Cluster_final.ipynb

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    "colab": {
      "name": "Cluster_final.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mathispuissant/StatApp/blob/main/Cluster_final.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mj-1at3bgWn3"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from json import loads \n",
        "import seaborn as sns\n",
        "\n",
        "import sys, os\n",
        "\n",
        "# Disable\n",
        "def blockPrint():\n",
        "    sys.stdout = open(os.devnull, 'w')\n",
        "\n",
        "# Restore\n",
        "def enablePrint():\n",
        "    sys.stdout = sys.__stdout__"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f8C6D1FUggfh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f52bdc7a-5d6b-4a07-a750-a13ba84abd99"
      },
      "source": [
        "%%time\n",
        "\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from json import loads \n",
        "from google.colab import drive"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "CPU times: user 34 µs, sys: 9 µs, total: 43 µs\n",
            "Wall time: 48.4 µs\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VmCquH-rghVo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "955e78fb-4c88-4c93-d0df-30d1b57ce628"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')\n",
        "\n",
        "velib_nombre = pd.read_csv(r\"/content/gdrive/My Drive/velib_sec.csv\", sep =\",\")\n",
        "velib_nombre = velib_nombre.set_index(\"station_id\")"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/gdrive; to attempt to forcibly remount, call drive.mount(\"/content/gdrive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HX4eixg0gWoB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "97e7ade2-a88b-4ede-f5ed-66c04a5cacb0"
      },
      "source": [
        "velib_nombre.head()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
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              "      <th>213688169</th>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
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              "      <td>3</td>\n",
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              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
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              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
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              "      <th>99950133</th>\n",
              "      <td>46</td>\n",
              "      <td>46</td>\n",
              "      <td>47</td>\n",
              "      <td>49</td>\n",
              "      <td>46</td>\n",
              "      <td>44</td>\n",
              "      <td>43</td>\n",
              "      <td>43</td>\n",
              "      <td>45</td>\n",
              "      <td>43</td>\n",
              "      <td>43</td>\n",
              "      <td>45</td>\n",
              "      <td>47</td>\n",
              "      <td>45</td>\n",
              "      <td>46</td>\n",
              "      <td>48</td>\n",
              "      <td>48</td>\n",
              "      <td>49</td>\n",
              "      <td>47</td>\n",
              "      <td>47</td>\n",
              "      <td>48</td>\n",
              "      <td>49</td>\n",
              "      <td>49</td>\n",
              "      <td>48</td>\n",
              "      <td>48</td>\n",
              "      <td>47</td>\n",
              "      <td>51</td>\n",
              "      <td>52</td>\n",
              "      <td>51</td>\n",
              "      <td>49</td>\n",
              "      <td>49</td>\n",
              "      <td>49</td>\n",
              "      <td>50</td>\n",
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              "      <td>50</td>\n",
              "      <td>49</td>\n",
              "      <td>49</td>\n",
