9yyy1kZWXxzDPPcPvtt1NeXt7kQYrvePttmDkTXn8dbr4ZXnkFRo0yqoYiI5vu56jkUJpKY19L9ZVyO8oDOX+qNd/mG/dzciAry+gDFht72T9SRC5Bgy8tbd++vVYSU6lly5a8+uqrfPLJJ00WmPiml1+Gxx4z1tyIizMSmlatYNkysyMT8Yz6Srlrdj+fOZNa3c9FxLMafEYmoAFNa4YMGdKoYMS3lZcbK5he2CM0IMDoLp2ebl5cIp5UXyn3hd3PVcotYo4maqkn/urCctNP9p6mogI6dXI9plMnY76MiD/SsgAivk2JjLhVs9x05tosADIOnTAxKhHv0rIAIr5NiYzUqa5y08BW5WBzMP+db1zKTfPzISrKjChFvEPLAoj4LjVHklrclZvaAp20iCqk9NsOzNuwjxFxUdiwsWkTTJ1qSqgiXlNZyp1x8Dgnvsxg2cQBDOoRqTMxIibTGRmppb5y07ABOZz5ZxcO7GjP31ILmTLF6AB8OZ2DRawmMMBWNRdGaxuJ+AadkZFa6is3bd0rl4qSFpzecS0/Tm1JvxshJaX2BGARERFvUCIjtdRXbgoQ1v9bwvp/q3JTERExnS4tSS0qNxUREatQIiO1qNxURESsQomM1EnlpiIiYgWaIyNuqdxURER8nc7ISL1UbioiIr5MiYyIiIhYlhIZERERsSwlMiIiImJZSmRERETEspTIiIiIiGUpkRERERHLUiIjIiIilqVERkRERCxLiYyIiIhYlhIZkUrJydCtG4SGws03w65dZkckIiIXYWoiM3/+fAYMGEDbtm2JjIxk7Nix7N+/3+WY0tJSkpKSaN++PW3atGH8+PHk5+ebFLH4rbffhpkzYc4c2LsX+vaFUaPg+HGzIxMRkXqYmsikpaWRlJRERkYGqamp2O12Ro4cSXFxcdUxM2bMYMOGDaxdu5a0tDSOHTvGuHHjTIxa/NLLL8Njj8GkSRAXB6+/Dq1awbJlZkcmIiL1MLX7dUpKisv9FStWEBkZSWZmJkOGDKGwsJClS5eyevVqhg0bBsDy5cvp1asXGRkZDBo0yIywxd+Ul0NmJsyaVb0tIACGD4f0dPPiEhGRizI1kampsLAQgIgIo9tyZmYmdrud4cOHVx3Ts2dPYmNjSU9PrzORKSsro6ysrOp+UVERAHa7Hbvd7snw/Vbl782vfn8VFUaSkpcHQUEEV1Rwvn17nBc8x4AOHbB9+SUVPvK8/XIcLEjj4Bs0Dr7Bk+PQ0Mf0mUTG4XAwffp0br31VuLj4wHIy8ujRYsWtGvXzuXYTp06kZeXV+fjzJ8/n3nz5tXa/vHHH9OqVasmj7s5SU1NNTuEpteqFaEFBYwCPv30U04VFFTtivv6azqcPs22v//dvPjq4JfjYEEaB9+gcfANnhiHkpKSBh3nM4lMUlIS2dnZ7Nixo1GPM2vWLGbOnFl1v6ioiC5dujBy5EjCwsIaG2azZLfbSU1NZcSIEQQHB5sdTuNs2AAPPwxOZ/U2pxMncMvs2TjXrIHERAAC162D667jrrvuMifWGvxqHCxM4+AbNA6+wZPjUHlF5WJ8IpGZOnUqH3zwAdu2baNz585V26OioigvL+f06dMuZ2Xy8/OJioqq87FCQkIICQmptT04OFgv9kay/O+wogKefBLcZPlB5eUwfTrcey/YbLBlC0ydSoCPPWfLj4Of0Dj4Bo2Db/DEODT08UytWnI6nUydOpX169ezefNmunfv7rK/f//+BAcHs2nTpqpt+/fv5/DhwyQkJHg7XLG67dvhu+/qP+bIEVi1CqZMgeJio4pJRER8lqmJTFJSEqtWrWL16tW0bduWvLw88vLyOHfuHADh4eE8+uijzJw5ky1btpCZmcmkSZNISEhQxZJcutzchh33k59AVhakpECnTh4NyUoqKuC556B7d2jZEq6+Gn77W9erdCIi3mbqpaUlS5YAcMcdd7hsX758OY888ggAixYtIiAggPHjx1NWVsaoUaN47bXXvByp+IXo6IYdl5oKNV6TAgsXwpIlsHIl9O4Ne/YYJ6zCw+GJJ8yOTkSaK1MTGWcD/pQLDQ0lOTmZ5ORkL0Qkfu2226BzZzh6tO7TCDabsf+227wfmwV8+qkxfejuu4373brBmjXq5CAi5lKvJWk+AgPh1VeNf9tsrvsq77/yinGc1HLLLbBpE3z1lXH/n/+EHTtgzBhz4xKR5s0nqpZEvGbcOFi3zqheunDib+fORhKj9hcuKhxOduUUcPxMKbf/MJTThRH07GkjMNCYM/PCC/Dgg2ZHKSLNmRIZaX7GjTOukWzfbkwAjo42LifpTIyLlOxc5m3YR25hKQDF+6Ip2taaXy48x4OjryAry6hWj4mBiRNNDVVEmjElMtI8BQZqQm89UrJzmbJqLxfOJDq1tRfhgw7y9slvucPWj4cfjubbb2H+fCUyImIezZERERcVDifzNuyj5nRopz0QbMbWeRv2UeFwEhgIDof3YxQRqaRERkRc7MopqLqcdKGWPfIp/LQHxYciOXLYxu/fOMvLL8MPfmBCkCIi39OlJRFxcfxM7SQGIGL4vzi9/ToKPu6NoySEV6Kc/PSnMHu2lwMUEbmAEhkRcRHZNrTO7QEhFUQM30fE8H0ArHlsEAlXt/dmaCIitejSkoi4GNg9gujwUGxu9tuA6PBQBnaP8GZYIiJ1UiIjIi4CA2zMSYwDqJXMVN6fkxhHYIC7VEdExHuUyIhILaPjo1nyUD+iwl0vM0WFh7LkoX6Mjm9g3yoREQ/THBnxC/PnwzvvwL//bXRmvuUWo8nhdde5HpeeDr/+NezcaSwlc8MNsHGj8T3ianR8NCPioqpW9o1sa1xO0pkYEfElSmTEL6SlQVISDBgA58/Dr34FI0fCvn3QurVxTHo6jB4Ns2bBH/4AQUFGv6AAnZd0KzDApgm9IuLTlMiIX0hJcb2/YgVERkJmJgwZYmybMQOeeAKeeab6uJpnbERExFr0t6j4pcJC42vE94U1x48bl5MiI43LTp06we23G92bRUTEupTIiGVVOJykHzrJe1lHST90kgqHsXy+w2E0M7z1VoiPN479+mvj69y58Nhjxhmcfv3gzjvhwAFTwhcRkSagS0tiSTU7M4OxtsmcxDjeS44mO9v1bEtlP6Cf/hQmTTL+feONsGkTLFtmTBYWERHrUSIjllNXZ2aAvMJSJkwsI+RoBbvSA+ncuXpf9PfVwnFxrt/TqxccPuzRcEVExIN0aUksxW1nZiecTO1NyVdRXPngTmK7uh7RrRvExMD+/a7f99VX0LWrR0MWEREP0hkZsRR3nZkLUuMp3hdD5Lg9nCwr4aNdp7ipWwTh4cYaMTYb/OIXMGcO9O1rrB+zcqWx7sy6dd5/HiIi0jSUyIiluOvMfPYz47RK/poEABKTje3Ll8Mjjxj/nj4dSkuNMuyCAiOhSU2Fq6/2cNAiIuIxSmTEUtx1Zu769Icu9911Zn7mGdd1ZERExNo0R0YsRZ2ZRUTkQkpkxFLUmVlERC6kREYsR52ZRUSkkubIiM9YsMBo6Pjkk/DKK/Ufq87MIiICSmTER+zeDW+8AX36NPx71JlZRER0aUlMd/YsPPggvPkmXHGF2dGIiIiVKJER0yUlwd13w/DhZkciIiJWo0tL4lUVDqfLvJacnRHs3Wtj926zIxMREStSIiNeU7Nj9fmiUI7/5TZeXVlIaGhHk6MTEREr0qUl8YrKjtUX9kkqzwvHXtyCn/2wPYFBToKCIC0NFi+GoCCoqDAxYBERsQQlMuJx7jpWh3Y9QfTkNGImbSc+aSeZe53cdJMx8TcrCwIDzYi2+Zk/HwYMgLZtITISxo517RJeUADTpsF11xkNOGNj4YknoLDQtJBFRKookRGPc9exOiCkghYdzxLc8SyFLU9S0rqA1q2hfXuIjzch0GYqLc2YcJ2RYTTRtNth5EgoLjb2Hztm3F56CbKzYcUKSEmBRx81NWwREUBzZMQL3HWsvtzjpGmlpLjeX7HCODOTmQlDhhhJ5f/9X/X+q6+GF16Ahx6C8+eNy4AiImbRR5B4nLuO1XUdt3WrZ2ORi6u8ZBRRT9/NwkIIC1MSIyLm08eQeFxlx+q8wtJa82TAaPYYpY7VXlWzDL6yvYPDAdOnw623ur+8d+IE/Pa38PjjXg1ZRKROSmTE4yo7Vk9ZtRcbuCQz6ljtfTXL4AGiw0OZkxjHe8nRZGfDjh11f29RkbF4YVwczJ3rnXhFROqjyb4+aNs2SEyEmBiw2eDdd90f+9//bRxzsSaLZlPHat9QVxk8QF5hKRMmlrFufQVbtkDnzrW/98wZGD3aqG5avx6Cg70UtIhIPXRGxgcVF0PfvjB5Mowb5/649euNSpOYGO/F1hjqWG0ud2XwTicUfNKbkq+iuOrxncR2TaD6XJmhqAhGjYKQEHj/fQht2LQnERGPUyLjg8aMMW71OXrUWNtj40bjVL9VqGO1edyVwRekxlO8L4bIcXs4WVbCR7tOcVO3CMLDjXVjioqMcuySEli1yrhfVGR8b8eOWu9HRMylRMaCHA54+GH4xS+gd2+zoxGrcFfefvazrgDkr0kAIDHZ2L58OTzyCOzdCzt3Gtt69HD93pwc6NbNA8GKiDSQEhkf4K6CxJ2FC42y1yee8GKQYnnuyuC7Pv2hy/01jw1yOWt2xx3G5ScREV+kRMZk9VWQ1DUBNjMTXn3V+CvZpqklcglUBi8i/khVSyaqr4Jkyqq9pGTn1vqe7dvh+HGj301QkHH79lv4+c91il/qV1kGDzWn8qoMXkSsS4mMSdxVkED1OivzNuyrte/hh+Hzz42mipW3mBhjvszGjZ6L19ddrPEhwJ/+BFddZUxOtdmMiap1HffTnxrL8LdsaRxz773w739765l4lsrgre9iyzM4nTB7NkRHG6/h4cPhwAFTQhXxCl1aMom7ChIAR3kg50+15tt8435OjpGwREQYZ2La1yj6CQ6GqCijO3FzVdn4cMAAo//Pr35lVNrs2wetWxvHlJQYZ7DGjYN16+Cdd2DBgtrH9e9vdOCOjTU6P8+daxyTk+MfFToqg7e2iy3P8OKLsHgxrFwJ3bvDc88ZpfP79qlsXvyTEhmT1NcgsTwvvKqCBGDmTOPrxIlGQz+p7WKND8FYen/6dNi61Uhkrr++7uMuXHq/Wzd4/nnjP45vvjHO1PgDlcFbV33LMzidxuKYzz5rnEkE+MtfoFMn48zNj37krShFvEeJjEnqa6QYGltQVUlSs4KkLt9805SR+YeGND5syHHFxUYZcvfu0KVL08Un4gk5OZCXZ1xOqhQeDjffDOnpSmTEPymRMYkqSBqvoY0Pax5X4YgA6m+Q+Npr8MtfGonMdddBaiq0aGHCkxSh4Us05OUZXzt1ct3eqVP1PhF/o0TGJGqk2DgNbXxY13GtTkYB/XnqKdw2SHzwQRgxAnJz4aWXYMIE+Mc/NMdAvK++1zpocraIqpZMpAqSy9PQxofZp+s+rqC4HID3P3TfIDE8HK65xpg3s26dUbW0fr3HnpJInS62RENNUVHG1/x81+35+dX7RPyNEpkmcLFyyLNnYepU4z/Mli0hLg5ef93YNzo+mh1PD2PNY4N49Uc3sOaxQex4epiSGDfqa3x4MtVofHjlgzu5sovD7XFFe7oDEP1fmcR2vfiStU6ncSsra5rnINIQDVmiAcDhqL7XvbuRsGzaVL2/qMhoMZGQgIhf0qWlJnCxcsiZM2HzZqPhXrdu8PHH8LOfGYnPPfeoguRSNLTx4R8/OMJ3R53YQgIICHYAUHE2hIJP4ijN6QhAXq6NP64qYuSAcLp1M5LMr7+Gt982yq07doTvvjNKtFu2hLvu8uYzlebO