code/SVM_from_scratch.ipynb

{
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  "metadata": {
    "colab": {
      "name": "SVM from scratch.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOjDP41NPSAZSSZsU7E5E9/",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/linlih/CS-Notes/blob/master/code/SVM_from_scratch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KYOsWnmErvk0",
        "colab_type": "text"
      },
      "source": [
        "## SVM From scratch\n",
        "\n",
        "参考自：sentdex\n",
        "https://www.youtube.com/watch?v=yrnhziJk-z8&list=PLQVvvaa0QuDfKTOs3Keq_kaG2P55YRn5v&index=28"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GTziWAZStRrI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tRpFUKwFqCSW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import style\n",
        "import numpy as np\n",
        "style.use('ggplot')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aXENDDCZzW3V",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Support_Vector_Machine:\n",
        "  \n",
        "  def __init__(self, visualization=True):\n",
        "    \"\"\"\n",
        "    初始化设置一些参数\n",
        "    显示以及颜色信息\n",
        "    \"\"\"\n",
        "    self.visualization = visualization\n",
        "    self.colors = {1:'r', -1:'b'}\n",
        "    if self.visualization:\n",
        "      self.fig = plt.figure()\n",
        "      self.ax = self.fig.add_subplot(1,1,1)\n",
        "\n",
        "  def fit(self, data):\n",
        "    \"\"\"\n",
        "    SVM的实现\n",
        "    \"\"\"\n",
        "    self.data = data\n",
        "    # { ||w||: [w, b]}\n",
        "    # 存放最优的参数\n",
        "    opt_dict = {}\n",
        "    \n",
        "    transforms = [[1, 1],\n",
        "            [-1, 1],\n",
        "            [-1, -1],\n",
        "            [1, -1]]\n",
        "    \n",
        "    all_data = []\n",
        "    # 将所有的数据展成一维的\n",
        "    for yi in self.data:\n",
        "      for featureset in self.data[yi]:\n",
        "        for feature in featureset:\n",
        "          all_data.append(feature)\n",
        "    \n",
        "    # 得到数据中最大的值和最小的值\n",
        "    self.max_feature_value = max(all_data)\n",
        "    self.min_feature_value = min(all_data)\n",
        "    all_data = None # 释放掉all_data的内存\n",
        "\n",
        "    # support vectors yi(xi.w+b) = 1\n",
        "\n",
        "    step_sizes = [self.max_feature_value * 0.1,\n",
        "            self.max_feature_value * 0.01,\n",
        "            # point of expense\n",
        "            self.max_feature_value * 0.001,]\n",
        "    \n",
        "    # extremely expesnsive\n",
        "    b_range_multiple = 5\n",
        "    # we dont need to take as mall of steps with b as we do w\n",
        "    b_mutiple = 5\n",
        "\n",
        "    latest_optimum = self.max_feature_value * 10\n",
        "\n",
        "    for step in step_sizes:\n",
        "      # 初始化w的值\n",
        "      w = np.array([latest_optimum, latest_optimum])\n",
        "      \n",
        "      # we can do this because convex\n",
        "      optimized = False\n",
        "      while not optimized:\n",
        "        # b的取值从 -max*range, max*range, 每次移动为 step * b_mutiple\n",
        "        for b in np.arange(-1*(self.max_feature_value * b_range_multiple),\n",
        "                   self.max_feature_value * b_range_multiple, \n",
        "                   step*b_mutiple):\n",
        "          # 4种不同的transform方式\n",
        "          for transformation in transforms:\n",
        "            w_t = w * transformation\n",
        "            found_option = True\n",
        "            # weakest link in SVM fundamentally\n",
        "            # SMO attempts to fix this a bit\n",
        "            # yi(xi.w+b) >= 1\n",
        "            # 遍历所有的数据\n",
        "            for i in self.data:\n",
        "              for xi in self.data[i]:\n",
        "                yi=i\n",
        "                if not yi*(np.dot(w_t, xi) + b) >= 1:\n",
        "                  found_option = False\n",
        "\n",
        "            if found_option:\n",
        "              opt_dict[np.linalg.norm(w_t)] = [w_t, b]\n",
        "        if w[0] < 0:\n",
        "          optimized = True\n",
        "          print('Optimized a step.')\n",
        "        else:\n",
        "          # w = [5, 5]\n",