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              "      <td>50</td>\n",
              "      <td>50</td>\n",
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              "      <td>31</td>\n",
              "      <td>31</td>\n",
              "      <td>29</td>\n",
              "      <td>29</td>\n",
              "      <td>28</td>\n",
              "      <td>28</td>\n",
              "      <td>28</td>\n",
              "      <td>27</td>\n",
              "      <td>25</td>\n",
              "      <td>26</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>23</td>\n",
              "      <td>23</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>26</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>24</td>\n",
              "      <td>26</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
              "      <td>24</td>\n",
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              "    <tr>\n",
              "      <th>516709288</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
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              "      <td>2</td>\n",
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              "      <td>2</td>\n",
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              "      <td>2</td>\n",
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              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
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              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>11</td>\n",
              "      <td>11</td>\n",
              "      <td>11</td>\n",
              "      <td>11</td>\n",
              "      <td>...</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>6</td>\n",
              "      <td>6</td>\n",
              "      <td>6</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36255</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>6</td>\n",
              "      <td>7</td>\n",
              "      <td>9</td>\n",
              "      <td>7</td>\n",
              "      <td>6</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>5</td>\n",
              "      <td>8</td>\n",
              "      <td>9</td>\n",
              "      <td>6</td>\n",
              "      <td>8</td>\n",
              "      <td>9</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>11</td>\n",
              "      <td>11</td>\n",
              "      <td>12</td>\n",
              "      <td>12</td>\n",
              "      <td>14</td>\n",
              "      <td>14</td>\n",
              "      <td>13</td>\n",
              "      <td>13</td>\n",
              "      <td>11</td>\n",
              "      <td>10</td>\n",
              "      <td>11</td>\n",
              "      <td>11</td>\n",
              "      <td>12</td>\n",
              "      <td>14</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>6</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>7</td>\n",
              "      <td>7</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>8</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37815204</th>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>11</td>\n",
              "      <td>12</td>\n",
              "      <td>14</td>\n",
              "      <td>13</td>\n",
              "      <td>13</td>\n",
              "      <td>12</td>\n",
              "      <td>14</td>\n",
              "      <td>14</td>\n",
              "      <td>14</td>\n",
              "      <td>15</td>\n",
              "      <td>16</td>\n",
              "      <td>17</td>\n",
              "      <td>18</td>\n",
              "      <td>20</td>\n",
              "      <td>20</td>\n",
              "      <td>21</td>\n",
              "      <td>24</td>\n",
              "      <td>27</td>\n",
              "      <td>29</td>\n",
              "      <td>29</td>\n",