3Wu9cnmGSmmZJVx1Veuq5RmmTzcq7a65prr8OibGWDNJxB8pkWkCF+tW/emnRun0HXcY9x9/HN54A3btMhIZabiGNj78eTJAV9rf9U/aXP8dAGeyYinZH1P1PSfWD2D695eLKhskhoYaqye/8gqcOmVMkhwyxBjDyEgPPSmROrh7rddcnmHx71qz+HfVyzNUTlJ//HE4fRoGDzaWJ9D8LvFXSmS84JZb4P33jTM2MTHGOiZffQWLFpkdmfU0tPHhc3f34rcffumyrd3gA7Qb7LrEac3y9pgY+PvfmyhYkUZw91q/cHkGqP0attngN78xbiLNgebIXIYKh5P0Qyd5L+so6YdOUuGof57FH/5gzIvp3Nko4R09GpKTqxdgk4arLFt3V8tlw6joeDihW4OOU3m7+KqGvtb1GpbmTonMJUrJzmXwws3c/2YGT76Vxf1vZjB44eY6GzxW+sMfICPDOCuTmQn/8z/GcvqffOLFwP1EQxsftggKUINEsTQ1+RRpGFMTmW3btpGYmEhMTAw2m413a5T7OJ1OZs+eTXR0NC1btmT48OEcMLH72eV0qz53zuj78/LLRmVTnz5GBdN99xnrk8ila2jZusrbxer0Gha5OFPnyBQXF9O3b18mT57MuDrKfV588UUWL17MypUr6d69O8899xyjRo1i3759hHp55trFSiFtVHardv1gsduNW0CNlDEwEBwODwXbDDS08aEaJIrV6TUsUj9TE5kxY8Ywxk25j9Pp5JVXXuHZZ5/l3u+7n/3lL3+hU6dOvPvuu/zITdOQsrIyyi5Y8KOoqAgAu92O3W6/7Fh35RRQcPYcIXV0P3aUB1J+qjXHThj3Dx6sYPduR1U55JAhgTz1lI3g4ApiY51s327jL38J5Pe/d2C3+342U/l7a8zvz1Nuig0DwgBwVJzHUdG443yZL49Dc2LWOPjDa7gp6f3gGzw5Dg19TJvT6bz4imBeYLPZWL9+PWO/X+zg66+/5uqrr+azzz7jhhtuqDru9ttv54YbbuDVV1+t83Hmzp3LvHnzam1fvXo1rVq18kTofPFFe557bnCt7UOHHubJJz/j1KkQ/vrXOLKyOnL2bAs6dixh5MhvueeeQ9j0R5WIiEgtJSUlPPDAAxQWFhIWFub2OJ9NZD799FNuvfVWjh07RnR09eWaCRMmYLPZePvtt+t8nLrOyHTp0oUTJ07U+4u4mF05BUxeufuixy2bOMDvqgjsdjupqamMGDGC4OBgs8NptjQOvkHj4Bs0Dr7Bk+NQVFREhw4dLprI+N06MiEhIYSEhNTaHhwc3Khf8qAekUS0aXnRbtWDekT67bXrxv4OpWloHHyDxsE3aBx8gyfGoaGP57Pl11HfdzjLr9H9LD8/v2qfN6kUUkRExPf4bCLTvXt3oqKi2HRB97OioiJ27txJgkndz1QKKSIi4ltMvbR09uxZDh48WHU/JyeHrKwsIiIiiI2NZfr06Tz//PNcc801VeXXMTExVfNozGC1Usht2+D3vzcW4svNhfXrXZvHzZ0Lb70FR44Yqw737w8vvAA332xWxCIiIg1naiKzZ88ehg4dWnV/5syZAEycOJEVK1bwy1/+kuLiYh5//HFOnz7N4MGDSUlJ8foaMjVZqVv1xTpzX3st/PGPcNVVxuJ9ixYZnZ8PHjS6P4uIiPgyUxOZO+64g/qKpmw2G7/5zW/4jbqfXbaLdeZ+4AHX+y+/DEuXwuefw513ejY2ERGRxvLZOTLifeXl8Kc/QXi4cRZHRETE1/ld+bUY7RQuZQ7PBx/Aj34EJSUQHQ2pqdChgxcDFhERuUxKZPxMSnYu8zbsc2lsGR0e+n3peN1VVUOHQlYWnDgBb74JEybAzp0QGemdmEVERC6XLi35kYt153andWvo0QMGDTLmxwQFGV9FRER8nRIZP3Gx7tyVHI6Ld6RwOOCCLg8iIiI+S5eW/MSunIJaZ2LA6Mx9/lTrqvtpmSVcdVVrIiKgfXtjzZh77jHmxpw4AcnJcPQo/PCH3oxeRETk8uiMjJ84fqZ2EgNQnhdO7orbyF1xGwCLf9eaG2+E2bMhMBD+/W8YP95YTyYxEU6ehO3boXdvb0YvIiJyeXRGxk9Etq17kcDQ2AK6Pv1h1f01jw1yWczvnXc8HpqIiIjH6IyMnxjYPYLo8NBaDS0r2TCqlwZ2j/BmWCIiIh6lRMZPqDu3iIg0R0pk/Ii6c4uISHOjOTJ+xmrduUVERBpDiYwfslJ3bhERkcbQpSURERGxLCUyIiIiYllKZERERMSylMiIiIiIZSmREREREctSIiMiIiKWpURGRERELEuJjIiIiFiWEhkRERGxLCUyIiIiYllKZERERMSylMiIiIiIZSmREREREctSIiMiIiKWpURGRERELEuJjIiIiFiWEhkRERGxLCUyIiIiYllKZERERMSylMiIiIiIZSmREREREctSIiMiIiKWpURGRERELEuJjIiIiFiWEhkRERGxLCUyIhazcGEAAwZA27YQGQljx8L+/XUf63TCmDFgs8G773ozShER71AiI2Ix27fbSEqCjAxITQW7HUaOhOLi2se+8oqRxIiI+KsgswMQkUvzwQcVBAdX/w2yYoVxZiYzE4YMqT4uKwv+539gzx6IjvZ6mCIiXqEzMiIWV1hofI2IqN5WUgIPPADJyRAVZU5cIiLeoERGxAIqHE525RQAsCungAqHEwCHA6ZPh1tvhfj46uNnzIBbboF77zUhWBERL9KlJREfl5Kdy7wN+yg4e44XB8LklbuJaNOSOYlxvJccTXY27NhRffz778PmzfDZZ+bFLCLiLUpkRHxYSnYuU1btxQmEBFZvzyssZcLEMkKOVrArPZDOnav3bd4Mhw5Bu3aujzV+PNx2G2zd6oXARUS8RJeWRHxUhcPJvA37cNbY7nTCydTelHwVxZUP7iS2q+sRzzwDn39uTPatvAEsWgTLl3shcBGxhG3bIDERYmLqXqLhkUeM7RfeRo82I9L66YyMiI/alVNAbmFpre3HN8Zz9l9XEjluDyfLSvho1ylu6hZBeDi0bGlM7q1rgm9sLHTv7oXARcQSiouhb1+YPBnGjav7mNGjXf8ACgnxTmyXQomMiI86fqZ2EgNQuLcbAPlrEgBITDa2L19u/AUlItIQY8YYt/qEhPh+5aMSGREfFdk2tM7t1/7qA8oqqle5W/PYIBKubl/vYzlrXp8SEWmArVuNdaquuAKGDYPnn4f29X/ceJ0SGREfNbB7BNHhoeQVltaaJwNgA6LCQxnYPaKOvSIitVUu5XD8TCmRbY3Pj8CAupf/Hj3auOTUvbtRQPCrXxlncNLTITCwzm8xhRIZER8VGGBjTmIcU1btpebHTOX9OYlxbj+EREQuVLmUw4Vz76LDQ5mTGAfUXv77Rz+q/vf110OfPnD11cZZmjvv9Hy8DaWqJREfNjo+miUP9SMq3PUyU1R4KEse6sfoePUeEJGLq1zKoWYBQV5hKVNW7W3QY1x1FXToAAcPeiLCy6czMiI+bnR8NCPiosg4eJwTX2awbOIABvWI1JkYEWkQd0s5ADipPsPrcFx4r7bvvoOTJ32vd5vOyIhYQGCArWouTH3XtEVEanK3lIOjPJDy/DDK8sMASMssISsLDh+Gs2fhF7+AjAz45hvYtMloedKjB4wa5d34L0aJjIiIiB9zt5RDeV44uStuI3fFbQAs/l1rbrwRZs82JvN+/jnccw9cey08+ij07w/bt/veWjK6tCQiIuLH3C3lEBpbQNenP6y6X3Mph40bPR5ak9AZGRERET9WuZSDuwvSNozqJasu5WCJRCY5OZlu3boRGhrKzTffzK5du8wOSURExBIql3KA2lN5/WEpB59PZN5++21mzpzJnDlz2Lt3L3379mXUqFEcP37c7NBEREQswZ+XcvD5OTIvv/wyjz32GJMmTQLg9ddf58MPP2TZsmU888wzJkcnIiJiDZVLOTR0ZV+r8OlEpry8nMzMTGbNmlW1LSAggOHDh5Oenl7n95SVlVFWVlZ1v6ioCAC73Y7dbvdswH6q8vem35+5NA6+QePgGzQOl++m2DDAKLl2VJzHUXH5j+XJcWjoY/p0InPixAkqKiro1KmTy/ZOnTrx73//u87vmT9/PvPmzau1/eOPP6ZVq1YeibO5SE1NNTsEQePgKzQOvkHj4Bs8MQ4lJSUNOs6nE5nLMWvWLGbOnFl1v6ioiC5dujBy5EjCwsJMjMy67HY7qampjBgxguDgYLPDabY0Dr5B4+AbNA6+wZPjUHlF5WJ8OpHp0KEDgYGB5Ofnu2zPz88nKiqqzu8JCQkhpI7VeoKDg/VibyT9Dn2DxsE3aBx8g8bBN3hiHBr6eD5dtdSiRQv69+/Ppk2bqrY5HA42bdpEQkKCiZGJiIiIL/DpMzIAM2fOZOLEidx0000MHDiQV155heLi4qoqJhEREWm+fD6Rue+++/jPf/7D7NmzycvL44YbbiAlJaXWBGARERFpfnw+kQGYOnUqU6dONTsMERER8TE+PUdGREREpD5KZERERMSyLHFpqTGcTifQ8Hp0qc1ut1NSUkJRUZHKHE2kcfANGgffoHHwDZ4ch8r/tyv/H3fH7xOZM2fOANClSxeTIxEREZFLdebMGcLDw93utzkvlupYnMPh4NixY7Rt2xabzdqNscxSuTrykSNHtDqyiTQOvkHj4Bs0Dr7Bk+PgdDo5c+YMMTExBAS4nwnj92dkAgIC6Ny5s9lh+IWwsDB9YPgAjYNv0Dj4Bo2Db/DUONR3JqaSJvuKiIiIZSmREREREctSIiMXFRISwpw5c+psxineo3HwDRoH36Bx8A2+MA5+P9lXRERE/JfOyIiIiIhlKZERERERy1IiIyIiIpalREZEREQsS4mMVNm2bRuJiYnExMRgs9l49913XfY7nU5mz55NdHQ0LVu2ZPjw4Rw4cMCcYP3Y/PnzGTBgAG3btiUyMpKxY8eyf/9+l2NKS0tJSkqiffv2tGnThvHjx5Ofn29SxP5pyZIl9OnTp2qhr4SEBD766KOq/RoD71uwYAE2m43p06dXbdM4eMfcuXOx2Wwut549e1btN3MclMhIleLiYvr27UtycnKd+1988UUWL17M66+/zs6dO2ndujWjRo2itLTUy5H6t7S0NJKSksjIyCA1NRW73c7IkSMpLi6uOmbGjBls2LCBtWvXkpaWxrFjxxg3bpyJUfufzp07s2DBAjIzM9mzZw/Dhg3j3nvv5V//+hegMfC23bt388Ybb9CnTx+X7RoH7+nduze5ublVtx07dlTtM3UcnCJ1AJzr16+vuu9wOJxRUVHO3//+91XbTp8+7QwJCXGuWbPGhAibj+PHjzsBZ1pamtPpNH7vwcHBzrVr11Yd8+WXXzoBZ3p6ullhNgtXXHGF889//rPGwMvOnDnjvOaaa5ypqanO22+/3fnkk086nU69F7xpzpw5zr59+9a5z+xx0BkZaZCcnBzy8vIYPnx41bbw8HBuvvlm0tPTTYzM/xUWFgIQEREBQGZmJna73WUsevbsSWxsrMbCQyoqKnjrrbcoLi4mISFBY+BlSUlJ3H333S6/b9B7wdsOHDhATEwMV111FQ8++CCHDx8GzB8Hv28aKU0jLy8PgE6dOrls79SpU9U+aXoOh4Pp06dz6623Eh8fDxhj0aJFC9q1a+dyrMai6X3xxRckJCRQWlpKmzZtWL9+PXFxcWRlZWkMvOStt95i79697N69u9Y+vRe85+abb2bFihVcd9115ObmMm/ePG677Tays7NNHwclMiI+LCkpiezsbJdr0eI91113HVlZWRQWFrJu3TomTpxIWlqa2WE1G0eOHOHJJ58kNTWV0NBQs8Np1saMGVP17z59+nDzzTfTtWtX/va3v9GyZUsTI9NkX2mgqKgogFqz0PPz86v2SdOaOnUqH3zwAVu2bKFz585V26OioigvL+f06dMux2ssml6LFi3o0aMH/fv3Z/78+fTt25dXX31VY+AlmZmZHD9+nH79+hEUFERQUBBpaWksXryYoKAgOnXqpHEwSbt27bj22ms5ePCg6e8HJTLSIN27dycqKopNmzZVbSsqKmLnzp0kJCSYGJn/cTqdTJ06lfXr17N582a6d+/usr9///4EBwe7jMX+/fs5fPiwxsLDHA4HZWVlGgMvufPOO/niiy/Iysqqut100008+OCDVf/WOJjj7NmzHDp0iOjoaNPfD7q0JFXOnj3LwYMHq+7n5OSQlZVFREQEsbGxTJ8+neeff55rrrmG7t2789xzzxETE8PYsWPNC9oPJSUlsXr1at577z3atm1bdY05PDycli1bEh4ezqOPPsrMmTOJiIggLCyMadOmkZCQwKBBg0yO3n/MmjWLMWPGEBsby5kzZ1i9ejVbt25l48aNGgMvadu2bdXcsEqtW7emffv2Vds1Dt7x1FNPkZiYSNeuXTl27Bhz5swhMDCQ+++/3/z3g8frosQytmzZ4gRq3SZOnOh0Oo0S7Oeee87ZqVMnZ0hIiPPOO+907t+/39yg/VBdYwA4ly9fXnXMuXPnnD/72c+cV1xxhbNVq1bOH/zgB87c3FzzgvZDkydPdnbt2tXZokULZ8eOHZ133nmn8+OPP67arzEwx4Xl106nxsFb7rvvPmd0dLSzRYsWziuvvNJ53333OQ8ePFi138xxsDmdTqfn0yURERGRpqc5MiIiImJZSmRERETEspTIiIiIiGUpkRERERHLUiIjIiIilqVERkRERCxLiYyIiIhYlhIZERERsSwlMiIiImJZSmRExGdVVFRwyy23MG7cOJfthYWFdOnShV//+tcAPPHEE/Tv35+QkBBuuOEGEyIVEbMokRERnxUYGMiKFStISUnhf//3f6u2T5s2jYiICObMmVO1bfLkydx3331mhCkiJlL3axHxaddeey0LFixg2rRpDBs2jF27dvHWW2+xe/duWrRoAcDixYsB+M9//sPnn39uZrgi4mVKZETE502bNo3169fz8MMP88UXXzB79mz69u1rdlgi4gOUyIiIz7PZbCxZsoRevXpx/fXX88wzz5gdkoj4CM2RERFLWLZsGa1atSInJ4fvvvvO7HBExEcokRERn/fpp5+yaNEiPvjgAwYOHMijjz6K0+k0OywR8QFKZETEp5WUlPDII48wZcoUhg4dytKlS9m1axevv/662aGJiA9QIiMiPm3WrFk4nU4WLFgAQLdu3XjppZf45S9/yTfffAPAwYMHycrKIi8vj3PnzpGVlUVWVhbl5eUmRi4i3mBz6vysiPiotLQ07rzzTrZu3crgwYNd9o0aNYrz58/zySefMHToUNLS0mp9f05ODt26dfNStCJiBiUyIiIiYlm6tCQiIiKWpURGRERELEuJjIiIiFiWEhkRERGxLCUyIiIiYllKZERERMSylMiIiIiIZSmREREREctSIiMiIiKWpURGRERELEuJjIiIiFjW/wdauUC424HlwQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        },
        {
          "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": [
        "belong"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9x1GvilkFPTC",
        "outputId": "7c5ba6ee-2a41-493c-a308-129affa20789"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: [0, 4, 6, 8, 9, 10, 11, 13, 14, 17, 18, 21, 22, 23, 24, 26, 27, 28, 29],\n",
              " 1: [1, 2, 3, 5, 7, 12, 15, 16, 19, 20, 25]}"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "_XymgWd0BoUg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!wget -N -q \"https://github.com/thomasfork/ipopt_linux/raw/main/ipopt-linux64.zip\"\n",
        "!unzip -o -q ipopt-linux64\n",
        "\n",
        "opt = SolverFactory('ipopt', executable='/content/ipopt')\n",
        "\n",
        "\n",
        "from pyomo import environ as pe\n",
        "import os\n",
        "\n",
        "os.environ['NEOS_EMAIL'] = 'XXXXXX@gmail.com'\n",
        "solver_manager = pe.SolverManagerFactory('neos')\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "s8zQrvAxJxfs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = AbstractModel()\n",
        "model.i = RangeSet(len(df))\n",
        "model.c = RangeSet(2)\n",
        "features = [f for f in df.columns if f not in ['y'] ]\n",