        "          # step = 1\n",
        "          # w - step = [4, 4]\n",
        "          w = w - step\n",
        "      \n",
        "      norms = sorted([n for n in opt_dict])\n",
        "      # ||w||: [w, b]\n",
        "      opt_choice = opt_dict[norms[0]]\n",
        "      self.w = opt_choice[0]\n",
        "      self.b = opt_choice[1]\n",
        "      latest_optimum = opt_choice[0][0]+step*2\n",
        "    # 打印最终的结果\n",
        "    for i in self.data:\n",
        "      for xi in self.data[i]:\n",
        "        yi = i\n",
        "        print(xi, ':', yi*(np.dot(self.w, xi)+self.b))\n",
        "\n",
        "  \n",
        "  def predict(self, features):\n",
        "    # sign( x.w+b )\n",
        "    classification = np.sign(np.dot(np.array(features), self.w)+self.b)\n",
        "    if classification != 0 and self.visualization:\n",
        "      self.ax.scatter(features[0], features[1], s=20, marker='x', c=self.colors[classification])\n",
        "    return classification\n",
        "  \n",
        "  def visualize(self):\n",
        "    [[self.ax.scatter(x[0], x[1], s=100, color=self.colors[i]) for x in data_dict[i]] for i in data_dict]\n",
        "    # hyperplane = x.w+b\n",
        "    # v = x.w+b\n",
        "    # psv = 1 positive support vector\n",
        "    # nsv = 1\n",
        "    # dec = 0\n",
        "    def hyperplane(x, w, b, v):\n",
        "      return (-w[0]*x-b+v) / w[1]\n",
        "    datarange = (self.min_feature_value*0.9, self.max_feature_value*1.1)\n",
        "    hyp_x_min = datarange[0]\n",
        "    hyp_x_max = datarange[1]\n",
        "\n",
        "    # (w*x+b) = 1\n",
        "    # positive support vector hyperplane\n",
        "    psv1 = hyperplane(hyp_x_min, self.w, self.b, 1)\n",
        "    psv2 = hyperplane(hyp_x_max, self.w, self.b, 1)\n",
        "    self.ax.plot([hyp_x_min, hyp_x_max], [psv1, psv2], 'k')\n",
        "\n",
        "    npsv1 = hyperplane(hyp_x_min, self.w, self.b, -1)\n",
        "    npsv2 = hyperplane(hyp_x_max, self.w, self.b, -1)\n",
        "    self.ax.plot([hyp_x_min, hyp_x_max], [npsv1, npsv2], 'k')\n",
        "\n",
        "    db1 = hyperplane(hyp_x_min, self.w, self.b, 0)\n",
        "    db2 = hyperplane(hyp_x_max, self.w, self.b, 0)\n",
        "    self.ax.plot([hyp_x_min, hyp_x_max], [db1, db2], 'y--')\n",
        "  \n",
        "    plt.show()\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ar5UPaCvy97g",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data_dict = {-1:np.array([[1, 7],\n",
        "              [2, 8],\n",
        "              [3, 8]]),\n",
        "        1:np.array([[5, 1],\n",
        "             [6, -1],\n",
        "             [7, 3],])}"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qREDWtLQFLQ0",
        "colab_type": "code",
        "outputId": "517646be-670d-4ac4-aa04-0d4fb2fab3de",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 218
        }
      },
      "source": [
        "#all_data = []\n",
        "for yi in data_dict:\n",
        "  for featureset in data_dict[yi]:\n",
        "    for feature in featureset:\n",
        "      #all_data.append(feature)\n",
        "      print(feature)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1\n",
            "7\n",
            "2\n",
            "8\n",
            "3\n",
            "8\n",
            "5\n",
            "1\n",
            "6\n",
            "-1\n",
            "7\n",
            "3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VPb3Or12zV3k",
        "colab_type": "code",
        "outputId": "0276d022-52d9-4898-c705-f8697792d76b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 416
        }
      },
      "source": [
        "svm = Support_Vector_Machine()\n",
        "svm.fit(data=data_dict)\n",
        "\n",
        "predict_us = [[0, 10],\n",
        "        [1, 3],\n",
        "        [3, 4],\n",
        "        [3, 5],\n",
        "        [5, 5],\n",
        "        [5, 6],\n",
        "        [6, -5],\n",
        "        [5, 8],]\n",
        "for p in predict_us:\n",
        "  svm.predict(p)\n",
        "svm.visualize()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Optimized a step.\n",
            "Optimized a step.\n",
            "Optimized a step.\n",
            "[1 7] : 1.2239999999999465\n",
            "[2 8] : 1.2239999999999465\n",