              "      <td>29</td>\n",
              "      <td>29</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>25</td>\n",
              "      <td>...</td>\n",
              "      <td>7</td>\n",
              "      <td>7</td>\n",
              "      <td>7</td>\n",
              "      <td>9</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "      <td>11</td>\n",
              "      <td>12</td>\n",
              "      <td>12</td>\n",
              "      <td>13</td>\n",
              "      <td>13</td>\n",
              "      <td>13</td>\n",
              "      <td>13</td>\n",
              "      <td>15</td>\n",
              "      <td>14</td>\n",
              "      <td>16</td>\n",
              "      <td>16</td>\n",
              "      <td>16</td>\n",
              "      <td>17</td>\n",
              "      <td>16</td>\n",
              "      <td>17</td>\n",
              "      <td>17</td>\n",
              "      <td>17</td>\n",
              "      <td>17</td>\n",
              "      <td>17</td>\n",
              "      <td>17</td>\n",
              "      <td>18</td>\n",
              "      <td>18</td>\n",
              "      <td>18</td>\n",
              "      <td>18</td>\n",
              "      <td>18</td>\n",
              "      <td>19</td>\n",
              "      <td>19</td>\n",
              "      <td>19</td>\n",
              "      <td>19</td>\n",
              "      <td>20</td>\n",
              "      <td>21</td>\n",
              "      <td>21</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 33343 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "            10/19/20;18:01:51  ...  02/15/21;21:58:37\n",
              "station_id                     ...                   \n",
              "213688169                   2  ...                  5\n",
              "99950133                   46  ...                 24\n",
              "516709288                   1  ...                  4\n",
              "36255                       0  ...                  9\n",
              "37815204                    5  ...                 21\n",
              "\n",
              "[5 rows x 33343 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-nrFXHqagWoD"
      },
      "source": [
        "velib_nombre=velib_nombre.dropna(axis=0)\n",
        "velib = velib_nombre.transpose()"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "id": "8cswrQNmgWoE"
      },
      "source": [
        "X = [ pd.to_datetime(date, format = r\"%m/%d/%y;%H:%M:%S\") for date in velib_nombre.columns]\n",
        "Y = [list(velib[station]) for station in velib.columns]\n"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ll5el34dgWoG"
      },
      "source": [
        "def mean_by_days(X, Y):\n",
        "    x = []\n",
        "    y = []\n",
        "\n",
        "\n",
        "    if not len(X) == len(Y):\n",
        "        return False\n",
        "\n",
        "\n",
        "    old_day = [X[0].day, X[0].month, X[0].year]\n",
        "    mean = 0\n",
        "    iteration = 0\n",
        "\n",
        "    for i in range(len(X)):\n",
        "        day = [X[i].day, X[i].month, X[i].year]\n",
        "\n",
        "        if  day == old_day:\n",
        "            mean += Y[i]\n",
        "            iteration += 1\n",
        "\n",
        "        else :\n",
        "\n",
        "            try:\n",
        "                y.append(mean / iteration)\n",
        "            except:\n",
        "                y.append(0)\n",
        "\n",
        "            x.append(str(old_day[0]) + \"/\" + str(old_day[1]))\n",
        "            \n",
        "            old_day = day\n",
        "            mean = 0\n",
        "            iteration = 0\n",
        "\n",
        "    return x, y\n"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AO4CVCs7gWoG"