        "model.x = Var(model.i, model.c, within = Binary)\n",
        "model.d = Var(model.i,model.c, bounds=(0,5000), within = Reals)\n",
        "M = 10000\n",
        "model.f = Set(initialize = features)\n",
        "model.mu = Var(model.c,model.f, bounds=(0,5000), within = Reals)\n",
        "\n",
        "def rule_c1(model,i,c):\n",
        "  Dic = sum( (model.mu[c,f]-df.loc[i-1,f])**2 for f in model.f)\n",
        "  return model.d[i,c] >= Dic - M*(1-model.x[i,c])\n",
        "model.C1 = Constraint(model.i, model.c, rule = rule_c1)\n",
        "\n",
        "def rule_c2(model,i):\n",
        "  return sum(model.x[i,c] for c in model.c) == 1\n",
        "model.C2 = Constraint(model.i, rule = rule_c2)\n",
        "\n",
        "def rule_obj(model):\n",
        "  return sum(model.d[i,c] for i in model.i for c in model.c)\n",
        "  #return sum(model.d[i,c] for (i,c) in model.d)\n",
        "\n",
        "model.obj = Objective(rule = rule_obj, sense = minimize)\n",
        "instance = model.create_instance()\n",
        "#results = opt.solve(instance)\n",
        "solver_manager = pe.SolverManagerFactory('neos')\n",
        "results = solver_manager.solve(instance, solver = \"cplex\")\n",
        "# CONOPT SNOPT KNITro\n",
        "\n",
        "\n",
        "from pyomo.opt import SolverStatus, TerminationCondition\n",
        "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
        "     print (\"this is optimal\")\n",
        "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
        "     print (\"do something about it? or exit?\")\n",
        "else:\n",
        "     print ('ERROR ' + str(results.solver))\n",
        "\n",
        "# CPLEX\n",
        "# Gurobi\n",
        "# Mosek (maybe)\n",
        "\n",
        "\n",
        "\n",
        "for (i,c), v in instance.x.items():\n",
        "  if v.value>0:\n",
        "    print(i,c)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XhQW-Hd3wHX9",
        "outputId": "ce106e0e-39e1-4549-d90d-9a0be9f429bc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "this is optimal\n",
            "1 2\n",
            "2 1\n",
            "3 1\n",
            "4 1\n",
            "5 2\n",
            "6 1\n",
            "7 1\n",
            "8 1\n",
            "9 2\n",
            "10 1\n",
            "11 2\n",
            "12 2\n",
            "13 1\n",
            "14 2\n",
            "15 2\n",
            "16 1\n",
            "17 1\n",
            "18 2\n",
            "19 2\n",
            "20 1\n",
            "21 1\n",
            "22 2\n",
            "23 2\n",
            "24 2\n",
            "25 2\n",
            "26 1\n",
            "27 2\n",
            "28 2\n",
            "29 2\n",
            "30 2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure()\n",
        "plt.scatter(df['x1'],df['x2'])\n",
        "plt.xlabel('X1')\n",
        "plt.ylabel('X2')\n",
        "plt.grid()\n",