            "[3 8] : 1.000000000000098\n",
            "[5 1] : 1.015999999998539\n",
            "[ 6 -1] : 1.6879999999980846\n",
            "[7 3] : 1.015999999998539\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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ff/1fvuUak+kmzGar73GzeUrExiaiyxdffOFbkz838rfddhu9e/eO9BDDRoIv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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rZl1H0zlS6hW",
        "colab_type": "text"
      },
      "source": [
        "# SMO算法\n",
        "\n",
        "ref: 《机器学习实战》"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rYIkgQFn23ZE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def load_data(filename):\n",
        "  dataMat, labelMat = [], []\n",
        "  fr = open(filename)\n",
        "  for line in fr.readlines():\n",
        "    lineArr = line.strip().split('\\t')\n",
        "    dataMat.append([float(lineArr[0]), float(lineArr[1])])\n",
        "    labelMat.append(float(lineArr[2]))\n",
        "  fr.close()\n",
        "  return dataMat, labelMat\n",
        "\n",
        "def clip(alpha, L, H):\n",
        "  if alpha < L:\n",
        "    return L\n",
        "  elif alpha > H:\n",
        "    return H\n",
        "  else: \n",
        "    return alpha\n",
        "\n",
        "def selectJrand(i, m):\n",
        "  j = i\n",
        "  while(j == i):\n",
        "    j = int(random.uniform(0, m))\n",
        "  return j\n",
        "\n",
        "def clipAlpha(aj, H, L):\n",
        "  if aj < L:\n",
        "    aj = L\n",
        "  elif aj > H:\n",
        "    aj = H\n",
        "  return aj"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LmTwHGipAWS5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from numpy import *\n",
        "def smoSimple(dataMatIn, classLabels, C, toler, maxIter):\n",
        "  dataMatrix = mat(dataMatIn)\n",
        "  labelMat = mat(classLabels).transpose()\n",
        "  b = 0\n",
        "  m, b = shape(dataMatrix)\n",
        "  alphas = mat(zeros((m, 1)))\n",
        "  iter = 0\n",
        "  while (iter < maxIter):\n",
        "    alphaPairsChanged = 0\n",
        "    for i in range(m):\n",
        "      fXi = float(multiply(alphas, labelMat).T * \\\n",
        "             (dataMatrix * dataMatrix[i, :].T)) + b\n",
        "      Ei = fXi - float(labelMat[i])\n",
        "      if ((labelMat[i] * Ei < -toler) and (alphas[i] < C)) or \\\n",
        "         ((labelMat[i] * Ei > toler) and \\\n",
        "          (alphas[i] > 0)):\n",
        "        j = selectJrand(i, m) # 随机选择第二个alpha\n",
        "        fXj = float(multiply(alphas, labelMat).T * \\\n",
        "               (dataMatrix*dataMatrix[j,:].T)) + b\n",
        "        Ej = fXj - float(labelMat[j])\n",
        "        alphaIold = alphas[i].copy()\n",
        "        alphaJold = alphas[j].copy()\n",
        "        if (labelMat[i] != labelMat[j]):\n",
        "          L = max(0, alphas[j] - alphas[i])\n",
        "          H = min(C, C + alphas[j] - alphas[i])\n",
        "        else :\n",
        "          L = max(0, alphas[j] + alphas[i] - C)\n",
        "          H = min(C, alphas[j] + alphas[i])\n",
        "        if L==H: print(\"L==H\"); continue\n",
        "        eta = 2.0 * dataMatrix[i,:] * dataMatrix[j,:].T - \\\n",
        "            dataMatrix[i,:] * dataMatrix[i,:].T -\\\n",
        "            dataMatrix[j,:] * dataMatrix[j,:].T\n",
        "        if eta >= 0 : print(\"eta>=0\"); continue\n",
        "        alphas[j] -= labelMat[j] * (Ei - Ej)/eta\n",
        "        alphas[j] = clipAlpha(alphas[j], H, L)\n",
        "        if (abs(alphas[j] - alphaJold) < 0.00001):\n",
        "          print(\"j not moving enough\"); continue\n",
        "        alphas[i] += labelMat[j] * labelMat[i] * \\\n",
        "               (alphaJold - alphas[j])\n",
        "        b1 = b - Ei - labelMat[i] * (alphas[i] - alphaIold) * \\\n",
        "           dataMatrix[i,:]* dataMatrix[i,:].T - \\\n",
        "           labelMat[j]*(alphas[j] - alphaJold) * \\\n",
        "           dataMatrix[i,:]*dataMatrix[j,:].T\n",
        "        b2 = b - Ej - labelMat[i] * (alphas[i] - alphaIold) * \\\n",
        "           dataMatrix[i,:]* dataMatrix[j,:].T - \\\n",
        "           labelMat[j]*(alphas[j] - alphaJold) * \\\n",
        "           dataMatrix[j,:]*dataMatrix[j,:].T\n",