      },
      "source": [
        "x, y = mean_by_days(X, Y[0])\n"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AqYXQfszgWoH"
      },
      "source": [
        "def average_day_by_hours (X, Y):\n",
        "    x = []\n",
        "    y = []\n",
        "    \n",
        "    if not len(X) == len(Y):\n",
        "        return False\n",
        "\n",
        "    hours = {}\n",
        "\n",
        "    for i in range(24):\n",
        "        hours[i] = []\n",
        "\n",
        "    for i in range(len(X)):\n",
        "        hours[X[i].hour].append(Y[i])\n",
        "\n",
        "    for i in range(24):\n",
        "        y.append(\n",
        "            sum(hours[i]) / len(hours[i])\n",
        "        )\n",
        "        x.append(i)\n",
        "\n",
        "    return x, y"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Krb5ZMEhgWoI"
      },
      "source": [
        "import statistics "
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ELhaUQMggWoI"
      },
      "source": [
        "def week_days_and_weekend_days(X, Y):\n",
        "    x = []\n",
        "    y_weekend = []\n",
        "    y_week = []\n",
        "\n",
        "    if not len(X) == len(Y):\n",
        "        return False\n",
        "\n",
        "    hours = {\"weekend\": {}, \"weekday\": {}}\n",
        "\n",
        "    for i in range(24):\n",
        "        hours[\"weekend\"][i] = []\n",
        "        hours[\"weekday\"][i] = []\n",
        "\n",
        "    for i in range(len(X)):\n",
        "\n",
        "        if X[i].weekday() < 5:\n",
        "            hours[\"weekday\"][X[i].hour].append(Y[i])\n",
        "        if not X[i].weekday() < 5:\n",
        "            hours[\"weekend\"][X[i].hour].append(Y[i])\n",
        "\n",
        "\n",
        "    for i in range(24):\n",
        "        y_week.append(\n",
        "np.array(hours[\"weekday\"][i])\n",
        "        )\n",
        "        y_weekend.append(\n",
        "np.array(hours[\"weekend\"][i])\n",
        "        )\n",
        "        x.append(i)\n",
        "\n",
        "\n",
        "    return x, y_week, y_weekend"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AIt20_OOgWoI"
      },
      "source": [
        "x, y_week, y_weekend = week_days_and_weekend_days(X, Y_m)\n",
        "y_week_mean, y_week_q1, y_week_q3 = [], [], []\n",
        "y_weekend_mean, y_weekend_q1, y_weekend_q3 = [], [], []\n",
        "\n",
        "\n",
        "for i in range(len(y_week)):\n",
        "    y_week_mean.append(np.mean(y_week[i]))\n",
        "    y_week_q1.append(np.percentile(y_week[i], 25))\n",
        "    y_week_q3.append(np.percentile(y_week[i], 75))\n",
        "\n",
        "for i in range(len(y_weekend)):\n",
        "    y_weekend_mean.append(np.mean(y_weekend[i]))\n",
        "    y_weekend_q1.append(np.percentile(y_weekend[i], 25))\n",
        "    y_weekend_q3.append(np.percentile(y_weekend[i], 75))\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3nQu9FwtgWoI"
      },
      "source": [
        "x, y_week, y_weekend = week_days_and_weekend_days(X, Y[0])\n"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_vyK6gcvgWoQ"
      },
      "source": [
        "# Kmean with a normalized and mean centered data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nHH2kxb4gWoQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4ccd705f-cc85-4f3c-f6de-b94939c9c20a"
      },
      "source": [
        "Y = []\n",
        "X = [ pd.to_datetime(date, format = r\"%m/%d/%y;%H:%M:%S\") for date in velib_nombre.columns]\n",
        "list_velib_wo_bike = []\n",
        "\n",
        "for i,k in enumerate(velib.columns):\n",
        "\n",
        "\n",
        "    if i % 200 == 0:\n",
        "        print(int(100 * i / len(velib.columns)))\n",
        "\n",
        "\n",
        "\n",
        "    y_week_mean = []\n",