        "for i in range(len(df)):\n",
        "  plt.text(df['x1'][i],df['x2'][i],s= str(i), c='blue')\n",
        "for k , [x0,y0] in clusters.items():\n",
        "  plt.scatter(x0,y0,c='red')\n",
        "  plt.text(x0,y0,s= str(k), c='red')\n",
        "\n",
        "\n",
        "for k in instance.c:\n",
        "  x0,y0 = instance.mu[k,'x1'].value,instance.mu[k,'x2'].value\n",
        "  plt.scatter(x0,y0,c='green')\n",
        "  plt.text(x0,y0,s= str(k), c='green')\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "hMO2mpk1ROPK",
        "outputId": "b238ae21-3d82-4a15-ec9b-1ef42f26e7ff"
      },
      "execution_count": null,
      "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": [
        "model = AbstractModel()\n",
        "model.i = RangeSet(len(df))\n",
        "model.j = RangeSet(len(df))\n",
        "\n",
        "features = [f for f in df.columns if f not in ['y'] ]\n",
        "model.x = Var(model.i, model.j, within = Binary)\n",
        "model.s = Var(model.j, within = Binary)\n",
        "#model.z = Var(model.i, model.j, within = Binary)\n",
        "model.z = Var(model.i, model.j,  bounds=(0,1), within = Reals)\n",
        "\n",
        "\n",
        "model.d = Var(model.i,model.j, bounds=(0,5000), within = Reals)\n",
        "M = 10000\n",
        "model.f = Set(initialize = features)\n",
        "\n",
        "def rule_c1(model,i,j):\n",
        "  Dic = sum( (df.loc[i-1,f]-df.loc[j-1,f])**2 for f in model.f)\n",
        "  #Dic = sum( abs(df.loc[i-1,f]-df.loc[j-1,f]) for f in model.f)\n",
        "  return model.d[i,j] >= Dic - M*(1-model.z[i,j])\n",
        "model.C1 = Constraint(model.i, model.j, rule = rule_c1)\n",
        "\n",
        "def rule_c2(model,i):\n",
        "  return sum(model.x[i,j] for j in model.j) == 1\n",
        "model.C2 = Constraint(model.i, rule = rule_c2)\n",
        "\n",
        "def rule_c3A(model,i,j):\n",
        "  return model.z[i,j] <= model.x[i,j]\n",
        "model.C3A = Constraint(model.i, model.j, rule = rule_c3A)\n",
        "\n",
        "def rule_c3B(model,i,j):\n",
        "  return model.z[i,j] <= model.s[j]\n",
        "model.C3B = Constraint(model.i, model.j, rule = rule_c3B)\n",
        "\n",
        "def rule_c3C(model,i,j):\n",
        "  return model.z[i,j] >= model.x[i,j] + model.s[j] -1\n",
        "model.C3C = Constraint(model.i, model.j, rule = rule_c3C)\n",
        "\n",
        "\n",
        "def rule_c4(model):\n",
        "  return sum(model.s[j] for j in model.j) == 2\n",
        "model.C4 = Constraint( rule = rule_c4)\n",
        "\n",
        "def rule_c5(model,i,j):\n",
        "  return model.x[i,j] <= model.s[j]\n",
        "model.C5 = Constraint(model.i, model.j, rule = rule_c5)\n",
        "\n",
        "\n",
        "\n",
        "def rule_obj(model):\n",
        "  return sum(model.d[i,j] for i in model.i for j in model.j)\n",
        "\n",