        "        if (0 < alphas[i]) and (C > alphas[i]):\n",
        "          b = b1\n",
        "        elif (0 < alphas[j]) and (C > alphas[j]):\n",
        "          b = b2\n",
        "        else:\n",
        "          b = (b1 + b2) / 2.0\n",
        "        alphaPairsChanged += 1\n",
        "        print(\"iter: %d i:%d, pairs changed %d\" % \\\n",
        "              (iter, i, alphaPairsChanged))\n",
        "    if (alphaPairsChanged == 0): iter += 1\n",
        "    else: iter = 0\n",
        "    print(\"interation number: %d\" % iter)\n",
        "  return b, alphas"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NJa-xLjfb9Dr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 222
        },
        "outputId": "0ec339f6-519f-4ceb-c3f1-46d614446232"
      },
      "source": [
        "\"!wget https://raw.githubusercontent.com/pbharrin/machinelearninginaction3x/master/Ch06/testSet.txt"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-03-16 13:18:44--  https://raw.githubusercontent.com/pbharrin/machinelearninginaction3x/master/Ch06/testSet.txt\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.0.133, 151.101.64.133, 151.101.128.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|151.101.0.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 2108 (2.1K) [text/plain]\n",
            "Saving to: ‘testSet.txt’\n",
            "\n",
            "testSet.txt         100%[===================>]   2.06K  --.-KB/s    in 0s      \n",
            "\n",
            "2020-03-16 13:18:49 (66.2 MB/s) - ‘testSet.txt’ saved [2108/2108]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EOF0HeWglDgy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "dataMat, labelMat = load_data('testSet.txt')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fLtxzq9ilL-v",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "8afd2549-9000-4f05-baaf-9972bffb4b52"
      },
      "source": [
        "b, alpas = smoSimple(dataMat, labelMat, 0.6, 0.001, 40)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "L==H\n",
            "iter: 0 i:1, pairs changed 1\n",
            "L==H\n",
            "L==H\n",
            "iter: 0 i:5, pairs changed 2\n",
            "L==H\n",
            "iter: 0 i:10, pairs changed 3\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "j not moving enough\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "iter: 0 i:0, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:10, pairs changed 2\n",
            "j not moving enough\n",
            "L==H\n",
            "L==H\n",
            "iter: 0 i:24, pairs changed 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:54, pairs changed 4\n",
            "j not moving enough\n",
            "iter: 0 i:62, pairs changed 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "iter: 0 i:0, pairs changed 1\n",
            "iter: 0 i:1, pairs changed 2\n",
            "iter: 0 i:5, pairs changed 3\n",
            "j not moving enough\n",
            "iter: 0 i:10, pairs changed 4\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "iter: 0 i:24, pairs changed 5\n",
            "L==H\n",
            "iter: 0 i:30, pairs changed 6\n",
            "iter: 0 i:46, pairs changed 7\n",
            "L==H\n",
            "j not moving enough\n",
            "iter: 0 i:55, pairs changed 8\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:94, pairs changed 9\n",
            "L==H\n",
            "iter: 0 i:99, pairs changed 10\n",
            "interation number: 0\n",
            "L==H\n",
            "L==H\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:13, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "iter: 1 i:7, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "iter: 1 i:54, pairs changed 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:82, pairs changed 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:20, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "iter: 0 i:30, pairs changed 2\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:57, pairs changed 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:82, pairs changed 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "iter: 1 i:10, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:54, pairs changed 2\n",
            "iter: 1 i:55, pairs changed 3\n",
            "j not moving enough\n",
            "iter: 1 i:79, pairs changed 4\n",
            "iter: 1 i:82, pairs changed 5\n",