        "    y_weekend_mean = []\n",
        "    y = list(velib[k]) \n",
        "\n",
        "    x, y_week, y_weekend = week_days_and_weekend_days(X, y)\n",
        "\n",
        "    \n",
        "\n",
        "    for j in range(len(y_week)):     \n",
        "        y_week_mean.append(np.mean(y_week[j]))\n",
        "        y_weekend_mean.append(np.mean(y_weekend[j]))\n",
        "\n",
        "    # normalizing and mean centering\n",
        "    y_week_mean -= np.mean(y_week_mean)\n",
        "    y_weekend_mean -= np.mean(y_weekend_mean)\n",
        "\n",
        "    if np.max(np.abs(y_week_mean)) == 0:\n",
        "        list_velib_wo_bike.append(k)\n",
        "\n",
        "    else:\n",
        "        Y.append(np.transpose(np.array([\n",
        "            y_week_mean / np.max(np.abs(y_week_mean)),\n",
        "            y_weekend_mean / np.max(np.abs(y_weekend_mean))\n",
        "        ])))\n",
        "\n",
        "Y = np.array(Y)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:35: RuntimeWarning: invalid value encountered in true_divide\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "14\n",
            "28\n",
            "42\n",
            "57\n",
            "71\n",
            "85\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q_h0dblygWoR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "239ecfb3-b2af-49b4-f26f-0b177b76b287"
      },
      "source": [
        "list_velib_wo_bike"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[2254322638,\n",
              " 213936755,\n",
              " 2515618216,\n",
              " 54000614,\n",
              " 1057319366,\n",
              " 1057383154,\n",
              " 653085678,\n",
              " 1063971944,\n",
              " 1074347188,\n",
              " 1074352578,\n",
              " 6297,\n",
              " 653159330,\n",
              " 1057387136,\n",
              " 213699079,\n",
              " 54000623]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lz91XUomgWoR"
      },
      "source": [
        "## cluster en folie"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DQGKG9IIgWoR"
      },
      "source": [
        "nb_clusters= [1,4]"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6_KX73FugWoS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0bb938ab-a3f4-4365-c8e4-8783c65a46ce"
      },
      "source": [
        "!pip install tslearn\n",
        "from tslearn.clustering import TimeSeriesKMeans\n",
        "\n",
        "clusters_Kmeans = {}\n",
        "for i in range(*nb_clusters):\n",
        "    clusters_Kmeans[i] = []\n",
        "    clusters_Kmeans[i].append(TimeSeriesKMeans(n_clusters= i, metric=\"dtw\", max_iter=20, n_init= 10))\n",
        "    clusters_Kmeans[i].append(clusters_Kmeans[i][0].fit_predict(Y))\n",
        "    print(i)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting tslearn\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/95/98/9a67e2869a8b1416eb6e6fd5e69c56f86869980403b18f30bdb5783ade9d/tslearn-0.5.0.5-cp37-cp37m-manylinux2010_x86_64.whl (790kB)\n",
            "\u001b[K     |████████████████████████████████| 798kB 4.9MB/s \n",
            "\u001b[?25hRequirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from tslearn) (1.4.1)\n",
            "Requirement already satisfied: numba in /usr/local/lib/python3.7/dist-packages (from tslearn) (0.51.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from tslearn) (1.19.5)\n",
            "Requirement already satisfied: Cython in /usr/local/lib/python3.7/dist-packages (from tslearn) (0.29.23)\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.7/dist-packages (from tslearn) (0.22.2.post1)\n",
            "Requirement already satisfied: joblib in /usr/local/lib/python3.7/dist-packages (from tslearn) (1.0.1)\n",
            "Requirement already satisfied: setuptools in /usr/local/lib/python3.7/dist-packages (from numba->tslearn) (56.1.0)\n",