        "model.obj = Objective(rule = rule_obj, sense = minimize)\n",
        "instance = model.create_instance()\n",
        "#results = opt.solve(instance)\n",
        "solver_manager = pe.SolverManagerFactory('neos')\n",
        "results = solver_manager.solve(instance, solver = \"cplex\")\n",
        "# CONOPT SNOPT KNITro\n",
        "\n",
        "\n",
        "from pyomo.opt import SolverStatus, TerminationCondition\n",
        "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
        "     print (\"this is optimal\")\n",
        "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
        "     print (\"do something about it? or exit?\")\n",
        "else:\n",
        "     print ('ERROR ' + str(results.solver))\n",
        "\n",
        "# CPLEX\n",
        "# Gurobi\n",
        "# Mosek (maybe)\n",
        "\n",
        "for j in instance.j:\n",
        "  if instance.s[j].value>0:\n",
        "    print(j)\n",
        "\n",
        "for (i,j), v in instance.x.items():\n",
        "  if v.value>0:\n",
        "    print(i,j)\n",
        "print(\"OF = \", value(instance.obj))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6_l_gVSpQv-F",
        "outputId": "cd471c1d-4cf2-4713-865a-6d548f464597"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "this is optimal\n",
            "21\n",
            "27\n",
            "1 27\n",
            "2 21\n",
            "3 21\n",
            "4 21\n",
            "5 27\n",
            "6 21\n",
            "7 21\n",
            "8 21\n",
            "9 27\n",
            "10 27\n",
            "11 27\n",
            "12 27\n",
            "13 21\n",
            "14 27\n",
            "15 27\n",
            "16 21\n",
            "17 21\n",
            "18 27\n",
            "19 27\n",
            "20 21\n",
            "21 21\n",
            "22 27\n",
            "23 27\n",
            "24 27\n",
            "25 27\n",
            "26 21\n",
            "27 27\n",
            "28 27\n",
            "29 27\n",
            "30 27\n",
            "OF =  6130.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "plt.figure()\n",
        "plt.scatter(df['x1'],df['x2'])\n",
        "plt.xlabel('X1')\n",
        "plt.ylabel('X2')\n",
        "plt.grid()\n",
        "for i in range(len(df)):\n",
        "  plt.text(df['x1'][i],df['x2'][i],s= str(i), c='blue')\n",
        "\n",
        "\n",
        "for j in instance.j:\n",
        "  if instance.s[j].value>0:\n",
        "    print(j)\n",
        "    x0,y0 = df['x1'][j-1],df['x2'][j-1]\n",
        "    plt.scatter(x0,y0,c='red')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "pFMcCeyMbOlY",
        "outputId": "a9261c99-4042-4a5a-8bcd-b3606e781893"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "21\n",
            "27\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "$$f = \\sum_i \\alpha_i k(X_i,x) y_i +b$$"
      ],
      "metadata": {
        "id": "5zpF-SZTz5l3"
      }
    }
  ]
}