            "iter: 1 i:96, pairs changed 6\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:46, pairs changed 1\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "iter: 0 i:0, pairs changed 1\n",
            "L==H\n",
            "iter: 0 i:10, pairs changed 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "iter: 0 i:52, pairs changed 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "iter: 0 i:0, pairs changed 1\n",
            "iter: 0 i:10, pairs changed 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:52, pairs changed 3\n",
            "iter: 0 i:54, pairs changed 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "iter: 0 i:10, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:69, pairs changed 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:54, pairs changed 2\n",
            "iter: 0 i:55, pairs changed 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:30, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:94, pairs changed 2\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:26, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:54, pairs changed 2\n",
            "iter: 1 i:55, pairs changed 3\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 2 i:45, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:69, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 2 i:23, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "iter: 1 i:17, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:30, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "iter: 0 i:17, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "iter: 1 i:23, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 2 i:52, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 2 i:69, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 9 i:54, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "iter: 1 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "iter: 0 i:52, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 13\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 14\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 15\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 16\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 17\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 18\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 18 i:69, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:55, pairs changed 1\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "L==H\n",
            "iter: 1 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "iter: 4 i:55, pairs changed 1\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "L==H\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 10 i:54, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 5 i:69, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 1 i:55, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 13\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 14\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 15\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 16\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 17\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 18\n",
            "j not moving enough\n",
            "iter: 18 i:54, pairs changed 1\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "iter: 0 i:55, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 13\n",
            "j not moving enough\n",
            "L==H\n",
            "j not moving enough\n",
            "interation number: 14\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 15\n",
            "j not moving enough\n",
            "iter: 15 i:52, pairs changed 1\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:54, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 0 i:52, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "iter: 12 i:55, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 13\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 14\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 15\n",
            "j not moving enough\n",
            "iter: 15 i:54, pairs changed 1\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 13\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 14\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 15\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 16\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 17\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 18\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 19\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 20\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 21\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 22\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 23\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 24\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 25\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 26\n",