            "Requirement already satisfied: llvmlite<0.35,>=0.34.0.dev0 in /usr/local/lib/python3.7/dist-packages (from numba->tslearn) (0.34.0)\n",
            "Installing collected packages: tslearn\n",
            "Successfully installed tslearn-0.5.0.5\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/tslearn/clustering/kmeans.py:17: UserWarning: Scikit-learn <0.24 will be deprecated in a future release of tslearn\n",
            "  \"Scikit-learn <0.24 will be deprecated in a \"\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "20LFJUGygWoS"
      },
      "source": [
        "list_inertia.append(clusters_Kmeans[i][0].inertia_)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p8Kvsq1_gWoT"
      },
      "source": [
        "### création médianes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "id": "OrI4l_LagWoT"
      },
      "source": [
        "for i in range(*nb_clusters):\n",
        "\n",
        "    clusters_Kmeans[i].append({})\n",
        "    for j in range(i):\n",
        "            clusters_Kmeans[i][2][j] = []\n",
        "\n",
        "    for index in range(len(clusters_Kmeans[i][1])):\n",
        "        num_cluster = clusters_Kmeans[i][1][index]    \n",
        "        clusters_Kmeans[i][2][num_cluster].append(Y[index])\n",
        "\n",
        "    for j in range(i):\n",
        "        q1_week = []\n",
        "        q1_weekend = []\n",
        "        q3_week = []\n",
        "        q3_weekend = []\n",
        "        for hour in range(24):\n",
        "            q1_week.append(np.percentile([vect[hour][0] for vect in clusters_Kmeans[i][2][j]], 25))\n",
        "            q1_weekend.append(np.percentile([vect[hour][1] for vect in clusters_Kmeans[i][2][j]], 25))\n",
        "            q3_week.append(np.percentile([vect[hour][0] for vect in clusters_Kmeans[i][2][j]], 75))\n",
        "            q3_weekend.append(np.percentile([vect[hour][1] for vect in clusters_Kmeans[i][2][j]], 75))\n",
        "        clusters_Kmeans[i].append([q1_week,\n",
        "        q1_weekend,\n",
        "        q3_week,\n",
        "        q3_weekend])\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TvftArQJgWoT"
      },
      "source": [
        "for j in range(*nb_clusters):\n",
        "    clusters = {}\n",
        "    for i in range(len(clusters_Kmeans[j][0].cluster_centers_)):\n",
        "        clusters[i] = [\n",
        "            [times[0] for times in clusters_Kmeans[j][0].cluster_centers_ [i]],\n",
        "            [times[1] for times in clusters_Kmeans[j][0].cluster_centers_ [i]]\n",
        "        ]\n",
        "\n",
        "    fig, axs = plt.subplots(len(clusters_Kmeans[j][0].cluster_centers_), 1, figsize=(10, 5 * j) )\n",
        "    x = [i for i in range(24)]\n",
        "\n",
        "\n",
        "    for i in range(len(clusters_Kmeans[j][0].cluster_centers_)):  \n",
        "        axs[i].plot(x, clusters[i][0], label = \"week\")\n",
        "        axs[i].plot(x, clusters[i][1], label = \"weekend\")\n",
        "\n",
        "        axs[i].legend()\n",
        "        axs[i].set_title(\"cluster \" + str(i))\n",
        "        axs[i].set_ylabel(\"taux d'occupation\")\n",
        "        axs[i].set_xlabel(\"heure\")\n",
        "\n",
        "    fig.savefig(\"results/Kmeans \" + str(j) + \" clusters\" \".jpg\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ROYecjKdgWoU"
      },
      "source": [
        "list_inertia = []\n",
        "for j in range(*nb_clusters):\n",
        "    list_inertia.append(clusters_Kmeans[j][0].inertia_)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6QbcW8hEgWoU",
        "outputId": "23c17b67-1eff-4fcd-a1a6-eb3045a11bd0"
      },
      "source": [
        "list_inertia"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[7.608265947929566,\n",