            "iter: 26 i:17, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "iter: 11 i:55, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 11\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 12\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 13\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 14\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 15\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 16\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 17\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 18\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 19\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 20\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 21\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 22\n",
            "j not moving enough\n",
            "iter: 22 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "iter: 7 i:17, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "iter: 1 i:29, pairs changed 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
            "iter: 10 i:55, pairs changed 1\n",
            "interation number: 0\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 1\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 2\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 3\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 4\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 5\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 6\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 7\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 8\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 9\n",
            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 10\n",
            "j not moving enough\n",
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            "j not moving enough\n",
            "j not moving enough\n",
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            "j not moving enough\n",
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            "j not moving enough\n",
            "j not moving enough\n",
            "interation number: 40\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SUXgp4QFhbLk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "alphas = np.array(alpas.ravel())[0]\n",
        "alphas"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n8UUi-cGj10i",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "16f632c7-b288-4ae2-81cb-9a7d281e96d3"
      },
      "source": [
        "b = np.array(b.ravel())[0]\n",
        "b"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-3.83300066])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mQRwE1taAveh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def get_w(alphas, dataset, labels):\n",
        "  ''' 通过已知数据点和拉格朗日乘子获得分割超平面参数w\n",
        "  '''\n",
        "  alphas, dataset, labels = np.array(alphas), np.array(dataset), np.array(labels)\n",
        "  yx = labels.reshape(1, -1).T*np.array([1, 1])*dataset\n",
        "  w = np.dot(yx.T, alphas)\n",
        "  return w.tolist()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ryzBeu-dosRh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 382
        },
        "outputId": "cc6dc91b-fcee-47da-b5f7-e857bc8e8ae4"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 分类数据点\n",
        "classified_pts = {'+1': [], '-1': []}\n",
        "for point, label in zip(dataMat, labelMat):\n",
        "    if label == 1.0:\n",
        "        classified_pts['+1'].append(point)\n",
        "    else:\n",
        "        classified_pts['-1'].append(point)\n",
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(111)\n",
        "# 绘制数据点\n",
        "for label, pts in classified_pts.items():\n",
        "    pts = np.array(pts)\n",
        "    ax.scatter(pts[:, 0], pts[:, 1], label=label)\n",
        "# 绘制分割线\n",
        "w = get_w(alphas, dataMat, labelMat)\n",
        "x1, _ = max(dataMat, key=lambda x: x[0])\n",
        "x2, _ = min(dataMat, key=lambda x: x[0])\n",