              " 5.393362054423828,\n",
              " 4.503982596865056,\n",
              " 4.123824789662627,\n",
              " 3.867275663668193,\n",
              " 3.681792106325219,\n",
              " 3.491649914116708]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gu5lEFvtgWoU"
      },
      "source": [
        "x = [1, 2, 3, 4, 5, 6, 7]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2QCcLkZKgWoU",
        "outputId": "4406c5d8-0646-4ccb-9c1f-aecb88c244da"
      },
      "source": [
        "plt.plot(x, list_inertia)\n",
        "plt.xlabel(\"nombre de clusters\")\n",
        "plt.ylabel(\"inertie\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'inertie')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 110
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
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fJYmIzxTwATKtKJsli2aTnzWI2x5bzZNv7/K7JBHxUVgD3sx2mtkGM1tvZhXhPJeEjBySyjP3zGLu2By+s/R9vvf7D7QNoEiMGogR/Hzn3FTnnJqTDZCMlEQeuW06d8wu4Rdv7eRrT1RQd+q032WJyADTFE1AxccZ/3jtRH5ww4W8ufUwn3/gLfWWF4kx4Q54B7xiZmvMbGFXLzCzhWZWYWYV1dXVYS4n9nxpZhGP3zGDquOn1FteJMaEO+BnO+cuBj4DLDazuZ1f4Jx7yDlX7pwrz83NDXM5sWl2aQ5LFs8mQ73lRWJKWAPeObffez4ELCG0K5T4YExuOksWzebiosHc+/R6/s8rW2jVxt4igRa2gDezNDPLaPsauIpQX3nxSXZaEk/cMZMby0fyk1e38RdPrVVveZEAC2ergmHAEjNrO8+vnXMvhfF80g1JCXH82+cnU5qXzr++uIm9R1fyiHrLiwRS2EbwzrlK59wU7zHJOfeDcJ1LesbMuHPuaB66tZxth+q5/r4VvL/vuN9liUg/022SMezKicN45u5LMUK95V9Wb3mRQFHAx7iJ+Zks/YvZjBuewd1PruFB9ZYXCQwFvJCXkcLTCy/hs5NH8G8vbuZbz6i3vEgQqB+8AF30lq8J9ZYfot7yIlFLI3hp19Zb/sc3TWX9nmMsuG8F2w7V+V2WiPSSAl4+4vqpod7yDU3N3HD/WyzfqhYSItFIAS9dmlaUzdLFod7ytz/2Dr9Ub3mRqKOAl3MqzE7l2UWXcvm4XP5BveVFoo4CXj5WenICD3+5nK/NCfWW/+rjFdSqt7xIVFDAy3nFxxnfuWYiP/zcZFZsO8wX1FteJCoo4KXbbp4xiie83vLX37eCip3qLS8SyRTw0iOXluawdPFssgYl8ucPr2LJur1+lyQi56CAlx4bnZvOkkWXMq0om796+l3+42X1lheJRAp46ZXBqUk8fscMbpo+kp++pt7yIpFIAS+9lpQQxw8/N5nvXH0BL75fxY0PreRg7Sm/yxIRjwJe+sTM+Nplo3m4rbf8T9VbXiRSKOClX3zS6y0fZ6He8i+9r97yIn5TwEu/6dxb/j//+CHHGpr8LkskZlkkbe5QXl7uKioq/C5D+ujU6Ra+9cx7/P7d/STGG/PH53FDWQHzJ+SRkhjvd3kigWJma5xz5V1+TwEv4eCc44P9tSxdt4/n391PdV0jGSkJXD15BAvKCphRPIS4OPO7TJGop4AXXzW3tPLW9iMsXbePlz6ooqGphYLBg7h+aj43lBUwdliG3yWKRC0FvESMhqZm/rjxIEvW7WP51sO0tDom5WdyQ1kB103JJy8zxe8SRaKKAl4iUnVdIy+8t58l6/bx3t7jxBnMLs3hhrICPjVpOGnJ2lFS5HwU8BLxth2q5/n1+1iybh97j55kUGI8V00axoKyAi4rzSEhXjd8iXRFAS9RwznHml1HWbJuHy+8d4DjJ0+Tk57ENReF5usvKszCTBdnRdoo4CUqNTa3sGxLNUvX7eNPmw7R1NLK6Jw0FpQVsGBqAaOGpvpdoojvFPAS9Y6fPM2LGw6wZN0+Vu0I9aEvL8pmQVkBV08eQXZaks8VivhDAS+Bsu/YydB8/dp9bD1UT2K8Mc9bTHWFFlNJjFHASyA559h4wFtMtX4/h7SYSmKQAl4Cr6XV8db2wyxZt4+X3g8tpsrPSuH6sgJuKCtgnBZTSUAp4CWmtC2mWrpuH294i6kmjvAWU03NZ5gWU0mAKOAlZh2ub+SFd0OLqd7tsJhqwdQCPnXhcNK1mEqinAJeBNheXc/z6/axZP0+9tScJCUxjqsmDueGsgLmjM0hUYupJAop4EU6cM6xdveZxVTHGk4zNC2Ja6fks6CsgClaTCVRRAEvcg5Nza28/mFoMdUfNx2kqbmVkpw0FkwNXZzVYiqJdAp4kW6oPXVmMdXblaHFVNO8xVSfmjSMvAxdnJXIo4AX6aF9x07y+/X7WbJuLx8erAdgdG4aM0uGMKNkCDNLhpI/eJDPVYoo4EV6zTnHpgN1LN9azaodNbyzs4a6U80AFGYP8sJ+CDNKhlI8NFVz9zLgFPAi/aSl1bG5qpbVO2raH0dOhDYWz8tIPivwx+alayWthJ2vAW9m8UAFsM85d83HvVYBL9HGOcf26npWeWG/qrKGqtpTAAxOTWR68ZD2aZ2JIzLV11763ccF/ECs8vgGsAnIHIBziQwoM6M0L4PSvAy+NLMI5xx7j55k1Y4aVlUeYfXOGv648SAA6ckJTCvKbh/lTy7MIjlBjdEkfMIa8GZWCFwN/AD4ZjjPJRIJzIyRQ1IZOSSVL0wrBKDq+ClW76xh9Y4jrN5Rw7+/vAWA5IQ4ykYNZmbJUGaWDKFsVDaDkhT40n/CPYL/EfAtQJ2eJGYNz0rhuin5XDclH4Aj9Y28s/NoaA5/5xF+8upWfuwgMd6YXJDFjJKhzBw9hGlF2WSmJPpcvUSzsM3Bm9k1wGedc4vMbB7w113NwZvZQmAhwKhRo6bt2rUrLPWIRKraU6dZs+soqypDo/z39h6nudURZzAxP5MZxUOZ4c3jD9HGJtKJLxdZzeyHwK1AM5BCaA7+OefcLed6jy6yisDJphbW7T7afuF27e6jNDa3AjBuWLoX9qFpHXXGFN9vk/y4EXxHCniRj2psbmHD3uPtgV+xs4YTTS0AFA1Nbb8tc2bJEAqzB+le/Bjj9100ItIHyQnxlBcPobx4CIvnQ3NLK5sO1LFqxxFW7ajhlY0H+W3FXgBGZKW0T+fMLBnKmNw0BX4M00InkSjX2urYeqie1V7gr9pRQ3VdIwBD05LaA39GyRAmDM8kXouvAsX3KZruUsCL9J1zjp1HGtoDf/WOGvYePQlARkoCk/IzmTA8k/HDM0KPYRmkaeOTqKUpGpEYYmaU5KRRkpPGjdNHAaHmaaH78I+y6UAtv63YQ4M3jw8wcsggxg/LZIIX+hOGZ1Cck6ZNUKKcRvAiMai1NbTidnNVLVuq6th8sI4tVXXsOHyCltZQJiTFxzE6N80L/TPhPyIrRfP6EUQjeBE5S1ycMWpoKqOGpnLVpOHtxxubW9h2qJ4PD9axuSoU+qt21LB0/f7212SmJJyZ3vGCf9ywDLIGaVFWpFHAi0i75IR4JuVnMSk/66zjxxtOs+VgHVuqatuD//l1+6lr3N3+mvyslLNCf/zwDMbkppOUoGkevyjgReS8slIT2+/EaeOcY//xU2eF/paqOt7cdpjTLaFpnoS40PWAtnn9tvAvGDxIrZQHgAJeRHrFzCgYPIiCwYO4YsKw9uOnW1qprD7RPuLfUlXH+j3HeOG9A+2vSUuKZ1xb6A87E/zZasXQr3SRVUQGRN2p03x4sN4b6Xuj/oN1HGs43f6avIzkj4z2S/PSSUlUl81z0UVWEfFdRkoi04qymVaU3X7MOcehukZviufMVM/jK3fR5PXfiTMozklrv5jbFv6jhqRq0dZ5KOBFxDdmxrDMFIZlpnD5uNz2480trew80nDWaH/j/lpefL+KtkmHQYmhaZ4LvBH/hBGhEf/gVE3ztNEUjYhEjYamZrZ60zybvPn9TQdqOdphmmdEVspZgT9xRCYlOWmB3S5RUzQiEgipSQlMGTmYKSMHtx9zzlFd18imqjo2H6hl04HQiH/51sM0d1i0NXZYOhOGZ3LBiAwmDM9kwogMctKT/fooA0IBLyJRzczIy0whr9M0T1NzK9ur69lcVcvmA3Vsqqpj+dZqnl27t/01OenJXuCfCf3SvPTA7JWrgBeRQEpKiOOCEZlcMCITys4cP1Lf6E3x1Hmj/dqzLuomxBljctOZ0GGkf8HwTIZlJkddiwYFvIjElKHpyVxamsylpTntx0IXdU+w6UBd+4i/YudRnu/QomFwamL7SH/iiFDwj83LiOiN0hXwIhLzEuLjKM3LoDQvg2u9zdEBjp88HWrGVlXLpgOhEf/T7+zh5OlQJ862Wzgv8O7Zb7uwGyk7ayngRUTOIWvQR1s0tLY6dtc0tIf+5qpa3t9/nD9sOLNSNyM51JCtbZrnghGh/vvpA9x3X7dJioj0g/rG5lAXzgNtI/7QVE9dY3P7a0YNSW0f6V/gPfd1wZZukxQRCbP05AQuHpXNxaPOXqm779jJM6Hv3cr5P5sO0tphwdaFBZn89q5Z/T6to4AXEQkTM6MwO5XC7FQ+OfFMQ7ZTp1vYerCeTd4F3Yam5rDM2SvgRUQGWEpiPJMLs5hcmHX+F/dBMNfuioiIAl5EJKgU8CIiAaWAFxEJKAW8iEhAKeBFRAJKAS8iElAKeBGRgIqoXjRmVg3s6uXbc4DD/ViOn4LyWYLyOUCfJRIF5XNA3z5LkXMut6tvRFTA94WZVZyr4U60CcpnCcrnAH2WSBSUzwHh+yyaohERCSgFvIhIQAUp4B/yu4B+FJTPEpTPAfoskSgonwPC9FkCMwcvIiJnC9IIXkREOlDAi4gEVNQHvJn93MwOmdn7ftfSF2Y20sxeM7NNZvaBmX3D75p6y8xSzGy1mb3rfZZ/8rumvjCzeDNbZ2Yv+F1LX5jZTjPbYGbrzSyqNz82s8Fm9oyZbfb+m5nld029YWbjvX8ebY9aM7u3335+tM/Bm9lcoB54wjl3od/19JaZjQBGOOfWmlkGsAZY4Jzb6HNpPWahvcfSnHP1ZpYIvAl8wzn3ts+l9YqZfRMoBzKdc9f4XU9vmdlOoNw5F/WLg8zscWC5c+4RM0sCUp1zx/yuqy/MLB7YB8x0zvV2wedZon4E75x7A6jxu46+cs4dcM6t9b6uAzYBBf5W1TsupN77Y6L3iMqRhJkVAlcDj/hdi4SYWSYwF3gUwDnXFO3h7vkEsL2/wh0CEPBBZGbFQBmwyt9Kes+b1lgPHAL+6JyL1s/yI+BbQKvfhfQDB7xiZmvMbKHfxfTBaKAaeMybOnvEzNL8Lqof3AQ81Z8/UAEfYcwsHXgWuNc5V+t3Pb3lnGtxzk0FCoEZZhZ102dmdg1wyDm3xu9a+sls59zFwGeAxd70ZjRKAC4GHnDOlQEngL/1t6S+8aaZrgN+158/VwEfQbz56meBXznnnvO7nv7g/eq8DPi0z6X0xmzgOm/u+jfAFWb2pL8l9Z5zbr/3fAhYAszwt6Je2wvs7fBb4TOEAj+afQZY65w72J8/VAEfIbwLk48Cm5xz/9fvevrCzHLNbLD39SDgk8Bmf6vqOefc3znnCp1zxYR+fX7VOXeLz2X1ipmleRfv8aYzrgKi8s4z51wVsMfMxnuHPgFE3c0IndxMP0/PQOhXnahmZk8B84AcM9sLfNc596i/VfXKbOBWYIM3dw3w9865/+djTb01AnjcuysgDvitcy6qbzEMgGHAktA4ggTg1865l/wtqU++DvzKm9qoBL7icz29ZmapwJXAXf3+s6P9NkkREemapmhERAJKAS8iElAKeBGRgFLAi4gElAJeRCSgFPAS1cysOFydRPvrZ5vZ98zsr3vxvsFmtqiv55fYpYCXmODdkx9tBgM9CngL0X/XAijgZYB4o+FNZvaw1yP+FW+VK2Y21czeNrP3zGyJmWV7x5eZ2X+a2Rvee6eb2XNmttXM/qXDj08ws8e99z/jLRxp63/+j2b2JvBFM7vKzFaa2Voz+53X96dzndO8PvYrgcUdjseb2b+b2TveebpclGJmX/a+/66Z/bKL7y8zs3Lv6xyvDQJmNslCPfTXe+8fC/wbMMY79u/e6/6mQw3/1Onv9n5gLTDSzH5hZu9bqP/7X/X0n5cEgwJeBtJY4D7n3CTgGPB57/gTwLedcxcBG4DvdnhPk3NuLvAg8Dyh0L0QuN3MhnqvGQ885L2/lrNHvaecc3OA/wG+A3zSa7hVAXyzixofA/7SOdd5A4mvAsedc9OB6cCdZlbS8QVmNgn4X8AVzrkpQE82bbkb+LHXoK2cUL+VvyXUPnaqc+5vzOwqQn+HM4CpwLQODcPGE9oToQzIAQqccxc65yZ7n0likAJeBtIO51xbG4Y1QLGZZQGDnXOve8cfJ9Tru83vvecNwAde3/xGQsvTR3rf2+OcW+F9/SQwp8P7n/aeLwEmAiu8VhC3AUUdi+uilo4j8KuAL3vvXQUMJRS2HV0BPCn8W2gAAAHvSURBVNO2oYZzrif7FKwE/t7Mvg0UOedOdvGaq7zHOkIj9QkdatjVYUOVSmC0mf3EzD5N6H96EoOivheNRJXGDl+3AIN68J7WTu9v5cy/v537bXT88wnv2Qj1pb/5Y85lXfysjt/7unPu5V6+v00zZwZWKW0HnXO/NrNVhDYXednMvkYoqDv//B8653521sHQ/gFtnxPn3FEzmwJ8itBvPH8G3HGeuiSANIIXXznnjgNHzewy79CtwOsf85aujLIze3LeTGiLwM7eBmabWSmEGjyZ2bhOtRwDjptZ228AX+rw7ZeBe7yWzpjZOPvoJhN/Av6sberIzIZ0UcdOYJr39RfaDprZaKDSOfdfhH5ruQioAzI61XBH27UDMysws7zOJzCzHCDOOfcs8A9Efytd6SWN4CUS3AY86F0c7U1nwE3AbWb2M2Ar8EDnFzjnqs3sduApM0v2Dn8H+LDTS78C/NzMGggFaptHgGJgrYVaMlYDCzqd4wMz+wHwupm1EJpKub3Tz/8P4LdmdivwaofjNwK3mNlpoAr4vnOuxsxWeLdqvujNw18ArAyVQD1wC6HfhjoqILTbUdsA7u86/31IbFA3SRGRgNIUjYhIQCngRUQCSgEvIhJQCngRkYBSwIuIBJQCXkQkoBTwIiIB9f8B6LhguIRy0UUAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SVZiirLYgWoU"
      },
      "source": [
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}