        "a1, a2 = w\n",
        "print(type(a1))\n",
        "print(a1)\n",
        "print(type(x1))\n",
        "print(x1)\n",
        "y1, y2 = (-b - a1*x1)/a2, (-b - a1*x2)/a2\n",
        "print(x1)\n",
        "print(y1)\n",
        "print([x1, x2])\n",
        "ax.plot(np.array([x1, x2]), np.array([y1, y2]))\n",
        "# 绘制支持向量\n",
        "for i, alpha in enumerate(alphas):\n",
        "  if abs(alpha) > 1e-3:\n",
        "    x, y = dataMat[i]\n",
        "    ax.scatter([x], [y], s=150, c='none', alpha=0.7,\n",
        "                linewidth=1.5, edgecolor='#AB3319')\n",
        "plt.show()"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'float'>\n",
            "0.8131488914872567\n",
            "<class 'float'>\n",
            "9.854303\n",
            "9.854303\n",
            "[15.71619496]\n",
            "[9.854303, -0.743036]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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tqsGXre6Szjqr1Igtp0aSi4a0dKmlztIwbAesgqUO9vK211Fx5p8b77hY/35b\nF/RQ3s04gUnZ/zAJDAe/YGMbgdl4jVUEcjz0ZxScKsdaVXHFj/uHdabHdTdddTZsa1itmg92HOel\nzzMBWHzLQO4Z29Np7YA9Va/FG+39C+DosulAy3vj2PuAGBkbyg+HbTfMqz+uEezV1NiOJKM1dtEQ\n03fXmK6pGWZTnLHk09RyRsP76y5xt2ZBzW1TnoFZr9dc2KOuU2Rg7RZERztH1o1p68PklpdaH+pN\nfZjaeA98pzxD34TbiSsr5WzKLiqLz6G8fQjqHkWnQQkoL+ctnRwpuMDipFR+PFbItf268OLceKI7\nOXcJqL6y/FNcPJUN2opfaDghcc5dUnElR2a2tmbrjgS/vfXvbXYCvuG4RmhNvxozeM5MvrUz8pZq\napZt5nh2f8uwITC8JszB+e+jq9+jZqi2WHnn+6O8+tVB/H28eHrGYOaPijYscM+m/UTuli8oOZx5\nxe0BXbrRffxkelx7I14+vnYe3TbZmtn6eik6BPhQVFplt2+NI7Nhe78l2GP2jNosjc3kPSPkzQ4R\nV37A2LvOqa3rqtr7Wd9g8PG/epZv1HvWnJpdKDOvhIWrU0jJLmbakG48P2soXTsGGDKW1prjG/9B\nTvIG/Dt1ofuEKYQNGIry9uZizgnytn3D+aMH6dhnIIP/5TG8A9rm+q499WfloYG+XKyspspyOVsa\nhq+9a6Q2vJDHiOe+bNal/P77juHtLuChPSzXmL3fvbVLPs3RnG2f9pZfZv53zXvTMOSNes+cfeWp\nVqqstvL6t1m8sSWL0EBfXr97JLfGdzd0ueTUPzeTk7yB7uMn03vuvVf0cw/uEU3XxPEU/LSdgx+8\nSebK1xm84HG3Wr6pvxwzYdk3V/VIb7jF0NEdKs2Zg0bV21svLmub+8Gaq42FiKHsrfXbuj3h9pqZ\neWgMNQdWYy7P1F35njWnZoPtO1nEzNe+Z3nyIWYkRPLVY9czPaGHoYFqqazgxOZ1hA1MoPf8+6+6\nYEediJHj6HXbnRRlplBy+IBh9Rilrp+NvV0v9QPc0Z4wxTYu1G2Lu7UacCXPCPk2FCKGm/JMzWy8\nvsa2NCbcXrMksrToyv4yrnzPmluzAcoqLfznpv3MeeMHisuqeO8Xibx6x3A6BRvX773OmZ+2Yykv\nJfrGmZc+TOw1+Oo2fhI+gcHk/ZBseF3OVL+fjT1hQZePNTjaE8beh0FYoK/DvXbaO89YrnHGfnd3\n4axrm7ryPTP5eqw7jpxlUVIKx86WcteYWJ68dSAdA1x3cPNcZir+nbrQsXd/oOnT4jsPG82ZvTtc\nVp8zOHIG6oXyyxfbcHSHim5IaK4AABIfSURBVL3L6y29bYiEuoM8I+Td4KLOdrXkoK0zjgG4+j1z\n5XGLWhcqqln2+X4+2H6C2PAgPnpoLOP7GN/IrCFLeSm+IaGXZvFNnRbvGxKKpbwcrbXbrMs7crZn\nlfXKi2040hTN3bYrtkWeEfJgSoi0mtldMN3xPXPQlgP5LFmTyqmSch6c2IvHb+pPkJ85f929AwIp\nKzh9KbSbOuhYdaEEb/8Atwl4sL9XvqGWnPpv9OXxPJ1nrMm7K0f7yQuHFZVW8viqffzi/Z0E+fuQ\n9OvxPD1jsGkBDxDWfygVhQWcP5YFNH7Q0VpVydl9OwkbMNSVJbaao/3d2+qp/55MQt5M7WlXkAt8\nkXaKG/+0lU/35vDbyX3Z+K8TGRnbyeyyiBh1Dd4BgeQkb0Rr3ehBx9M7tlJdeoHuE6eYVG3LNLzw\nSFigL77eV/4mIjtgzOE5yzXuyBktEQQF5yt49rM0NqXmMSSyIyt/OZohkaFml3WJt38A0VNmcnzj\nKo59+hGzZtV02264znyt9ykOrPuI0L6DCe07qIlnbXts9V2XtXTzecYZr+7K7DN13ZzWmrV7cnhu\nQwallRYendKPBdf1xrcNtgPWWnN07Yec+u5LAiN60H1iwzNev6X4YBodevZhyIL/wCco2OyShRvx\n/DNe3ZU77woyWW5RGUvWprLlQAGjenbipXkJ9O3adtsBK6XoNeceQuL6krt1M0fXfnDF/X5h4cTe\nOp/I66fh7effojFk5ixskZm8cCtWq+bjnSd4cVMmFqtm4c0DuO+aOLzdrB3wxZwTlObloK0W/EI7\nEdpnoN0zYR3RFtvfCteRmbzwCMfPXmRRUgrbjxQyoW9nls1NICbcuHbARgqOiiU4KtZpz+dul6QT\nriMhL9o8i1Xz/g9HeeXLA/h6e/HSvHhuT4xxq33kRnO3S9IJ15GQF23awdPnWbg6hb0ni7hxUFf+\nMDue7qHGtAN2Z+52STrhOm1vG4IQQJXFyp+TDzH9z99xorCU5XcO5+37EiXg7XC04Zdof2QmL9qc\n1Oxinli9j8y888wcFsnSmYPp3KFlO07aC+nxIuwxLOSVUkuBh4CC2puWaK03GTWecH/lVRaWJx9i\nxdYjdA724+37Epk6uJvZZbkN6fEibDF6Jv+q1voVg8cQHmDXsUIWJqVwpOAidyTGsGT6IEID3eta\np0K0RbJcI0x1saKalzcfYOX/HSMqLJAPHhzLxH6ubwcshKcyOuQfUUrdB+wCHtdanzN4POFGvjtU\ncOlqQvdfE8cT0wYQ7C/zDiGcqVX/opRSXwPdbdz1O+CvwPOArv3zj8AvbTzHAmABQGys804OEW1X\ncVkVL2zMYNWubHpHBPOPh68hMS7c7LKE8EguaWuglIoDNmitG22SbUpbg5ZcmUm02JfpeTy1Lo2z\nFytZcF1vHp3SjwAH+pALIewzpa2BUqqH1vpU7bdzgDSjxmoxs6/M1I6cvVDB0vUZrN+Xy8DuIbx7\n/2jio9tOO2AhPJWRC6D/pZQaTs1yzTHgYQPHapnGrswkIe8UWms+25fL79dncKG8msen9ufh6/vg\n5yPn4QnhCoaFvNb6XqOe22nkykyGyisu56l1qXy9P5/hMWG8PD+Bft1CzC5LiHalfW9lkCszGUJr\nzSc7T/LCpv1UWaw8NX0QD0zo5XbtgIXwBO075Kc8Y/vKTFOeMa8mN3eysJTFa1L4Iess43qHs2xu\nAnFd5CpHQpilfYe8XJnJaSxWzcptx3h58wG8vRQvzBnKXaNj8ZLZuxCmat8hDzWBLqHeKln5F1iU\nlMLu4+eYNCCCF+bES4tbIdoICXnRYlUWKyu2HmF58iGC/Lx59Y5hzB4eJRfzEKINkZAXLZKeW8zC\n1Smk55YwPb4HS28bQkSItAMWoq2RkBfNUlFt4bXkLN7852HCgvx48+cjuXloD7PLEkLYISEvHPbT\niXMsXJ1CVv4F5o2M5ukZgwgL8jO7LCFEIyTkRZNKK6t5ZfNB3t92lB4dA/jbA6O5YUBXs8sSQjhA\nQl40atvhMyxOSuVEYSn3juvJolsG0kHaAQvhNuRfq7CppLyKFzdl8vGPJ4jrHMQnC8Yxtndns8sS\nQjSThLy4yjeZp1myJo388+U8fF1vHpvaX9oBC+GmJOTFJYUXK3lufTrr9uYyoFsIb907imExYWaX\nJYRoBQl5gdaajamnePbTdIrLqnh0Sj9+M6mvtAMWwgNIyLdz+SXlPLUujS8zTpMQHcqHD41lYPeO\nZpclhHASCfl2SmvN6t3ZPL8hg4pqK0/eMpAHJ/bCx1tm70J4Egn5dij7XClL1qax9WABY+LCWTYv\nnt4RHcwuSwhhAAn5dsRq1Xyw4zgvfZ4JwPOzhnDP2J7SDlgIDyYh304cKbjA4qRUfjxWyLX9uvDi\n3HiiOwWZXZYQwmAS8h6u2mLlne+P8upXB/H38eLl+QnMHxUt7YCFaCck5D1YZl4JC1enkJJdzLQh\n3Xh+1lC6dgwwuywhhAtJyHugymorr3+bxRtbsugY4Mvrd4/k1vjuMnsXoh1q1X45pdTPlFLpSimr\nUiqxwX1PKqWylFIHlFLTWlemcNS+k0XMfO17licfYkZCJF/9+/VMT+ghAS9EO9XamXwaMBd4q/6N\nSqnBwJ3AECAS+Fop1V9rbWnleMKO8ioLf/rqIO98d4SuIQG894tEJg/sZnZZQgiTtSrktdb7AVuz\nxFnA37XWFcBRpVQWMAb4v9aMJ2zbceQsi5JSOHa2lLvGxPLkrQPpGOBrdllCiDbAqDX5KGB7ve+z\na2+7ilJqAbAAIDY21qByPNOFimqWfb6fD7afIDY8iI8eGsv4Pl3MLksI0YY0GfJKqa+B7jbu+p3W\n+tPWFqC1XgGsAEhMTNStfb72YsuBfJasSeVUSTkPTuzF4zf1J8hPjqMLIa7UZCporW9swfPmADH1\nvo+uvU20UlFpJc9v2E/ST9n07dqB1b8az6iencwuSwjRRhk19fsM+Egp9SdqDrz2A340aKx244u0\nUzy1Lp2i0kp+O7kvj0zui7+PXMxDCGFfq0JeKTUHeA2IADYqpfZqradprdOVUquADKAa+I3srGm5\ngvMVPPtZGptS8xgS2ZGVvxzNkMhQs8sSQrgBpXXbWQZPTEzUu3btMruMNkNrzdo9OTy3IYPSSguP\nTunHgut64yvtgIUQ9SildmutE23dJ0fq2qjcojKWrE1ly4ECRvXsxEvzEujbVdoBCyGaR0K+jbFa\nNR/vPMGLmzKxWDXPzhzMfdfE4S3tgIUQLSAh34YcP3uRRUkpbD9SyIS+nXlxTgKxnaUdsBCi5STk\n2wCLVfP+D0d55csD+Hp5sWxuPHeMjpF+M0KIVpOQN9nB0+dZuDqFvSeLuHFQV/4wO57uodIOWAjh\nHBLyJqmyWPnrlsP85ZssOgT4sPzO4dw2LFJm70IIp5KQN0FqdjFPrN5HZt55Zg6LZOnMwXTu4G92\nWUIIDyQh70LlVRaWJx9ixdYjdA724+37Epk6WNoBCyGMIyHvIruOFbIwKYUjBRe5PTGa300fTGig\ntAMWQhhLQt5gFyuqeXnzAVb+3zGiwgL53wfHcG2/CLPLEkK0ExLyBvr+0BkWr0khp6iM+6+J44lp\nAwj2l7dcCOE6kjgGKC6r4oWNGazalU3viGD+8fA1JMaFm12WEKIdkpB3si/T83hqXRpnL1by6xv6\n8OiUfgT4SjtgIYQ5JOSd5OyFCpauz2D9vlwGdg/h3ftHEx8t7YCFEOaSkG8lrTWf7cvl9+szOF9e\nxb9P7c+vru+Dn4+0AxZCmE9CvhXyist5al0qX+/PZ3hMGP81P4H+3ULMLksIIS6RkG8BrTWf7DzJ\nC5v2U2Wx8tT0QTwwoZe0AxZCtDkS8s10srCUxWtS+CHrLON6h7NsbgJxXYLNLksIIWySkHeQxapZ\nue0YL28+gLeX4oU5Q7lrdCxeMnsXQrRhEvIOyMq/wKKkFHYfP8ekARG8MCeeyLBAs8sSQogmScg3\nospiZcXWIyxPPkSQnzd/un0Yc0ZESTtgIYTbaFXIK6V+BiwFBgFjtNa7am+PA/YDB2p/dLvW+let\nGcvV0nOLWbg6hfTcEm6N787vbxtKRIi0AxZCuJfWzuTTgLnAWzbuO6y1Ht7K53e5imoLryVn8eY/\nDxMW5MebPx/JzUN7mF2WEEK0SKtCXmu9H/CY5YufTpxj4eoUsvIvMG9kNE/PGERYkJ/ZZQkhRIsZ\nuSbfSym1BygBntJaf2fgWK1SWlnNK5sP8v62o/ToGMDfHhjNDQO6ml2WEEK0WpMhr5T6Guhu467f\naa0/tfOwU0Cs1vqsUmoUsE4pNURrXWLj+RcACwBiY2Mdr9xJth0+w+KkVE4UlnLvuJ4sumUgHaQd\nsBDCQzSZZlrrG5v7pFrrCqCi9uvdSqnDQH9gl42fXQGsAEhMTNTNHaulSsqreHFTJh//eIK4zkH8\nfcE4xvXu7KrhhRDCJQyZsiqlIoBCrbVFKdUb6AccMWKslvgm8zRL1qSRf76cBdf15rEb+xPoJ+2A\nhRCep7VbKOcArwERwEal1F6t9TTgOuA5pVQVYAV+pbUubHW1rXTuYiW/X5/Our25DOgWwlv3jmJY\nTJjZZQkhhGFau7tmLbDWxu1JQFJrntuZtNZsTD3Fs5+mU1xWxaNT+vGbSX2lHbAQwuN5/BHG/JJy\nnlqXxpcZp0mIDuXDh8YysHtHs8sSQgiX8NiQ11qzenc2z2/IoKLaypO3DOTBib3w8ZbZuxCi/fDI\nkM8+V8qStWlsPVjA6LhOvDQvgd4RHcwuSwghXM6jQt5q1Xyw4zgvfZ4JwHOzhvDzsT2lHbAQot3y\nmJC/WFHNA+/v5MdjhVzbrwsvzo0nulOQ2WUJIYSpPCbkg/y86dk5iJ8lRjN/VLTH9NMRQojW8JiQ\nV0rx8s+GmV2GEEK0KbLVRAghPJiEvBBCeDAJeSGE8GAS8kII4cEk5IUQwoNJyAshhAeTkBdCCA8m\nIS+EEB5Mae2yK+41SSlVABw3uw4bugBnzC7CYPIaPUd7eJ3yGq/UU2sdYeuONhXybZVSapfWOtHs\nOowkr9FztIfXKa/RcbJcI4QQHkxCXgghPJiEvGNWmF2AC8hr9Bzt4XXKa3SQrMkLIYQHk5m8EEJ4\nMAl5IYTwYBLyTVBK3ayUOqCUylJKLTa7HmdTSsUopb5VSmUopdKVUo+aXZNRlFLeSqk9SqkNZtdi\nBKVUmFJqtVIqUym1Xyl1jdk1OZtS6rHav6dpSqmPlVIBZtfkDEqp95RS+UqptHq3hSulvlJKHar9\ns1NLnltCvhFKKW/gdeAWYDBwl1JqsLlVOV018LjWejAwDviNB77GOo8C+80uwkDLgS+01gOBYXjY\na1VKRQH/CiRqrYcC3sCd5lblNH8Dbm5w22IgWWvdD0iu/b7ZJOQbNwbI0lof0VpXAn8HZplck1Np\nrU9prX+q/fo8NcEQZW5VzqeUigamA++YXYsRlFKhwHXAuwBa60qtdZG5VRnCBwhUSvkAQUCuyfU4\nhdZ6K1DY4OZZwMrar1cCs1vy3BLyjYsCTtb7PhsPDMA6Sqk4YASww9xKDPHfwELAanYhBukFFADv\n1y5JvaOUCja7KGfSWucArwAngFNAsdb6S3OrMlQ3rfWp2q/zgG4teRIJeQGAUqoDkAT8m9a6xOx6\nnEkpNQPI11rvNrsWA/kAI4G/aq1HABdp4a/3bVXtmvQsaj7QIoFgpdTPza3KNXTNXvcW7XeXkG9c\nDhBT7/vo2ts8ilLKl5qA/1BrvcbsegwwAbhNKXWMmiW3yUqpD8wtyemygWytdd1vYaupCX1PciNw\nVGtdoLWuAtYA402uyUinlVI9AGr/zG/Jk0jIN24n0E8p1Usp5UfNQZ7PTK7JqZRSipp13P1a6z+Z\nXY8RtNZPaq2jtdZx1Pw//EZr7VEzQK11HnBSKTWg9qYpQIaJJRnhBDBOKRVU+/d2Ch52cLmBz4D7\na7++H/i0JU/i47RyPJDWulop9QiwmZoj+e9prdNNLsvZJgD3AqlKqb21ty3RWm8ysSbRMr8FPqyd\nkBwBHjC5HqfSWu9QSq0GfqJmV9gePKS9gVLqY+AGoItSKht4FlgGrFJKPUhNC/bbW/Tc0tZACCE8\nlyzXCCGEB5OQF0IIDyYhL4QQHkxCXgghPJiEvBBCeDAJeSGE8GAS8kII4cH+P5nGiHbUncCZAAAA\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-_9jCYmKjzai",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}